Posterior Analytics and Physics

Source

Source: The Works of Aristotle Translated into English, ed. W. D. Ross: vol. 1 (Oxford: Clarendon Press, 1928; Analytica Posteriora trans. G. R. G. Mure) and vol. 2 (1930; Physica trans. R. P. Hardie and R. K. Gaye), via the Internet Archive (in.ernet.dli.2015.5162 and in.ernet.dli.2015.2601) Source URL: https://archive.org/details/in.ernet.dli.2015.5162 Translator: G. R. G. Mure; R. P. Hardie and R. K. Gaye (1928) Public domain basis: Public domain in the United States (published 1928 and 1930; the 95-year US term has expired). Both works complete; translators' notes partly retained; Bekker line numbers and indexes removed. OCR text. Physics: https://archive.org/details/in.ernet.dli.2015.2601

Posterior Analytics

G. R. G. MURE. M.A.

FBLLOW AND TUTOR OP MBRTON COLLEGE

PREFACE

I DOUBT whether I should have undertaken to translate the Posterior Analytics had I not been encouraged by a promise of assistance from Professor Joachim. That promise he has most generously fulfilled, and if this translation has any value it is largely because it embodies an amount of his constructive criticism far too great for detailed acknowledgement. I have, however, also received a number of valuable suggestions from the Editor, and the errors from which these two scholars were unable to save me probably constitute the remainder of the book.

I have taken Bekker’s text as a foundation, noting departures from it, and in this connexion I have to thank Professor J. A. Smith for the gift of a photograph of Cod. A of the Posterior Analytics. The notes are perhaps too numerous for a translation, certainly too few to form anything resembling a commentary. I have not known how to avoid this compromise.

Finally my thanks are due to the late Mr. H. Heighten, who read about half the proofs and made several suggestions which I have adopted, and to Mr. Joseph of New College for the loan of his notes on Professor Cook Wilson's lectures on the Posterior Analytics.

October 5, 1935.

CONTENTS

CHAP.

1. The student’s need of pre-existent knowledge. Its nature.

2. The nature of scientific knowledge. The conditions of demonstration. The meaning of Contradiction, Enunciation, Proposition, Basic truth, Thesis, Axiom, Hypothesis, Definition.

3. Two erroneous views of scientific knowledge. The futility of circular demonstration.

4. Types of attribute : * True in every instance *, ‘ Essential ‘ Commensurate and universal * Accidental

5. Causes through which we erroneously suppose a conclusion commensurate and universal when it is not. How to avoid this error.

6. The premisses of demonstration must be necessary and essential.

7. The premisses and conclusion of a demonstration must fall within a single genus. The three constituent elements of demonstration.

8. Only eternal connexions can be demonstrated.

9. Demonstration must proceed from the basic premisses peculiar to each science, except in the case of subalteruate sciences.

10. The different sorts of basic truth.

11. The function of the common axioms in demonstration.

12. The scientific premiss in interrogative form. Formal fallacy.

The growth of a science.

13. The difference between knowledge of the fact and knowledge of the reasoned fact.

14. The first figure is the true type of scientific syllogism.

15. Immediate negative propositions.

16. Ignorance as erroneous inference when the premisses are immediate.

I7« Ignorance as erroneous inference when the premisses are mediate.

18. Ignorance as the negation of knowledge, e.g. such as must result from the lack of a sense.

19. Can demonstration develop an indefinite regress of premisses,

(1) supposing the primary attribute fixed? (2) supposing the ultimate subject fixed ? (3) supposing both primary attribute and ultimate subject fixed ?

20. If (i) and (a) are answered negatively, the answer to (3) must be in the negative.

If affirmative demonstration cannot develop an indefinite r^ress, then negative demonstration cannot.

CONTENTS

CHAP.

22. Dialectical and analytic proofs that the answer to both (i) and

(2) is in the negative.

23. Corollaries.

24. The superiority of universal to particular demonstration.

25. The superiority of affirmative to negative demonstration.

26. The superiority of affirmative and negative demonstration to reductio ad impossibile»

27. The more abstract science is the prior and the more accurate science.

28. What constitutes the unity of a science.

29. How there may be several demonstrations of one connexion.

30. Chance conjunctions are not demonstrable.

31. There can be no demonstration through sense-perception.

32. Different sciences must possess different basic truths.

33. The relation of opinion to knowledge.

34. Quick wit : the faculty of instantaneously hitting upon the middle term.

1. The four possible forms of inquiry.

2. They all concern the middle term.

3. The difference between definition and demonstration,

4. Essential nature cannot be demonstrated.

5. Essential nature cannot be inferred by division.

6. Attempts to prove a thing’s essential nature either hypothetically or through the definition of its contrary beg the question.

7. Definition does not touch the question of existence; demonstration proves existence. Hence definition cannot demonstrate.

8. Yet only demonstration can reveal the essential nature of things which have a cause other than themselves — i.c. attributes.

9. That which is self-caused— the basic premisses — is grasped immediately.

10. Types of definition.

11. The several causes as middle terms.

12. The question of time in causal inference.

13. How to obtain the definition of a substance. The use of division for this purpose.

14. How to select a connexion for demonstration.

1 5. One middle will often serve to prove several connexions.

16. If the effect is present, is the cause also present? Plurality of causes is impossible where cause and effect are commensurate.

17. Different causes may produce the same effect, but not in things specifically identical.

18. The true cause of a connexion is the proximate and not the more universal cause.

t9» How the individual mind comes to know the basic truths.

I All instruction given or received by way of argument 71*^ proceeds from pre-existent knowledge. This becomes evident upon a survey of all the species of such instruction. The mathematical sciences and all other speculative disciplines are acquired in this way, and so are the two forms of dialectical reasoning, syllogistic and inductive ; for each 5 of these latter makes use of old knowledge to impart new, the syllogism assuming an audience thatacceptsits premisses, induction ^ exhibiting the universal as implicit in the clearly known particular. Again, the persuasion exerted by rhetorical arguments is in principle the same, since they use either example, a kind of induction, or enthymeme, a form 10 of syllogism.

The pre-existent knowledge required is of two kinds.

In some cases admission of the fact must be assumed, in others comprehension of the meaning of the term used, and sometimes both assumptions are essential. Thus, we assume that every predicate can be either truly affirmed or truly denied of any subject,^ and that * triangle means so and so ; as regards ‘ unit ’ we have to make the double assumption of the meaning of the word and the existence of the 15 thing. The reason is that these several objects are not equally obvious to us. Recognition of a truth may in some cases

' The sense of Mynv implied in the use of eVaytayiJ by Aristotle is probably that of ‘leading the pupil on* from the particular to the universal by making him recognize the latter as implicit in the former.

* i. e. the law of excluded middle.

® Elsewhere rpiy^vov as a rule appears as one of the subjects of which the geometer assumes the meaning and being and demonstrates properties: here it seems to be instanced as a property, of which only the meaning is assumed. This chapter is, however, preliminary, and probably Aristotle is only drawing the distinction, which appears in ch. 10, 76'> 16 ff., between tacit and explicit assumptions. Possibly, however, Aristotle is thinking of ‘ triangular * as an attribute of number, cf. note on 73* 40, or as a particular modification of ariptia koX ypuppau the wp&ra of space.

contain as factors both previous knowledge and also knowledge acquired simultaneously with that recognition — knowledge, this latter, of the particulars actually falling under the universal and therein already virtually known. For example, the student knew beforehand that the angles 30 of every triangle are equal to two right angles ; but it was only at the actual moment at which he was being led on to recognize this as true in the instance before him that he came to know ‘ this figure inscribed in the semicircle * to be a triangle.^ For some things (viz. the singulars finally reached which are not predicable of anything else as subject) are only learnt in this way, i.e. there is here no recognition through a middle of a minor term as subject to a major. Before he was led on to recognition or before he actually as drew a conclusion, we should perhaps say that in a manner he knew, in a manner not.

If he did not in an unqualified sense of the term know the existence of this triangle, how could he know without qualification that its angles were equal to two right angles ? No : clearly he knows not without qualification but only in the sense that he knows universally. If this distinction is not drawn, we are faced with the dilemma in the Meno : ^ either a man will learn nothing or what he already knows ; 30 for we cannot accept the solution which some people offer. A man is asked, ‘ Do you, or do you not, know that every pair is even ? ’ He says he docs know it. The questioner then produces a particular pair, of the existence, and so a fortiori of the evenness, of which he was unaware. The solution which some people offer is to assert that they do not know that every pair is even, but only that everything

* Though he uses syllogistic terms, Aristotle is hardly describing syllogism, but rather the conversion of a universal known €£» into actual knowledge. The ' major premiss " here is a previously known universal (in Aristotle’s example * the angles of all triangles are together equal to two right angles ’), the * minor * is the recognition of a singular (in the example, ‘ this is a triangle ’), and the * conclusion *, with which the minor is simultaneous, is the recognition of this singular as an instance embodying the universal (* the angles of this triangle in the semi-circle are equal to two right angles ’). Hence hv yv&aiv in ^ 19 refers to ocra, and means * the singulars of which he has knowledge as a f in that he knows the universal

* Plato, Menoy So E.

which they know to be a pair is even : yet what they know 71^ to be even is that of which they have demonstrated evenness, i.e. what they made the subject of their premiss, viz. not merely every triangle or number which they know to be such, but any and every number or triangle without reservation. For no premiss is ever couched in the form * every number which you know to be such *, or ‘ every rectilinear figure which you know to be such ^ : the predicate is always construed as applicable to any and every instance of the 5 thing. On the other hand, I imagine there is nothing to prevent a man in one sense knowing what he is learning, in another not knowing it. The strange thing would be, not if in some sense he knew what he was learning, but if he were to know it in that precise sense and manner in which he was learning it.^

2 We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows, when we think 10 that we know the cause on which the fact depends, as the cause of that fact and of no other, and, further, that the fact could not be other than it is. Now that scientific knowing is something of this sort is evident — witness both those who falsely claim it and those who actually possess it, since the former merely imagine themselves to be, while the latter are also actually, in the condition described. Consequently the proper object of unqualified scientific knowledge is something 15 which cannot be other than it is.

There may be another manner of knowing as well — that will be discussed later.* What I now assert is that at all events we do know by demonstration. By demonstration I mean a syllogism productive of scientific knowledge, a syllogism, that is, the grasp of which is eo ipso such knowle(^e. Assuming then that my thesis as to the nature of scientific knowing is correct, the premisses of demonstrated knowledge ao must be true, primary, immediate, better known than and prior to the conclusion, which is further related to them as effect to cause. Unless these conditions are satisfied, the

^ Cf. An, Pk ii^ ch. 21,

* Cf. the following chapter and more particularly ii, ch. 19.

basic truths will not be ‘appropriate*^ to the concliislon. Syllogism there may indeed be without these conditions, but such syllogism, not being productive of scientific knowledge, will not be demonstration. The premisses must be 25 true : for that which is non-existent cannot be known — we cannot know, e.g., that the diagonal of a square is commensurate with its side.^ The premisses must be primary and indemonstrable ; otherwise they will require demonstration in order to be known, since to have knowledge, if it be not accidental knowledge, of things which are demonstrable, means precisely to have a demonstration of them. The premisses must be the causes of the conclusion, better known 30 than it, and prior to it ; its causes, since we possess scientific knowledge of a thing only when we know its cause ; prior, in order to be causes ; antecedently known, this antecedent knowledge being not our mere understanding of the meaning, but knowledge of the fact as well.^ Now ‘ prior * and ‘ better known* are ambiguous terms, for there is a difference between what is prior and better known in the order of 72* being and what is prior and better known to man. I mean that objects nearer to sense are prior and better known to man ; objects without qualification prior and better known are those further from sense. Now the most universal causes* are furthest from sense and particular causes are 5 nearest to sense, and they are thus exactly opposed to one another. In saying that the premisses of demonstrated knowledge must be primary, I mean that they must be the ‘ appropriate * basic truths, for I identify primary premiss and basic truth. A ‘ basic truth ' in a demonstration is an immediate proposition. An immediate proposition is one which has no other proposition prior to it. A proposition is either part of an enunciation, i.e. it predicates a single

' i.e. within the same genus. Cf. i, ch. 7.

* Within the conditions of dnSditfig here laid down, false premisses would give a false conclusion corresponding to a bv w? yl^Cdof such as bidfx€T(}ot-^<rvfii*€rpot, which is not anything iv roU npdypaaty. Such a ufi du cannot be the object of demonstration.

* Cf. 71* II ff. False anddafif is a contradiction in terms. Though false premisses may yield a true conclusion, a syllogism in which this occurs is not aTrddii^if but gives only the 3ri : cf. Aft. Pr. ii, a. 53^ 7-10.

attribute of a single subject. If a proposition is dialectical, it assumes either part indifferently ; if it is demonstrative, it jo lays down one part to the definite exclusion of the other because that part is true. The term ‘ enunciation ’ denotes either part of a contradiction indifferently. A contradiction is an opposition which of its own nature excludes a middle. The part of a contradiction which conjoins a predicate with a subject is an affirmation ; the part disjoining them is a negation, I call an immediate basic truth of syllogism a ‘thesis* when, though it is not 15 susceptible of proof by the teacher, yet ignorance of it does not constitute a total bar to progress on the part of the pupil : one which the pupil must know if he is to learn anything whatever is an axiom. I call it an axiom because there are such truths and we give them the name of axioms par excellence} If a thesis assumes one part or the other of an enunciation, i.e. asserts either the existence or the 20 non-existence of a subject, it is a hypothesis ; ^ if it does not so assert, it is a definition. Definition a ‘thesis* or a ‘ laying something down since the arithmetician lays it down that to be a unit is to be quantitatively indivisible ; but it is not a hypothesis, for to define what a unit is is not the same as to affirm its existence.

Now since the required ground of our knowledge— i.e. of n our conviction of a fact is the possession of such a syllogism as we call demonstration, and the ground of the syllogism is the facts constituting its premisses, we must not only know the primary premisses — some if not all of them — beforehand, but know them better than the conclusion ; for the cause of an attribute’s inherence in a subject always itself inheres in the subject more firmly than that attribute; e.g. the cause of our loving anything is dearer to us than the object of our love. So since the primary premisses are the cause 30

' sc, because the quantitative axioms — ignorance of which is a bar only to maikematical knowledge— are also called axioms.

* ‘ Hypothesis ’ to Aristotle and Plato means an assumption not calling lor proof within the sphere of the special science in which it functions, not a ‘ working hypothesis *.

* For Aristotle's view of the relation of belief to knowledge see i| ch. 33.

basic truths will not be ‘appropriate*^ to the conclusion. Syllogism there may indeed be without these conditions, but such syllogism, not being productive of scientific knowledge, will not be demonstration. The premisses must be 25 true : for that which is non-existent cannot be known — we cannot know, e.g., that the diagonal of a square is commensurate with its side.^ The premisses must be primary and indemonstrable ; otherwise they will require demonstration in order to be known, since to have knowledge, if it be not accidental knowledge, of things which are demonstrable, means precisely to have a demonstration of them. The premisses must be the causes of the conclusion, better known 30 than it, and prior to it ; its causes, since we possess scientific knowledge of a thing only when we know its cause ; prior, in order to be causes ; antecedently known, this antecedent knowledge being not our mere understanding of the meaning, but knowledge of the fact as well.^ Now ‘ prior * and ‘ better known* are ambiguous terms, for there is a difference between what is prior and better known in the order of 72* being and what is prior and better known to man. I mean that objects nearer to sense are prior and better known to man ; objects without qualification prior and better known are those further from sense. Now the most universal causes* are furthest from sense and particular causes are 5 nearest to sense, and they are thus exactly opposed to one another. In saying that the premisses of demonstrated knowledge must be primary, I mean that they must be the ‘ appropriate * basic truths, for I identify primar}" premiss and basic truth. A ‘ basic truth * in a demonstration is an immediate proposition. An immediate proposition is one which has no other proposition prior to it. A proposition is either part of an enunciation, i.e. it predicates a single

* i. e. within the same genus. Cf. i, ch. 7.

* Within the conditions of here laid down, false premisses would give a false conclusion corresponding to a fxff tv as such as iJiaficTpof—crv/ificrpof, which is not anything fvrotfTrpaypao't)/. Such a ov cannot be the object of demonstration.

* Cf. 71® II ff. False dn6dii(is is a contradiction in terms. Though false premisses may yield a true conclusion, a syllogism in which this occurs is not dirttafis but gives only the Su : cf. An, Pr, ii. 2. 53'* 7-10.

BOOK 1. 2 attribute of a single subject. If a proposition is dialectical, it assumes either part indifferently ; if it is demonstrative, it fo lays down one part to the definite exclusion of the other because that part is true. The term ‘ enunciation ' denotes either part of a contradiction indifferently. A contradiction is an opposition which of its own nature excludes a middle. The part of a contradiction which conjoins a predicate with a subject is an affirmation ; the part disjoining them is a negation. I call an immediate basic truth of syllogism a ^thesis’ when, though it is not 15 susceptible of proof by the teacher, yet ignorance of it does not constitute a total bar to progress on the part of the pupil : one which the pupil must know if he is to learn anything whatever is an axiom. I call it an axiom because there are such truths and we give them the name of axioms par excellence} If a thesis assumes one part or the other of an enunciation, i.e. asserts either the existence or the 20 non-existence of a subject, it is a hypothesis ; ^ if it does not so assert, it is a definition. Definition is a ‘ thesis * or a ‘ laying something down *, since the arithmetician lays it down that to be a unit is to be quantitatively indivisible ; but it is not a hypothesis, for to define what a unit is is not the same as to affirm its existence.

Now since the required ground of our knowledge — i.e. of 25 our conviction of a fact is the possession of such a syllogism as we call demonstration, and the ground of the syllogism is the facts constituting its premisses, we must not only know the primary premisses — some if not all of them — beforehand, but know them better than the conclusion : for the cause of an attribute’s inherence in a subject always itself inheres in the subject more firmly than that attribute; e.g. the cause of our loving anything is dearer to us than the object of our love. So since the primary premisses are the cause 30

' sc. because the quantitative axioms— ignorance of which is a bar only to mathematical knowledge— are also called axioms.

* ‘Hypothesis’ to Aristotle and Plato means an assumption not calling for proof within the sphere of the special science in which it functions, not a ‘working hypothesis’.

* For Aristotie^s view of the relation of belief to knowledge see i» ch. 33.

30 method by which induction produces knowledge.^ But if we accept this extension of its meaning, our definition of unqualified knowledge will prove faulty ; for there seem to be two kinds of it. Perhaps, however, the second form of demonstration, that which proceeds from truths better known to us, is not demonstration in the unqualified sense of the term."

The advocates of circular demonstration are not only faced with the difficulty we have just stated : in addition their theory reduces to the mere statement that if a thing exists, then it does exist — an easy way of proving anything.

35 That this is so can be clearly shown by taking three terms,*' for to constitute the circle it makes no difference whether many terms or few or even only two are taken. Thus by direct proof, if A is, B must be ; if B is, C must be ; therefore if A is, C must be. Since then — by the circular 73^ proof — if A is, B must be, and if B is, A must be, A may be substituted for C above. Then ' if B is, A must be ' = ‘if B is, C must be’, which above gave the conclusion ‘ if A is, C must be’ : but C and A have been identified.* Con-

^ Placing a comma after yvMfUfioiTqmv in 27, and taking et /X17 . . . in

28 ff. as qualifying d^vparop in ^ 25. Aristotle seems to mean that circular demonstration is impossible unless demonstration is taken to include a type of argument based on truths prior only in the sense of ‘ prior to us ^ such as induction, where we grasp the particular and recognize in it the universal, which is however drrXws TrpoTf f)op. The next sentence, €t 5’ ovrojff . . . , seems to confirm this interpretation, which does, however, involve a verbal contradiction, olop to. Trpds rd 6’ (i7rXwr may be a marginal gloss crept into the text. The Greek would be less harsh without it.

* Sc". ‘ and therefore our definition is not faulty

® sc. to constitute the valid syllogism which Aristotle sets up in '^37-9 to illustrate the tautology of the circular demonstration when reduced to explicit syllogism-

* TovTo 8’ on Tov A opTos TO F (<m seems to mean that * B implies C’ taken in conjunction with ‘ A implies B ’ gave the conclusion ‘ A implies C\ Aristotle tries to show the circular proof tautologous by reducing it to syllogism, apparently arguing thus : ‘ B implies implies

*A implies C* is valid syllogism (a schema for comparison) : while according to the circular proof A necessitates B and B necessitates A. If A-B, B-A (‘A implies B\ ^ B implies A') are to be made the premisses of a syllogism, there is nothing but A to take the place of C in the schema— no major term different from the minor : B-A is all we have to fill the place of the major premiss B-C. Now, in the schema^ B-C (taken in conjunction with the minor premiss A-B^ which is common to both syllogisms) gave the conclusion A-C. But Cis now A (a restatement of the fact that B-C has become B-A). Therefore the conclusion is A- A.

BOOK L 3 sequently the upholders of circular demonstration are in the position of saying that if A is, A must be — a simple way of 5 proving anything. Moreover, even such circular demonstration is impossible except in the case of attributes that imply one another, viz. * peculiar * ^ properties.

Now, it has been shown that the positing of one thing — be it one term or one premiss — never involves a necessary consequent : ^ two premisses constitute the first and smallest lo foundation for drawing a conclusion at all and therefore a fortiori for the demonstrative syllogism of science. If, then, A is implied in B and C, and B and C are reciprocally implied in one another and in A^ it is possible, as has been shown in my writings on the syllogism,*^ to prove all the assumptions on which the original conclusion rested, by circular demonstration in the first figure. But it has also 15 been shown that in the other figures either no conclusion is possible, or at least none which proves both the original premisses.** Propositions the terms of which are not convertible cannot be circularly demonstrated at all, and since convertible terms occur rarely in actual demonstrations, it is clearly frivolous and impossible to say that demonstration is reciprocal and that therefore everything can be demonstrated.

4 Since the object of pure scientific knowledge cannot be other than it is, the truth obtained by demonstrative knowledge will be necessary. And since demonstrative knowledge is only present when we have a demonstration, it follows that demonstration is an inference from necessary premisses. So we must consider what are the premisses of demonstration — i. e. what is their character : and as a 25 preliminary, let us define what we mean by an attribute ‘ true in every instance of its subject \ an ‘ essential *

' T<) idiov is defined in To/>, i, 102** iS as 6 ^19 drjXoljitp t6 rifiv eij/aif fx6v<a d* vmipxd Kn\ apTiKaTrjyopflrai rov rrpaypaTOi. ra idia in this sense are in fact ra tcaO’ avra crvfx^t^rfK6ra as Aristotle elsewhere calls them : but Aristotle often uses tdiop more widely to include also elements in the Ti €ivat and even as in An, Post, ii, ch. 6. 9s® 8 to differentiate these from other characters of a substance.

* Ibid, ii, cc. 5 and 6.

attribute, and a ^ commensurate and universal ' ^ attribute. I call ‘ true in every instance ’ what is truly predicable of all instances — not of one to the exclusion of others — and at all times, not at this or that time only ; e. g. if animal is 30 truly predicable of every instance of man, then if it be true to say * this is a man \ * this is an animal ' is also true, and if the one be true now the other is true now. A corresponding account holds if point is in every instance predicable as contained in line. There is evidence for this in the fact that the objection we raise against a proposition put to us as true in every instance is either an instance in which, or an occasion on w^hich, it is not true. Essential attributes are (i) such as belong to their subject as elements 35 in its essential nature (e. g. line thus belongs to triangle, point to line ; for the very being or ‘ substance ’ of triangle and line is composed of these elements, which are contained in the formulae defining triangle and line) : (a) such that, while they belong to certain subjects, the subjects to which they belong are contained in the attribute’s own defining formula. Thus straight and curved belong to line, odd and 40 even, prime and compound, square and oblong, to niimber; ^ 73^ and also the formula defining any one of these attributes contains its subject — e. g. line or number as the case may be.

Extending this classification to all other attributes, I distinguish those that answer the above description as belonging essentially to their respective subjects ; whereas attributes related in neither of these two ways to their subjects I call accidents or ‘ coincidents ’ ; ^ e. g. musical or white is a ‘ coincident ' of animal.

5 Further (a) that is essential which is not predicated of a subject other than itself: e. g. ‘the walking [thing] * walks

* koBSXov is not always u§ed by Aristotle in the strict sense here defined. It has therefore seemed advisable to add * commensurate * in translating it where it is used in the strict sense.

* The reference is to a method of naming numbers according to the geometrical arrangements of which their units are capable. Cf, Plato, Tkeaetetus^ 147E-148B.

* (rvfjLp€pr)K6s is elsewhere except in i,cc. 19 and 22 translated * accident which less adequately covers the sense of the word here and in that chapter. For the meaning expressed by * coincident * cf. 28-29, and is white in virtue of being something else besides ; ^ whereas substance, in the sense of whatever signifies a * this somewhat is not what it is in virtue of being something else besides. Things, then, not predicated of a subject I call essential ; things predicated of a subject I call accidental or ‘ coincidental

In another sense again (b) a thing consequentially ^ con- ro nected with anything is essential ; one not so connected is ‘ coincidental An example of the latter is ‘ While he was walking it lightened ’ : the lightning was not due to his walking ; it was, we should say, a coincidence. If, on the other hand, there is a consequential connexion, the predication is essential ; e. g. if a beast dies when its throat is being cut, then its death is also essentially connected with the cutting, because the cutting was the cause of death, not 15 death a ‘ coincident ' of the cutting.

So far then as concerns the sphere of connexions scientifically known in the unqualified sense of that term, all attributes which (within that sphere) are essential either in the sense that their subjects are contained in them, or in the sense that they are contained in their subjects, are necessary as well as consequentially connected with their subjects.^ For it is impossible for them not to inhere in their subjects — either simply or in the qualified sense that one or other of a pair of opposites must inhere in the subject ; e. g. in line must be either straightness or cuivature, 20 in number either oddness or evenness. For within a single identical genus the contrary of a given attribute is either its privative or its contradictory; e. g. within number what is not odd is even, inasmuch as within this sphere even is a

^ sc, the unexpressed subject. Aristotle's point cannot be rendered in English, which seldom uses an adjective or participle substantially.

Cf. Me^, z, ch. 10, where Aristotle distinguishes to from the ndOot

\€vk6tt}s.

* i.e. any ikis which is designable as characterized under the Category of Substance. Cf. Prof. J. A. Smith in C/ass, Rev,y vol xxxv,

® hC avTcJ implies a connexion really wider than causation, and would include e. g. the inherence of mathematical properties.

* So Zabarella and Pacius, taking Aristotle’s meaning to be that only types (i) and (2) have the degree of necessity requisite for scientific knowledge — a view borne out by i, ch. 22, 84* 7-28.

t46S4<4 Q necessary consequent of not-odd. So, since any given predicate must be either affirmed or denied of any subject,^ essential attributes must inhere in their subjects of necessity.^

35 Thus, then, we have established the distinction between the attribute which is ‘ true in every instance ' and the * essential ’ attribute.

I* term * commensurately universar an attribute which belongs to every instance of its subject, and to every instance essentially and as such ; from which it clearly follows that all commensurate universals inhere necessarily in theit subjects. The essential attribute, and the attribute that belongs to its subject as such, are identical. E. g. point 30 and straight belong to line essentially, for they belong to line as such ; and triangle as such has two right angles, for it is essentially equal to two right angles.

An attribute belongs commensurately and universally to a subject when it can be shown to belong to any random instance of that subject and when the subject is the first thing to which it can be shown to belong. Thus, e. g., (i) the equality of its angles to two right angles is not a commensurately universal attribute of figure. For though it 33 is possible to show that a figure has its angles equal to two right angles, this attribute cannot be demonstrated of any figure selected at haphazard, nor in demonstrating does one take a figure at random — a square is a figure but its angles arc not equal to two right angles. On the other hand, any isosceles triangle has its angles equal to two right angles, yet isosceles triangle is not the primary subject of this attribute but triangle is prior. So whatever can be shown

^ i. e. the law of excluded middle.

- Aristotle argues as follows : Essential attributes of type (2) which inhere in their subjects as disjunctive pairs of opposites are necessary because the disjunction covers the whole ground of the subject. The disjunction covers the whole ground because the subject is Within a single genus, and the law of excluded middle here ‘ invests the contrary with the character of the contradictory* or privativc~~i. e. though this law onl^ entitles you either to affirm or deny a predicate, yet here the affirmation of one predicate is i'Pjso facto the denial of its opposite and vice versa; ‘number is odd or not-odd* must mean ‘number is odd or even * ; ‘animal is seeing or not-seeing' is identical with ‘animal i? seeing or blind’.

BOOK 1. 4 73»> to have its angles equal to two right angles, or to possess 40 any other attribute, in any random instance of itself and primarily — that is the first subject to which the predicate in question belongs commensurately and universally, and the 74^ demonstration, in the essential sense, of any predicate is the proof of it as belonging to this first subject commensurately and universally: while the proof of it as belonging to the other subjects to which it attaches is demonstration only in a secondary and unessential sense. Nor again (12) is equality to two right angles a commensurately universal attribute of isosceles ; »t is of wider application.^

5 We must not fail to observe that we often fall into error because our conclusion is not in fact primary and commen- 5 surately universal in the sense in which we think we prove it so. We make this mistake (i) when the subject is an individual or individuals above which there is no universal to be found : (2) when the subjects belong to different species and there is a higher universal, but it has no name :

(3) when the subject which the demonstrator takes as a whole is really only a part of a larger whole ; for then the demonstration will be true of the individual instances 10 within the part and will hold in every instance of it, yet the demonstration will not be true of this subject primarily and commensurately and universally. When a demonstration is true of a subject primarily and commensurately and universally, that is to be taken to mean that it is true of a given subject primarily and as such. Case (3) may be thus exemplified. If a proof were given that perpendiculars to the same line are parallel, it might be supposed that lines thns perpendicular were the proper subject of the demonstration because being parallel is true of every instance of them. But it is not so, for the parallelism depends not 15 on these angles being equal to one another because each is a right angle, but simply on their being equal to one another. An example of (i) would be as follows: if isosceles were the only triangle, it would be thought to

^ If olbi in 2 is the right reading, it seems necessary to regard Kai'roi (73^34) . . . /cad* avr<S (74*2) as a parenthesis, however clumsy.

In ® 36 I place a comma-after have its angles equal to two right angles qua isosceles. An instance of (a) would be the law that proportionals alternate.^ Alternation used to be demonstrated separately of numbers, lines, solids, and durations,^ though it could 30 have been proved of them all by a single demonstration. Because there was no single nanie to denote that in which numbers, lengths, durations, and solids are identical, and because they differed specifically from one another, this property was proved of each of them separately. To-day, however, the proof is commensurately universal, for they do not possess this attribute qua lines or qua numbers, but qua manifesting this generic character which they are postulated 25 as possessing universally. Hence, even if one prove of each kind of triangle that its angles are equal to two right angles, whether by means of the same or different proofs; still, as long as one treats separatelj^ equilateral, scalene, and isosceles, one does not yet know, except sophistically, that triangle has its angles equal to two right angles, nor does one yet know that triangle has this property commensurately and universally, even if there is no other species of triangle but these. For one does not know that triangle as such has this property, nor even that ‘ all ’ triangles have it — unless ‘air means ‘each taken singly’: if ‘all* means ‘ as a whole class then, though there be none in which one does not recognize this property, one does not know it of ‘ all triangles ’.

When, then, does our knowledge fail of commensurate universality, and when is it unqualified knowledge? If triangle be identical in essence with equilateral, i.c. with each or all equilaterals, then clearly we have unqualified knowledge:^ if on the other hand it be not, and the attribute belongs to equilateral qua triangle; then our 35 knowledge fails of commensurate universality. ‘ But *, it will be asked, ‘does this attribute belong to the subject of which

' i,e. the law by which if A : B : : C : Dy then A : C :: B : D,

* The reference is perhaps Jo ;(poi/ot as the time-units of music and metre.

• sc, of the attribute 'equal to two right angles* which, known to inhere in equilateral, would then be known to inhere in a primary subject, i. e. fully known.

it has been demonstrated qua triangle or qua isosceles? What is the point at which the subject to which it belongs is primary ? (i. e. to what subject can it be demonstrated as belonging commensurately and universally ?) ' Clearly this point is the first term in which it is found to inhere as the elimination of inferior differentiae proceeds. Thus the angles of a brazen isosceles triangle are equal to two right angles : but eliminate brazen and isosceles and the attribute remains. * But* — you may say — ‘ eliminate figure or limit, 74^^ and the attribute vanishes.’ True, but figure and limit are not the first differentiae whose elimination destroy*', the attribute. ‘Then what is the first?’ If it is triangle, it will he in virtue of triangle that the attribute belongs to all the other subjects of which it is predicable, and triangle is the subject to which .it can be demonstrated as belonging commensurately and universally.

6 Demonstrative knowledge must rest on necessary basic 5 truths; for the object of scientific knowledge^ cannot be other than it is. Now attributes attaching essentially to their subjects attach necessarily to them : for essential attributes are either elements in the essential nature of their subjects, or contain their subjects as elements in their own essential nature. (The pairs of opposites which the latter class includes are necessary because one member or the other necessarily inheres.) It follows from this that pre- 10 misses of the demonstrative syllogism must be connexions essential in the sense explained: for all attributes must inhere essentially or else be accidental, and accidental attributes are not necessary to their subjects.

We must either state the case thus, or else premise that the conclusion of demonstration is necessary^ and that a demonstrated conclusion cannot be other than it is, and then infer that the conclusion must be developed* from 15 necessary premisses. For though you may reason from true premisses without demonstrating, yet if your premisses are necessary you will assuredly demonstrate — in such necessity

' i. e. that which is known by demonstration.

* Reading dpayfcawv* you have at once a distinctive character of demonstration. That demonstration proceeds from necessary premisses is also indicated by the fact that the objection we raise against a professed demonstration is that a premiss of it 20 is not a necessary truth — whether we think it altogether devoid of necessity, or at any rate so far as our opponent's previous argument goes. This shows how natve it is to suppose one's basic truths rightly chosen if one starts with a proposition which is (i) popularly accepted and (2) true, such as the sophists' assumption that to know is the same as to possess knowledge.^ For (i) popular acceptance or rejection is no criterion of a basic truth, which can only be the primary law of the genus constituting the subject matter 25 of the demonstration; and (2) not all truth is ‘appropriate’.^ A further proof that the conclusion must be the development of necessary premisses is as follows. Where demonstration is possible, one who can give no account which includes the cause has no scientific knowledge. If, then, we suppose a syllogism in which, though A necessarily inheres in Cf yet i?, the middle term of the demonstration, is not necessarily connected with A and C, then the man who argues 30 thus has no reasoned knowledge of the conclusion, since this conclusion does not owe its necessity to the middle term ; for though the conclusion is necessary, the mediating link is a contingent fact. Or again, if a man is without knowledge now, though he still retains the steps of the argument, though there is no change in himself or in the fact and no lapse of memory on his part ; then neither had he knowledge previously. But the mediating link, not being necessary, 35 may have perished in the interval ; and if so, though there be no change in him nor in the fact, and though he will still retain the steps of the argument, yet he has not knowledge, and therefore had not knowledge before. Even if the link has not actually perished but is liable to perish, this situation is possible and might occur. But such a condition cannot be knowledge.

75^ When the conclusion is necessary, the middle through which it was proved may yet quite easily be non-necessary.

You can in fact infer the necessary even from a non-neressary premiss, just as you can infer the true from the not true. On the other hand, when the middle is necessary the conclusion must be necessary; just as true premisses always 5 give a true conclusion. Thus, if A is necessarily predicated of B and B of C, then A is necessarily predicated of C. But when the conclusion is non-neccssary the middle cannot be necessary either. Thus: let A be predicated nonnecessarily of C but necessarily of B, and let Z? be a 10 necessary predicate of C ; then A too will be a necessary predicate of C, which by hypothesis it is not.

To sum up, then : demonstrative knowledge must be knowledge of a necessary nexus, and therefore must clearly be obtained through a necessary middle term ; otherwise its possessor will know neither the cause nor the fact that his conclusion is a necessary connexion. Blither he will mistake 15 the non-necessary for the necessary and believe the necessity of the conclusion without knowing it, or else he will not even believe it — in which case he will be equally ignorant, whether he actually infers the mere fact through middle terms or the reasoned fact and from immediate premisses.'

Of accidents that are not essential according to our definition of essential there is no demonstrative knowledge ; for since an accident, in the sense in which I here speak of it, 20 may also not inhere, it is impossible to prove its inherence as a necessary conclusion. A difficulty, however, might be raised as to why in dialectic, if the conclusion is not a necessary connexion, such and such determinate premisses should be proposed in order to deal with such and such determinate problems. Would not the result be the same if one asked any questions whatever and then merely stated one’s conclusion ? The solution is that determinate questions 35 have to be put, not because the replies to them affirm facts which necessitate facts affirmed by the conclusion, but because these answers are propositions which if the answerer affirm,

^ So Zabarella, taking Aristotle to mean that you may construct a formally perfect syllogism, inferring the fact, or even the reasoned fact, from wnat are actually true and necessary premisses ; yet because you do not realiae their necessity, you have not knowledge. One would, however, have expected avXXoyicnjrm for tldfj in • 16.

he must affirm the conclusion — and affirm it with truth if they are true.

Since it is just those attributes within every genus which are essential and possessed by thieir respective subjects as such that are necessary, it is clear that both the conclusions 30 and the premisses of demonstrations which produce scientific knowledge are essential.^ For accidents are not necessary : and, further,^ since accidents are not necessary one does not necessarily have reasoned knowledge of a conclusion drawn from them (this is so even if the accidental premisses are invariable but not essential, as in proofs through signs ; ^ for though the conclusion be actually essential, one will not know it as essential nor know its reason) ; but to have 35 reasoned knowledge of a conclusion is to know it through its cause. We may conclude that the middle must be consequentially connected with the minor, and the major with the middle.

It follows that we cannot in demonstrating pass from one 7* genus to another. We cannot, for instance, prove geometrical truths by arithmetic. For there are three elements in 40 demonstration : (i) what is proved, .the conclusion — an attribute inhering essentially in a genus; (2) the axioms,® 75“ U. axioms ^hich are premisses of demonstration ; (3) the subject-genus whose attributes, i. e. essential properties, are revealed by the demonstration. The axioms which are premisses of demonstration may be identical ® in two or

' The implied minor premiss required for this conclusion is the already proved fact that tne conclusions and premisses of demonstration are necessary. I take ov8' el » 32 — dtSn ^ 34 as a parenthesis.

* A further reason for excluding accidental pmmisses from demonstration : they cannot give reasoned knowledge of a conclusion, i. e. 35) knowledge of it through its cause (and this, Aristotle implies, was one of the first conditions of demonstration. Cf. yi'* 10, 11).

* Usually proofs from effect to cause, cf. i, ch. 13, 78*30 ff,

* Zabarella begins ch. 7 at 75* 2l»— perhaps a better division.

® It is not clear whether by cf Aristotle implies that the quantitative axioms can be premisses of demonstration— a view perhaps supported by i, ch. 9, 75^40, 41 if the interpretation of Bryson's quadrature of the circle suggested in my note on 76*3 is correct— or whether, like such axioms as the laws of contradiction and excluded middle, they are implied as canons regulating all mathematical demonstrations but do not serve as premisses, I have with hesitation adopted the former alternative here and in ch. 10, 14.

* tear ayaXoyiav

BOOK L 7 75^ more sciences : but in the case of two different genera such as arithmetic and geometry you cannot apply arithmetical demonstration to the properties of magnitudes unless the 5 magnitudes in question are numbers.^ How in certain cases transference is possible I will explain later.^

Arithmetical demonstration and the other sciences likewise possess, each of them, their own genera; so that if the demonstration is to pass from one sphere to another, the genus must be either absolutely or to some extent^ the same. If this is not so, transference is clearly impossible, 10 because the extreme and the middle terms must be drawn from the same genus : * otherwise, as predicated, they will not be essential and will thus be accidents. That is why it cannot be proved by geometry that opposites fall under one science, nor even that the product of two cubes is a cube.

Nor can the theorem of any one science be demonstrated by means of another science, unless these theorems are related 15 as subordinate to superior (e. g. as optical theorems to geometry or harmonic theorems to arithmetic). Geometry again ® cannot prove of lines any property which they do not possess qua lines, i. e. in virtue of the fundamental truths of their peculiar genus : it cannot show, for example, that the straight line is the most beautiful of lines or the contrary of the circle ; for these qualities do not belong to lines in virtue of their peculiar genus, but through some property which it shares with other genera. 30

8 It is also clear that if the premisses from which the syllogism proceeds are commensurately universal, the conclusion of such demonstration — demonstration, i. e., in the unqualified sense — must also be eternal. Therefore no attribute can be demonstrated nor known by strictly scientific knowledge to inhere in perishable things. The proof can only be accidental, because the attribute's connexion 35 with its perishable subject is not commensurately universal

® i. e. in the case of subaltcmate sciences : cf. e, g. 75^ 15 ff.

^ sc, * in all the demonstrations of the science.’

® Aristotle has given two examples of the vicious transference of a middle term from one science to another : he now gives two exampk^s of the vicious transience of a complete major premiss.

but temporary and special. If such a demonstration is made, one premiss must be perishable and not commensurately universal (perishable ^ because only if it is perishable will the conclusion be perishable ; not commensurately universal, because the predicate will be predicable of some instances of the subject and not of others) ; so that the conclusion can only be that a fact is true at the moment— not commen- 30 surately and universally. The same is true of definitions, since a definition is either a primary premiss ^ or a conclusion of a demonstration, or else only differs from a demonstration in the order of its terms. Demonstration and science of merely frequent occurrences — e. g. of eclipse as happening to the moon — are, as such,*^ clearly eternal : whereas so far as they are not eternal they are not fully commensurate.*

35 Other subjects too have properties attaching to them in the same way as eclipse attaches to the moon.

It is clear that if the conclusion is to show an attribute 9 inhering as such, nothing can be demonstrated except from its * appropriate ' ® basic truths. Consequently a proof even from- true, indemonstrable, and immediate premisses does 40 not constitute knowledge. Such proofs are like Bryson's method of squaring the circle ; for they operate by taking as their middle a common character— a character, therefore, 76* which the subject may share with another — and consequently they apply equally to subjects different in kind. They therefore afford knowledge of an attribute only as inhering accidentally, not as belonging to its subject as such : otherwise they would not have been applicable to another genus.®

* i.e. the minor premiss in a basic syllogism of a science. Cf. ii. ch. 10.

* sc. * as far as they are demonstration and science ’ — the thesis which the chapter establishes. In so far as eclipse, demonstrated through its proximate cause, is regarded as embodying an unalterable nexus of cause and effect, the demonstration is genuine demonstration.

* In so far as the eclipse so demonstrated is a particular event, the demonstration is not fully commensurate and so not truly universal.

* Cf. note on 5^1^23.

* The usual explanation of Bryson’s method, viz. that he argued that a circle is the mean area between the areas of the circumscribed and inscribed squares, renders it improbably futile. A more probable account (cf. Heath, Greek Mathematics^ vol. i. 22^-5) is as follows : Bryson circumscribed regular polygons about a circle and inscribed

Our knowledge of any attributes connexion with a subject is accidental unless we know that connexion through the middle term in virtue of which it inheres, and as an 5 inference from basic premisses essential and ‘ appropriate * to the subject — unless we know, e. g., the property of possessing angles equal to two right angles as belonging to that subject in which it inheres essentially, and as inferred (rom basic premisses essential and ‘appropriate' to that subject: so that if that middle term also belongs essentially to the minor, the middle must belong to the same kind as the major and minor terms. The only exceptions to thi'' rule are such cases as theorems in harmonics which are demonstrable by arithmetic. Such theorems arc proved by the 10 same middle terms as arithmetical properties, but with a qualification — the fact falls under a separate science (for the subject genus is separate), but the rcasuned fact concerns the superior science, to which the attributes essentially belong. Thus, even these apparent exceptions show that no attribute is strictly demonstrable except from its ‘appropriate* basic truths, which, however, in the case of 15 these sciences have the requisite identity of character.

It is no less evident that the peculiar basic truths of each inhering attribute are indemonstrable ; for basic truths from which they might be deduced would be basic truths of all regular polygons within it, in each case increasing the number of sides so that the area of the resulting polygon more and more nearly approached that of the circle, arguing that eventually the external and internal polygons would approximate so closely that there could be only one polygon mean in area between them, which would consequently coincide in area with the circle. He may then have reasoned thus: ‘Things which are greater and less than the same things respectively are eoual. The mean polygon is greater than all the internal polygons ana less than all the external polygons; so is the circle : therdore they are equal/ Now the axiom contained by the major premiss is true, but requires specification within each science to be effective ; e. g. in arithmetic it can only prove a number equal to itself, while in geometry it must be stated as ‘ Commensurate magnitudes See/. The difficulty of this explanation is that in Blench.

172® 2-7 Aristotle condemns Bryson's quadrature as ‘ eristic because it can be extended outside the sphere of geometp^ altogether ; leaving one to suppose that had Bryson reduced the application of the axiom to geometry and stated it as ^ Mc^itudes which are, &c.', the proof would have been valid, whereas in fact it requires a further reduction within geometry to connect it with the minor premiss. It is also highly questionable whether Aristotle held that a quantitative axion' could serve as major premiss of demonstration, cf. note on 75*42.

that is, and the science to which they belonged would possess universal sovereignty.^ This is so because he knows better whose knowledge is deduced from higher causes, for his acknowledge is from prior premisses when it derives from causes themselves uncaused : hence, if he knows better than others or best of all, his knowledge would be science in a higher or the highest degree. But, as things are, demonstration is not transferable to another genus, with such exceptions as we have mentioned of the application of geometrical demonstrations to theorems ^ in mechanics or optics, or of 25 arithmetical demonstrations to those of harmonics.

It is hard to be sure whether one know's or not ; for it is hard to be sure whether one s knowledge is based on the basic truths appropriate to each attribute — the differentia of true knowledge. We think we have scientific knowledge if we have reasoned from true and primary premisses. But that is not so ; the conclusion must be homogeneous with 30 the basic facts of the science.

I call the basic truths of every genus those elements in it 10 the existence of which cannot be proved. As regards both these primary truths and the attributes dependent on them the meaning of the name is assumed. The fact of their existence as regards the primary truths must be assumed ; but it has to be proved of the remainder,^ the attributes. Thus we assume the meaning alike of unity, straight, and 35 triangular; but while as regards unity and magnitude^ we assume also the fact of their existence, in the case of the remainder proof is required.

* Cf. Met, B, cc. 2 and 3. Aristotle must surely mean that there is no such dominant science. This interpretation, however, leaves the relation of science to metaphysics— to which a reference is clearly implied — obscure. Zabarella; ‘notandum est Aristotclem non negare metaphysicum posse probare aliarum scientiarum principia, id namque non negari potest ; sed solum negare quod in illis scientiis quarum sunt principia, id fieri queat: ex principiis enim metaphysicis possunt probari principia geometrica, non tamen in ipsa geometria sed in metaphysica * ; i. e. as opposed to the relation of subaltcmate sciences. Pacius retains the discussion within the limits of a single science, but not without violence to the text.

* firjxnvtKaSj oirrtxnc, and ap^oviKas should almost certainly be neuter plurals. * sc. the remainder of the genus ; vide 75* 42-*^ l.

* Unless piyeBos stands for the genus of which tlBv and rpiyavov are species, the insertion of it is odd— though not without parallel. For rpiymop a$ apparently an attribute vide note on 71* 15.

Of the basic truths used in the demonstrative sciences some are peculiar to each science, and some are common, but common only in the sense of analogous, being of use only in so far as they fall within the genus constituting the province of the science in question.

Peculiar truths are,e.g., the definitions of line and straight ; 40 common truths are such as ‘take equals from equals and equals remain*. Only so much of these comrnon truths is required as falls within the genus in question : for a truth of this kind will have the same force even if not used 76^ generally but applied by the geometer only to magnitudes, or by the arithmetician only to numbers. Also peculiar to a science are the subjects the existence as well as the meaning of which it assumes, and the essential attributes of which it investigates, e.g. in arithmetic units, in geometry points and 5 lines. Both the existence and the meaning of the subjects are assumed by these sciences ; but of their essential attributes only the meaning is assumed. For example arithmetic assumes the meaning of odd and even, square and cube, geometry that of incommensurable, or of deflection or verging ^ of lines, whereas the existence of these attributes is demonstrated by means of the axioms and from previous conclusions to as premisses. Astronomy too proceeds in the same way.

For indeed every demonstrative science has three elements :

(i) that which it posits, the subject genus whose essential attributes it examines; (2) the so-called axioms, which are primary premisses* of its demonstration ; (3) the attributes, 15 the meaning of which it assumes. Yet some sciences may very well pass over some of these elements ; e. g. we might not expressly posit the existence of the genus if its existence were obvious (for instance, the existence of hot and cold is more evident than that of number) ; or we might omit to assume expressly the meaning of the attributes if it were well understood. In the same way the meaning of axioms, 20 such as ‘Take equals from equals and equals remain’, is well known and so not expressly assumed.* Nevertheless in the nature of the case the essential elements of demonstration are three: the subject, the attributes, and the basic premisses *

' Vtde Heath, Euc/tW, vol. i, p. 150. * Cf. note on 75* 42.

That which expresses necessary self-grounded fact, and which we must necessarily believe/ is distinct both from the hypotheses^ of a science and from illegitimate postulate I say * must believe *, because all syllogism, and therefore a fortiori demonstration, is addressed not to the spoken 25 word, but to the discourse within the soul,^ and though we can always raise objections to the spoken word, to the inward discourse we cannot always object. That which is capable of proof but assumed by the teacher without proof is, if the pupil believes and accepts it, hypothesis, though only in a limited sense hypothesis — that is, relatively to the 30 pupil ; if the pupil has no opinion or a contrary opinion on the matter, the same assumption is an illegitimate postulate. Therein lies the distinction between hypothesis and illegitimate postulate : the latter is the contrary of the pupil s opinion,* demonstrable, but assumed and used without demonstration.

35 The definitions — viz. those which are not expressed as statements that anything is or is not ^ — are not hypotheses : but it is in the premisses of a science that its hypotheses are contained. Definitions require only to be understood, and this is not hypothesis — unless it be contended that the pupiFs hearing is also an hypothesis required by the teacher. Hypotheses, on the contrary, postulate facts on the being of which depends the being of the fact inferred. Nor are 40 the geometer's hypotheses false, as some have held, urging that one must not employ falsehood and that the geometer is uttering falsehood in stating that the line which he draws is a foot long or straight, when it is actually neither. The 77® truth is that the geometer does not draw any conclusion from the being of the particular line of which he speaks, but from what his diagrams symbolize. A further distinction is that all hypotheses and illegitimate postulates are either universal or particular, whereas a definition is neither.®

' sc. axioms. ^ Cf. note on 72* 20,

* Cf, Plato, Theaetetus, 189 E ff * Omitting ^ after

® It seems easier to read ovbiv for with Waitz, but one would then expect Xiyovcriv.

® A opos is not strictly a judgement at all ; it is the unity of the constitutive moments of an Uropov eldot set out as a formula or X6yos,

It

II So ^ demonstration does not necessarily imply the being 5 of Forms nor a One beside a Many, but it does necessarily imply the possibility of truly predicating one of many; since without this possibility we cannot save the universal, and if the universal goes, the middle term goes with it, and so demonstration becomes impossible. We conclude, then, that there must be a single identical term unequivocally predicable of a number of individuals.

The law that it is impossible to affirm and deny simul- 10 taneously the same predicate of the same subject is not expressly posited by any demonstration except when the conclusion also has to be expressed in that form ; in which case the proof lays down as its major premiss that the major is truly affirmed of the middle but falsely denied.

It makes no difference, however, if we add to the middle, or again to the minor term, the corresponding negative. For grant a minor term of which it is true to predicate man — 15 even if it be also true to predicate not-man of it — still grant simply that man is animal and not not-animal, and the conclusion follows: for it will still be true to say that Callias—even if it be also true to say that not-Callias—is animal and not not-animal.^ The reason is that the major

^ Zabarella inserts the first paragraph of this chapter down to

6^<ji>vvnov in *9

* i. e. if the required conclusion is ‘Callias is animal and not notanimal ^ the syllogism is adequate in the form Man is animal and not not-animal,

Callias is man,

Callias is animal and not not-animal.

There is no need to add * and not not-man * to the middle or * and not not-Callias’ to the minor, for even if the opposites which these additions would exclude were taken as true, the same conclusion would follow ;

Man and also not-man (cat, dog, &c.) is animal and not notanimal,

Callias and also not-Callias (Plato, Socrates, &c.) is man-andalso-not-man (i. e. belongs to a genus wider than man and narrower than animal).

Callias is animal and not not-animal.

The major once made definite, the width of the middle, provided it is narrower than the major, does not matter, and the width of the minor, provided it is narrower than the middle, is unimportant.

The construction in ** 15-17 perhaps presents two anacolutha : (^i) die antecedent to ov seems to be the subject to an unexpressed verb presumably fW (could itvat have dropped out between flmitf and ft

It term is predicable not only of the middle, but of something other than the middle as well, being of wider application ;

30 so that the conclusion is not affected even if the middle isextended to cover the original middle term and also what is not the original middle term.'

The law that every predicate can be either truly affirmed or truly denied of every subject is posited by such demonstration as uses reductio ad impossibile, and then not always universally, but so far as it is requisite ; within the limits, that is, of the genus — the genus, I mean (as I have already 35 explained ^), to which the man of science applies his demonstrations. In virtue of the common elements of demonstration— I mean the common axioms which are used as premisses of demonstration,^ not the subjects nor the attributes demonstrated as belonging to them — all the sciences have communion with one another, and in communion with them all is dialectic and any science which might attempt a universal proof of axioms such as the law of 30 excluded middle, the law that the subtraction of equals from equals leaves equal remainders, or other axioms of the same kind. Dialectic has no definite sphere of this kind, not being confined to a single genus. Otherwise its method would not be interrogative ; for the interrogative method is barred to the demonstrator, who cannot use the opposite facts to prove the same nexus. This was shown in my work 35 on the syllogism.*^

If a syllogistic question ^ is equivalent to a proposition 12 embodying one of the two sides of a contradiction, and if

Km ?), and {b) a main clause, * the conclusion follows must be supplied.

To avoid (a) I have with hesitation taken the antecedent to Kao oC as subject to ibbBr) in the first 9I clause, and ibdBri as followed by the infinitive dvai in the third d clause.

' Lit. ‘even if the middle is itself and also what is not itself’; i. e. you may pass from the middle term man to include not-man without affecting the conclusion. Cf. previous note.

* An. Pr. I. I. The ‘opposite facts’ arc those which would be expressed in the alternatively possible answers to the dialectical question, the dialectician’s aim being to refute his interlocutor whether the latter answers the question first put to him affirmatively or in the negative.

• i. c. a premiss put in the form of a question.

BOOK 1. la each science has its peculiar propositions from which its peculiar conclusion is developed, then there is such a thing as a distinctively scientific question, and it is the interrogative form of the premisses from which the 'appropriate’ conclusion of each science is developed. Hence it is clear 40 that not every question will be relevant to geometry, nor to medicine, nor to any other science: only those questions will be geometrical which form premisses for the proof of 77*^ the theorems of geometry or of any other science,^ such as optics, which uses the same basic truths as geometry. Of the other sciences the like is true. Of these questions the geometer is bound to give his account, using the basic truths of geometry in conjunction with his previous conclusions ; of the basic truths the geometer, as. such, is not 5 bound to give any account The like is true of the other sciences. There is a limit, then, to the questions which wc may put to each man of science ; nor is each man of science bound to answer all inquiries on each several subject, but only such as fall within the defined field of his own science.

If, then, in controversy with a geometer qua geometer the disputant confines himself to geometry and proves anything from geometrical premisses, he is clearly to be applauded ; 10 if he goes outside these he will be at fault, and obviously cannot even refute the geometer except accidentally.^ One should therefore not discuss geometry among those who are not geometers, for in such a company an unsound argument will pass unnoticed. This is correspondingly true in the other sciences. 15

Since there are ' geometrical ^ questions, does it follow that there are also distinctively * ungeometrical * questions ? Further, in each special science — geometry for instance — what kind of error® is it that may vitiate questions, and yet not exclude ^ them from that science ? Again, is the erroneous conclusion one constructed from premisses opposite to

' Reading % A cV rwv with C and Bonitz.

’ Placing a colon instead of a comma after AtiKPvU) a comma instead of a full stop after in '>ll, and a colon instead of a comma after crvfjL^tfirjKds in 12.

® Reading noiav*

* Omitting $ dyfco/nfVpijTa with A, B, and C. So Waitz.

20 the true premisses,^ or is it formal fallacy though drawn from geometrical premisses ? ^ Or, perhaps, the erroneous conclusion is due to the drawing of premisses from another science; e.g. in a geometrical controversy a musical question is distinctively ungeometrical, whereas the notion that parallels meet is in one sense geometrical, being ungeometrical in a different fashion : the reason being that ‘ ungeometrical *, like * unrhythmical is equivocal, meaning in the 35 one case not geometry at all,^ in the other bad geometry? It is this error, i. e. error ^ based on premisses of this kind — 'of' the science but false — that is the contrary® of science. In mathematics the formal fallacy is not so common, because it is the middle term in which the ambiguity lies,® since the major is predicated of the whole of the middle 30 and the middle of the whole of the minoi (the predicate of course never has the prefix 'all ') ; and in mathematics one can, so to speak, see these middle terms with an intellectual vision, while in dialectic the ambiguity may escape detection. E.g. ‘Is every circle a figure?’ A diagram shows that this is so, but the minor premiss ‘ Are epics circles ? ' ^ is shown by the diagram to be false.

If a proof has an inductive minor premiss, one should not 35 bring an * objection ' against it. For since every premiss must be applicable to a number of cases (otherwise it will not be true in every instance, which, since the syllogism proceeds from universals, it must be), then assuredly the same is true of an ‘ objection ' ; since premisses and ‘ objections' are so far the same that anything which can be validly advanced as an ‘ objection ’ must be such that it could take the form of a premiss, either demonstrative or 40 dialectical.® On the other hand, arguments formally illo-

^ i. c. wrong in its matter.

* Placing a note of interrogation after kctA yiotfitrpiau dc.

^ Reading aurj; kqI 17 with A, B, C, and Waitz.

® tvapTia : but not contradictory. The ignorance contradictory to scien9e is blank nescience, cf. i, ch. 18.

* Reading a<l to dirrSv with A, B, and C first hand.

’ The reference is to ra xvxXticd, the cycle of post-Homeric epics supplementing Homer.

* The connexion of this section 77'»34-9 is not very clear.

gical do sometimes occur through taking as middles mere attributes of the major and minor terms. An instance of this is Caeneus’ proof that fire increases in geometrical 78* proportion : * Fire he argues, ‘ increases rapidly, and so does geometrical proportion*. There is no syllogism so, but there is a syllogism if the most rapidly increasing proportion is geometrical and the most rapidly increasing proportion is attributable to fire in its motion. Sometimes, 5 no doubt, it is impossible to reason from premisses predicating mere attributes : but sometimes it is possible, though the possibility is overlooked.^ If false premisses could never give true conclusions ‘ resolution ’ would be easy, for premisses and conclusion would in that case inevitably reciprocate.^ I might then argue thus Met be an existing fact ; let the existence of A imply such and such facts actually known to me to exist, which we may call I can now, since they reciprocate, infer A from B.

Reciprocation of premisses and conclusion is more fre- 10 quent in mathematics, because mathematics takes definitions, but never an accident, for its premisses — a second characteristic distinguishing mathematical reasoning from dialectical disputations.

A science expands not by the interposition of fresh middle

Zabarella inserts it at the end of ch. 17. I take it as an obiter dictum on (uaracTis, and Aristotle as saying that the proper way to attack a proof containing an inductive minor premiss is not to urge an Hvcrraais^ for in science an €varra(Ti9, like a positive premiss of science, must be universal and must lead to the conclusion opposite to the inference it attacks. Hence if the tvcrraats is another inductive premiss, it is equally unscientific — it docs not demonstrate an opposite conclusion ; if it is universal, it is gratuitous, for all one need do, Aristotle implies, is to point out that the original ‘proof* proves nothing, because it has a premiss which is not KaddXov.

^ It is possible, i.e. nov of course by mere conversion to the first figure, but when, as in the above hypothetical example, a fresh truth ignored in the invalid' argument can be brought m to amend the paralogism and produce a syllogism in the first figfure.

* Paralogism occurs because, though true premisses must give a true conclusion, the converse docs not hold. If it did, premisses and conclusion would reciprocate, and it would be as easy to ‘resolve* a conclusion into its premisses as to see what conclusion must follow from given premisses.

* The premisses regarded as an antecedent.

^ The conclusion regarded as a consequent.

D % terms, but by the apposition of fresh extreme terms.^ E.g.

IS A is predicated of B, 5 of C, C of A and so indefinitely. Or the expansion may be lateral: e.g. one major, A, may be proved of two minors, C and E. Thus let A represent number — a number or number taken indeterminately ; B determinate odd number ; C any particular odd number, ao We can then predicate A of C. Next let D represent determinate even number, and E even number. Then A is predicable of E.^

Knowledge of the fact differs from knowledge of the 13 reasoned fact. To begin with, they differ within the same science and in two ways: (i) when the premisses of the 25 syllogism are not immediate (for then the proximate cause is not contained in them — a necessary condition of knowledge of the reasoned fact): (2) when the premisses are immediate, but instead of the cause the better known of the two reciprocals is taken as the middle ; for of two reciprocally predicable terms the one which is not the cause may quite easily be the better known and so become the

* i.e. the old conclusion forms one premiss of the new syllogism and supplies the middle term :

A—B That which has sensation, sleeps,

Animal has sensation ;

A — C Animal sleeps.

Then ( i ) if the apposed term is a minor,

A-~C Animal sleeps,

C—D That which expels fatigue -products is animal ;

A — D That which expels fatigue-products sleeps.

(2) if the apposed term is a major,

D—A That which sleeps expels fatigue-products.

A — C Animal sleeps ;

j) — c Animal expels fatigue-products,

Cf. note on An. Pr. 26* 29.

Aristotle here and in the passage immediately following, where he speaks of lateral expansion, is thinking of the scientist as setting out the body of his results in systematic form, as in fact writing a textbook: in passages such as i, ch. 22, 85*^1 ff. which regard the expansion of a science as proceeding by the insertion of fresh middle terms between the terms of a npo^Xrjfjiay he has in mind actual scientific discovery or at any rate a systematization of results prior to the final setting out of the science in its logical order.

* i. e. A A — B and A — D are the two major

/\ premisses with A for predicate which y \ produce respectively the conclusions

^ \ A--C and A--E,

Diiddlc term of the demonstration. Thus (2) (a) you might prove as follows that the planets are near because they do 30 not twinkle : let C be the planets, B not twinkling, A proximity. Then B is predicable of C ; for the planets do not twinkle. But A is also predicable of B^ since that which does not twinkle is near — we must take this truth as having been reached by induction or sense-perception. Therefore 35 A is 3. necessary predicate of C; so that we have demonstrated that the planets are near. This syllogism, then, proves not the reasoned fact but only the fact ; since they are not near because they do not twinkle, but, because they are near, do not twinkle. The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact. Thus : let C be the planets, B proximity, A not twinkling. Then B is an 78'* attribute of C, and A — not twinkling — of B^ Consequently A is predicable of C, and the syllogism proves the reasoned fact, since its middle term is the proximate cause. Another example is the inference that the moon is spherical from its manner of waxing. Thus : since that which so waxes is 5 spherical, and since the moon so waxes, clearly the moon is spherical. Put in this form^ the syllogism turns out to be proof of the fact, but if the middle and major be reversed it is proof of the reasoned fact ; since the moon is not spherical because it waxes in a certain manner, but w^axes in such a manner because it is spherical. (Let C be the moon, B 10 spherical, and A waxing.) Again (^), in cases where the cause and the effect are not reciprocal and the effect is the better known, the fact is demonstrated but not the reasoned fact. This also occurs (i) when the middle falls outside the major and minor,' for here too the strict cause is not given, and so the demonstration is of the fact, not of the reasoned fact. For example, the question *Why does 15 not a wall breathe?’ might be answered, ‘ Because it is not an animal ' ; but that answer would not give the strict cause, because if not being an animal causes the absence of respiration, then being an animal should be the cause of respiration,

' sc. in the second figure {vtWs 78*^ 24), in which the middle is predicate in both j^remisses. Cf. An, Pr, i, ch. 5, 26'»39.

according to the rule that if the negation of x causes the ao non-inherence of the affirmation of x causes the inherence of jK ; e.g. if the disproportion of the hot and cold elements is the cause of ill health, their proportion is the cause of health ; and conversely, if the assertion of x causes the inherence of the negation of x must cause ys non-inherence. But in the case given this consequence does not result; for not every animal breathes, A syllogism with this kind of cause takes place in the second figure. Thus : let A be animal, 35 B respiration, C walk Then A is predicable of all B (for all that breathes is animal), but of no C\ and consequently B is predicable of no (7; that is, the wall does not breathe. Such causes are like far-fetched explanations, which precisely consist in making the cause too remote, as in Anacharsis’ 30 account of why the Scythians have no flute-players ; namely because they have no vincs.^

Thus, then, do the syllogism of the fact and the syllogism of the reasoned fact differ within one science and according to the position of the middle terms. But there is another way too in which the fact and the reasoned fact differ, and that is ^ when they are investigated respectively by different 35 sciences. This occurs in the case of problems related to one another as subordinate and superior, as when optical problems are subordinated to geometry, mechanical problems to stereometry, harmonic problems to arithmetic, 40 the data of observation to astronomy. (Some of these 79*^ sciences bear almost the same name ; e. g. mathematical and nautical astronomy, mathematical and acoustical harmonics.) Here it is the business of the empirical observers to know the fact, of the mathematicians to know the reasoned fact ; for the latter are in possession of the demonstrations giving the causes, and are often ignorant of the 5 fact : just as we have often a clear insight into a universal, but through lack of observation are ignorant of some of its particular instances. These connexions have a perceptible existence though they are manifestations of forms. For

^ i.e. they have no flute-players, •.* they do not indulge in wine, *.* they have no grapes, they have no vines.

• In 78*^ 35 read ry hC aXXi;? for rh hC AWrjt with n and p.

• sc. 'which require two sciences for their proof'. Cf. 78'*3S.

the mathematical sciences concern forms: they do not demonstrate properties of a substratum, since, even though the geometrical subjects are predicable as properties of a perceptible substratum, it is not as thus predicable that the mathematician demonstrates properties of them.^ As lo optics is related to geometry, so another science is related to optics, namely the theory of the rainbow. Here knowledge of the fact is within the province of the natural philosopher, knowledge of the reasoned fact within that of the optician, either qua optician or* qua mathematical optician. Many sciences not standing in this mutual relation enter into it at points ; e. g. medicine and geometry ; it is the physician’s business to know that circular wounds heal more 15 slowly, the geometer’s to know the reason why.^

H Of all the figures the most scientific is the first. Thus, it is the vehicle of the demonstrations of all the mathematical sciences, such as arithmetic, geometry, and optics, and practically of all sciences that investigate causes : for 30 the syllogism of the reasoned fact is either exclusively or generally speaking and in most cases in this figure— a second proof that this figure is the most scientific ; for grasp of a reasoned conclusion is the primary condition of knowledge. Thirdly, the first is the only figure which enables us to pursue knowledge of the essence of a thing. In the 35 second figure no affirmative conclusion is possible, and knowledge of a thing’s essence must be affirmative ; while in the third figure the conclusion can be affirmative, but cannot be universal, and essence must have a universal character : e. g, man is not two-footed animal in any qualified sense, but universally. Finally, the first figure has no need of the others, while it is by means of the first that the 30 other two figures are developed, and have their intervals

^ Cf. 2-5 and note thereon.

’ Reading tj toO Kara for ^ Kara in 79* 12, with the MSS. Bekker’s omission of toO is an obvious misprint.

* Perhaps because they expose the maximum amount of raw surface, or possibly because a wound forming an acute angle heals most easily— i.e. by first or second intention X granulation — and therefore a circular wound least easily.

close-packed ^ until immediate premisses are reached. Clearly, therefore, the first figure is the primary condition of knowledge.

Just as an attribute A may (as we saw) be atomically 15 connected with a subject B, so its disconnexion may be atomic. I call ‘ atomic * connexions or disconnexions which 35 involve no intermediate term ; since in that case the connexion or disconnexion will not be mediated by something other than the terms themselves. It follows that if either A or Bj or both A and B, have a genus, their disconnexion cannot be primary. Thus : let C be the genus of A. Then, if C is not the genus of B — for A may well have a genus 40 which is not the genus of B — there will be a syllogism proving A's disconnexion from B thus:

79"^ all A is C, no B is Cy no B is A»

Or if it is B which has a genus Z?, we have all B is A no D is Ay no B is Ay by syllogism ;

5 and the proof will be similar if both A and B have a genus. That the genus of A need not be the genus of B and vice versa, is shown by the existence of mutually exclusive coordinate series of predication. If no term in the series A CD ... is predicable of any term in the series BEF . . ., and if G — a term in the former series — is the genus of Ay 10 clearly G will not be the genus of B\ since, if it were, the series would not be mutually exclusive. So also if B has a genus, it will not be the genus of A. If, on the other hand, neither A nor B has a genus and A does not inhere in By this disconnexion must be atomic. If there be a middle term, one or other of them is bound to have

' Cf. i, ch. 23, 84^ 19 ff., and also note on 78® 14. nvKvmcris means the filling up with middle terms of the mediable loosely connected or interval between the terms of a npofiXrjfia or proposition requiring proof—a process which continues until each term is immediately connected with its neighbour, and basic premisses are reached. Then only is the original npo^XrjfAa genuinely proved.

BOOK I. 15 79"^ a genus, for the syllogism will be either in the first or the 15 second figure. If it is in the first, B will have a genus — for the premiss containing it must be affirmative ; ^ if in the second, either A or B indifferently, since syllogism is possible if either is contained in a negative premiss,^ but not if both premisses are negative.

Hence it is clear that one thing may be atomically disconnected from another,^ and we have stated when and how this is possible.

16 Ignorance — defined not as the negation of knowledge but as a positive state of mind — is error produced by inference.

(1) Let us first consider propositions asserting a predicates 25 immediate connexion with or disconnexion from a subject. Here,^ it is true, positive error may befall one in alternative ways ; for it may arise where one directly believes a connexion or disconnexion as well as where one's belief is acquired by inference. The error, however, that consists in a direct belief is without complication ; but the error resulting from inference — which here concerns us — takes many forms. Thus, let A be atomically disconnected from all B : then the conclusion inferred through a middle term 30 Cy that all B is A^ will be a case of error produced by syllogism. Now, two cases are possible. Either {a) both premisses, or {p) one premiss only, may be false, {d) If neither A is an attribute of any C nor C of any B, whereas the contrary was posited in both cases, both premisses will be false. (C may quite well be so related to A and B that 35 C is neither subordinate to A nor a universal attribute of B : for B^ since A was said to be primarily disconnected from i?, cannot have a genus, and A need not necessarily be a universal attribute of all things. Consequently both

' i. e. in Celarent.

^ i. e. in Cesare or Camestres.

^ Reading 5XXo with MSS. and WaiU. The omission of dXXo in Bekker is clearly a misprint.

^ H€v in ^ 25 is not answered till 81^38. It has seemed necessary to expand the translation of ^ 25-39, ^ 26 appears to contradict ^ 24; but really Aristotle begins to discuss error resulting from inference and is led by the mention of immediate propositions to comment in passing upon error in direct apprehension.

40 premisses may be false.^) On the other hand, {b) one of the premisses may be true, though not either indifferently but 80® only the major ; since, B having no genus, the premiss C-B will always be false, while A-C may be true. This is the case if, for example, A is related atomically to both C and B ; because when the same term is related atomically to more terms than one, neither of those terms will belong to the other.^ It is, of course, equally the case if A-C is 5 not atomic.^

Error of attribution, then, occurs through these causes and in this form only — for we found that no syllogism of universal attribution was possible in any figure but the first.^ On the other hand, an error of non-attribution may occur either in the first or in the second figure. Let us therefore first explain the various forms it takes in the first 10 figure and the character of the premisses in each case.

{c) It may occur when both premisses are false; e.g. supposing A atomically connected with both C and B^

* e. g. All quantity is substance,

All quality is quantity ;

All quality is substance.

Had B a genus, disconnexion from B would have been mediated by it.

* e. g. All body is substance— atomic,

B C All quality is body ;

All quality is substance-atomic.

The reference cannot be to the impossibility of predicating co-ordinate species of one another, because B is stated to have no genus. We must therefore suppose Karrjyopfiv here to include negation as well as affirmation (cf. 82^^ 14 and note) ; e. g. substance is primarily affirmed of body and denied of quality, therefore quality and body cannot be predicated cither of the other. Aristotle then adds that this is only one case, and that as long as the minor premiss is atomic the major need not be atomic ; e. g. in the above example man or stone might be substituted for body.

* e. g. All man is substance — mediable,

All quality is man ;

All quality is substance— atomic.

An, Pr, i. I.

8o» if it be then assumed that no C h and all B is C, both premisses are false.^

{d) It is also possible when one is false. This may be either premiss indifferently. A-C may be true, C-B false 15 -A-C true because A is not an attribute of all things, C-B false because C, which never has the attribute A, cannot be an attribute of B\'^ for if C-B were true, the premiss A-C would no longer be true, and besides if both premisses were true, the conclusion would be true.^ ao Or again, C-B may be true and A-C false ; e. g. if both C and A contain B as genera, one of them must be subordinate to the other, so that if the premiss takes the form No Cis yJ , it will be false.'^ This makes it clear that whether either or both premisses are false, the conclusion will equally be 25 false.

In the second figure the premisses cannot both be wholly false; for if all B is A, no middle term can be with truth universally affirmed of one extreme and universally denied of the other : but premisses in which the middle is affirmed 50 of one extreme and denied of the other are the necessary condition if one is to get a valid inference at all.'* There-

' e. g. No cat is animal,

All man is cat ;

.*. No man is animal.

* Reading abvvnrov vnap^tiP with codd.

* e. g. No stone is animal, (possibly true animal is not true of

B C all things, as is, e.g., being or one.)

All man is stone ; (false stone, which is never animal, B A cannot be an attribute of man.)

.‘.No man is animal.

eg.

No living thii^ is animal,

All man is living ;

. No man is animal.

Here * living * must be a genus of animal because both animal and living arc predicable of man as genera. If living and animal were co-ordinate, they could not both be prcdicable of man.

* sc. In this figure.

fore if, taken in this way, they are wholly false, their contraries conversely should be wholly true. But this is impossible.^ On the other hand, there is nothing to prevent both premisses being partially false ; e. g. if actually 35 some A is C and some B is C, then if it is premised that all A is C and no B is C, both premisses are false, yet partially, not wholly, false.'^ The same is true if the major is made negative instead of the minor. Or one premiss may be wholly false, and it may be either of them. Thus, supposing that actually an attribute of all /I must also be an 40 attribute of all B,^ then if C is yet taken to be a universal 80** attribute of all A but universally non-attributable to B, C-A will be true but C-B false.* Again, actually that which is an attribute of no B will not be an attribute of all A either ; for if it be an attribute of all A, it will also be an attribute of all B, which is contrary to supposition ; but if C be nevertheless assumed to be a universal attribute of 5 Ay but an attribute of no By then the premiss C-B is true

' e. g, in Camestres, All animal is immortal,

No man is immortal,

BA gives the false conclusion No man is animal : but if the contraries of these premisses were wholly true they would form a syllogism in Cesare — A C

No animal is immortal,

All men are immortal ly . A gising the same conclusion — No man is animal -which would have to be true.

^ e.g. All animals are biped,

No mammals are biped ;

No mammals are animal.

® sc, as must be the case on our initial assumption that in fact all B is A,

* e. g. All animal is living,

No man is living ;

No man is animal.

but the major is false.^ The case is similar if the major is made the negative premiss. For in fact what is an attribute of no A will not be an attribute of any B either ; and if it be yet assumed that C is universally non-attributable to A, but a universal attribute of B, the premiss C-A is true but the minor wholly false.^ Again, in fact it is lo false to assume that that which is an attribute of all B is an attribute of no for if it be an attribute of all B, it must be an attribute of some A. If then C is nevertheless assumed to be an attribute of all B but of no C-B will be true but false.^

It is thus clear that in the case of atomic propositions erroneous inference will be possible not only when both 15 premisses are false but also when only one is false.

17 (2) In the case of attributes not atomically connected with or disconnected from their subjects, (a) (i) as long as the false conclusion is inferred through the ‘ appropriate ’ middle, only the major and not both premisses can be false. By 20 ‘ appropriate middle ' I mean the middle term through which the contradictory— i.e. the true — conclusion is inferrible.* Thus, let A be attributable to B through a middle term C: then, since to produce a conclusion the premiss C-B must be taken affirmatively, it is clear that this premiss must

* e. g. All animal is stone,

No man is stone ;

No man is animal.

* e. g. No animal is stone,

B C All man is stone ;

No man is animal.

* e.g. No animal is living,

All man is living ;

No man is animal.

* Cf. note on 71^3. This definition is a corollary of the definition there given of ^ appropriate *.

35 always be true, for its quality is not changed,^ But the major A-Cis false, for it is by a change in the quality of A-C that the conclusion becomes its contradictory — i. e. true.^ Similarly (ii) if the middle is taken from another series of predication ; e. g. suppose D to be not only contained within A as a. part within its whole but also predicable of all B, Then the premiss D-B must remain unchanged, but 30 the quality of A-B must be changed ; so that B-B is always true, A-B always false.® Such error is practically identical with that which is inferred through the ‘ appropriate * middle. On the other hand, (3) if the conclusion is not inferred through the 'appropriate’ middle — (i) when the middle is subordinate to A but is predicable of no B, both premisses 35 must be false, because if there is to be a conclusion both must be posited as asserting the contrary of what is actually the fact, and so posited both become false : e.g. suppose that actually all B is A but no B is B; then if these premisses are changed in quality, a conclusion will follow and both 40 of the new premisses will be false.^ When, however, (ii) 8l*the middle B is not subordinate to Ay A-B will be true, B-B false — A-B true because A was not subordinate

' i. e. it does not become negative instead of affirmative in the false syllogism.

* c. g. Nothing rational laughs,

All man is rational ;

B A .'. No man laughs.

Change the quality of the minor and there is no inference ; change the quality of the major and the contradictory and true conclusion follows.

’ e. g. Nothing that walks upright laughs,

All men walk upright ;

B A .*. No man laughs.

Change the quality of the minor and there is no inference ; change the qu^ity of the major and the contradictory— true — conclusion follows.

* e.g. No brute is living,

All men are brutes ;

.’. No man is living.

to D, D-B false because if it had been true, the conclusion too would have been true; but it is ex hypothesi false.^

When the erroneous inference is in the second figure, both 5 premisses cannot be entirely false; since if B is subordinate to there can be no middle predicable of all of one extreme and of none of the other, as was stated before.^ One premiss, however, may be false, and it may be either of them. Thus, if C is actually an attribute of both A and B, but is assumed 10 to be an attribute of A only and not of B, C-A will be true, C-B false : ^ or again if C be assumed to be attributable to B but to no -<4, C-B will be true, C-A false.

We have stated when and through what kinds of premisses 15 error will result in cases where the erroneous conclusion is negative. If the conclusion is affirmative, {a) (i) it may be inferred through the ‘appropriate* middle term. In this case both premisses cannot be false since, as we said before,^ C-B must remain unchanged if there is to be a conclusion, and consequently A-C^ the quality of which is changed, will always be false. This is equally true if (ii) the middle ao is taken from another series of predication, as was stated to be the case also with regard to negative error ; ® for D-B must remain unchanged, while the quality of A-D must be converted, and the type of error is the same as before.

{b) The middle may be inappropriate. Then (i) if Z? is 35 subordinate to A^ A-D will be true, but D-B false; since A may quite well be predicable of several terms no one of

* Cf.8o*29.

No stone is living,

All man is stone ;

.'.No man is living.

Every living thing is substance, B C

No man is substance ;

No man is living.

* Cf. 80^17-26.

» Cf, 80^26-32.

which can be subordinated to another.' If, however, (ii) D is not subordinate. to obviously A-D^since it is affirmed, will always be false, while may be either true or

30 false ; for A may very well be an attribute of no Z>, whereas all B is D, e. g. no science is animal, all music is science. Equally well A may be an attribute of no Z?, and D of no B,

It emerges, then, that if the middle term is not subordinate to the major, not only both premisses but either singly may be false.

35 Thus we have made it clear how many varieties of erroneous inference are liable to happen and through what kinds of premisses they occur, in the case both of immediate and of demonstrable truths.

It is also clear that the loss of any one of the senses entails 18 the loss of a corresponding portion of knowledge, and that, since we learn either by induction or by demonstration, this 40 knowledge cannot be acquired. Thus demonstration de- 81'* velops from universals, induction from particulars ; but since it is possible to familiarize the pupil with even the so-called mathematical abstractions only through induction — i. e. only because each subject genus possesses, in virtue of a determinate mathematical character, certain properties which can be treated as separate even though they do not exist in 5 isolation ^ — it is consequently impossible to come to grasp universals except through induction. But induction is impossible for those who have not sense-perception. For it is sense-perception alone which is adequate for grasping the particulars : they cannot be objects of scientific knowledge, because neither can universals give us knowledge of

^ e. g. All brutes are quadrupeds,

All men are brutes ;

.*. All men are quadrupeds.

* Reading rrfv AB with MSS.

* Cf. 79* 6-10. Ta (jLadrffxariKd or rh as Aristotle calls them, exist only as properties of sensible objects, not pet se as separate entities, although they can be isolated by abstraction and thus constitute the subjects of mathematical demonstration. Consequently it is only by tVayaryiJ from sensible objects that the universal can be elicited ana known ; vide Met K. io6i* 28.

them without induction, nor can we get it through induction without sense-perception.^

19 Every syllogism is effected by means of three terms. 10 One kind of syllogism serves to prove that A inheres in C by showing that A inheres in B and in C; the other is negative and one of its premisses asserts one term of another, while the other denies one term of another. It is clear, then, that these are the fundamentals and so-called hypotheses of syllogism. Assume them as they have been stated, and 15 proof is bound to follow — proof that A inheres in C through B, and again that A inheres in B through some other middle term, and similarly that B inheres in C, If our reasoning aims at gaining credence and so is merely dialectical, it is obvious that we have only to see that our inference is based on premisses as credible as possible : so that if a middle ao term between A and B is credible though not real, one can reason through it and complete a dialectical syllogism. If, however, one is aiming at truth, one must be guided by the real connexions of subjects and attributes. Thus:^ since there are attributes which are predicated of a subject essentially or naturally ^ and not coincidentally ^ — not, that is, 35 in the sense in which we say ‘ That white (thing) is a man*, which is not the same mode of predication as when we say ‘ The man is white * : the man is white not because he is something else but because he is man, but the white is man because * being white ' coincides with ‘ humanity * within one substratum — therefore there are terms such as are naturally subjects of predicates. Suppose, then, C such a term not 3^ itself attributable to anything else as to a subject, but the proximate^ subject of the attribute B — i. e. so that B-C is immediate ; suppose further E related immediately to F, and Fto B, The first question is, must this series terminate,

' viiie ii, ch. 19 and notes thereon.

* Placing a colon after ovt<os.

* i. e. predication in which the predicate is essentially adjectival ; cf. ch. 4, yy 5-10. Such predication is called by the Latin commentators ‘ predicatio naturalis ’,'lind is further discussed in ch. 22.

® In ch. 21, 82*^39 ff. Aristotle from the alternative point of view defines such a subject as iJararov.

8i^ or can ft proceed to infinity? The second question is as follows : Suppose nothing is essentially predicated of but 35 A is predicated primarily of H and of no intermediate prior term, and suppose H similarly related to G and G to B ; then must this series also terminate, or can it too proceed to infinity? There is this much difference between the questions : the first is, is it possible to start from that which is not itself attributable to anything else but is the subject 40 of attributes, and ascend to infinity ? The second is the problem whether one can start from that which is a predicate but not itself a vSubject of predicates, and descend to infinity ? A third question is, if the extreme terms arc fixed, can there be an infinity of middles ? I mean this : suppose for example that A inheres in Cand B is intermediate between them, but 5 between B and A there are other middles, and between these again fresh middles ; can these proceed to infinity or can they not ? This is the equivalent of inquiring, do demonstrations proceed to infinity, i.e. is everything demonstrable ? Or do ultimate subject and primary attribute limit one another ?

I hold that the same questions arise with regard to 10 negative conclusions and premisses : viz. if A is attributable to no By then either this predication will be primary, or there will be an intermediate term prior to B to which A is not attributable — G, let us say, which is attributable to all B — and there may still be another term H prior to Gy which is attributable to all G, The same questions arise, I say, because in these cases too either the series of prior terms to which A is not attributable ^ is infinite or it terminates.

15 One cannot ask the same questions in the case of reciprocating terms, since when subject and predicate arc convertible^ there is neither primary nor ultimate subject, seeing that all the reciprocals ^ua subjects stand in the same relation to one another, whether we say that the subject has an infinity of attributes or that both subjects and attributes — and we raised the question in both cases — are infinite in

^ Reading ov;^ indpxft with D ; or else Wdpxuv is used generally to include negation.

• Reading dvriKaTrjyopovpevott with D. So Waitz.

number. These questions then cannot be asked — unless, indeed, the terms can reciprocate by two different modes, by accidental predication in one relation and natural 20 predication in the other.^

20 Now," it is clear that if the predications terminate in both the upward and the downward direction (by ‘ upward ’ I mean the ascent to the more universal, by ‘ downward’ the descent to the more particular), the middle terms cannot be infinite in number. For suppose that A is predicated of and that the intermediates — call them BB'B'*, . .—are 35 infinite, then clearly you might descend from A and find one term predicated of another ad since you have an infinity of terms between you and F\ and equally, if you ascend from /q there are infinite terms between you and A, It follows that if these processes are impossible there cannot be an infinity of intermediates between A and l\ Nor is it of any eftcct to urge that some terms of the 30 series AB. . . are contiguous^ so as to exclude intermediates, while others cannot be taken into the argument at all:^ whichever terms of the series . . . I take, the number of intermediates in the direction cither of A or oiF must be finite or infinite: where the infinite series starts, whether from the first term or from a later one, is of no moment, for the succeeding terms in any case are infinite 35 in number.

21 Further,^’ if in affirmative demonstration the series terminates in both directions, clearly it will terminate too

' The possibility of * unnatural ’ predication is ruled out in ch. 22.

* Ch. 20 consists of a hypothetical argument to the effect that if the first and second questions asked in ch. 19 are answered in the negative, then the answer to the third question must also be in the negative.

* I read ABZ with VVaitz. Codd. ABC read ABB, not, as Bekker indicates, AB ; cod. M, AB.

^ Cf. note on 95^4.

® The objector apparently argues that even if in fact the number of terms between A and F is infinite, yet in thought we can reach from A to F since some of the intermediate terms will be contiguous and the rest—the possibly infinite series of middles separating two terms — may elude our apprehension altogether, so that for our thought these two terms constitute an immediate proposition.

® The hypothetical argument of the last chapter is now extended to cover negation.

8a‘ in negative demonstration. Let us assume that we cannot proceed to infinity either by ascending from the ultimate term (by ^ ultimate term ' I mean a term such as F was, 82^ not itself attributable to a subject but itself the subject of attributes), or by descending towards an ultimate from the primary term (by ^ primary term ’ I mean a term predicable of a subject but not itself a subject If this assumption is justified, the scries will also terminate in the case of negation. For a negative conclusion can be proved in all 5 three figures. In the first figure it is proved thus : no B is all C is B. In packing the interval B-C we must reach immediate propositions — as is always the case with the minor premiss * — since B-C is affirmative. As regards the other premiss it is plain that if the major term is denied of a term D prior to By D will have to be predicable of all By JO and if the major is denied of yet another term prior to /J, this term must be predicable of all B. Consequently, since the ascending series is finite, the descent will also terminate and there will be a subject of which ^ is primarily nonpredicable.^ In the second figure the syllogism is, all is By no C is By no C is A, If proof of this* is required, 15 plainly it may be shown either in the first figure as above, in the second as here, or in the third. The first figure has been discussed, and we will proceed to display the second, proof by which will be as follows : all B is DyXjo C \s D , . ., since it is required that B should be a subject of which a predicate is affirmed. Next, since D is to be proved not to belong to Cy then D has a further predicate which is denied of C. 30 Therefore, since the succession of predicates affirmed of an

* sc* a predicate above which is no wider universal.

* Because Celarent is the only mood of the first figure in which negative is possible.

* Interchanging AcnVo) and in and 12 with Waitz. If we keep the text, 7 t6 Kar<a 6b(k must mean the series of subjects descending from the primary, most universal predicate of C, through Byto C; and in that case Aiistotle^s argument is : ‘The minor premiss, B-C, being affi mative, the number of B^s — and .*. of Cs— predicates is finite; but it is this series which must contain the subject of which A is primarily denied : therefore looking at the series from the opposite point of view as ascending towards the term of which A is primarily denied (7 6B6t)y it is eaually finite.* So Zabarella ; but this interpretation is artificial, and 82" 21 below confirms Waitz*s reading.

* sc, * that no C is iff

8a^ ever higher universal terminates,* the succession of predicates denied terminates too.^

The third figure shows it as follows : all B is some B is not C, some A is not C. This premiss, i. e. C-B, will be proved either in the same figure or in one of the two figures discussed above. In the first and second figures the 35 series terminates. If we use the third figure, we shall take as premisses, all E is B, some E is not C, and this premiss again will be proved by a similar prosyllogism. But since it is assumed that the series of descending subjects also terminates, plainly the series of more universal non-predicables will terminate also. Even supposing that the proof is not confined to one method, but employs them all and is now in the first figure, now in the second or third — even so 30 the regress will terminate, for the methods are finite in number, and if finite things arc combined in a finite number of ways, the result must be finite.

Thus it is plain that the regress of middles terminates in the case of negative demonstration, if it docs so also in the case of affirmative demonstration. That in fact the regress terminates in both these cases may be made clear by the 35 following dialectical considerations.

^ In the case of predicates constituting the essential nature of a thing, it clearly terminates, seeing that if definition is possible, or in other words, if essential form is knowable,

^ i. e. each of the successive prosyllogisms required to prove the negative minors contains an affirmative major in which the middle is affirmed of a subject successively * higher' or more universal than the subject of the first syllogism. Thus :

Syllogism : All B \% D Prosyllogisms : AU D 'xst E All E is F

No C is D No C is E No C is F

No C is ^ No C is Z> NoC isE

Z>, Ei &c., are successively more universal subjects ; and the series of affirmative majors containing them must ex hypothesi terminate.

* Since the series of affirmative majors terminates and since an affirmative major is required for each prosyllogism, we shall eventually reach a minor incapable of proof and therefore immediate.

* This chapter attempts to answer the first and second questions raised in ch. 19. So obscure is it that it has seemed best to add a series of foot-notes constituting an analysis of the argument. This has been expanded where it has appeared possible to supplement the text of the translation, and contracted where the contrary was the case. Direct comment has been included only in parentheses contained In square brackets.

Sa"

and an infinite series cannot be traversed, predicates constituting a thing’s essential nature must be finite in 83* number.^ But as regards predicates generally we have the following prefatory remarks to make, (i) We can affirm without falsehood ‘ the white (thing) is walking and ‘ that big (thing) is a log’ ; or again, ‘the log is big’, and ‘the man walks’. But the affirmation differs in the two cases.

5 When I affirm * the white is a log ’, I mean that something which happens to be white is a log— not that white is the substratum in which log inheres, for it was not qua white or q7ia a species of white that the white (thing) came to be a log, and the white (thing) is consequently not a log except incidentally. On the other hand, when I affirm ‘ the log is white ’, I do not mean that something else, which happens lo also to be a log, is white (as 1 should if I said ‘ the musician is white *, which would mean ‘ the man who happens also to be a musician is white ’) ; on the contrary, log is here the substratum — the substratum which actually came to be white, and did so qua wood or qtm a species of wood and qua nothing else.

If we must lay down a rule, let us entitle the latter kind 15 of statement predication, and the former not predication at all, or not strict but accidental predication. ‘White’ and ‘ log * will thus serve as types respectively of predicate and subject.

We shall assume, then, that the predicate is invariably 30 predicated strictly and not accidentally of the subject, for on such predication demonstrations depend for their force. It follows from this that when a single attribute is predicated of a single subject, the predicate must affirm of the subject either some element constituting its essential nature, or that it is in some way qualified, quantified, essentially related, active, passive, placed, or dated.'^

^ If the attributes in a series of predication such as we are discussing are substantiaj, they must be finite in number, because they are then the elements constituting the definition of a substance.

* The first of three statements preliminary to a proof that predicates which are accidental— other than substantial — cannot be unlimited in number : Accidental is to be distinguished from essential or natural predication [cf. i, ch. 4, 73'> 15 ff. and An. Pr. i, ch. 25, 43* 2^-6]. The former is alien to demonstration : hence, provided that a single attribute is

BOOK L 22

(2) Predicateswhichsignify substance signify that the subject is identical with thepredicateor withaspeciesof the predicate. Predicates not signifying substance which are predicated 35 of a subject not identical with themselves or with a species of themselves are accidental or coincidental ; q. g. white is a coincident of man, seeing that man is not identical with white or a species of white, but rather with animal, since man is identical with a species of animal. These predicates which 30 do not signify substance must be predicates of some other subject, and nothing can be white which is not also other than white. The Forms we can dispense with, for they are mere sound without sense ; and even if there ‘are such things, they are not relevant to our discussion, since demonstrations are concerned with predicates such as we have defined.^ 35

(3) If is a quality of B cannot be a quality of A — a quality of a quality. Therefore A and B cannot be predicated reciprocally of one another in strict predication : they can be affirmed without falsehood of one another, but not genuinely predicated of each other For one alternative is that they should be substantially predicated of one another, i. e. B would become the genus or differentia of /I— the 83^ predicate now become subject But it has been shown that in these substantial predications neither the ascending predicates nor the descending subjects form an infinite series; c. g. neither the scries, man is biped, biped is animal, &c., nor the series predicating animal of man, man of Callias, Callias of a further subject as an element of its predicated of a single subject, all genuine predicates fall either under the category of substance or under one of the adjectival categories.

^ Second preliminary statement : The precise distinction of substantive from adjectival predication makes clear (implicitly) the two distinctions, (a) that between natural' and accidental predication, (b) that between substantival and adjectival predication, which falls within natural predication. [For ‘ coincidentar, ‘coincident’, see note on 73^ 4.] This enables us to reject the Platonic Forms.

I In *^30 read n, and for repcTtV/zara in *^33 cf. ProbL 518^ 29.)

* Third preliminary statement merging into the beginning of the proof proper : Reciprocal predication cannot produce an indefinite regress because it is not natural predication.

[iroidrrjs in 83*37 seems to be equivalent to ‘character’ and to cover all the categories, cf. MeL A. 1020* 33-^ 2. ovtw? in * 38 is most naturally taken as meaning ‘in strict or natural predication’, but may mean ‘ so as to produce an indefinite regress The latter is, however, an mplicit consequence of the predication being unnatural.]

5 essential nature, is infinite. For all such substance is definable, and an infinite series cannot be traversed in thought : consequently neither the ascent nor the descent is infinite, since a substance whose predicates were infinite w^ould not be definable. Hence they will not be predicated each as the genus of the other; for this would equate a lo genus with one of its own species. Nor (the other alternative) can a quale be reciprocally predicated of a quale^ nor any term belonging to an adjectival category of another such term, except by accidental predication ; for all such predicates are coincidents and are predicated of substances.^ On the other hand— in proof of the impossibility of an infinite ascending series — every predication displays the subject as somehow qualified or quantified or as characterized under one of the other adjectival categories, or else 15 is an element in its substantial nature: these latter are limited in number, and the number of the widest kinds under which predications fall is also limited, for every predication must exhibit its subject as somehow qualified, quantified, essentially related, acting or suffering, or in some place or at some time.^

I assume first that predication implies a single subject and a single attribute, and secondly that predicates which are not substantial are not predicated of one another. We assume this because such predicates are all coincidents, and

^ Expansion of third preliminary statement : Reciprocals A and B might be predicated of one another (a) substantially ; but it has been proved already that because a definition cannot contain an infinity of elements substantial predication cannot generate infinity ; and it would disturb the relation of genus and species : (^) as qualia or qttanta &c. ; but this would be unnatural predication, because all such predicates are adjectival, i. e. accidents, or coincidents, of substances.

[ou5e firjv in 83^ 10, though an anacoluthon, answers § ... rot in » 39. ndura yap . , . Kan^yoptirai in and 12 seems to be Aristotle’s proof that the descending series in the predication of accidents terminates ; sc. because it ends in an individual substance.]

* The ascent of predicates is also finite ; because all predicates fall under one or other of the categories, and (a) the series of predicates under each category terminates when the category is reached, and (d) the number of the categories is limited, [(a) seems to mean that an attribute as well as a substance is definable by genus and differentia, and the elements in its definition must terminate in an upward direction at the category, and can therefore no more form an infinite series than can the elements constituting the definition of a substance.]

BOOK I. aa 83'> though some are essential coincidents, others of a different type, yet we maintain that all of them alike are predicated ao of some substratum and that a coincident is never a substratum— since we do not class as a coincident anything which does not owe its designation to its being something other than itself, but always hold that any coincident is predicated of some substratum other than itself, and that another group of coincidents may have a different substratum, Subject to these assumptions then, neither the ascending nor the descending series of predication in which ^5 a single attribute is predicated of a single subject is infinite.^ For the subjects of which coincidents are predicated are as many as the constitutive elements of each individual substance, and these we have seen are not infinite in number, while in the ascending series are contained those constitutive elements with their coincidents — both of which are finite.^ We conclude that there is a given subject {D) of which some attribute {C) is primarily predicable ; that there must be an attribute {B) primarily predicable of the first attribute, and that the series must end with a term {A) not predicable of any term prior to the last 3^ subject of which it was predicated and of which no term prior to it is predicable.^

' To reinforce this brief proof that descent and ascent are both finite we may repeat the premisses on which it depends. These are (i) the assumption that predication means the predication of one attribute of one subject, and (2) our proof that accidents cannot be reciprocally predicated of one another, because that would be unnatural predication. It follows from these premisses that both ascent and descent are finite. [Actually (2) only reinforces the proof that the descent terminates.]

* To repeat again the proof that both ascent and descent are finite :

The subjects cannot be more in number than the constituents of a definable form, and these, we know, are not infinite in number : hence the descent is finite. The series regarded as an ascent contains subjects and ever more universal accidents, and neither subjects nor accidents are infinite in number.

* Formal restatement of the last conclusion. [This is obscure: apparently Aristotle here contemplates a hybrid series: category, accident, further specified accident . . . substantial genus, subgenus . . . infima species^ individual substance.

If tnis interpretation of the first portion of the chapter is at all correct, Aristotle’s first proof that the first two questions of ch. 19 must be answered in the negative is roughly as follows : The ultimate subject of all judgement is an individual substance, a concrete singular. Of such concrete singulars you can predicate substantially only the elements

The argument we have given is one of the so-called proofs ; an alternative proof follows. Predicates so related to their subjects that there are other predicates prior to them predicable of those subjects are demonstrable; but of demonstrable propositions one cannot have something s5 better than knowledge, nor can one know them without demonstration. Secondly, if a consequent is only known through an antecedent (viz. premisses prior to it) and we neither know this antecedent nor have something better than knowledge of it, then we shall not have scientific knowledge of the consequent. Therefore, if it is possible through demonstration to know anything without qualification and not merely as dependent on the acceptance of certain premisses — i. e. hypothetically — the series of intermediate 84^ predications must teiminate. If it docs not terminate, and beyond any predicate taken as higher than another there remains another still higher, then every predicate is demonstrable. Consequently, since these demonstrable predicates are infinite in number and therefore cannot be traversed, we shall not know them by demonstration. If, therefore, we have not something better than knowledge of 5 them, we cannot through demonstration have unqualified but only hypothetical science of anything.^ constituting their injima species. These are limited in number because they form an intelligible synthesis. So far, then, as substantial predicates are concerned, the questions are answered. But these elements are also the subjects of which accidents, or coincidents, are predicated, and therefore as regards accidental predicates, at any rate, the descending series of subjects terminates. The ascending series of attributes also terminates, (i) because each higher attribute in the series can only be a higher genus of the accident predicated of the ultimate subject of its genus, and therefore an element in the accident’s definition ; (2) because the number of the categories is limited.

We may note that the first argument seems to envisage a series which, viewed as an ascent, starts with a concrete individual of which the elements of its definition are predicated successively, specific differentia being followed by proximate genus, which latter is the starting-point of a succession of ever more universal attributes terminating in a category j and that the second argument extends the scope of the dispute to the sum total of all the trains of accidental predication which one concrete singular substance can beget. It is, as so often in Aristotle, difficult to be sure whether he is regarding the injima species or the concrete singular — the Trpwriy ovala of the Categories — as the ultimate subject of judgement. I have assumed that he means the latter.]

^ The former proof was dialectical. So is that which follows in this paragraph. If a predicate inheres in a subject but is sub-

BOOK 1. 22

As dialectical proofs of our contention these may carry conviction, but an analytic process will show more briefly that neither the ascent nor the descent of predication can be infinite in the demonstrative sciences which are the Jo object of our investigation. Demonstration proves the inherence of essential attributes in things. Now attributes may be essential for two reasons : either because they are elements in the essential nature of their subjects, or because their subjects are elements in their essential nature. An example of the latter is odd as an attribute of number — though it is number's attribute, yet number itself is an 15 element in the definition of odd ; of the former, multiplicity or the indivisible, which are elements in the definition of number. In neither kind of attribution can the terms be infinite.^ They are not infinite where each is related to the term below it as odd is to number, for this would mean the inherence in odd of another attribute of odd in whose nature odd was an essential element : but then number 20 will be an ultimate subject of the whole infinite chain of attributes, and be an element in the definition of each of them. Hence, since an infinity of attributes such as contain their subject in their definition cannot inhere in a single thing, the ascending series is equally finite.'-^ Note, moreordinate to a higher predicate also predicable of that subject [i. e. not to a wider predicate but to a middle term giving logically prior premisses and in that sense higher], then the inherence can be known by demonstration and only by demonstration, liut that means that it is known as the consequent of an antecedent. Therefore, if demonstration gives genuine knowledge, the series must terminate; i.e. every predicate is demonstrable and known only as a consequent and therefore hypothetically, unless an antecedent known per se is reached.

^ Analytic proof [i. e. a proof from the appropriate dpx"* ^he subject which Aristotle is here treating, namely ra draXi^Tt»ca ; cf. the frequent corresponding use of (j}V(TtK^s, Note, however, that t« dmXvriKd have no proper place in Aristotle’s classification of the sciences : there is no special yeVo? of reality forming their subject-matter]. Demonstration proves the inherence in subjects of attributes essential either (i) because they are elements in their subject’s definition, e.g. multiplicity or the indivisible [reading in 84* 16 ddiaiperov with the first hand of D. Number mmrrXrjOos ddiaipfVwK, cf. Met, 22] ; or (2) because their subjects are elements in their definition, as e.g. odd [mpiTToy in ^14 is really an abbreviatioii for n^pirrov Ka\ Spnov, cf. i, ch. 4, 73® 39] 1^ relation to number. Attribution of neither type of attribute can beget an infinite series.

* As regards type (2) [the opening of the chapter has disposed ot type (i)] ; in any scries of such predicates any given term will contain over, that all such attributes rriust so inhere in the ultimate subject— e. g. its attributes in number and number in them— as to be commensurate with the subject and not of wider 25 extent. Attributes which are essential elements in the nature of their subjects are equally finite : otherwise definition would be impossible. Hence, if all the attributes predicated are essential and these cannot be infinite, the ascending series will terminate, and consequently the descending series too.^

If this is so, it follows that the intermediates between any two terms are also always limited in number.* An imme- 30 d lately obvious consequence of this is that demonstrations necessarily involve basic truths, and that the contention of some — referred to at the outset — that all truths are demonstrable is mistaken. For if there are basic truths, (a) not all truths are demonstrable, and (i) an infinite regress is impossible ; since if either (^) or (3) were not a fact, it would mean that no interval was immediate and 35 indivisible, but that all intervals were divisible. This is true because a conclusion is demonstrated by the interposition, not the apposition, of a fresh term. If such interposition could continue to infinity there might be an infinite number of terms between any two terms ; but this is im- 8^^ possible if both the ascending and descending series of predication terminate ; and of* this fact, which before was shown dialectically, analytic proof has now been given.'^ in its definition all the lower terms, and the series will therefore terminate at the bottom in the ultimate subject. But since every term down to and including the ultimate subject is contained in the definition of any given term, if the series ascend infinitely there must be a term containing an infinity of terms in its definition. But this is impossible, and therefore the ascent terminates.

^ Note too that either type of essential attribute must be commensurate with its subject, because the first defines, the second is defined by, its subject ; and consequently no subject can possess an infinite number of essential predicates of either type, or definition would be impossible. Hence if the attributes predicated are all essential, the scries terminates in both directions. [This passage merely displays the ground underlying the previous argument that the ascent of attributes of type {2) is finite, and notes in passing its more obvious and already stated application to attributes of type (i).]

* It follows that the intermediates between a given subject and a given attribute must also be limited in number.

’ Corollary: (a) demonstrations necessarily involve basic truths,

It is an evident corollary of these conclusions that if the same attribute A inheres in two terms C and D predicable either not at all, or not of all instances, of one another, it 5 does not always belong to them in virtue of a common middle term. Isosceles and scalene possess the attribute of having their angles equal to two right angles in virtue of a common middle ; for they possess it in so far as they are « both a certain kind of figure, and not in so far as they differ from one another. But this is not always the case; for, were it so, if we take B as the common middle in virtue of which A inheres in C and Z>, clearly B would inhere in C 10 and D through a second common middle, and this in turn would inhere in C and D through a third, so that between two terms an infinity of intermediates would fall — an impossibility. Thus it need not always be in virtue of a common middle term that a single attribute inheres in several subjects, since there must be immediate intervals. Yet if the attribute to be proved common to two subjects 15 is to be one of their essential attributes, the middle terms involved must be within one subject genus and be derived from the same group of immediate premisses ; for we have seen that processes of proof cannot pass from one genus to another.^

It is also clear that when A inheres in B, this can be demonstrated if there is a middle term. Further, the 20 ‘ elements ’ of such a conclusion are the premisses containand therefore (^) not all truths, as we saw [84^32] that some maintain, are demonstrable [cf. 72^ 6]. If either (a) or {5} were not a fact, since conclusions are demonstrated by the interposition of u middle and not by the apposition of an extreme term [cf. note on 78* 15], no premiss would be an immediate indivisible interval. This closes the analytic argument.

[Thus the nerve of the dialectical and analytic arguments is the same : they differ only in that the former covers all syllogism. The basis of Aristotle’s contention is that predication is always a synthesis of determinate elements, a concrete whole which is essentially not aneipov. Unfortunately for Aristotle’s point this contention, however sound, involves the reciprocal interdependence of the elements of such a synthesis and, ultimately, of all the terms of a series of predication.

It may prove that the series of predication cannot contain an infinity of terms, but it does not prove that it is terminated by self-evident apya/, true within their own four comers. It is questionable how far Aristotle’s logical system can survive this chapter.]

ing the middle in question, and they are identical in number with the middle terms, seeing that the immediate propositions— or at least such immediate propositions as are universal— are the ‘elements*. If, on the other hand, there is no middle term, demonstration ceases to be possible : we are on the way to the basic trutlis. Similarly if A does not inhere in this can be demonstrated if there is a middle 35 term or a term prior to B in which A does not inhere : otherwise there is no demonstration and a basic truth is reached.^ There are, moreover, as many ‘ elements * of the demonstrated conclusion as there are middle terms, since it is propositions containing these middle terms that are the basic premisses on which the demonstration rests ; and as there arc some indemonstrable basic truths asserting that ‘ this is that ’ or that this inheres in that so there are 30 others denying that ‘ this is that * or that ‘ this inheres in that ’ — in fact some basic truths will affirm and some will deny being.

When wc are to prove a conclusion, we must take a primary essential predicate — suppose it C — of the subject B^ and then suppose A similarly predicable of C, If we proceed in this manner, no proposition or attribute which falls beyond A is admitted in the proof: the intei*val is constantly condensed until subject and predicate become 35 indivisible, i.c. one. We have our unit when the premiss becomes immediate,^ since the immediate premiss alone is a single premiss in the unqualified sense of ‘single*. And as in other spheres the basic element is simple but not identical in all — in a system of weight it is the mina, in music the quarter-tone, and so on — so in syllogism the unit 85^ is an immediate premiss, and in the knowledge that demonstration gives it is an intuition.^ In syllogisms, then, which prove the inherence of an attribute, nothing falls outside the major term. In the case of negative s)dlogisms on the other hand, (1) in the first figure nothing falls outside the

' Placing a full stop after dpxn in ^ 26.

* Placing a comma after yfvrjrm in ^ 36.

’ uovt grasps immediately an indivisible reality — e.g. the W Avai of a substance the elements of which are not predicated of one another Cf. 77*4, S8^3S-7, and notes thereon.

major term whose inherence is in question ; e. g. to prove through a middle C that A does not inhere in B the premisses required are, all 5 is C^noCisA, Then if it has 5 to be proved that no C is A, a middle must be found between A and C ; and this procedure will never vary.

(2) If we have to show that £ is not D by means of the premisses, all Z? is C; no Ey or not all if is C ; then the middle will never fall beyond E, and E is the subject of which D is to be denied in the conclusion.

(3) In the third figure the middle will never fall beyond 10 the limits of the subject and the attribute denied of it.

24 Since demonstrations may be either commensurately universal or particular,^ and either affirmative or negative ; the question arises, which form is the better? And the same 15 question may be put in regard to so-callcd ‘direct’ demonstration and reciuctio ad inipossibile. Let us first examine the commensurately universal and the particular forms, and when we have cleared up this problem proceed to discuss ‘ direct ’ demonstration and reductio ad inipossibile.

The following considerations might lead some minds to 20 prefer particular demonstration.

(i) The superior demonstration is the demonstration which gives us greater knowledge (for this is the ideal of demonstration), and we have greater knowledge of a particular individual when we know it in itself than when we know it through something else; e.g. wc know Coriscus the musician better when we know that Coriscus is musical than 35 when we know only that man is musical, and a like argument holds in all other cases. But commensurately universal demonstration, instead of proving that the subject itself actually is Xy proves only that something else is .r— e.g. in attempting to prove that isosceles is Xy it proves not that isosceles but only that triangle is x — whereas particular demonstration proves that the subject itself is x. The demonstration, then, that a subject, as such, possesses an attribute is superior. If this is so, and if the particular

^ Second figurfe, Camestres or Baroco.

* The distinction is that of whole and part, genus and species ; not that of universal and singular.

rather than the commensurately universal form so demon- 30 strates, particular demonstration is superior.

{%) The universal has not a separate being over against groups of singulars. Demonstration nevertheless creates the opinion that its function is conditioned by something like this — some separate entity belonging to the real world ; that, for instance, of triangle or of figure or number, over 35 against particular triangles, figures, and numbers. But demonstration which touches the real and will not mislead is superior to that which moves among unrealities and is delusory. Now commensurately universal demonstration is of the latter kind : if we engage in it we find ourselves reasoning after a fashion well illustrated by the argument that the proportionate is what answers to the definition of some entity which is neither line, number, solid, nor plane, 85" but a proportionate apart from all these. Since, then, such a proof is characteristically commensurate and universal, and less touches reality than does particular demonstration, and creates a false opinion, it will follow that commensurate and universal is inferior to particular demonstration.

We may retort thus, (i) The first argument applies no more to commensurate and universal than to particular 5 demonstration. If equality to two right angles is attributable to its subject not qua isosceles but qua triangle, he who knows that isosceles possesses that attribute knows the subject as qua itself possessing the attribute, to a less degree than he who knows that triangle has that attribute. To sum up the whole matter ; if a subject is proved to possess qua triangle an attribute which it does not in fact possess qua triangle, that is not demonstration : but if it does possess it qua triangle, the rule applies that the greater knowledge is his who knows the subject as possessing its attribute qua that in virtue of which it actually does possess it. Since, io then, triangle is the wider term, and there is one identical definition of triangle — i.e. the term is not equivocal — and since equality to two right angles belongs to all triangles, it is isosceles qua triangle and not triangle qua isosceles which has its angles so related. It follows that he who knows a connexion universally has greater knowledge of it as it in

BOOK I. 24 85^ fact is than he who knows the particular ; and the inference is that commensurate and universal is superior to particular demonstration,

{%) If there is a single identical definition — i.e. if the ^5 commensurate universal is unequivocal — then the universal will possess being not less but more than some of the particulars, inasmuch as it is universals which comprise the imperishable, particulars that tend to perish.

(3) Because the universal has a single meaning, we are not therefore compelled to suppose that in these examples it has being as a substance apart from its particulars — any more than we need make a similar supposition in the other cases of unequivocal universal predication, viz. where the predicate signifies not substance but quality, essential related- ao ness, or action. If such a supposition is entertained, the blame rests not with the demonstration but with the hearer.

(4) Demonstration is syllogism that proves the cause, i. e. the reasoned fact, and it is rather the commensurate universal than the particular which is causative (as may be shown thus : that which possesses an attribute through its own essential nature is itself the cause of the inherence, 35 and the commensurate universal is primary;^ hence ^ the commensurate universal is the cause). Consequently commensurately universal demonstration is superior as more especially proving the cause, that is the reasoned fact.

(5) Our search for the reason ceases, and we think that we know, when the coming to be or existence of the fact before us is not due to the coming to be or existence of some other fact, for the last step of a search thus conducted is eo ipso the end and limit of the problem. Thus : ‘ Why did he io come ? * ‘To get the money — wherewith to pay a debt — that he might thereby do what was right.’ When in this regress we can no longer find an efficient or final cause, we regard the last step of it as the end of the coming — or being or coming to be — and we regard ourselves as then only having full knowledge of the reason why he came.

If, then, all causes and reasons are alike in this respect, 35 * And therefore also essential ; cf. i, ch. 4, 73** 26 ff,

«45 *4 4 Y and if this is the means to full knowledge in the case of final causes such as we have exemplified, it follows that in the case of the other causes also full knowledge is attained when an attribute no longer inheres because of something else. Thus, when we learn that exterior angles are equal to four right angles because they are the exterior angles of an isosceles, there still remains the question ‘ Why has 86^ isosceles this attribute?* and its answer * Because it is a triangle, and a triangle has it because a triangle is a rectilinear figure.* If rectilinear figure possesses the property for no further reason,^ at this point we have full knowledge — but at this point our knowledge has become commensurately universal, and so we conclude that commensurately universal demonstration is supeiior.

(6) The more demonstration becomes particular the more it sinks into an indeterminate manifold, while universal

5 demonstration tends to the simple and determinate. But objects so far as they are an indeterminate manifold are unintelligible, so far as they are determinate, intelligible : they are therefore intelligible rather in so far as they are universal than in so far as they are particular. From this it follows that univei sals are more demonstrable : but since relative and correlative increase concomitantly, of the more demonstrable there will be fuller demonstration. Hence the commensurate and universal form, being more truly 10 demonstration, is the superior.

(7) Demonstration which teaches two things is preferable to demonstration which teaches only one. He who possesses commensurately universal demonstration knows the particular as well, but he who possesses particular demonstration docs not know the universal. So that this is an additional reason for preferring commensurately universal demonstration. And there is yet this further argument:

(8) Proof becomes more and more proof of the commensurate universal as its middle term approaches nearer to the

15 basic truth, and nothing is so, near as the immediate premiss which is itself the basic truth. If, then, proof from the basic truth is more accurate than proof not so derived, ^ i. e. for no reason other than its own nature.

BOOK 1. 34 demonstration which depends more closely on it is more accurate than demonstration which is less closely dependent.

But commensurately universal demonstration is characterized by this closer dependence, and is therefore superior. Thus, if A had to be proved to inhere in /), and the middles were B and C, B being the higher term would render the demonstration which it mediated the more universal. 20

Some of these arguments, however, are dialectical. The clearest indication of the precedence of commensurately universal demonstration is as follows *. if of two propositions, a prior and a posterior, we have a grasp of the prior, we havea kind of knowledge — a potential grasp — of the posterior as well. For example, if one knows that the angles of all *’5 triangles are equal to two right angles, one knows in a sense — potentially — that the isosceles’ angles also are equal to two right angles, even if one does not know that the isosceles is a triangle ; but to grasp this posterior proposition is by no means to know the commensurate universal either potentially or actually. Moreover, commensurately universal demonstration is through and through intelligible ; particular demonstration issues in sense-perception. 30

25 The preceding arguments constitute our defence of the superiority of commensurately universal to particular demonstration. That affirmative demonstration excels negative may be shown as follows.

(1) We may assume the superiority ceteris paribus of the demonstration which derives from fewer postulates or hypotheses— in short from fewer premisses ; for, given that all 35 these are equally well known, where they are fewer knowledge will be more speedily acquired, and that is a desideratum.

The argument implied in our contention that demonstration from fewer assumptions is superior may be set out in universal form as follows.* Assuming that in both cases alike the middle terms are known, and that middles which are prior are better known than such as are posterior, we ma}' suppose two demonstrations of the inherence of A in the one proving it through the middles C and D, the other 86**

through F and G, Thcn^ A-D is known to the same degree as A-E (in the second proof), but A~D is better known than and prior to A-E (in the first proof) ; since A-E is proved through A-D, and the ground is more certain than the conclusion.^

5 Hence demonstration by fewer premisses is ceteris paribus superior. Now both affirmative and negative demonstration operate through three terms and two pro. misses, but whereas the former assumes only that something is, the latter assumes both that something is and that something else is not, and thus operating through more kinds of premiss ^ is inferior.

10 (2) It has been proved ^ that no conclusion follows if both premisses are negative, but that one must be negative, the other affirmative. So we are compelled to lay down the following additional rule: as the demonstration expands, the affirmative premisses must increase in number, but there ^5 cannot be morethan one negative premiss in each complete proof.^ Thus, suppose no is yJ, and all C is B. Then, if both the premisses are to be again expanded, a middle must be interposed. Let us interpose D between A and and E between B and C, Then clearly E is affirmatively 30 related to iPand C, while D is affirmatively related to B but negatively to A ; for all B is A but there must be no D which is A. Thus there proves to be a single negative premiss, A-D. In the further prosyllogisms too it is the same, because in the terms of an affirmative syllogism the middle is always related affirmatively to both extremes ; in 25 a negative syllogism it must be negatively related only to one of them, and so, this negation comes to be a single negative premiss, the other premisses being affirmative. If,

* Reading o/iotW with Boethius and vet. Interp. So Waitz.

* The two proofs are (i) A—B (2) A—F

® ‘ Specie non numero pluia*, Zabarella. ^ An, Pk i, ch. 7.

^ i. e. in one syllogism and two prosyllogisms proving its premisses.

BOOK 1. 25 then, that through which a truth is proved is a better known and more certain truth, and if the negative proposition is proved through the affirmative and not vice versa, affirmative demonstration, being prior and better known and more certain, will be superior.

(3) The basic truth of demonstrative syllogism is the 30 universal immediate premiss, and the universal premiss asserts in affirmative demonstration and in negative denies: and the affirmative proposition is prior to and better known than the negative (since affirmation explains denial and is prior to denial, just as being is prior to not-being). It follows 35 that the basic premiss of affirmative demonstration is superior to that of negative demonstration, and the demonstration which uses superior basic premisses is superior.

(4) Affirmative demonstration is more of the nature of a basic form of proof, because it is a sine qua non of negative demonstration.

26 Since affirmative demonstration is superior to negative, it 87® is clearly superior also to reductio ad impossibile. We must first make certain what is the difference between negative demonstration and reductio ad impossibile. Let us suppose that no B is A, and that all C is the conclusion necessarily follows that no Cis A. If these premisses are assumed, 5 therefore, the negative demonstration that no C is is direct, Reductio ad impossibik.oxi the other hand, proceeds as follows Supposing we are to prove that A docs not inhere in we have to assume that it does inhere, and further that B inheres in C, with the resulting inference that A^ inheres in C. This we have to suppose a known and admitted impossibility; and we then infer that A cannot inhere in B, lo Thus if the inherence of -5 in C is not questioned, A*s inherence in 5 is impossible.

The order of the terms is the same in both proofs : they differ according to which of the negative propositions is the better known, the one denying -^4 of ^ or the one denying A of C, When the falsity of the conclusion ^ is the better

^ i. e. the impossibility of A~Cy the conclusion of the hypothetical syllogism.

87* ANA LYT I C A POST K R 10 R A

15 known, wc use rcductio ad iinpossibilc \ wlicn the major prenaiss of the syllogism is the more obvious, we use direct demonstration. All the same the proposition denying A of B is, in the order of being, prior to that denying A of C\ for premisses are prior to the conclusion which follows from them, and ‘ no C is * is the conclusion, ‘ no B is A ’ one of 20 its premisses. For the destructive result of redactio ad impossibile is not a proper conclusion, nor arc its antecedents proper premisses. On the contrary ; the constituents of syllogism arc premisses related to one another as whole to part or part to whole,' whereas the premisses A-C :ind A - B 25 are not thus related to one another. Now the superior demonstration is that which proceeds from better known and prior premisses, and while both these forms depend for credence on the not being of something, )’ct the source of the one is prior to that of the other. Therefore negative demonstration will have an unqualified superiority to reduct io ad impossibile^ and affirmative demonstration, being superior to negative, will consequently be superior also to rcductio ad 30 impossibile.

The science which is knowledge at once of the fact and 27 of the reasoned fact, not of the fact by itself without the reasoned fact, is the more exact and the prior science.

A science such as arithmetic, which is not a science of properties qua inhering in a substratum, is more exact than and prior to a science like harmonics, which is a science of properties inhering in a substratum ; and similarly a science like arithmetic, which is constituted of fewer basic elements, is more exact than and prior to geometry, which requires 35 additional elements. What I mean by ‘ additional elements ’ is this : a unit is substance without position, while a point is substance with position ; the latter contains an additional element.

* Deleting commas after and limv in ^22, In An. Pr. 25^32-5 Aristotle detines the first figure as that in which the middle term is contained in the major as in a whole and the minor is contained in the middle as in a whole. Hence major premiss is related to minor as whole to part. 'I'he first figure is perfect because it displays the natural organic movement of thought from minor through middle to major. Reduciio ad Unpossibile perverts this natural movement and its * premisses’ do not stand in this organic relation.

a8 A single science is one whose domain is a single genus, viz. all the subjects constituted out of the primary entities of the genus — i.e. the parts of this total subject — and their essential properties.

One science differs from another when their basic truths have neither a common source nor arc derived those of the one science ' from those of the other. This is verified when 87^ we reach the indemonstrable premisses of a science, for they must be within one genus with its conclusions : and this again is verified if the conclusions proved by means of them fall within one genus — i. c. are homogeneous.

29 One can have several demonstrations of the same 5 connexion not only by taking from the same series of predication middles which are other than the immediately cohering term ^ — e. g. by taking C, D, and F sevcrall)' to prove A-B — but also by taking a middle from another series. Thus let A be change, D alteration of a property, B feeling pleasure, and G relaxation. Wc can then without falsehood predicate D of B and A of D, for he who is pleased jo suffers alteration of a property, and that which alters a property changes. Again, wc can predicate A of G without falsehood, and G q{ B \ for to feel pleasure is to relax, and to relax is to change. So the conclusion can be drawn through middles which arc different, i. c. not in the same series — yet not so that neither of these middles is prcdicable of the other, for they must both be attributable to some one 1 ; subject.

A further point worth investigating is how many ways of proving the same conclusion can be obtained by varying the figure.

30 There is no knowledge by demonstration of chance conjunctions; for chance conjunctions exist neither by necessity nor as general connexions but comprise what 20 comes to be as something distinct from these. Now demonstration is concerned only with one or other of these two ; for all reasoning proceeds from necessary or general premisses, the conclusion being necessary if the premisses

^ Reading urtpai.

35 are necessary and general if the premisses arc general. Consequently, if chance conjunctions are neither general nor necessary, they are not demonstrable.

Scientific knowledge is not possible through the act of 31 perception. Even if perception as a faculty is of ' the such ' and not merely of a ‘ this somewhat V yet one must at any rate actually perceive a * this somewhat and at a definite 30 present place and time : but that which is commensurately universal and true in all cases one cannot perceive, since it is not ‘ this * and it is not ‘ now * ; if it were, it would not be commensurately universal- -the term we apply to what is always and everywhere. Seeing, therefore, that demonstrations are commensurately universal and universals imperceptible, we clearly cannot obtain scientific knowledge by 35 the act of perception : nay, it is obvious that even if it were possible to perceive that a triangle has its angles equal to two right angles, we should still be looking for a demonstration— we should not (as some ^ say) possess knowledge of it ; for perception must be of a particular, whereas scientific knowledge involves the recognition of the commensurate universal. So if we were on the moon, and saw the earth 40 shutting out the sun^s light, we should not know the cause 88® of the eclipse : we should perceive the present fact of the eclipse, but not the reasoned fact at all, since the act of perception is not of the commensurate universal. I do not, of course, deny that by watching the frequent recurrence of this event we might, after tracking the commensurate universal, possess a demonstration, for the commensurate universal is elicited from the several groups of singulars,

5 The commensurate universal is precious because it makes clear the cause ; so that in the case of facts like these which have a cause other than themselves universal knowledge ® is more precious than sense-perceptions and than intuition. (As regards primary truths there is of course a different account to be given.'*) Hence it is clear that knowledge of

• Protagoras is perhaps referred to.

’ i. e. demonstration through the commensurate universal.

things demonstrable ’ cannot be acquired by perception, unless the term perception is applied to the possession of 10 scientific knowledge through demonstration. Nevertheless certain points do arise with regard to connexions to be proved which are referred for their explanation to a failure in sense-perception : there are cases when an act of vision would terminate our inquiry, not because in seeing we should be knowing, but because we should have elicited the universal from seeing ; if, for example, we saw the pores in the glass and the light passing through, the reason of the 15 kindling would be clear to us^ because we should at the same time see it in each instance and intuit that it must be so in all instances.

32 All syllogisms cannot have the same basic truths. This may be shown first of all by the following dialectical considerations, (i) Some syllogisms are true and some false ; for though a true inference is possible from false 20 premisses, yet this occurs once only — I mean if A, for instance, is truly predicable of C, but the middle, is false, both A-B and being false ; nevertheless, it middles are taken to prove these premisses, they will be false because every conclusion which is a falsehood has false premisses, 25 while true conclusions have true premisses, and false and true differ in kind. Then again, (2) falsehoods are not all derived from a single identical set of principles : there are falsehoods which are the contraries of one another and cannot coexist, e; g. * justice is injustice \ and * justice is cowardice * ; * man is horse*, and ‘man is ox * ; ‘the equal is greater*, and ‘the equal is less.* From our established principles we may argue the 30 case as follows, confining ourselves therefore to true conclusions. Not even all these are inferred from the same basic truths ; many of them in fact have basic truths which differ genetically and are not transferable; units, for instance, which are without position, cannot take the place of points, which have position. The transferred terms could only fit

* A theory of the concentration of rays through a burning-glass which was not Aristotle’s.

35 in as middle terms or as major or minor terms, or else have some of the other terms between them, others outside them.^

Nor can any of the common axioms — such, I mean, as the law of excluded middle — serve as premisses for the proof of all conclusions. For the kinds of being are different, and some attributes attach to quanta and some to qnalia only; and proof is achieved by means of^ the common axioms taken in conjunction with these several kinds and their attributes.

Again, ^ it is not true that the basic truths are much fewer 5 than the conclusions, for the basic truths are the premisses, and the premisses are formed by the apposition of a fresh extreme term or the interposition of a fresh middle. Moreover, the number of conclusions is indefinite, though the number of middle terms is finite ; and lastly some of the basic truths arc necessary, others variable.

^ i. e. the transference of from one science to another must mean that the terms of which they consist will appear in the second science either always as middles or always as majors or always as minors, or else now as middies between terms native to the second science, now as extreme terms linked by middles native to the second science: therefore the second science would contain a demonstration the terms of which were not wdihin one genus, and therefore not predicable kuS^ niro of one another — as Aristotle has shown passim^ cf. e.g. 75^10-12. The usually assumed reference to the figures of syllogism seems irrevelant.

* N.B. 5id, not eV : i.e. if demonstration is to be possible, you require premisses containing the genus and its properties, as well as the Koiva a^iwfxara as regulative canons.

* The argument from ert at 3 to in ^8 appears to be as follows : * (Actually, the conclusions are many ; but if the dpxnl of all demonstration were the same, there would only be a few conclusions.) But it is not true that the much few’er than the conclusions, for the die premisses, and the premisses are formed either (i) by the apposition of fresh extreme terms, or (2) by the interpolation of fresh middles (and therefore in (i) you get a fresh dpxf) for every fresh conclusion, the other premiss being a previous conclusion (cf. note on 78^14); while in (2) the premisses become each in turn a conclusion). Moreover the number of conclusions is indefinite (.*. once again that of the dpxal cannot be small) — though of course (if you are proceeding by TrvKuaxris of a didarj^pa requiring mediation) the middle terms (required before you reach immediate premisses) are not indefinite in number. Finally there are variable as well as necessary dpx<n (and therefore once move the number cannot be small).’

The last sentence is a final argument that the dpx<d are not few in number, and is admissible because the whole treatment is dialectical, cf. 88^ 19.

Looking at it in this way wc see that, since the number of conclusions is indefinite, the basic truths cannot be identical or^ limited in number. If, on the other hand, identity is used 10 in another sense, and it is said, c. g these and no other are the fundamental truths of geometry, these the fundamentals of calculation, these again of medicine * ; would the statement mean anything except that the sciences have basic truths ? To call them identical because they are self-identical is absurd, since everything can be identified with everything in that sense of identity. Nor again can the contention 15 that all conclusions have the same basic truths mean that from the mass of all possible premisses any conclusion may be drawn. That would be exceedingly naive, for it is not the case in the clearly evident mathematical sciences, nor is it possible in analysis, since it is the immediate premisses which are the basic truths, and a fresh conclusion is only formed by the addition of a new immediate premiss - : but if it be 20 admitted that it is these primary immediate premisses which are basic truths, each subjcct-genus will provide one basic truth.’^ If, however, it is not argued that from the mass of all possible premisses any conclusion may be proved, nor yet admitted that basic truths differ so as to be generically different for each science, it remains to consider the possibility that, while the basic truths of all knowledge are within one genus, special premisses are required to prove special conclusions. But that this cannot be the case has 25 been shown by our proof that the basic truths of things generically different themselves differ generically. For fundamental truths are of two kinds, those which are premisses of demonstration^ and the subject-genus; and though the former are common, the latter — number, for instance, and magnitude — are peculiar.

* Reading fj with D.

* Such a suggestion would be stupid (i) because you can see at once — so clear are they— that the demonstrations which build up the mathematical sciences by synthesis from their basic elements do not all start from the same apx^^ ; and (2) because in analysis of a conclusion into its ultimate premisses (=*from the complementary point of view nvKyuiarit of a diaarfjpn) different reached in different sciences.

* sc\ ‘at least one— its own definition’.

30 Scientific knowledge and its object differ from opinion 33 and the object of opinion in that scientific knowledge is commensurately universal and proceeds by necessary connexions, and that which is necessary cannot be otherwise.

So though there are things which are true and real and yet can be otherwise, scientific knoivlcdge clearly does not concern them : if it did, things which can be otherwise would 35 be incapable of being otherwise. Nor are they any concern of rational intuition — by rational intuition I mean an originative source of scientific knowledge — nor of indemonstrable knowledge/ which is the grasping of the 89^ immediate premiss. Since then rational intuition, science, and opinion, and what is revealed by these terms, are the only things that can be ‘true’, it follows that it is opinion that is concerned with that which may be true or false, and can be otherwise : opinion in fact is the grasp of a premiss which is immediate but not necessary. This view also fits 5 the observed facts, for opinion is unstable, and so is the kind of being we have described as its object. Besides, when a man thinks a truth incapable of being otherwise he always thinks that he knows it, never that he opines it. He thinks that he opines when he thinks that a connexion, though actually so, may quite easily be otherwise ; for he believes *0 that such is the proper object of opinion, while the necessary is the object of knowledge.

In what sense, then, can the same thing be the object of both opinion and knowledge ? And if any one chooses to maintain that all that he knows he can also opine, why should not ^ opinion be knowledge? For he that knows and he that opines will follow the same train of thought through the same middle terms until the immediate premisses are 15 reached; because it is possible to opine not only the fact but also the reasoned fact, and the reason is the niiddle term ; so that, since the former knows, he that opines also has knowledge.

The truth perhaps is that if a man grasp truths that

^ t/ovff (cf. notes on 85*1 and 77*4) grasps the individual nature, rv ri tjv tlvui or the definition, as a unity ; im<rTr,ixtj immdduKTOf gives this as a premiss.

* Reading (crnu for tarip with A, B, C, and Waitz.

cannot be other than they arc, in the way in which he grasps ^ the definitions through which demonstrations take place, he will have not opinion but knowledge : if on the other hand he apprehends these attributes as inhering in their subjects, but not in virtue of the subjects’ substance and essential nature, he possesses opinion and not genuine 20 knowledge ; and his opinion, if obtained through immediate premisses, will be both of the fact and of the reasoned fact; if not so obtained, of the fact alone. The object of opinion and knowledge is not quite identical ; it is only in a sense identical, just as the object of true and false opinion is in a sense identical. The sense in which some maintain that 25 true and false opinion can have the same object leads them to embrace many strange doctrines, particularly the doctrine that what a man opines falsely he does not opine at all. There are really many senses of * identical *, and in one sense the object of true and false opinion can be the same, in another it cannot. Thus, to have a true opinion that the diagonal is commensurate with the side would be absurd : 30 but because the diagonal with which they are both concerned is the same, the two opinions have objects so far the same: on the other hand, as regards their essential definable nature these objects differ. The identity of the objects of knowledge and opinion is similar. Knowledge is the apprehension of, e. g., the attribute ‘ animal ’ as incapable of being otherwise, opinion the apprehension of * animal ’ as capable of being otherwise — e. g. the apprehension that 35 animal is an element in the essential nature of man is knowledge ; the apprehension of animal as predicable of man but not as an element in man’s essential nature is opinion : man is the subject in both judgments, but the mode of inherence differs.

This also shows that one cannot opine and know the same thing simultaneously ; for then one would apprehend the samii thing as both capable and incapable of being otherwise — an impossibility. Knowledge and opinion of 89*^ the same thing can coexist in two different people in the sense we have explained, but not simultaneously in the * {leading txa with MSS.

same person. That would involve a man’s simultaneously apprehending, e. g,, (i) that man is essentially animal — i. e. cannot be other than animal — and (2) that man is not 5 essentially animal, that is, we may assume,^ may be other than animal.

Further consideration of modes of thinking and their distribution under the heads of discursive thought, intuition, science, art, practical wisdom, and metaphysical thinking, belongs rather partly to natural science, partly to moral philosophy.

10 Quick wit is a faculty of hitting upon the middle term 34 instanlaneousl3^ It would be exemplified by a man who saw that the moon has her bright side always turned towards the sun, and quickly grasped the cause of this, namely that she borrows her light from him ; or observed somebody in conversation with a man of wealth and divined that he was borrowing money, or that the friendship of these people sprang from a common enmity. In all these instances he has seen the major and minor terms and then , - grasped the causes, the middle terms.

Let A represent ^ bright side turned sunward B ‘ lighted from the sun C the moon. Then B, * lighted from the sun ’, is predicable of C, the moon, and Ay * having her bright side towards the source of her light’, is predicable of B.

20 So A is prcdicable of C through B,

^ Reading eo-rw with B, C, and Waitz,

BOOK 11

1 The kinds of question vvc ask arc as many as the kinds of things which we know. They are in fact four: — (i) whether the connexion of an attribute with a thing is a fact,

(2) what is the reason of the connexion, (3) whether a thing exists, (4) what is the nature of the thing. Thus, when our 25 question concerns a complex of thing and attribute^ and we ask whether the thing is thus or otherwise qualified — whether, e.g., the sun suffers eclipse or not — then we are asking as to the fact of a connexion. That our inquiry ceases with the discovery that the sun does suffer eclipse is an indication of this ; and if we know from the start that the sun suffers eclipse, we do not inquire whether it does so or not. On the other hand, when we know the fact we ask the reason ; as, for example, when we know that the sun is being eclipsed and that an earthquake is in progress, it is the reason of 30 eclipse or earthquake into which wc inquire.

Where a complex is concerned, then, those are the two questions we ask ; but for some objects of inquiry we have a different kind of question to ask, such as whether there is or is not a centaur or a God. (By ‘ is or is not * I mean ‘ is or is not, without further qualification ’ ; as opposed to ‘ is or is not (e. g.) white ’.) On the other hand, when we have ascertained the thing's existence, we inquire as to its nature, asking, for instance, ‘ what, then, is God ? * or ‘ what is man ? 35

2 These, then, are the four kinds of question wc ask, and it is in the answers to these questions that our knowledge consists.'-^

' So Zabarella and Pacius explain etk apiOfiou Stvrfs, Waitz takes it as meaning ‘enumerating the alternative possibilities’.

* In ch. I Aristotle has distinguished four forms of inquiry, and the enumeration is taken to be exhaustive. These were: (i) r6 ort, ‘Is S P}* (2) TO a*drt, ‘Why is 5 Pr (3) u cVrt, ‘Does 5 exist ? ^

(4) Tt eVrt, ‘What is 6*?’. (i) answered affirmatively provokes (2), and (3) answered affirmatively provokes (4). In ch. 2 we learn that all four questions are questions as to the cause ; that * Is S P?^ means ‘ Has P-S a cause ? ’, and that ‘ Poes *5* exist ? ’ means ‘ Has S a

Now when vve ask whether a connexion is a fact, or whether a thing without qualification is^ we are really asking whether the connexion or the thing has a ‘ middle ’ ; ^ and when we have ascertained cither that the connexion is a fact or that the thing is — Le. ascertained either the partial or the 90^ unqualified being of the thing — and are proceeding to ask the reason of the connexion or the nature of the thing, then we are asking what the * middle* is.

(By distinguishing the fact of the connexion and the cause ? ’ ; and again that ^ Why is S PV means * What is the cause of P-S ? *, and ‘ What is 5 ? ’ means ‘ What causes S ? *

This is obscurely worked out because Aristotle is hampered by his theory of predication. On the one hand (A) all four questions ask the cause of the being of S\ which is a substance; (i) and (2) ask respectively ‘Is there a cause’ and ‘What is the cause' of S having being as the subject of an attribute ’ — i. e. they seek a cause of part ofS's being, 5’s being in so far as 5 is P] while (3) and (4) ask respectively ‘ Is there a cause * and ‘ What is the cause * of S having being as a substance — i. e. they inquire as to a cause of the complete unqualified (fin-Xwy) being of .S\ On the other hand, (B) (i) and (2) in asking the cause of S being P, are really asking ‘ What is the enuse of Z' ? for P's being consists in its inherence in .S', This seems to distinguish (i) and (2) as concerning the cause of attributes from (3) and (4) as concerning the cause of substances. But you can also ask (3) and (4) of an attribute — 6* need not be a substance — e.g. in 90*^5, given as an instance of a op, is an attribute, aad in ^ 15 (f. (where n itrriv fK\€iylrn ; is shown to be equivalent to Bid tL €(mp eKXnyffis ; and to have the same fxicrop) Bid ri 7 (rtXtjvrj ; is given as the equivalent of

In 1. 31 to the end of the chapter it seems doubtful whether, as I have taken the passage, Aristotle is saying that to know what a thing is is to know what causes it, equally as regards S qua S and S qiu\ P {i,e. equally as regards the complete and the partial being of a substance) ; or equally as regards the being of S and the being of P.

The source of this obscurity is Aristotle’s struggle— necessitated by his view of predication— to distinguish grammatical subject and predicate as substance and attribute, which consequently tend to become two kinds of thing. The same struggle is seen in the fluctuation of the meaning of xmoKfi^fvop^ which means now the complete substance, {a) as a totality of the elements constituting its definition and of its essential properties, [b) as a totality of its defining attributes only ; now (c) a mere substratum which alone remains when you remove all its attributes from a substance.

* ‘Middle’: in this chapter is extended to mean ‘proximate cause’; it is wider than the middle term of a syllogism. It is, or rather is reflected by, the middle term of a syllogism in the case of the definition of an attribute, because the definition of an attribute is a X<5yof of it as inhering in the subject, and the middle term which proves, also causes, or reflects the cause of, this inherence ; but the cause of a substance possessing unqualified being is not something other than itself, but its Xoyos, its definition by genus and differentia; and this cannot be the middle term of a syllogism, because such definition is not demonstrable (cf, ii> ch. 4).

existence of the thing as respectively the partial and the unqualified being of the thing, I mean that if wc ask ‘does the moon suffer eclipse ? ’, or ‘ docs the moon wax ? *, the question concerns a part of the thing s being ; for what we are asking in such questions is whether a thing is this or that, i.c. has or has not this or that attribute : whereas, if we ask whether the moon or night exists, the question concerns the unqualified being of a thing.)

We conclude that in all our inquiries we are asking cither 5 whether there is a ‘ middle ’ or what the ‘ middle ’ is : for the ‘ middle’ here is precisely the cause, and it is the cause that we seek in all bur inquiries. Thus, ‘ Does the moon suffer eclipse ? ’ means ‘ Is there or is there not a cause producing eclipse of the moon?’, and when we have learnt that there is, our next question is, ‘ What, then, is this cause ? * ; for the cause through which a thing not is this or that, i. e. has this or that attribute, but without qualification is — and the 10 cause through which ^ it is — not is without qualification, but ts this or that as having some essential attribute or some accident— are both alike the ‘middle’. By that which is without qualification I mean the subject, e. g. moon or earth or sun or triangle ; by that which a subject is (in the partial sense) I mean a property, e. g. eclipse, equality or inequality, interposition or non-interposilion. For in all these examples it is clear that the nature of the thing and the reason of the fact are identical: the question ‘What is 15 eclipse? ’ and its answer ‘ The privation of the moon’s light by the interposition of the earth ’ are identical with the question ‘ What is the reason of eclipse ? ’ or ‘ Why does the moon suffer eclipse?’ and the reply ‘Because of the failure of light through the earth's shutting it out’. Again, for ‘ What is a concord ? A commensurate numerical ratio of a high and ^ a low note ’, we may substitute ‘ What reason makes a high and a low note concor^dant ? Their relation 20 according to a commensurate numerical ratio.* ‘Are the high and the low note concordant?* is equivalent to ‘Is

' Reading toC ilvai, for to ilvai with Bonltz in 90^ 9,

G their ratio commensurate ? * ; and when we find that it is commensurate, we ask ‘ What, then, is their ratio?’.

Cases in which the ‘middle’ is sensible show that the 25 object of our inquiry is always the ‘middle’: we inquire, because we have not perceived it, whether there is or is not a ‘middle’ causing e. g. an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too ; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth s screening the sun’s light, and from this would arise the universal.

Thus, as we maintain, to know a tiling’s nature is to know the reason why it is ; and this is equally true of things in so far as they are said without qualification to as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to two right angles, or greater or less.

?>5 It is clear, then, that all questions are a search for a 3 ‘ middle '. Let us now state how essential nature is revealed, and in what way it can be reduced to demonstration ; ^ what definition is, and what things arc definable. And let us first discuss certain difficulties which these (questions raise, 90^' beginning what we have to say with a point most intimately connected with our immediately preceding remarks, namely the doubt that might be felt as to whether or not it is possible to know the same thing in the same relation, both by definition and by demonstration. It might, I mean, be urged that definition is held to concern essential nature and is in every case universal and affirmative ; whereas, on the 5 other hand, some conclusions are negative and some are not universal ; e.g. all in the second figure are negative, none in the third are universal. And again, not even all affirmative conclusions in the first figure are definable, e. g. ‘ every triangle has its angles equal to two right angles ’. An argument

* Cf. 94*11-14.

ROOK II. 3 proving this difference between demonstration and definition is that to have scientific knowledge of the demonstrable ^ is identical with possessing a demonstration of it: hence if 10 demonstration of such conclusions as these is possible, there clearly cannot also be definition of them. If there could, one might know such a conclusion also in virtue of its definition without possessing the demonstration of it ; for there is nothing to stop our having the one without the other.

Induction too will sufficiently convince us of this difference; for never yet by defining anything — essential attribute or ,3 accident— did we get knowledge of it. Again, if to define is to acquire knowledge of a substance, at any rate such attributes arc not substances.

It is evident, then, that not everything demonstrable can be defined. What then? Can everything definable be demonstrated, or not? There is one of our previous arguments v^ich covers this too. Of a single thing qua 20 single there is a single scientific knowledge. Hence, since to know the demonstrable scientifically is to possess the demonstration of it, an impossible consequence will follow : — possession of its definition without its demonstration will give knowledge of the demonstrable.

Moreover, the basic premisses of demonstrations are definitions, and it has already been shown ^ that these will be found indemonstrable ; either the basic premisses will be 25 demonstrable and will depend on prior premisses, and the regress will be endless ; or the primary truths will be indemonstrable definitions.

Rut if the definable and the demonstrable are not wholly the same, may they yet be partially the same? Or is that impossible, because there can be no demonstration of the definable? There can be none, because definition is of the 30 essential nature or being of something, and all demonstrations evidently posit and assume the essential nature — mathematical demonstrations, for example, the nature of

* Reading a7r<)5<i/icroi*~with Waitz, who confirmed by aTro^fiKtoy (A,

13, and C) in * 21, A reads (irro5fi»criic«i^, B, D, M, n, u awodmeritemt

90^ ANAT.YTICA POSTERIORA unity and the odd, and all the other sciences likewise. Moreover, every demonstration proves a predicate of a subject as attaching or as not attaching to it, but in defini- .^5 tion one thing is not predicated of another; we do not, c. g., predicate animal of biped nor biped of animal, nor yet figure of plane— plane not being figure nor figure planed Again, to pjovc essential nature is not the same as to 91® prove the fact of a connexion. Now definition reveals essential nature, demonstration rev^eals that a given attribute attaches or docs not attacli to a given subject ; but different things require different demonstrations^ — unless the one demonstration is related to the other as part to whole.

I add this because if all triangles have been proved to possess angles equal to two right angles, then this attribute has been proved to attach to isosceles ; for isosceles is a part of 5 which all triangles constitute the whole. But in the case before us the fact and the essential nature are not so related to one another, since the one is not a part of the other.

So it emerges that not all the definable is demonstrable nor all the demonstrable definable; and’we may draw the general conclusion that there is no identical object of which it is possible to possess both a definition and a demonstration, ro It follows obviously that definition and demonstration are neither identical nor contained cither within the other: if they were, their objects would be redated either as identical or as whole and part.

So much, then, for the first stage of our problem. The 4 next step is to raise the question whether syllogism — i. e. demonstration — of the definable nature is possible or, as our recent argument assumed,^ impossible.

‘ sc. within the definitory In the definition of fo)oi-

^UovvXoyiKovy the three ‘ moments ’ are severally and collectively predicable of avOpoTroSy but they are not, when considered as moments constituting the definition of avOfmno^y predicable of each other.

2 Aristotle argues that what definition reveals and what ordinary demonstration reveals are different. 'I herefore if definition is a kind of demonstration it is at any rate not the ordinary kind, and the * definable ’ has not been shown to -be the ‘ demonstrable ’ in the sense reauired.

• Aristotle has been assuming that diToSct^ty is only of ro on. Cf. e.g. 9o'^3i~9i*2.

We might argue it impossible on the following grounds : —

(a) syllogism proves an attribute of a subject through the middle term; on the other hand (d) its definable nature is both 15 ‘ peculiar ' ^ to a subject and predicated of it as belonging to its essence. But in that case ( i) the subject, its definition, and the middle term connecting them must be reciprocally predi* cable of one another; forifyi is ‘ peculiar’ to C, obviously is ‘peculiar’ to B and B to C — in fact all three terms arc ‘peculiar’ to one another: and further (2) if A inheres in the essence of all B and B is predicated universally of all C as belonging to C*s essence, A also must be predicated of C as belonging to its essence.

If one does not take this relation as thus duplicated — if, that is, A is predicated as being of the essence of />, but B is not of the essence of the subjects of which it is predicated— A will not necessarily be predicated of Cas belonging to its essence. So both premisses ivi// predicate essence, and consequently B also will be predicated of C as its essence. Since, therefore, botli premisses do predicate 25 essence — i. e. definable form— (T’s definable form will appear in the middle term before the conclusion is drawn.

We may generalize by supposing that it is possible to prove the essential nature of man. Let Cbe man, A man'^s 'essential nature —two-footed animal, or aught else it may be. Then, if we are to syllogize, A must be predicated of all B. But this premiss will be mediated by a fresh definition, which consequently will also be the essential 3^ nature of man.* Therefore the argument assumes what it has to prove, since B too is the essential nature of man. It is, however, the case in which there are only the two premisses — i. e. in which the premisses arc primary and immediate — which we ought to investigate, because it best illustrates the point under discussion.

Thus they who prove the essential nature of soul or man 35

* sc, ‘ and an indefinite regress occurs \ This argument is a corollary of the proof in 91*^ 15-26 that if the proposition predicating A— its definition— of C can be a conclusion, there must be a middle term, and since A, B, and C are reciprocally predicable, B too, as well A, will be a definition of C or anything else through reciprocating terms beg the question. It would be begging the question, for example, to contend that the soul is that which causes its own life, and that what causes its own life is a self-moving number ; for one would have to postulate that the soul is a selfmoving number in the sense of being identical with it.^ For if A is predicable as a mere consequent of B and B o{ C, A will not on that account be the definable form of C: A will merely be what ^ it was true to say of C, Even if A is predicated of all B inasmuch as B is identical with a species of A, still it w'ill not follow: being an animal is predicated 5 of being a man — since it is true that in all instances to be human is to be animal, just as it is also true that eveiy man is an animal — but not as identical with being man.''

We conclude, then, that unless one takes both the premisses as predicating essence, one cannot infer that A is the definable form and essence of C\ but if one does so take them, in assuming B one w ill have assumed, before drawing the conclusion, what the definable form of C is ; ^ so that 10 there has been no inference, for one has begged the question.

Nor, as w'as said in my formal logic, ^ is the method of 5 division a process of inference at all, since at no point does the characterization of the subject follow necessarily from the premising of certain other facts ^ : division demonstrates 15 as little as does induction. For in a genuine demonstration the conclusion must not be put as a question nor depend on a concession, but must follow necessarily from its premisses, even if the respondent deny it. The definer asks ‘ Is man animal or inanimate?* and then* assumes — he has not

' orrtp dpiBfxop ttvni nvrov nlrov Kivovvra alone would mean * to be of the genus self-moving number' ; as qualified by m to niro ov it means ‘fully identical with and completely definable as self-moving number’.

* Bywater’s ot4 rVrl to ri elvai is easier.

® Cf. An, Pr, i, ch. 31, iv Tjj dpaXvcrfi rfj TTfpi Ta axripara means literally ‘in that part of the logical^ resolution of conclusions into their premisses which concerns the figures

* A reminder of the definition of av\\oyicrp6t^ An. Pr, i, 24^^ 18-20.

’ i.e. when the respondent has replied ‘ animal inferred — that man is animal. Next, when presented with an exhaustive division of animal into terrestrial and aquatic, he assumes that man is terrestrial. Moreover, that man is jo the complete formula, terrestrial-animal, does not follow necessarily from the premisses : this too is an assumption, and equally an assumption whether the division comprises many differentiae or few. (Indeed as this method of division is used by those who proceed by it, even truths that can be inferred actually fail to appear as such.) ^ For why should not the whole of this formula be true of man, and yet not 25 exhibit his essential nature or definable form ? Again, what guarantee is there against an unessential addition, or against the omission of the final or of an intermediate determinant of the substantial being ?

The champion of division might here urge that though these lapses do occur, yet w^e can solve that difficulty if all the attributes we assume are constituents of the definable form, and if, postulating the genus, we produce by division the requisite uninterrupted sequence of terms, ^ and omit nothing ; and that indeed we cannot fail to fulfil these 30 conditions if what is to be divided falls whole into the division at each stage, and none of it is omitted ; and that this — the dividendum — must without further question be (ultimately) incapable of fresh specific division.'^ Never-

* The terms of a series are when nothing of the same kind as they intervenes between them, cf. Phys. vi. 231^ 23 and note on 95^ 4. The completed duup€ais of a must present a set of terms such that between any two terms which are next to one another, either horizontally or vertically, no term of the same genus intervenes. Thus, if a yepos A is divided into B and C, B and C must be : if B and C are divided respectively into B^ B"^ and O (?, each of these pairs must be and also the pairs AB^ BB\ and^C, C’C',

CC®, must each be

® Omitting yap and du in ^32 with A.- rovro in ^32 refers to the subject of €pniirrfi in '^31. The divider is supposed to argue that if the process of division fulfils certain conditions — which, if at each stage it exhausts the dividendum, it cannot fail to do — then its final result must be an Sropov tldos — the essentially definable. In the next sentence Aristotle does not dispute that dimpfcnt may reach an aropov ASos but denies that it does so by a process of inference. fJSij in ^ 32 seems to mean ‘ without more ado * without having any further condition to fulfil* : B Adr)f Wailz

ANALYTICA POSTER lORA theless, we reply, division does not involve inference; if it gives knowledge, it gives it in another way. Nor is there any absurdity in this : induction, perhaps, is not demonstration any more than is division, yet it docs make 35 evident some truth. Yet to state a definition reached by division is not to state a conclusion : as, when conclusions are drawn without their appropriate middles, the alleged necessity by which the inference follows from the premisses is open to a question as to the reason for it, so definitions reached by division invite the same question. Thus to the 92® question ‘ What is the essential nature of man ? ’ the divider replies * Animal, mortal, footed, biped, wingless ’ ; and when at each step he is asked * Why ? \ he will say, and, as he thinks, prove by division, that all animal is mortal or immortal : but such a formula taken in its entirety is not definition ; so that even if division docs demonstrate its formula, definition at any rate docs not turn out to be a 5 conclusion of inference.

Can we nevertheless actually demonstrate what a thing 6 essentially and substantially is, but hypothetically, i. e. by premising (i) that its definable form is constituted by the ‘ peculiar ^ ^ attributes of its essential nature; (2) that such and such are the only attriljutcs of its essential nature, and that the complete synthesis of them is peculiar to the thing ; and thus —since in this synthesis consists the being of the thing—obtaining our conclusion ? Or is the truth 10 that, since proof must be through the middle term, the definable form is once more assumed in this minor premiss too ?

Further, just as in syllogizing we do not premise what syllogistic inference is (since the premisses from which we conclude must be related as whole and part),^ so the definable form must not fall within the syllogism but remain outside the premisses posited. It is only against a doubt »5 as to its having been a syllogistic inference at all that we

* A reminder of a necessary condition of syllogism. If the definition of syllogism is premised the conclusion would have to affirm some subject to be of the nature of syllogism.

have to defend our argument as conforming to the defini> tioii of syllogism. It is only when some one doubts whether the conclusion proved is the definable form that we have to defend it as conforming to the definition of definable form which wc assumed. Hence syllogistic inference must be possible even without the express statement of what syllogism is or what definable form is.^

The following type of hypothetical proof also begs the 20 question. If evil is definable as the divisible, and the defini* tion of a thing^s contrary — if it has one — is the contrary of the thing’s definition ; ^ then, if good is the contrary of evil and the indivisible of the divisible, we conclude that to be good is essentially to be indivisible. The question is begged because definable form is assumed as a premiss, and as a premiss which is to prove definable form. ‘ But not the same definable form you may object.^ That I admit, for 35 in demonstrations also we premise that ‘this' is predicable of ‘that * but in this premiss the term we assert of the minor is neither the major itself nor a term identical in definition, or convertible, with the major.

Again, both proof by division and the syllogism just described are open to the question why man should be animal-biped-terrestrial and not merely animal and terrestrial, since what they premise does not ensure that the 30 predicates shall constitute a genuine unity and not merely belong to a single subject as do musical and grammatical when predicated of the same man.

7 How then by definition shall we prove substance or essential nature ? We cannot show it as a fresh fact 35 necessarily following from the assumption of premisses admitted to be facts—thc method of demonstration : wc may not proceed as by induction to establish a universal on the evidence of groups of particulars which offer no excep-

* Reading ^ n uym with A.

^ The full Greek would be d kokw to ftVai fori ru Simptrc^ emti, rco 5’ €pavTi<p TO (Jpal tori to rep fvavriep flvm. . . It would however be easier to read d to (so B and Waitz) kqk^ {sc> that) ecrri to dunperep civoi, to d* (paPTicp (sc, duot) rd tw evavrito €ipat,

* Placing a colon after

ANALYTICA I>OSTERIORA tion, beaiuse induction proves not what the essential nature 9^^ of a thing is but that it has or has not some attribute. Therefore, since presumably one cannot prove essential nature by an appeal to sense perception ' or by pointing with the finger, what other method remains ?

To put it another way: how shall we by definition prove essejitial nature ? He who knows what human — or any other 5 — nature is, must know also that man exists ; for no one knows the nature of what does not exist — one can know the meaning of the phrase or name ‘goat-stag’ but not what the essential nature of a goat-stag is. But further, if definition can prove what is the essential nature of a thing, can it also prove that it exists? And how will it prove them both by the same process,^ since definition exhibits one 10 single thing and demonstration another single thing, and what human nature is and the fact that man exists are not the same thing ? Then too we hold that it is by demonstration that the being of everything must be proved — unless indeed to be were its essence ; and, since being is not a genus,^ it is not the essence of anything. Hence the being of anything as fact is matter for demonstration ; and this 15 is the actual procedure of the sciences, for the geometer assumes the meaning of the w^ord triangle, but that it is possessed of some attribute* he proves. What is it, then, that we shall prove in defining essential nature ? Triangle ? In that case a man will know by definition what a thing’s nature is without knowing whether it exists. But that is impossible.

Moreover it is clear, if we consider the methods of defining actually in use, that definition does not prove that 30 the thing defined exists : since even if there does actually

^ Cf, for this use of cucr^rjertt e, g. Af^t. 1025^* ii, 1064^8, Met, 13S6* 32 (best MSS.).

* Placing a comma after ri eVn and a note of interrogation after ert <crn, and reading koI nuts rco nvrw Xoyw with A and B. So W^aitz,

* Triangle is for the geometer most naturally a subject and not an attribute : and in that case ort 6’ tem should mean not ‘ that it exists but ‘ that it has some attribute’, e.g. equality to two right angles. It is tempting to read ecrrl W.

Cf., however, note on 71* 15, and it is possible that Aristotle is speaking loosely in this dialectical passage.

exist something ^ which is equidistant from a centre/^ yet why should the thing named in the definition exist ? Why, in other words, should this be the formula defining circle?

One might equally well call it the definition of mountain copper. For definitions do not carry a further guarantee that the thing defined can exist or that it is what they claim to define : one can always ask why. 25

Since, therefore, to define is to prove either a thing’s essential nature or the meaning of its name, we may conclude that definition, if it in no sense proves essential nature, is a set of words signifying precisely what a name signifies.

But that were a strange consequence ; for (i) both what is not substance and what does not exist at all would be definable, since even non-existents can be signified by a name: (2) all sets of words or sentences would be defini- 3° tions, since any kind of sentence could be given a name ; so that we should all be talking in definitions, and even the Iliad would be a definition: (3) no demonstration^ can prove that any particular name means any particular thing: neither, therefore, do definitions, in addition to revealing the meaning of a name, also reveal that the name has this meaning. It appears then from these considerations that 35 neither definition and syllogism nor their objects are identical, and further that definition neither demonstrates nor proves anything, and that knowledge of essential nature is not to be obtained either by definition or by demonstration.

8 We must now start afresh and consider which of these 93^ conclusions are sound and which are not, and what is the nature of definition, and whether essential nature is in any sense demonstrable and definable or in none.

Now to know its essential nature is, as we said,® the same as to know the cause of a thing's existence, and the proof

' Reading n laov for to Icrov, with A and D.

- An abbreviated definition of circle, cf. Euclid, Ete7n, i, Defs. xv and xvi.

* Accenting lore.

* Omitting imarrj^r) with A, B, D, and supposing dfroieifu to be understood.

* sc, ‘as on this assumption it would have to do\

* ii, ch. 2. In 93*4 read tov tl with A, C, and B corr.

5 of this depends on the fact that a thing must have a cause. Moreover, this cause is cither identical with the essential nature of the thing or distinct from it ; ‘ and if its cause is distinct from it, the essential nature of the thing is either demonstrable or indemonstrable. Consequently, if the cause is distinct from the thing’s essential nature and demonstration is possible, the cause must be the middle term, and, the conclusion proved being universal and affirmative, the proof is in the first figure. So the method just examined of proving it through another essential nature 10 would be one way of proving essential nature, because a conclusion containing essential nature must be inferred through a middle which is an essential nature just as a ‘peculiar’ * property must be inferred through a middle which is a ‘peculiar' property; so that of the two definable natures of a single thing this method will prove one and not the other.^

Now it was said before^ that this method could not amount to demonstration of essential nature — it is actually 15 a dialectical proof of it — so let us begin again and explain by what method it can be demonstrated. When we are aware of a fact we seek its reason, and though sometimes the fact and the reason dawn on us simultaneously, yet we cannot apprehend the reason a moment sooner than the fact ; and clearly in just the same way we cannot apprehend a thing's definable form without apprehending that it exists, 20 since while we are ignorant whether it exists we cannot know its essential nature. Moreover we are aware whether a thing exists or not sometimes through apprehending an element in its character, and sometimes accidentally,^ as,

' ‘distinct from it‘; i.e. in the case oi firopei ties, with the definition of which Aristotle is alone concerned in this chapter. The being of a property consists in its inherence in a substance through a middle which defines it. Cf. the following chapter.

* ®I2 ru)v ri f)t> €ipni : Aristotle speaks of two moments of the definable form as two essential natures. His argument amounts to this : that if the conclusion contains the whole definition, the question has been begged in the premisses (cf. ii, ch. 4). Hence syllogism— and even so merely dialectical syllogism— is only possible if premisses and conclusion each contain a part of the definition. * ii, ch. 2.

® The distinction is that between genuine knowledge of a connexion for example, when wc are aware of thunder as a noise in the clouds, of eclipse as a privation of hght, or of man as some species of animal, or of the soul as a self-moving thing. As often as we have accidental knowledge that the thing exists, we must be in a wholly negative state 25 as regards awareness of its essential nature ; for we have not got genuine knowledge even of its existence, and to search for a thing’s essential nature when we are unaware that it exists is to search for nothing. On the other hand, whenever we apprehend an element in the thing’s character there is less difficulty. Thus it follows that the degree of our knowledge of a thing’s essential nature is determined by the sense in which we are aware that it exists. Let us then take the following as our first instance of being aware of an element in the essential nature. Let A be eclipse, (7 30 the moon, B the earth’s acting as a screen. Now to ask whether the moon is eclipsed or not is to ask whether or not B has occurred. But that is precisely the same as asking whether A has a defining condition ; ^ and if this condition actually exists, we assert that A also actually exists. Or again we may ask which side of a contradiction the defining condition necessitates : does it noake the angles of a triangle equal or not equal to two right angles ? When we have found the answer, if the premisses are immediate,^ we know fact and reason- together ; if they are not im- 35 mediate, wc know the fact without the reason, as in the following example : let C be the moon, A eclipse, B the fact that the moon fails to produce shadows ^ though she is full and though no visible body intervenes between us and through its cause and accidental knowledge of it through a middle not the cause.

* Xayop varies in meaning from mere ‘statement* to ‘the formula giving TO TL ^}v €Lmt of a substance *, but always the underlying unity of its meanings is the rationality, the intelligible connexion, which discourse-verbal or held by the soul with herself — exhibits in varying degrees. Here it is equivalent to ‘ proximate cause The fact that Xoyoj also means ‘definition* assists Aristotle to identify cause and definition. ‘ Defining condition ’ perhaps to some degree covers the two senses.

* i.e. that there is no moonlight casting shadows on the earth on a clear night at full moon.

her. Then if />’, failure to produce shadows in spite of the 93 absence of an intervening body, is attributable to C, and A, eclipse, is attributable to B, it is clear that the moon is eclipsed, but the reason why is not yet clear, and we know that eclipse exists, but we do not know what its essential nature is. J3ut wlicn it is clear that A is attributable to C and we proceed to ask the reason of this fact, we are 5 inquiring what is the nature of B : is it the earth’s acting as a screen, or the moon’s rotation or her extinction? But B is the definition of the other term, viz., in these examples, of the major term A ; for eclipse is constituted by the earth acting as a screen. Thus, (i) *What is thunder?’ ‘The quenching of fire in cloud’, and (2) ‘Why does it thunder?’ Because fire is quenched in the cloud are equivalent.

10 Let Che cloud, A thunder, B the quenching of fire. Then A is attributable to C, cloud, since fire is quenched in it ; and A^ noise, is attributable to B ; and B is assuredly the definition of the major term A. If there be a further mediating cause of B, it will be one of the remaining partial definitions of A,

15 We have stated then how essential nature is discovered and becomes known, and wc see that, while there is no syllogism— i.e. no demonstrative syllogism— of essential nature, yet it is through syllogism, viz. demonstrative syllogism, that essential nature is exhibited. So we conclude that neither can the essential nature of anything which has a cause distinct from itself be known without demonstration, nor can it be demonstrated; and this is what we 20 contended in our preliminary discussions.^

Now while some things have a cause distinct from them- 9 selves, others have not. Hence it is evident that there are essential natures which are immediate, that is are basic premisses ; and of these not only that they are but also ivhat they are must be assumed or revealed in some other way. This too is the actual procedure of the arithmetician,

25 who assumes both the nature and the existence of unit. On the other hand, it is possible (in the manner explained) to

exhibit through demonstration the essential nature of things which have a * middle’,^ i. e. a cause of their substantial being other than that being itself ; but we do not thereby demonstrate it.

lO Since definition is said to be the statement of a thing's nature, obviously one kind of definition will be a statement of the meaning of the name, or of an equivalent nominal 30 formula. A definition in this sense tells you, e.g., the meaning of the phrase ' triangular character When we are aware that triangle exists, we inquire the reason why it exists. But it is difficult thus to learn the definition of things the existence of which we do not genuinely know — the cause of this difficulty being, as wc said before;* that we only know accidentally whether or not the thing exists, Moreover, a statement may be a unity in either of two ways, by conjunction, like the I/iad, or because it exhibits a single predicate as inhering not accidentally in a single subject."^

That then is one way of defining definition. Another kind of definition is a formula exhibiting the cause of a thing’s existence. Thus the former signifies without proving, but 94 the latter will clearly be a ^//(^.rf-demonstration of essential nature, differing from demonstration in the arrangement of its terms. For there is a difference between stating why it thunders, and stating what is the essential nature ol thunder ; since the first statement will be ‘ Because fire is quenched in the clouds', while the statement of what the nature of thunder is will be ' The noise of fire being quenched in the clouds’. Thus the same statement takes 5 a different form: in one form it is continuous'* demonstration, in the other definition. Again, thunder can be defined

* Cf., however, ii, ch. 2, and note on 89*^ 38. Aristotle here uses /icVo*' in the more restricted sense.

* i. e. as treated by geometry ; that is, as abstracted a materia and treated as a subject. Cf. 81’’ 25.

^ Presumably a reason for there being a kind of definition other than nominal. The reference is obviously to 92*’ 32.

* Demonstration, like a line, is continuous because its premisses are parts which are conterminous (as linked by middle terms), and there IS a movement from premisses to conclusion. Definition resembles rather the indivisible simplicity of a point.

as noise in the clouds, which is the conclusion of the demonstration embodying essential nature. On the other hand the definition of immediates is an indemonstrable

10 positing of essential nature.

We conclude then that definition is {a) an indemonstrable statement of essential nature, or [b) a syllogism of essential nature differing from demonstration in grammatical form, or (c) the conclusion of a demonstration giving essential nature.

Our discussion has therefore made plain (i) in what sense and of what things the essential nature is demon-

15 strable, and in what sense and of what things it is not; {2) what arc the various meanings of the term definition, and in what sense and of what things it proves the essential nature, and in what sense and of what things it does not ; (3) what is the relation of definition to demonstration, and how far the same thing is both definable and demonstrable and how far it is not

30 We think we have scientific knowledge when we know ii the cause, and there are four causes : (i) the definable form, (2) an antecedent which necessitates a consequent,^ (3) the

^ By this Aristotle appears to mean the material cause ; cf. Physics ii, 195®- 18, 19, where the premisses of a sylU^gism are said to be the material cause of the conclusion. In this chapter Aristotle gives no separate example of formal cause as the middle term of demonstration, and seems rather, in virtue of a d fferent classification of cause, to regard the middle of demonstration as alivays a formal cause because it defines the major ter n, and as generically embracing material, efficient, and final causes. But as the transition is neither explicit nor complete, this is confusing. In the Metaphysics Aristotle teaches that formal, final, and efficient causes coalesce (cf. e. g. Met, 1044^1, 1070'^ 26), while the material cause remains distinct. The treatment of causation here is presumably earlier than the teaching of the Metaphysics^ though in the last part of the chapter Aristotle is moving towards the position he there adopts. Possibly he felt that if the middle of must reflect the full proximate cause of a connexion, then the four causes could not remain wholly distinct from one another, and hence his attempt here to unite them under the formal cause. He may subsequently have been induced to omit the material cause from this unification from a consideration of the unknowable and merely potential nature of Even here the example he gives of a material cause is not what one expects, i. e, not one such as, e. g., bricks taken as the material cause of a house. Aristotle’s difficulty is due to the fact that he is trying to equate scientific conceptions of causation, which he should have recognized as oIkPim or at least as axioms not transferable without modification from spheres which they were formulated

KOOK IL II efficient cause, ^ (4) the final cause. Hence each of these can be the middle term of a proof, for^(^^) though the inference from antecedent to necessary consequent does not hold if only one premiss is assumed — two is the minimum 35 — still when there are two it holds on condition that they have a single common middle term. So it is from the assumption of this single middle term that the conclusion follows necessarily. The following example will also show this.^ Why is the angle in a semicircle a right angle ? — or from what assumption does it follow that it is a right angle ? Thus, let A be right angle, /> the half of two right angles,

C the angle in a semicircle. Then B is the cause in virtue 3^ of .vhich Aj right angle, is attributable to C, the angle in a semicircle, since B^A and the other, viz'. C, for C is half of two right angles. Therefore it is the assumption of B, the half of two right angles, from which it follows that A is attributable to C, i.e. that the angle in a semicircle is a right angle. Moreover, B is identical with (d) the defining form of A^ since it is what A's definition^ signifies. More- 35 over, the formal cause has already been shown to be the middle.^ (c) ‘ Why did the Athenians become involved in the Persian war?’ means ‘What cause originated the waging of war against the Athenians?’ and the answer is, ‘ Because they raided Sardis with the Eretrians ’, since 94^ this originated the war. Let A be war, B unprovoked raiding, C the Athenians, Then B, unprovoked raiding, is true of Cf the Athenians, and A is true of B^ since men make war on the unjust aggressor. So A, having war 5 waged upon them, is true of By the initial aggressors, and to explain, with the logical category of ground and consequent, which for him takes the narrowly specialized form of inherence of attribute in subject. Two thousand years later Leibniz was still making the same attempt.

^ j; T4 TTpiror should be tluis accented.

* sc. ‘ lest you should suppose that (2) could not be a middle \

* sc. * that (2) can appear as a middle ’.

^ Cf. Euclid, Elem. i, Def. x, but Aristotle may be referring to some earlier definition. The proof here given that the angle in a semicircle is a right angle is not that of Euclid iii. 31 ; cf. Heath, Greek MathematieSy i. pp. 339, 340.

* riie reference is to 93^3fF., and other passages such as 94*5 ft*., where the middle is shown to define the major.

B is true of C, the Athenians, who were the aggressors. Hence here too the cause — in this case the efficient cause — is the middle term, {d) This is no less true where the cause is the final cause. E. g. why does one take a walk after supper? For the sake of one’s health. Why does a house lo exist ? For the preservation of one’s goods. The end in view is in the one case health, in the other preservation. To ask the reason why one must walk after supper is precisely to ask to what end one must do it. Let C be walking after supper, B the non-regurgitation of food, A health. Then let walking after supper possess the property of preventing 15 food from rising to the orifice of the stomach, and let this condition be healthy ; since it seems that B, the non-regurgitation of food, is attributable to C, taking a walk, and that health, is attributable to B. What, then, is the cause through which A. the final cause, inheres in C? It is the non-regurgitation of food ; but B is a kind of definition 30 of A, for A will be explained by it. Why is B the cause of A's belonging to C? Because to be in a condition such as B is to be in health. The definitions must be transposed, and then the detail will become clearer.^ Incidentally, here the order of coming to be is the reverse of what it is in proof through the efficient cause: in the efficient order the middle term must come to be first, whereas in the teleo- 25 logical order the minor, C, must first take place, and the end in view comes last in tirne.'^

^ The argument from 94^8 is roughly as follows : —

Health A, digestion /►’, walking (\

The final cause A inheres in C through the efficient cause B. (A-B, B-C, A-^C.)

(But the final cause naturally appears as the effect of the efficient cause ; which means that) B^ the efficient cause, is a kind of definition of Ay the final cause.

(Since A is B^s final cause, just as much as B is A*s efficient cause, A is also a kind of definition of B, Hence) we can transpose A and B^ and prove the inherence of B in *C through A, (B-A, A-C, .*. B-C)

This seems to foreshadow the doctrine of the ultimate identity of final, efficient, and formal cause, cf. note on 94*^ 22.

* The actual yeveais or order of events is walking — digestion — health. The terms of the syllogism through the efficient cause reflect C B A these stages as follows: minor — middle — major. In the syllogism through

C B A final cause they appear as minor— major— middle. Aristotle should,

BOOK 11. n

The same thing may exist for an end and be necessitated as well. For example, light shines through a lantern (j) because that which consists of relatively small particles necessarily passes through pores larger than those particles — assuming that light does issue by penetration — and (2) for 30 an end, namely to save us from stumbling. If, then, a thing can exist through two causes, can it come to be through two causes—as for instance if thunder be a hiss and a roar necessarily produced by the quenching of fire, and also designed, as the Pythagoreans say, for a threat to terrify those that lie in Tartarus?^ Indeed, there are very many such cases, mostly among the processes and products 35 of the natural world for nature, in different senses of the term ‘nature*, produces now for an end, now by necessity.

Necessity too is of two kinds. It may work in accordance with a thing’s natural tendency, or by constraint and in 95^ opposition to it; as, for instance, by necessity a stone is borne both upwards and downwards, but not by the same necessity.

Of the products of man’s intelligence some are never due to chance or necessity but always to an end, as for example a house or a statue ; others, such as health or safety, may 5 result from chance as well.

It is mostly in cases where the issue is indeterminate (though only where the production does not originate in however, have said of the middle in the efficient order not det yfVftrOin TTfmTovy but that it must come to be before the major.

‘ in the efficient order *, and Aristotle is comparing the order of steps in a tiov\(v(Tis (an dvaXvais of an end into its means, cf. e. g. E»A\ 1112*^

1 1-24) with the actual order of events reflected by the syllogism through the efficient cause. In this case he naturally says that in the teleological order the middle — health, the end in view — is conceived first (cf. E. i\\ loc. cit.). The objection to this second view is that Aristotle is unlikely to speak of di/aXtcric as a ycwir ; in the passage quoted from E.N, he contrasts dvdXvais and ycVctrir.

* Placing a comma after fvd^x^Tai in 32 and a note of interrogation after (pofiawtu in '’34. -

* avvuTTafA€voi$ : probably the natural processes by which e.g. ofioiofitprj are formed from orotxfia. This is an instance of dual causation in yiYPia^at, cf. 94^* 3 1, avi/earuxriv : probably natural products ^ua maintaining themselves in befng (e.g. plants and animals)— an instance of dual causation in dvai, cf. ibid.

95*" ANALYTICA TOSTERIORA chance, and the end is consequently good),^ that a result is due to an end, and this is true alike in nature or in art. By chance, on the other hand, nothing comes to be for an end.

10 The effect may be still coming to be, or its occurrence 12 may be past or future, yet the cause will be the same as when it is actually existent — for it is the middle which is the cause ‘‘^—except that if the effect actually exists the cause is actually existent, if it is coming to be so is the cause, if its occurrence is past the cause is past, if future the cause is future. For example, the moon was eclipsed because the earth intervened, is becoming eclipsed because the earth is 15 in process of intervening, will be eclipsed because the earth will intervene, is eclipsed because the earth intervenes.

To take a second example: assuming that the definition of ice is solidified water, let C be water, A solidified, B the middle, which is the cause, namely total failure of heat. Then B is attributed to C, and Ay solidification, to B : ice 20 forniis when B is occurring, has formed vv'hen B has occurred, and will form when B shall occur.

This sort of cause, then, and its effect come to be simultaneously when they are in process of becoming, and exist simultaneously when they actually exist ; and the same holds good when they arc past and when they are future. But what of cases where they are not simultaneous ? Can causes and effects different from one another form, as they seem to us to form, a continuous succession, a past effect resulting from a past cause different from itself, a future effect from a future cause different from it, and an effect which is comingto-be from a cause different from and prior to it? Now on this theory it is from the posterior event that we reason (and this though these later events actually have their source of origin in previous events — a fact which shows that also when the effect is coming-to-be we still reason from the posterior event), and from the prior event we cannot reason

' Bracketing 95** 7 orav . . . • 8 ayaB6v and reading a comma after in ^ 7. * The end is consequently good e. a genuine end,

* Bracketing ru yaft fniaov alriov and following it with a colon. Aristotle means that he is hi^re only dealing with causes which can be middle terms of demonstration, i.e, which reciprocate with their effects.

(we cannot argue that because an event A has occurred, 3^ therefore an event /> has occurred subsequently to A but still in the past — and the same holds good if the occurrence is future) ’ — cannot reason because, be the time interval definite or indefinite, it will never be possible to infer that because it is true to say that A occurred, therefore it is true to say that B, the subsequent event, occurred; for in the interval between the events, though A has already occurred, the latter statement will be false. And the same argument 35 applies also to future events;^ i.e. one cannot infer from an event which occurred in the past that a future event will occur. The reason of this is that the middle must be homogeneous, past when the extremes are past, future when they are future, coming to be when they are coming-to-be, actually existent when they are actually existent ; and there cannot be a middle term homogeneous with extremes respectively past and future. And it is a further difficulty in this theory that the time interval can be neither indefinite 40 nor definite, since during it the inference will be false/' We 95^^ have also to inquire what it is that holds events together so that the coming-to-be now occurring in actual things follows upon a past event. It is evident, wc may suggest, that a past event and a present process cannot be * contiguous.’,^ Treating as parentheses ® 28 apxh 5e . , . *29 wcrnirw? and *30

^ Placing a comma after uroyL^vov in *36.

® i. e. a further difficulty created by taking cause and effect as ‘ punctual ’ events is that, since time is continuous and not composed of atomic * nows ’, there must be a time interval between any two such ‘ punctual * events. But during this interval the inference must be false, because the causal nexus cannot leap the gap nor, ex hypothesis persist through it. In fact such an account of cause and effect does not correspond to the real connexions in things. Cf. e. g. Physics vi.

^ Terms are <</)«{ ‘ successive ’, if they are next one another and nothing of the same kind intervenes. Terms aie ‘ contiguous \ if they are €(#)cfr;p and also in contact; e. g. boats at the -start of a bumping race are t ; houses in a row of houses any and every pair of which share a party- wall are ixoynpn. If the members of any series are conterminous — i. e. if any point at which you divide the series is a term of the series— they are <TVPtx^) or ‘continuous’. Cf.

Met, io68^3off.

Aristotle asks whether it is possible, while regarding time as continuous, yet to suppose that within any duration, past or future, two disjunct or ‘ punctual ’ events can be connected as cause and effect ; and further whether an event now occurring, not itself ‘ punctuar but a specious present, can have as its cause a ‘ punctual ’ past event.

95** ANALYTICA POSTER lORA for not even two past events can be ' cotitiguoii.s P'or past 5 events are limits and atomic; so just as points are not ‘ contiguous ’ neither are past events, since both are indivisible. For the same reason a past event and a present process cannot be ‘contiguous*, for the process is divisible, the event indivisible. Thus the relation of present process to past event is analogous to that of line to point, since a 10 process contains an infinity of past events. These questions, however, must receive a more explicit treatment in our general theory of change.'

The following must suffice as an account of the manner in which the middle would be identical with the cause on the supposition that coming-to-be is a series of consecutive events: for^ in the terms of such a scries too the middle 15 and major terms must form an immediate premiss; c. g. we argue that, since C has occurred, therefore A occurred : and C"s occurrence was posterior, A's prior; but C is the source of the inference because it is nearer to the present moment, and the starting-point of time is the present. We next argue that, since D has occurred, therefore C occurred. Then we conclude that, since /> has occurred, therefore A 20 must have occurred ; and the cause is C, for since /) has occurred C must have occurred, and since Chas occurred A must previously have occurred.

If wc get our middle term in this way, will the series terminate in an immediate premiss, or since, as we said, no two events are ‘ contiguous*, will a fresh middle term always intervene because there is an infinity of middles? No: though no two events are ‘ contiguous *, yet we must start from a premiss consisting of a middle and the present ev^ent 25 as major.-' The like is true of future events too, since if it

' Cf. Physics vi.

^ i.e. Aristotle has haH in this chapter to explain (i) how syllogisms concerning a process of events can be brought into line with other demonstrations equally derivable from immediate primary premisses, and (2) in what sense the middle term contains the cause, lie has in fact had (i) to show that in these syllogisms inference must find its primary premiss in the efifect, and (2) to imply that the ‘ cause ’ which appears as middle when cause and effect are not simultaneous is a causa cognoscendi and not essendi»

* Waitz reads an in 25 for ana fiiVov (D ano Tov fiiijov) : * from

BOOK 11. 12 is true to say that D will exist, it must be a prior truth to say that A will exist, and the cause of this conclusion is C\ for if D will exist, C will exist prior to Z>, and if C will exist, A will exist prior to it. And here too the same infinite divisibility mi^^ht be urged, since future events are ;o not ‘ contiguous But here too an immediate basic premiss must be assumed. And in the w^orld of fact this is so : if a house has been built, then blocks must have been quarried and shaped. The reason is that a house having been built necessitates a foundation having been laid, and if a foundation has been laid blocks must have been shaped beforehand. 35 Again, if a house will be built, blocks w’ill similarly be sliaped beforehand ; and proof is through the middle in the same way, for the foundation will exist before the house.

Now w'e observe in Nature a certain kind of circular process of coming-to-be; and this is possible only if the middle and extreme terms ^ are reciprocal, since conversion is conditioned by reciprocity in the terms of the proof. This— the convertibility of conclusions and premisses — has 96^ been proved in our early chapters,^ and the circular process is an instance of this. In actual fact it is exemplified thus: when the earth had been moistened an exhalation was bound to rise, and when an exhalation had risen cloud was bound to form, and from the formation of cloud rain necessarily resulted, and by the fall of rain the earth was necessarily moistened: but this wms the starting-point, so 5 that a circle is completed ; for posit any one of the terms and another follows from it, and from that another, and from that again the first.

Some occurrences are universal (for they arc, or come-tobe what they are, always and in every case) ; others again are not always what they are but only as a general rule : 10 for instance, not every man can grow a beard, but it is the general rule. In the case of such connexions the middle term too must be a general rule. For if A is predicated an immediate premiss, i. e. the primary “ now ” * ; but np^rou is used in ^’15 as«* major term \

^ VVe should perhaps read upot with A and Waitz; but* the sense is the same.

* i, ch. 3 and An. Pr. ii, cc. 3-5, 8-10.

universally of /> and B of C, A too must be predicated always and in every instance of (7, since to hold in every 15 instance and always is of the nature of the universal. But we have assumed a connexion which is a general rule ; consequently the middle term B must also be a general rule.

So connexions which embody a general rule — i.e. which exist or come to be as a general rule — will also derive from immediate basic premisses.

30 We have already explained how essential nature is set 13^ out in the terms of a demonstration, and the sense in which it is or is not demonstrable or definable; so let us now discuss the method to be adopted in tracing the elements predicated as constituting the definable form.

Now of the attributes which inhere always in each several thing there are some which are wider in extent than it but 35 not wider than its genus (by attributes of wider extent I mean all such as are universal attributes of each several subject, but in their application aie not confined to that subject).- I.e. while an attribute may inhere in every triad, yet also in a subject not a triad — as being inheres in triad but also in subjects not numbers at all — odd on the other hand is an attribute inhering in every triad and of wider 30 application (inhering as it does also in pentad),^ but which does not extend beyond the genus of triad ; for pentad is a number, but nothing outside number is odd. It is such attributes which we have to select, up to the exact point at which they are severally of wider extent than the subject but collectively coextensive with it ; for this synthesis must be the substance of the thing. For example every 35 triad possesses the attributes number, odd, and prime in both senses, i.e. not only as possessing no divisors, but also as not being a sum of numbers. This, then, is precisely what triad i.s, viz. a number, odd, and prime in the former and also the latter sense of the term : for these attributes taken severally

‘ This chapter treats only the definition of substances.

^ Bracketing Ka\ . . . vnupxft I. 30, and following the bracket with a comma.

apply, the first two to all odd numbers, the last to the dyad 96*^ also as well as to the triad, but, taken collectively, to no other subject. Now since we have shown above ^ that attributes predicated as belonging to the essential nature are necessary and that universals are necessary, and since the attributes which we select as inhering in triad, or in any other subject whose attributes wc select in this way, arc predicated as belonging to its essential nature, triad will thus possess these 5 attributes necessarily. Further, that the synthesis of them constitutes the substance of triad is shown by the following argument. I f it is not identical with the being of triad, it must be related to triad as a genus named or nameless. It will then be of wider extent than triad — assuming that wider potential extent is the character of a genus. If on the other hand 10 this synthesis is applicable to no subject other than the individual triads, it will be identical with the being of triad, because we rpakc the further assumption that the substance of each subject is the predication of elements in its essential nature down to the last differentia characterizing the individuals. It follows that any other synthesis thus exhibited will likewise be identical with the being of the subject.

The author of a hand-book ^ on a subject that is a generic 15 whole should divide the genus into its first infimae species — number e. g. into triad and dyad — and then endeavour to seize their definitions by the method we have described — the definition, for example, of straight line or circle or right angle. After that, having established what the category is to which the subaltern genus belongs — quantity or quality, for instance — he should examine the properties ‘peculiar'^ ao to the species, working through the proximate^ common differentiae. He should proceed thus because the attributes of the genera compounded of the infimae species will be clearly given by the definitions of the species ; since the basic element of them all® is the definition, i. e. the simple

* With the remainder of the chapter compaie An. Pr. 1, ch. 25, where the treatment covers all syllogism.

^ TTpeiro)!/ appears to mean ‘first in a scale ascending towards the genus ’. ® sc. genera and species.

iufuna specks^ and the attributes inhere essentially in the simple infiniae species^ in the genera only in virtue of these.

35 Divisions according to differentiae are a useful accessory to this method. What force they have as proofs we did, indeed, explain above, ^ but that merely towards collecting the essential nature they may be of use we will proceed to show. They might, indeed, seem to be of no use at all, but rather to assume everything at the start and to be no better 30 than an initial assumption made without division. But, in factjthe order in which theattributes are predicated does make a difference — it matters whether wc say animal — tame — biped, or biped — animal- tame. For if every definable thing consists of two elements and ‘ animal-tame ’ forms a unity, and again out of this and the further differentia man^(or whatever else is the unity under construction) is constituted, then the elements we assume have necessarily been reached 35 by division. Again, division is the only possible method of avoiding the omission of any element of the essential nature. Thus, if the primary genus is assumed and we then take one of the lower divisions, the dividendum will not fall whole into this division: e. g. it is not all animal wdiich is either whole-winged or split-winged but all winged animal, 97*^ for it is winged animal to which this differentiation " belongs. The primary differentiation of animal is that within which all animal falls. The like is true of every other genus, whether outside animal or a subaltern genus of animal ; e. g. the primary differentiation of bird is that within which falls every bird, of fish that within which falls every fish. So, if we proceed in this way, we can be sure that nothing 5 has been omitted : by any other method one is bound to omit something without knowing it.

^ luv opicTfxov K(u TO (ittXoOi' : 1. c. the vifima species ^ which is ‘ simple * because below it are only dBulfpopa, and which is the essentially definable.

* ii, cb. 5 and Afi. Pr. i, ch. 31, where duiipicris is shown not to be inference.

^ Aristotle tends to use Bia<t)opd and dmipforis indifferently in this chapter. This is natural, since a subject which obtains its 6ia(f>opd by falling on one side of a dialpfais is tpso qualified by its distinction from the other side.

BOOK ir. 13

To define and divide one need not know the whole of existence. Yet some hold it impossible to know the differentiae distinguishing each thing from every single other thing without knowing every single other thing ; and one cannot, they say, know each thing without knowing its differentiae, since everything is identical with that from 10 which it docs not differ, and other than that from which it differs. Now first of all this is a fallacy : not every differentia precludes identity, since many differentiae inhere in things specifically identical, though not in the substance of these nor essentially. Secondly, when one has taken one’s differing pair of opposites and assumed that the two sides exhaust the genus, and that the subject one seeks to define 15 is present in one or other of them, and one has further verified its presence in one of them ; then it does not matter whether or not one knows all the other subjects of which the differenti^je are also predicated. For it is obvious that when by this process one reaches subjects incapable of further differentiation one will possess the formula defining the sub* stance. Moreover, to postulate that the division exhausts the genus is not illegitimate if the opposites exclude a middle ; 20 since if it is the differentia of that genus, anything contained in the genus must lie on one of the two sides.

In establishing a definition by division one should keep three objects in view : (i) the admission only of elements in the definable form, (a) the arrangement of these in the right order, (3) the omission of no such elements. The first is 25 feasible because one can establish genus and differentia through the topic of the genus, ^ just as one can conclude the inherence of an accident through the topic of the accident.^ The right order will be achieved if the right term is assumed as primary, and this will be ensured if the term selected is predicable of all the others but not all they of it; since 30 there must be one such term. Having assumed this we at once proceed in the same way with the lower terms ; for our second term will be the first of the remainder, our third the first of those which follow the second in a * contiguous ' series, since when the higher term is excluded, that term of

* Cf, Topics iv. ^ Cf. Topics ii. * Cf. note on 95^* 4* the renuiinder which is ‘ contiguous ’ to it will be primary, and so on. Our procedure makes it clear that no elements 35 in the definable form have been omitted : we have taken the differentia that comes first in the order of division, pointing out that animal, e.g., is divisible exhaustively into A and B, and that the subject accepts one of the two as its predicate. Next we have taken the differentia of the whole thus reached, and shown that the whole we finally reach is not further divisible — Le. that as soon as we have taken the last differentia to form the concrete totality, this totality admits 97 of no division into species. For it is clear that there is no superfluous addition, since all these terms we have selected are elements in the definable form ; and nothing lacking, since any omission would have to be a genus or a differentia. Now the primary term is a genus, and this term taken in conjunction with its differentiae is a genus: moreover the differentiae are all included, because there is now no further 5 differentia ; if there were, the final concrete would admit of division into species, which, we said, is not the case.

To resumeour account of the right method of investigation:^ We must start by observing a set of similar — i. e. specifically identical — individuals, and consider what element they have in common. We must then apply the same process to another set of individuals which belong to one species '^ and are generically but not specifically identical with the former 10 set. When we have established what the common element is in all members of this second species, and likewise in members of further species, we should again consider whether the results established possess any identity, and persevere until we reach a single formula, since this will be the definition of the thing. But if we reach not one formula but two or more, evidently the dejimendnm cannot be one thing but must be more than one. I may illustrate my meaning as follows. If we were inquiring what the essential nature of pride is, we should examine instances of proud men we know of to see what, as such, they have in common ; e. g.

’ Aristotle resumes the discussion broken in 96^ 25 by the digression on diaiptais and deals with the question of defining a y<Voy.

* Reading avroU with A (?). » Reading ri mina.

if Alcibiades was proud, or Achilles and Ajax were proud, we should find, on inquiring what they all had in common, that it was intolerance of insult ; it was this which drove Alcibiades to war, Achilles to wrath, and Ajax to suicide. 20 Wc should next examine other cases, Lysander, for example, or Socrates, and then if these have in common indifference alike to good and ill fortune, I take these two results and inquire what common element have equanimity amid the vicissitudes of life and impatience of dishonour. If they have none, there will be two genera^ of pride. Besides, every 25 definition is always universal and commensurate:^ the physician does .not prescribe what is healthy for a single eye, but for all eyes or for a determinate species of eye. It is also easier by this method to define the single species than the universal, and that is why our procedure should be from the several species to the universal genera — this for the further reason too that equivocation is less readily 30 detected in genera than in infimac species. Indeed, perspicuity is essential in definitions, just as inferential movement^ is the minimum required in demonstrations ; and we shall attain perspicuity if we can collect separately the definition of each species^ through the group of singulars which we have established — e. g. the definition of similarity not unqualified but restricted to colours and to figures ; 35 the definition of acuteness, but only of sound— and so proceed to the common universal with a careful avoidance of equivocation. We may add that if dialectical disputation must not employ metaphors, clearly metaphors and metaphorical expressions are precluded in definition : otherwise dialectic would involve metaphors.®

14 In order to formulate the connexions we wish to prove 98®

' fUrj here must mean yivrj^ an apparent reversion to Plato’s indiscriminate use of the terms, and contrary to Aristotle's general usage elsewhere.

* This sentence explains why the absence of a common element means that there are two genera : a definition, being commensurate, cannot embrace subjects with nothing in common.

* Reading avWiXoyiaBaij with B and Waitz.

* y(P€i here must be equivalent to cf. note on 97^’ 25.

® sc, as sometimes involving definition.

we have to select our analyses and divisions.' The method of selection consists in laying down the common genus of all our subjects of investigation — if c.g. they are animals, we lay down what the properties are which inhere in every animal. 7'hese established, we next lay down the pro[)ei ties 5 essentially connected with the first of the remaining classes — e. g. if this first subgenus is bird, the essential properties of every bird — and so on, always characterizing the proximate subgenus.^ This will clearly at once enable us to say in virtue of what character^ the subgenera — man, e. g., or horse — possess their properties. Let A be animal, lo B the properties of every animal, C D E various species of animal. Then it is clear in virtue of what character B inheres in D — namely A — and that it inheres in C and F. for the same reason : and throughout ihe remaining subgenera always the same rule applies.

We are now taking our examples from the traditional class-names, but we must not confine ourselves to considering these. We must collect any other common character which 15 we observe, and then consider with what species it is connected and what properties belong to it. For example, as the common properties of horned animals we collect the possession of a third stomach and only one row of teeth. Then since it is clear in virtue of what character they possess these attributes— namely their horned character — the next question is, to what species does the possession of horns attach ?

30 Yet a further method of selection is by analogy: for we cannot find a single identical name to give to a squid^s pounce, a fish*s spine, and an animal's bone, although these

^ av.iTo/iiJ seems to mean that analysis of a subject, for the purpose of eliciting its properties, which w'ould precede the process of division exhibiting the true generic character in virtue of which the subject possesses those properties. Bonitz, however, takes it as equivalent to hinliifais (Index s. v.).

* i. e. the subgenera. Cf. the previous chapter.

® Placing commas after opvidi *6 and tyyvTara ^7.

* Aristotle in this chapter is explaining how to select the true primary subject— cf. i, 4 ad fin.— of a property ; not how to find the middle term— with which he deals, e.g., in cc. i 5-18— and hia W here means quatenus^ not propter quod.

BOOK II. 14 98*^ too possess common properties as if there were a single osseous nature.

15 Some connexions that require proof are identical in that they possess an identical * middle^ ^ — g, a whole group might be proved through * reciprocal replacement ’ ^ — and of as these one class are identical in genus, namely all those whose difference consists in their concerning different subjects or in their mode of manifestation. This latter class may be exemplified by the questions as to the causes respectively of echo, of reflection, and of the rainbow : the connexions to be proved which these questions embody are identical generically, because all three are forms of repercussion ; but specifically they are different.

Other connexions that require proof only differ in that the ‘middle' of the one is subordinate to the ‘ middle' of .^0 the other. For example : Why does the Nile rise towards the end of the month ? Because towards its close the month is more stormy. Why is the month more stormy towards its close? Because the moon is waning. Here the one cause is subordinate to the other.

16 The question might be raised with regard to cause and 35 effect whether when the effect is present the cause also is present ; whether, for instance, if a plant sheds its leaves or the moon is eclipsed, there is present also the cause of the eclipse or of the fall of the leaves — the possession of broad leaves, let us say, in the latter case, in the former the 98^ earth's interposition.'^ For, one might argue, if this cause is not present, these phenomena will have some other cause :

if it is present, its effect will be at once implied by it — the eclipse by the earth's interposition, the fall of the leaves by the possession of broad leaves;^ but if so, they will be logically coincident and each capable of proof through the other. Let me illustrate : Let A be deciduous character, 5

® Cf. Waitz ad ioc.

® Placing a dash instead of a full stop after form in ^38.

* Placing a colon instead of a full stop after (pvWoppoti in ^ 4.

in the latter case equality of the ratios of the sides and equality of the angles, in the case of colours identity of the 15 act of perceiving them, or something else of the sort. Again, connexions requiring proof which are identical by analogy have middles also analogous.

The truth is that cause, effect, and subject are reciprocally predicable in the following way. If the species are taken severally, the effect is wider than the subject (e. g. the possession of external angles equal to four right angles is an attribute wider than triangle or square), but it is co- 20 extensive with the species taken collectively (in this instance with all figures whose external angles are equal to four right angles). And the middle likewise reciprocates, for the middle is a definition of the major ; which is incidentally the reason why all the sciences are built up through definition.

Wc may illustrate as follows. Deciduous is a universal attribute of vine, and is at the same time of wider extent than vine ; and of fig, and is of wider extent than fig : but it is not wider than but coextensive with the totality of the a5 species. Then if you take the middle which is proximate,^ it is a definition of deciduous. I say that, because you will first reach a middle ^ next the subject,® and a premiss asserting it ^ of the whole subject, and after that a middle — the coagulation of sap or something of the sort — proving the connexion of the first middle with the major ; ® but it is the coagulation of sap at the junction of leaf-stalk and stem which defines deciduous.^

^ sc. to TO <f>v\\oppo€ip, the major. * sc. broad-leaved,

* Vine, fig, &c. * One should perhaps read o rt,

• Aristotle contemplates four terms : (i) deciduous, (2) coagulation, (3) broad-leaved, (4) vine, fig, &c.

If we get the middle proximate to (i) it is a definition of (i). But in investigating vines, figs, Sec. according to the method of chapter 13, we shall first find a common character of them in broadleaved, and, taking this as a middle, we shall prove that vine, fig, &c., gua broad-leaved, are deciduous. But this proof is not demonstration, because broad-leaved is not a definition of deciduous. So our next step will be to find a middle-rrcoagulation— mediating the major premiss of this proof, and demonstllate that broad -leaved plants, gua liable to coagulation, are deciduous. This is strict demonstration, because coagulation defines deciduous.

If an explanation in formal terms of the inter-relation of 30 cause and effect is demanded, wc shall offer the following.

Let A be an attribute of all 5, and B of every species of /?, but so that both A and B are wider than their respective subjects. Then B will be a universal attribute of each species of D (since I call such an attribute universal even if it is not commensurate, and I call an attribute primary universal if it is commensurate,^ not with each species severally but with their totality),® and it extends beyond each of them taken separately. Thus, B is the cause of A*s 35 inherence in the species of D : consequently A must be of wider extent than B ; otherwise why should B be the cause of A*s inherence in D any more than A the cause of B's inherence in D 7 Now if A is an attribute of all the species of Ej all the species of E will be united by possessing some common cause other than B : otherwise how shall we be able to say that A is predicable of all of which E is predicable, while E is not predicable of all of which A can be predicated? I mean how can there fail to be some special cause of A's inherence in £, as there was of A*s inherence in all the species of Then are the species of E, too, united by possessing some common cause ? This cause we must look for. Let us call it C,^

We conclude, then, that the same effect may have more than one cause, but not in subjects specifically identical.

For instance, the cause of longevity in quadrupeds is lack of 5 bile, in birds a dry constitution— or certainly something different

If immediate premisses are not reached at once, and there

* The parenthesis should clearly terminate at ^vTt(rrp€(f>n * 35.

* The schema of Aristotle’s argument in this paragraph is :

® It seems best to begin this chapter at n ^ 7, and place a comma after irXtUn in °8. The after rr^tpop in **9 will tnen be roughly parallel to e.g.Po/.iil i6,.ia87*> 13 (cf. Bonitz, Ind. though the apodosis is not here an antithesis.

is not merely one middle but several middles, i. e. several causes; is the cause of the property’s inherence in the several species the middle which is proximate to the primary

10 universal,^ or the middle which is proximate to the species ? ^ Clearly the cause is that nearest to each species severally in which it is manifested, for that is the cause of the subject s falling under the universal. To illustrate formally: C is the cause of B's inherence in D , hence C is the cause of A*s inherence in A B of A's inherence in C, while the cause of A's inherence in B is B itself.

»5 As regards syllogism and demonstration, the definition 19 of, and the conditions required to produce each of them, are now clear, and* with that also the definition of, and the conditions required to produce, demonstrative knowledge, since it. is the same as demonstration. As to the basic premisses, how they become known and what is the developed state of knowledge of them is made clear by raising some preliminary problems.

ao We have already said ^ that scientific knowledge through demonstration is impossible unless a man knows the primary immediate premisses. But there are questions which might be raised in respect of the apprehension of these immediate premisses: one might not only ask whether it is of the same kind as the apprehension of the conclusions, but also whether there is or is not scientific knowledge of both; or scientific knowledge of the latter, and of the former a different kind of knowledge; and, further, whether the

^5 developed states of knowledge arc not innate but come to be in us, or arc innate but at first unnoticed. Now it is strange if wc possess them from birth ; for it means that wc possess apprehensions more accurate than demonstration and fail to notice them. If on the other hand wc acquire them and do not previously possess them, how could we apprehend and learn without a basis of preexistent knowledge? For that is impossible, as we used

30 to find in the case of demonstration. So it emerges that neither can we possess them from birth, nor can they come

* i. c. the property.

* the subject.

^ i, ch. I, lo be in us if we are without knowledge of them to the extent of having no such developed state at all. Therefore we must possess a capacity of some sort, but not such as to rank higher in accuracy than these developed states. And this at least is an obvious characteristic of all animals, for they possess a congenital discriminative capacity which is called 35 sense-perception. But though sense-perception is innate in all animals, in some the sense-impression comes to persist, in others it does not. So animals in which this persistence does not come to be have either no knowledge at all outside the act of perceiving, or no knowledge of objects of which no impression' persists ; animals in which it does come into being have perception and can continue to retain the senseimpression in the soul : and when such persistence is lOO* frequently repeated' a further distinction at once arises between those which out of the persistence of such senseimpressions develop a power of systematizing them and those which do not. So out of sense-perception comes to be what we call memory, and out of frequently repeated memories of the same thing develops experience ; for a 5 number of memories constitute a single experience.^ From experience again— i.e. from the universal now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all — originate the skill of the craftsman and the knowledge of the man of science, skill in the sphere of coming to be and science in the sphere of being.

We conclude that these states of knowledge are neither Innate in a determinate form, nor developed from other 10 higher states of knowledge, but from sense-perception. It is like a rout in battle stopped by first one man making a stand and then another, until the original formation has been restored. The soul is so constituted as to be capable of this process.

Let us now restate the account given already^ though with insufficient clearness. When one of a number of 15 logically indiscriminable particulars has made a stand, the

* Reading ytifOfAtvtav with D in 100*^ i.

* Cf, A 980* a8. Afi/, A I should be comparccLwith this chapter.

loo^ earliest universal is present in the soul : for though the act of sense-perception is of the particular, its content is uniloo'* versal — is man, for example, not the man Callias.^ A fresh stand is made among these rudimentary universals, and the process does not cease until the indivisible concepts, the true universals,^ are established : e. g. such and such a species of animal is a step towards the genus animal,^ which by the same process is a step towards a further generalization.

Thus it is clear that we must get to know the primary premisses by induction ; for the method by which even sense- 5 perception implants the universal is inductive. Now of the thinking states by which we grasp truth, some are unfailingly true, others admit of error — opinion, for instance, and calculation, whereas scientific knowing and intuition^ are always true : further, no other kind of thought except intuition is more accurate than scientific knowledge, whereas primary premisses are more knowable than demonstrations, and all 10 scientific knowledge is discursive. From these considerations it follows that there will be no scientific knowledge of the primary premisses, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premisses — a result which alsofollows from the fact that demonstration cannot be the originative source of demonstration, nor, consequently, scientific knowledge of scientific knowledge. If, therefore, it is the only other kind of true thinking except scientific knowing, intuition 15 will be the originative source of scientific knowledge. And the originative source of science grasps the original basic premiss, while science as a whole is similarly related as originative source to the whole body of fact.®

' Removing the brackets, reading a colon after KaB6\ov 16 and a full stop after KaXXiov Mfmnov in ^ I.

* i. e, the categories, which arc par excellence universal and are indivisible because not constituted of genus and differentia, cf. Met, 1084^* 14 and 1023^’ 24, For this sense of cf. the use of uropa in Met, 994'* 21.

” Following (tZov with a comma.

* Cf. note on 85* i.

* i. e. the conclusions.

Physics

us* and ‘knowable’ without qualification. So in the present inquiry we must follow this method and advance from what so is more obscure by nature, but clearer to us, towards what is more clear and more knowable by nature.

Now what is to us plain and obvious at first is rather confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from generalities to particulars ; for it is a whole 35 that is best known to sense-perception, and a generality is a kind of whole, comprehending many things within it, 184* like 1 parts. Much the same thing happens in the relation 10 of the name to the formula. A name, e g. ‘round’, means vaguely a sort of whole : its definition analyses this into its particular senses. Similarly a child begins by calling all men ‘ father \ and all women ‘mother’, but later on distinguishes each of them.

15 The principles in question must be either (a) one or 2 (i) more than one.

If (a) one, it must be either (i) motionless, as Parmenides and Melissus assert, or (ii) in motion, as the physicists hold, some declaring air to be the first principle, others water.

If ( 6 ) more than one, then either (i) a finite or (ii) an infinite plurality. If (i) finite (but more than one), then 30 either two or three or four or some other number. If (ii) infinite, then either as Democritus believed one in kind, but differing in shape or form; or different in kind and even contrary. 2

A similar inquiry is made by those who inquire into the number of existents : for they inquire whether the ultimate constituents of existing things 3 are one or many, and if many, equivalent phrase is n p6r€pov rfj The knowledge with which an inquiry starts is always the causa cognoscendi of the conclusion : it may, or may not, be knowledge of the causa essendi .

1 Reading in 1 . 26 axrrrep ptpq, with E.

2 i84 b 21. Both Anaxagoras and the Pythagoreans recognized contraries as principles, but it is chiefly the former who is referred to here. Contraries are * the most different of the things in the same genus ' {Met. A. 1018*27). Thus while the atoms of Democritus were the same in kind, the principles of Anaxagoras not only differed in kind, but were even contrary to each other.

8 Reading in 1 . 23 «cri ir pdrrcw (qrovcri with Bonitz.

i84 b whether a finite or an infinite plurality. So they too are inquiring whether the principle or element is one or many. 1

Now to investigate whether Being is one and motionless 25 is not a contribution to the science of Nature. For just as 185* the geometer has nothing more to say to one who denies the principles of his science — this being a question for a different science 2 or for one common to all — so a man investigating principles cannot argue with one who denies their existence. For if Being is just one, and one in the way mentioned, there is a principle no longer, since a principle must be the principle of some thing or things.

To inquire therefore whether Being is one in this sense 5 would be like arguing against any other position maintained for the sake of argument (such as the Heraclitean thesis, or such a thesis as that Being is one man) or like refuting a merely contentious argument — a description which applies to the arguments both of Melissus and of Parmenides : their premisses are false and their conclusions do not follow. Or 10 rather the argument of Melissus is gross and palpable and offers no difficulty at all : accept one ridiculous proposition and the rest follows — a simple enough proceeding.

We physicists, on the other hand, must take for granted that the things that exist by nature are, either all or some of them, in motion — which is indeed made plain by induction . 3 Moreover, no man of science is bound to solve every kind of difficulty that may be raised, but only as 15 many as are drawn falsely from the principles of the science : it is not our business to refute those that do not arise in this way: just as it is the duty of the geometer to refute the squaring of the circle by means of segments, but it is not his duty to refute Antiphon's proof . 4 At the same

1 Perhaps Aristotle is thinking of Plato’s account in the Sophist (242-6) of preceding views about the number and nature of ra ovra (a term which includes more objects than those of physics).

2 Another special science, if there is one, to which geometry is subordinate, as optics (e. g.) is to geometry.

8 «Vay« yij, the process by which a man is led on from the apprehension of particular or partial forms of a universal to the apprehension of the universal in its complete and purified form.

4 The former method was suggested by Hippocrates of Chios, and i85 r time the holders of the theory of which we are speaking do incidentally raise physical questions, though Nature is not their subject : so it will perhaps be as well to spend a few words on them, especially as the inquiry is not without scientific interest.

ao The most pertinent question with which to begin will be this 1 : In what sense is it asserted that all things are one? For 4 is * is used in many senses. Do they mean that all things 4 are* substance or quantities or qualities ? And, further, are all things one substance — one man, one horse, or one 35 soul — or quality and that one and the same — white or hot or something of the kind ? These are all very different doctrines and all impossible to maintain.

For if both substance and quantity and quality are, then, whether these exist independently of each other or not, Being will be many.

If on the other hand it is asserted that all things are quality or quantity, then, whether substance exists or not, 50 an absurdity results, if indeed the impossible can properly be called absurd. For none of the others can exist independently: substance alone is independent : for everything is predicated of substance as subject. 2 Now Melissus says that Being is infinite. It is then a quantity. For the infinite is in the category of quantity, whereas substance or quality or affection cannot be infinite except through rested on the rather obvious geometrical fallacy of supposing that if a particular kind of lunule can be squared, another kind can be squared also. Antiphon’s method was that of exhaustion. He drew a square in the circle, and then isosceles triangles on its sides, and so on, and inferred that ultimately the inscribed polygon was equal in area to the circle. This involves a denial of the geometrical principle that every geometrical magnitude can be divided ad infinitum , and gives only an approximate result. See Heath, Greek Mathematics , i. 183-200, 221-3, and Diels, Vorsokratiker 8 , i. 298!, ii. 294 f.

1 omitting I 8 u v in 1 . 22 with FI Simp.

2 Aristotle is assuming the doctrine of the Categories which distinguishes the different types of predication, i. e. the different senses in which ‘is* is used. Only things which are in the full sense, i. e. substances ( nverim ), have independent existence: other things are attributes (ovuPtfirjKoru) of them, and exist only when they are predicated of a subject (vnoK€ifj.epou) which is a substance. Thus it is self-contradictory to speak of an attribute which exists unsupported by a substance.

BOOK I. 2 18 5 a a concomitant attribute, 1 that is, if at the same time i85 b they are also quantities. For to define the infinite you must use quantity in your formula, but not substance or quality. 2 If then Being is both substance and quantity, it is two, not one : if only substance, it is not infinite and has no magnitude ; for to have that it will have to be a quantity. 3

Again, ‘one* itself, no less than ‘being’, is used in many 5 senses, so we must consider in what sense the word is used when it is said that the All is one.

Now we say that (a) the continuous is one or that (< b ) the indivisible is one, or (c) things are said to be ‘one’, when their essence is one and the same, as ‘ liquor * and ‘drink’.

If (a) their One is one in the sense of continuous, it is many, for the continuous is divisible ad infinitum . 1Q

There is, indeed, a difficulty about part and whole, perhaps not relevant to the present argument, yet deserving consideration on its own account — namely, whether the part and the whole are one or more than one, and how they can be one or many, and, if they are more than one, in what sense they are more than one. 4 (Similarly with the parts of wholes which are not continuous.) Further, if each of 15 the two parts is indivisibly one with the whole, the difficulty arises that they will be indivisibly one with each other also.

But to proceed: If (b) their One is one as indivisible,

1 Kara aviifii&rjKos, of which the Latin equivalent was per accidens.

It is usually opposed to Ka0* avr6 (per se) or fj uvto (quatenus ipsum).

Thus a triangle, through its own nature ( ku 6 ’ mrd), or as such (fj airo), has its angles equal to two right angles. On the other hand, the white (object) is six feet high, not in virtue of its whiteness (kq 0 % mVd), but through an attribute which is not necessarily involved in whiteness ( Kara avjx^ffirjKos). (In Posterior Analytics, i. 4, Aristotle draws a distinction between aM and »/ avro which may here be neglected.)

8 The point of the paragraph is that Melissus at least is obviously committed to a dualism, since he emphasizes the infinity of the one being.

4 Aristotle seems to have in view a possible objection to the statement that the continuous is many. It might be said that the continuous is many only potentially, not actually.

i85 b nothing will have quantity or quality, 1 and so the one will not be infinite, as Melissus says — nor, indeed, limited, as Parmenides says, for though the limit is indivisible, the limited is not. 2

But if (i c ) all things are one in the sense of having the 20 same definition, like 4 * raiment ’ and 4 dress ', then it turns out that they are maintaining the Heraclitean doctrine, for it will be the same thing 4 to be good * and 4 to be bad ’, and 4 to be good * and 4 to be not good and so the same thing will be 4 good * and 4 not good ’, and man and horse ; in fact, their view will be, not that all things are one, but that they are nothing ; and that 4 to be of such-and-such a quality * is the same as 4 to be of such-and-such a size \

25 Even the more recent of the ancient thinkers were in a pother lest the same thing should turn out in their hands both one and many. So some, like Lycophron, 3 were led to omit 4 is’, others to change the mode of expression and say 4 the man has been whitened * instead of 4 is white \ and 30 4 walks’ instead of 4 is walking*, for fear that if they added the word 4 is * they should be making the one to be many — as if 4 one* and 'being* were always used in one and the same sense. What 4 is* may be many either in definition (for example 4 to be white * is one thing, 4 to be musical* another, yet the same thing 4 may be both, so the one is many) or by division, as the whole and its parts. i86 a On this point, indeed, they Were already getting into difficulties and admitted that the one was many— as if there was any difficulty about the same thing being both one and many, provided that these are not opposites ; for 4 one’ may mean either 'potentially one* or 'actually one \ 6

1 Indivisible unity is inconsistent with any type of predication, which always involves a subject and a predicate, and in particular with the predication of quantity.

2 e.g. a point which terminates a line is indivisible, though the line is not.

8 An orator and a pupil of Gorgias. For what is known of him see Zeller i 6 . 1323, n. 3,

4 Reading in 1 . 33 to avr 6 t with E.

* So that there is no contradiction in supposing that a thing is (say)

4 actually one but 4 potentially many ’, at the same time.

3 If, then, we approach the thesis in this way it seems impossible for all things to be one. Further, the arguments 5 they use to prove their position are not difficult to expose. For both of them reason contentiously — I mean both Melissus and Parmenides. [Their premisses are false and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all : admit one ridiculous proposition and the rest follows — a simple enough proceeding.] 1

The fallacy of Melissus is obvious. 2 For he supposes that 10 the assumption 4 what has come into being always has a beginning* justifies, the assumption ‘what has not come into being has no beginning*. Then this also is absurd, that in every case there should be 3 a beginning of the thing — not of the time and not only in the case of coming to be in the full sense but also in the case of coming to have a quality 4 — as if change never took place suddenly. 15 Again, does it follow that Being, if one, is motionless? Why should it not move, the whole of it within itself, as parts of it do which are unities, e. g. this water? Again, why is qualitative change impossible ? But, further, Being cannot be one in form, though it may be in what it is made of. (Even 20 some of the physicists hold it to be one in the latter way, though not in the former.) Man obviously differs from horse in form, and contraries from each other.

The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view : the answer to him being that 4 this is not true ’ and ‘ that does not follow*. His assumption that one is used in a single sense only is false, because it is used in several. His conclusion »5 does not follow, because if we take only white things, and if ‘white* has a single meaning, none the less what is white will be many and not one. For what is white will not be

1 The words in brackets are probably wrongly inserted from 185“ 9-12.

4 See Diels, Vorsokratiker * , i. 187-90. Aristotle wishes to say that there is always a beginning of the time, but not always of the thing.

i86 a one either in the sense that it is continuous or in the sense that it must be defined in only one way. ‘ Whiteness ’ will be different from ‘ what has whiteness ’. Nor does this mean that there is anything that can exist separately, over 30 and above what is white. For ‘ whiteness ’ and * that which is white’ differ in definition, not in the sense that they are things which can exist apart from each other. But Parmenides had not come in sight of this distinction.

It is necessary for him, then, to assume not only that ‘ being’ has the same meaning, of whatever it is predicated, but further that it means (1) what just is 1 and (2) what is just one }

It must be so, 1 * 3 for (1) an attribute is predicated of some 35 subject, so that the subject to which * being ’ is attributed will not be, as it is something different from ‘ being ’. i86 b Something, therefore, which is not will be. Hence ‘substance’ 4 will not be a predicate of anything else. 5 For the subject cannot be a beings unless ‘being’ means several things, in such a way that each is something. But ex hypothesi ‘ being’ means only one thing.

If, then, ‘substance’ is not attributed to anything, but 5 other things are attributed to it, how does ‘ substance * mean what is rather than what is not ? For suppose that * substance ’ is also ‘ white Since the definition of the latter is different (for being cannot even be attributed to white, as nothing is which is not ‘substance’), it follows that ‘white’ is not-being— and that not in the sense of a particular not-being, but in the sense that it 10 is not at all. Hence ‘ substance * is not ; for it is true to say that it is white, 6 which we found to mean

1 i. e. substance.

a i. e. indivisible unity.

* It is necessary to supply some such intermediate step as this :

‘ If being is not thus identified with substantial being, it is an attribute, and then the following difficulty occurs — *.

4 Or that which just is.

5 Consequently to make being = substance does not obviously involve a plurality (duality) of beings, as identifying it with an attribute does.

6 Aristotle assumes throughout the possibility of predication.

not-being. If to avoid this 1 we say that even ‘white’ means substance, it follows that ‘being’ has more than one meaning.

In particular, then, Being will not have magnitude, if it is substance. For each of the two parts 2 must be in a different sense.

(2) Substance is plainly divisible into other substances, if we consider the mere nature of a definition. For instance, 15 if ‘ man ’ is a substance, ‘ animal ’ and ‘ biped ’ must also be substances. For if not substances, they must be attributes — and if attributes, attributes either of (a) man or of ( b ) some other subject. But neither is possible.

(a) An attribute is either that which may or may not belong to the subject or that in whose definition the subject 20 of which it is an attribute is involved . 3 Thus ‘ sitting ’ is an example of a separable attribute, while 4 snubness 9 contains the definition of ‘ nose ’, to which we attribute snubness. Further, the definition of the whole is not contained in the definitions of the contents or elements of the definitory formula ; that of 4 man ’ for instance in ‘ biped *, or that of

4 white man ’ in * white ’. If then this is so, and if 4 biped ’ is 25 supposed to be an attribute of 4 man ’, it must be either separable, so that 4 man ’ might possibly not be 4 biped ’, or the definition of 4 man ’ must come into the definition of ‘ biped ’ — which is impossible, as the converse is the case. 3 ®

(b) If, on the other hand, we suppose that 4 biped’ and 4 animal ’ are attributes not of man but of something else, and are not each of them a substance, then 4 man ’ too will be an attribute of something else. But we must assume that substance 4 is not the attribute of anything, and that the subject of which both 4 biped * and 4 animal ’ and each separately 5 are predicated is the subject also of the complex 4 biped animal ’.

Are we then to say that the All is composed of indivisible 35

1 Sc. to avoid the self-contradiction involved in saying to 5 ntp hv

OVK tv,

9 Which are, at the least, involved in its having magnitude.

4 Omitting n in 1 . 34, with E 1 I Phil. Simp.

6 Placing a comma after, not before, ko\ evdrtpov (11. 34-5).

187* substances ? 1 Some thinkers did, in point of fact, give way to both arguments. To the argument that all things are one if being means one thing, they conceded that not-being is ; to that from bisection, they yielded by positing atomic magnitudes. 2 But obviously it is not true that if being means one thing, and cannot at the same time mean the 5 contradictory of this, there will be nothing which is not, for even if what is not cannot be without qualification, there is no reason why it should not be a particular not-being. To say that all things will be one, if there is nothing besides Being itself, is absurd. For who understands ‘being itself to be anything but a particular substance? But if this is so, there is nothing to prevent there being many beings, as has been said.

! ° It is, then, clearly impossible for Being to be one in this sense.

The physicists on the other hand have two modes of 4 explanation.

The first set make the underlying body 3 one — either one of the three 4 or something else which is dense;* than fire *5 and rarer than air 5 — then generate everything else from this, and obtain multiplicity by condensation and rarefaction. Now these are contraries, which may be generalized into ‘excess and defect*. (Compare Plato’s 4 Great and Small * — except that he makes these his matter, the one his form, while the others treat the one which underlies as matter and the contraries as differentiae, i. e. forms), ao The second set assert that the contrarieties are contained in the one and emerge from it by segregation, for example Anaximander and also all those who assert that ‘ what is * is one and many, like Empedocles and Anaxagoras ; for they

1 Taking aduupertov apn to nav in 1 . 35 as a question.

2 See Diels, Vorsokratiker *, i. 170 f. t 181-3.

3 i87 a 13 omitting op, of which there is no trace in Simplicius.

4 Water, air, or fire. Aristotle points out elsewhere {Met, A. 988° 30) that no one made earth the substratum.

5 Aristotle sometimes mentions a theory that the substratum is between water and air, and once a theory that it is between water and fire. A substance between air and fire is mentioned by Aristotle in fouf other passages besides the present. See Zeller i 6 . 283-91, Diels, Vors} i. 415. 32-416. 27.

i&f too produce other things from their mixture by segregation, These differ, however, from each other in that the former imagines a cycle of such changes, the latter a single series. Anaxagoras again made both his * homoeomerous * 1 35 substances and his contraries infinite in multitude, whereas Empedocles posits only the so-called 1 2 3 * elements.

The theory of Anaxagoras that the principles are infinite in multitude was probably due to his acceptance of the common opinion of the physicists that nothing comes into being from not-being. For this is the reason why they use the phrase ‘ all things were together * and the coming 30 into being of such and such a kind of thing is reduced to change of quality, while some spoke of combination and separation. 8 Moreover, the fact that the contraries proceed from each other led them to the conclusion. The one, they reasoned, must have already existed in the other ; for since everything that comes into being must arise either from what is or from what is not, and it is impossible for it to arise from what is not (on this point all the physicists agree), they thought that the truth of the alternative necessarily 35 followed, namely that things come into being out of existent things, i.e. out of things already present, but imperceptible to our senses because of the smallness of their bulk. So 187* they assert that everything has been mixed in everything, because they saw everything arising out of everything.

But things, as they say, appear different from one another and receive different names according to the nature of the particles which are numerically predominant among the innumerable constituents of the mixture. For nothing, they say, is purely and entirely white or black or sweet, 5 bone or flesh, but the nature of a thing is held to be that of which it contains the most.

Now (1) the infinite qua infinite is unknowable, so that what

1 6 fx(HOfx(pfj is Aristotle’s term for substances which are divisible into parts like themselves. It means primarily the ‘tissues’ of plants and animals, e.g, flesh, as distinguished from the opyavun ptpr) % such as the hand. It includes the metals, but not the four elements.

8 Aristotle himself regards the four * elements ’ as complex.

3 Putting only a comma after dWoiovaOat in 1 . 30. Cf. Diels, ib. 388.

i87 b is infinite in multitude or size is unknowable in quantity, and what is infinite in variety of kind is unknowable in io quality. But the principles in question are infinite both in multitude and in kind. Therefore it is impossible to know things which are composed of them ; for it is when we know the nature and quantity of its components that we suppose we know a complex.

Further (2) if the parts of a whole may be of any size in the 15 direction either of greatness or of smallness (by ‘parts* I mean components into which a whole can be divided and which are actually present in it), it is necessary that the whole thing itself may be of any size. Clearly, therefore, 1 since it is impossible for an animal or plant to be indefinitely big or small, neither can its parts be such, or the whole will be the same. But flesh, bone, and the like are the parts 20 of animals, and the fruits are the parts of plants. Hence it is obvious that neither flesh, bone, nor any such thing can be of indefinite size in the direction either of the greater or of the less.

Again (3) according to the theory all such things are already present in one another and do not come into being but are constituents which are separated out, and a thing receives its designation from its chief constituent. Further, anything may come out of anything — water by segregation 35 from flesh and flesh from water. Hence, since every finite body is exhausted by the repeated abstraction of a finite body, it seems obviously to follow that everything cannot subsist in everything else. For let flesh be extracted from water and again more flesh be produced 2 from the remainder by repeating the process of separation : then, even though the quantity separated out will continually decrease, still it 30 will not fall below a certain magnitude. 3 If, therefore, the process comes to an end, everything will not be in everything else (for there will be no flesh in the remaining water) ; if on the other hand it does not, and further extraction is always possible, there will be an infinite multitude of finite

8 Anaxagoras would deny this.

equal 1 particles in a finite quantity — which is impossible. Another proof may be added : Since every body must 35 diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that from the minimum quantity of flesh no body can be separated out ; for the flesh left would 188 be less than the minimum of flesh. 2

Lastly (4) in each of his infinite bodies there would be already present infinite flesh and blood and brain — having a distinct existence, however, from one another, and no less real than the infinite bodies, and each infinite: which is contrary to reason.

The statement that complete separation never will take 5 place is correct enough, though Anaxagoras is not fully aware of what it means. For affections are indeed inseparable. If then colours and states had entered into the mixture, and if separation took place, there would be a ‘white’ ora ‘healthy’ which was nothing but white or healthy, i. e. was not the predicate of a subject. So his ‘ Mind’ is an absurd person aiming at the impossible, if he is supposed to wish to separate them, and it is impossible 10 to do so, both in respect of quantity and of quality — of quantity, because there is no minimum magnitude, 3 and of quality, because affections are inseparable.

Nor is Anaxagoras right about the coming to be of homogeneous bodies. 4 It is true there is a sense in which clay is divided into pieces of clay, but there is another in which it is not. Water 6 and air are, and are generated, 15 1 from ’ each other, but not in the way in which bricks come 4 from ’ a house and again a house 4 from 9 bricks 6 ; and it is better to assume a smaller and finite number of principles, as Empedocles does. 7

1 Aristotle supposes for simplicity that the finite amounts which are extracted are equal.

2 For Anaxagoras there is no minimum. — It seems best to read fXarro)!' in 1 . i with Simplicius.

8 Omitting in 1 . 16, perhaps with Them, and Simp.

6 i. e. by segregation and aggregation respectively. Water comes from air by change of quality. »

T If we accept the possibility of transmutation, it is not necessary to assume an infinite multitude of principles.

All thinkers then agree in making the contraries 5 principles, both those who describe the All as one and

20 unmoved (for even Parmenides treats hot and cold as principles under the names of fire and earth) 1 and those too who use the rare and the dense. The same is true of Democritus also, with his plenum 2 and void, both of which exist, he says, the one as being, the other as not-being. Again he speaks of differences in position, shape, and order, and these are genera of which the species are contraries, namely, of position, above and below, before and behind ;

25 of shape, angular and angle-less, straight and round. 3

It is plain then that they all in one way or another identify the contraries with the principles. And with good reason. For first principles must not be derived from one another nor from anything else, while everything has to be derived from them. But these conditions are fulfilled by the primary contraries, which are not derived from anything else because they are primary, nor from each other because they are contraries.

30 But wc must see how this can be arrived at as a reasoned result, as well as in the way just indicated.

Our first presupposition must be that in nature nothing acts on, or is acted on by, any other thing at random, nor may anything come from anything else, unless we mean that it does so in virtue of a concomitant attribute.

35 For how could 4 white * come from 4 musical unless 4 musical ’ happened to be an attribute of the not-white 4 or of the black? No, ‘white’ comes from ‘not-white' —and not from any 4 not-white but from black or some i88 b intermediate colour. 6 Similarly, ‘musical’ comes to be from ‘ not-musical’, but not from any thing other than musical, but from 4 unmusical ’ or any intermediate state there may be.

2 Reading in 1 . 22 nXrjpa for arepah', with E 1 I Simp. Phil. Them.

8 Reading in 1 . 25 with MS. Par. 1859, Phil., and Simp., y^ycma^W ay<av iov, €v 6 v mpifapts.

4 Reading in 1 . 36 T<j>pr) Afww, with E and Simp.

8 According to Aristotle, the colours form a scale between black and white.

Nor again do things pass into the first chance thing ;

‘ white 1 does not pass into ‘ musical 1 (except, it may be, in virtue of a concomitant attribute), but into ‘notwhite * — and not into any chance thing which is not white, but into black or an intermediate colour ; ‘musical' passes into ‘not- musical* — and not into any chance thing others than musical, but into 1 unmusical ’ or any intermediate state there may be.

The same holds of other things also : even things which are not simple but complex follow the same principle, but the io opposite state has not received a name, so we fail to notice the fact. What is in tune must come from what is not in tune, and vice versa ; the tuned passes into untunedness — and not into any untunedness, but into the corresponding opposite. It does not matter 1 whether we take attune- 15 ment, order, or composition for our illustration ; the principle is obviously the same in all, and in fact applies equally to the production of a house, a statue, or any other complex.

A house comes from certain things in a certain state of separation instead of conjunction, a statue (or any other thing that has been shaped) from shapelessness — each of 20 these objects being partly order and partly composition.

If then this is true, everything that comes to be or passes away comes from, or passes into, its contrary or an intermediate state. But the intermediates are derived from the contraries — colours, for instance, from black and white. Everything, therefore, that comes to be by a natural 35 process is either a contrary or a product of contraries.

Up to this point we have practically had most of the other writers on the subject with us, as I have said already 2 ; for all of them identify their elements, and what they call their principles, with the contraries, giving no reason indeed for the theory, but constrained as it were by the truth itself. They differ, however, from one another in that 30 some assume contraries which are more primary, others contraries which are less so: some those more knowable

1 Reading in 1. 15 ftiafopa d' ov&V, with the MSS.

i88 b in the order of explanation, others those more familiar to sense. For some make hot and cold, or again moist and dry, the conditions of becoming; while others make odd 35 and even, or again Love and Strife ; and these differ from each other in the way mentioned.

Hence their principles are in one sense the same, in another different ; different certainly, as indeed most people 189* think, but the same inasmuch as they are analogous ; for all are taken from the same table of columns, 1 * * some of the pairs being wider, others narrower in extent. In this way then their theories are both the same and different, some better, some worse; some, as I have said, take as their contraries what is more knowable in the order of explanation,

5 others what is more familiar to sense. (The universal is more knowable in the order of explanation, the particular in the order of sense: for explanation has to do with the universal, sense with the particular.) ‘ The great and the small/ for example, belong to the former class, 4 the dense and the rare * to the latter.

10 It is clear then that our principles must be contraries.

The next question is whether the principles are two or 6 three or more in number.

One they cannot be, for there cannot be one contrary. Nor can they be innumerable, because, if so, Being will not be knowable : and in any one genus there is only one contrariety, and substance is one genus : also a finite number 15 is sufficient, and a finite number, such as the principles of Empedocles, is better than an infinite multitude ; for Empedocles professes to obtain from his principles all that Anaxagoras obtains from hisinnumerableprinciples. Lastly, some contraries are more primary than others, and some arise from others— -for example sweet and bitter, white and black — whereas the principles must always remain principles.

1 The following is the table given Limit . . . Unlimited Odd . . . Even

This will suffice to show that the principles are neither 20 one nor innumerable.

Granted, then, that they are a limited number, it is plausible to suppose them more than two. For it is difficult to see how either density should be of such a nature as to act in any way on rarity or rarity on density. The same is true of any other pair of contraries ; for Love does not gather Strife together and make things out of it, nor does 25 Strife make anything out of Love, but both act on a third thing different from both. Some indeed assume more than one such thing from which they construct the world of nature.

Other objections to the view that it is not necessary to assume a third principle as a substratum may be added.

(1) We do not find that the contraries constitute the substance of any thing. But what is a first principle ought 30 not to be the predicate of any subject. If it were, there would be a principle of the supposed principle: for the subject is a principle, and prior presumably to what is predicated of it. Again (2) we hold that a substance is not contrary to another substance. How then can substance be derived from what are not substances? Or how can non-substance be prior to substance ?

If then we accept both the former argument 1 and this one, 2 we must, to preserve both, assume a third somewhat 35 as the substratum of the contraries, such as is spoken of by i8g b those who describe the All as one nature — water or fire or what is intermediate between them. What is intermediate seems preferable ; for fire, earth, air, and water are already 3 involved with pairs of contraries. There is, therefore, much to 5 be said for those who make the underlying substance different from these four ; of the rest, the next best choice is air, as presenting sensible differences in a less degree than the others ; and after air, water. All, however, agree in this, that they differentiate their One by means of the contraries, such as density and rarity and more and less, which may 10

1 Th?t the contraries are principles (ch. 5).

3 Reading in 1, 4 nvp yap fjbq, with E Them. Simp.

i89 b of course be generalized, as has already been said, 1 into excess and defect. Indeed this doctrine too (that the One and excess and defect are the principles of things) would appear to be of old standing, though in different forms ; for the early thinkers made the two the active and the one the passive principle, whereas some of the more recent 15 maintain the reverse.

To suppose then that the elements are three in number would seem, from these and similarconsiderations, a plausible view, as I said before. 2 On the other hand, the view that they are more than three in number would seem to be untenable.

For the one substratum is sufficient to be acted on ; but if 20 we have four contraries, there will be two contrarieties, and we shall have to suppose an intermediate nature for each pair 3 separately. 4 If, on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be superfluous. Moreover, it is impossible that there should be more than one primary contrariety. For substance is a single genus of being, ’so that the principles can differ only as prior and posterior, not in 25 genus ; in a single genus there is always a single contrariety, all the other contrarieties in it being held to be reducible to one.

It is clear then that the number of elements is neither one nor more than two or three; but whether two or three is, as I said, a question of considerable difficulty.

30 We will now give our own account, 6 approaching the 7 question first with reference to becoming in its widest sense : for we shall be following the natural order of inquiry if we speak first of common characteristics, and then investigate the characteristics of special cases. 6

We say that one thing comes to be from another thing, and one sort of thing from another sort of thing, both in

8 i89 b 2o reading kKartpa with Philoponus and Pacius.

4 So that one of these substrata would be superfluous.

i89 b the case of simple and of complex things. I mean the following. We can say (i) the ‘man becomes musical',

(a) what is ‘ not-musical becomes musical V or (3) the * not- 35 musical man becomes a musical man \ Now what becomes 190® in (1) and (2) — ‘ man * and * not musical * — I call simple , and what each becomes — ‘ musical ’ — simple also. But when (3) we say the ‘not-musical man becomes a musical man both what becomes and what it becomes are complex .

As regards one of these simple ‘ things that become ’ we 5 say not only ‘this becomes so-and-so 1 , 2 but also ‘from being this, comes to be so-and-so as ‘ from being notmusical comes to be musical * ; as regards the other we do not say this in all cases, as we do not say (1) ‘ from being a man he came to be musical ’ but only ‘ the man became musical *.

When a ‘simple’ thing is said to become something, in one case (1) it survives through the process, in the other (2)' it does not. For the man remains a man and is such even JO when he becomes musical, whereas what is not musical or is unmusical does not continue to exist, either simply or combined with the subject.

These distinctions drawn, one can gather from surveying the various cases of becoming in the way we are describing that, as we say, there must always be an underlying something, namely that which becomes, and that this, though 15 always one numerically, in form at least is not one. (By that I mean that it can be described in different ways.) For ‘ to be man ’ is not the same as ‘ to be unmusical One part survives, the other does not : what is not an opposite survives (for ‘ man * survives), but ‘ not-musical 9 3 or ‘ unmusical * does not survive, nor does the compound of the two, namely 20 ‘ unmusical man \

We speak of * becoming that from this’ instead of ‘this becoming that ’ more in the case of what does not survive the change — ‘ becoming musical from unmusical ', not ‘ from

1 Omitting in 1 . 35 n, with E Them. Phil. Simp.

* Omitting in 1 . 6 n, with E l Them. Phil.

i90 a man ’ — but there are exceptions, as we sometimes use the 25 latter form of expression even of what survives ; we speak of 4 a statue coming to be from bronze \ not of the ‘ bronze becoming a statue \ The change, however, from an opposite which does not survive is described indifferently in both ways, ‘ becoming that from this * or ‘ this becoming that r . 30 We say both that ‘ the unmusical becomes musical and that 1 from unmusical he becomes musical’. And so both forms are used of the complex, ‘ becoming a musical man from an unmusical man and 1 an unmusical man becoming a musical man \

But there are different senses of ‘coming to be*. In some cases we do not use the expression ‘ come to be but 1 come to be so-and-so \ Only substances are said to * come to be ’ in the unqualified sense.

Now in all cases other than substance it is plain that there must be some subject, namely, that which becomes. For we know that when a thing comes to be of such 35 a quantity or quality or in such a relation, time, or place, a subject is always presupposed, since substance alone is not predicated of another subject, but everything else of substance.

i$o b But that substances too, and anything else that can be said ‘to be’ without qualification, come to be from some substratum, will appear on examination. For we find in every case something that underlies from which proceeds that which comes to be ; for instance, animals and plants from seed.

5 Generally things which come to be, come to be in different ways: (1) by change of shape, as a statue 1 ; (a) by addition, as things which grow; (3) by taking away, as the Hermes from the stone ; (4) by putting together, as a house ; (5) by alteration, as things which 1 turn ’ in respect of their material substance. 2

1 Sc. a bronze statue. *k is probably a gloss.

* The first four modes of becoming are cases of artificial production^. The fifth seems to include both mere change of quality (dXXotuvi?) ancj generation in the full sense (AnXr) yeVe<nr), which presumably is aiways| accompanied by dXXotva is. Milk ‘turning’ would be merely a cas<|

It is plain that these are all cases of coming to be from a substratum.

Thus, clearly, from what has been said, whatever comes 10 to be is always complex. There is, on the one hand, (a) something which comes into existence, and again (b) something which becomes that — the latter ( b ) in two senses, either the subject or the opposite. By the ‘opposite' I mean the ‘unmusical’, by the ‘subject’ ‘ man’, and similarly I call the absence of shape or form or order the ‘opposite', 15 and .the bronze or stone or gold the ‘subject’.

Plainly then, if there are conditions and principles which constitute natural objects and from which they primarily are or 1 have come to be — have come to be, I mean, what each is said to be in its essential nature, not what each is in respect of a concomitant attribute — plainly, I say, everything comes to be from both subject and form. For 30 ‘musical man’ is composed (in a way ) 2 of ‘man* and ‘musical’: you can analyse it 3 into the definitions of its elements. It is clear then that what comes to be will come to be from these elements.

Now the subject is one numerically, though it is two in form. (For it is the man, the gold — the ‘ matter ’ 4 generally — that is counted, for it is more of the nature of a ‘ this *, and 35 what comes to be does not come from it in virtue of a concomitant attribute 6 ; the privation, on the other hand, and of change of quality (aXXmaurtf), not of change of substance (AnXrj y«Vf oris) : water turning into wine, or Karaixrjpta becoming avtipw ror, would be an example of the latter. Since Aristotle is carefully working up to the conception of matter (vXrj), the words Kara rrjv iX^v are used inadvertently, or are a later addition to explain rpenofxfm.

1 Omitting the comma after tlai in 1. 18.

2 The relation of attribute to subject is only analogous to that of form to matter.

8 Omitting the first rovs X6yovs in 1 . 22, with Diels.

4 Aristotle here introduces vXrj as his technical term for ‘matter’. Literally the word means 4 wood f or 4 timber’, and Aristotle no doubt has in view the simplest example of a maker, the rtKrmtf.

5 Every transition is of the form XA->XA\ where X is substance. J± r (or XA') is said to come to be from A' without qualification (ArrXm), On the other hand, A f comes to be from A , in virtue of an attribute (Kara ovfAfitfirjKvs), namely A , which X possesses. The contrast is between ‘ coming to be * without qualification, and ‘ coming to be in virtue of an attribute’. If A f is a quality, A is the contrary quality the contrary are incidental 1 in the process.) And the positive form is one* — the order, the acquired art of music, or any similar predicate.

There is a sense, therefore, in which we must declare the principles to be two, and a sense in which they are three ; 30 a sense in which the contraries are the principles — say for example the musical and the unmusical, the hot and the cold, the tuned and the untuned — and a sense in which they are not, since it is impossible for the contraries to be acted on by each other. But this difficulty also is solved by the fact that the substratum is different from the contraries, 35 for it is itself not a contrary. The principles therefore are, in a way, not more in number than the contraries, but as it were two, nor yet precisely two, since there is a difference 191* of essential nature, but three. For 4 to be man ’ is different from 4 to be unmusical 7* and 4 to be unformed ’ from 4 to be bronze \

We have now stated the number of the principles of natural objects which are subject to generation, and how the number is reached : and it is clear that there must be a substratum for the contraries, and that the contraries 5 must be two. (Yet in another way of putting it this is not necessary, as one of the contraries will serve to effect the change by its successive absence and presence.)

The underlying nature is an object of scientific knowledge, by an analogy. For as the bronze is to the statue, the 10 wood to the bed, or the matter and the formless before receiving form to any thing which has form, so is the underlying nature to substance, i. e. the 4 this' or existent.

This then is one principle (though not one or existent 4 in the same sense as the 4 this ’), and the definition was one as we agreed 6 ; then further there is its contrary, the priva-

(or intermediate). But if A ' is substance (as well as X), A is called the privation (crTiprjms) of A\

3 i.e. counts as principle No. 2.

8 Altering the reading of the MSS. in 1. 13 ($ 6 U yos ) to 6 \6yot. \6yos is used by Aristotle as equivalent to rfdos of i9o b 28.

tion. In what sense these are two, and in what sense more, has been stated above. Briefly, we explained first 1 *5 that only the contraries were principles, and later 2 that a substratum was indispensable, and that the principles were three ; our last statement 3 has elucidated the difference between the contraries, the mutual relation of the principles, and the nature of the substratum. Whether the form or the substratum is the essential nature of a physical object is not yet clear. 4 But that the principles are three, and in what sense, and the way in which each is a principle, is clear.

So much then for the question of the number and the nature of the principles.

8 We will now proceed 5 to show that the difficulty of the early thinkers, as well as our own, is solved in this way alone.

The first of those who studied science were misled in their search for truth and the nature of things by their inex- *5 perience, 0 which as it were thrust them into another path.

So they say that none of the things that are either comes to be or passes out of existence, because what comes to be must do so either from what is or from what is not, both of which are impossible. For what is cannot come to be 3° (because it is already), and from what is not nothing could have come to be (because something must 7 be present as a substratum). So too they exaggerated the consequence of this, and went so far as to deny even the existence of a plurality of things, maintaining that only Being itself is. Such then was their opinion, and such the reason for its adoption.

Our explanation on the other hand is that the phrases ‘something comes to be from what is or from what is not \

‘ what is not or what is does something or has something 35 done to it or becomes some particular thing are to be taken (in the first way of putting our explanation) in the

4 This is discussed below, Bk. II, Ch. 1.

8 Reading in 1. 24 with El.

f Sc. of logical analysis. So Themistius and Philoponus.

7 Reading in l. 31 falv, with Bonitz.

i9i b i 9 * b same sense as 4 a doctor does something or has something done to him ‘ is or becomes something from being a doctor'. These expressions may be taken in two senses, and s^ too, clearly, may ‘from being', and ‘being acts or is acted on \ A doctor builds a house, not qua doctor, but qua 5 housebuilder, and turns gray, not qua doctor, but qua darkhaired. On the other hand he doctors or fails to doctor qua doctor. But we are using words most appropriately when we say that a doctor does something or undergoes something, or becomes something from being a doctor, if he does, undergoes, or becomes qua doctor. Clearly then also ‘ to come to be so-and-so from not-being ’ means ‘ qua not-being \

10 It was through failure to make this distinction that those thinkers gave the matter up, and through this error that they went so much farther astray as to suppose that nothing else comes to be or exists apart from Being itself, thus doing away w r ith all becoming.

We ourselves are in agreement with them in holding that nothing can be said without qualification to come from what is not. But nevertheless we maintain that a thing may * come to be from what is not ' — that is, in a qualified 15 sense. For a thing comes to be from the privation, which in its own nature is not-being, — this not surviving as a constituent of the result. Yet this causes surprise, and it is thought 1 impossible that something should come to be in the way described from what is not.

In the same way we maintain that nothing comes to be from being, and that being does not come to be except in a qualified sense. In that way, however, it does, just as animal might come to be from animal, and an animal of ao a certain kind from an animal of a certain kind. Thus, suppose a dog to come to be from a horse. The dog would then, it is true, come to be from animal 2 (as well as from an animal of a certain kind) but not as animal , for that is already there. But if anything is to become an animal, not in a qualified sense, it will not be from animal ;

and if being, not from being — nor from not-being either, for 25 it has been explained 1 that by 4 from not-being * we mean from not-being qua not-being.

Note further that we do not subvert the principle that everything either is or is not.*

This then is one way of solving the difficulty. Another consists in pointing out that the same things can be explained in terms of potentiality and actuality. But this has been done with greater precision elsewhere. 3

So, as we said, the difficulties which constrain people 30 to deny the existence of some of the things we mentioned 4 are now solved. For it was this reason which also caused some of the earlier thinkers to turn so far aside from the road which leads to coming to be and passing away and change generally. If they had come in sight of this nature, 5 all their ignorance would have been dispelled.

9 Others, 0 indeed, have apprehended the nature in question, 35 but not adequately.

In the first place they allow that a thing may come to be without qualification from not-being, accepting on this point the statement 7 of Parmenides. Secondly, they think 19a® that if the substratum is one numerically, it must have also only a single potentiality 8 — which is a very different thing.

Now we distinguish matter and privation, and hold that one of these, namely the matter, is not-being only in virtue of an attribute which it has, while the privation in its own nature is not-being ; and that the matter is nearly, in 5 a sense is, substance, while the privation in no sense is. They, on the other hand, identify their Great and Small

8 Met, Bk. e, and X 1017“ 35- b 9.

4 e. g. becoming and plurality.

4 The Platonists.

7 That if a thing does not come to be from being, it must come to be from not-being.

• dvvdfmi rfdu above (i9o b 24). In Aristotle’s theory, the substratum plays a double part.

alike with not-being, and that whether they are taken together as one or separately. Their triad is therefore of quite a different kind from ours. For they got so far jo as to see that there must be some underlying nature, but they make it one — for even if one philosopher 1 makes a dyad of it, which he calls Great and Small, the effect is the same, for he overlooked the other nature . 2 For the one which persists is a joint cause, with the form, of what comes to be — a mother, as it were . 3 But the negative part 15 of the contrariety may often seem, if you concentrate your attention on it as an evil agent, not to exist at all.

For admitting with them that there is something divine, good, and desirable, we hold that there are two other principles, the one contrary to it, the other such as of its own nature to desire and yearn for it. But the consequence of their view is that the contrary desires its own extinction. 20 Yet the form cannot desire itself, for it is not defective ; nor can the contrary desire it, for contraries are mutually destructive. The truth is that what desires the form is matter, as the female desires the male and the ugly the beautiful — only the ugly or the female not per se but per accidens .

25 The matter comes to be and ceases to be in one sense, while in another it does not. As that which contains the privation, it ceases to be in its own nature, for what ceases to be — the privation — is contained within it. But as potentiality it does not cease to be in its own nature, but is necessarily outside the sphere of becoming and ceasing to be. For if it came to be, something must have existed as a primary substratum from which it should come and 30 which should persist in it ; but this is its own special nature , 4 so that it will be before coming to be. (For my definition of matter is just this — the primary substratum of each thing, from which it comes to be without qualification, and which persists in the result.) And if it ceases to be it will pass into that at the last, so it will have ceased to be before ceasing to be.

1 Plato. 8 The privation. 8 Cf. Tim, 50 D, 51 a.

4 Reading avrrjs in 1 . 30 with I and Phil.

The accurate determination of the first principle in respect of form, whether it is one or many and what it is or what they are, is the province of the primary type of 35 science 1 ; so these questions may stand over till then . 2 But of the natural, i.e. perishable , 3 forms we shall speak ig 2 b in the expositions which follow . 4

The above, then, may be taken as sufficient to establish that there are principles and what they are and how many there are. Now let us make a fresh start and proceed.

1 Metaphysics or ‘ First philosophy * (irpuir) (fithmcxfila) as it is often called. 2 Met, A. 7-9.

5 Omitting in 1 . 1 twv after *««, with E Them. Phil.

4 i.e. the remaining treatises of 1 second philosophy’ viz.

the rest of the Physics , the De Caelo , De Gen . et Corr, } See. (especially De Gen. et Corr. II).

Of things that exist, 1 some exist by nature, some from I other causes.

4 By nature 9 the animals and their parts exist, and the io plants and the simple bodies (earth, fire, air, water) — for wc say that these and the like 2 exist ‘ by nature*.

All the things mentioned present a feature in which they differ from things which are not constituted by nature. Each of them has within itself a principle 3 of motion and *5 of stationariness (in respect of place, or of growth and decrease, or by way of alteration). On the other hand, a bed and a coat and anything else of that sort, qua receiving these designations— i. e. in so far as they are products of art — have no innate impulse to change. But in so far as they happen to be composed of stone or 20 of earth or of a mixture of the two, they do have such an impulse, 4 and just to that extent — which seems to indicate that fiature is a source or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not in virtue of a concomitant attribute.

I say ‘not in virtue of a concomitant attribute because (for instance) a man who is a doctor might cure himself. Nevertheless it is not in so far as he is a patient that he 25 possesses the art of medicine: it merely has happened that the same man is doctor and patient — and that is why these attributes are not always found together. So it is with all other artificial products. None of them has in itself the source of its own production. But while in some cases (for instance houses and the other products of manual

1 ra Zvrn = substances, which consist of matter and form. Such of them as exist by nature (<f>vau) are the objects of Physical Science.

1 Inorganic compounds are included (1. 20).

* Reading in 1 . 13 f. tovtw uev yap tKacrrov tv coutw apyn p cvei, with E Al. Them. Phil.

4 A bed, e. g., tends to fall to the ground or to rest there, not qua bed, but qua made of a heavy material.

labour) that principle is in something else external to the thing, in others — those which may cause a change in them- 30 selves in virtue of a concomitant attribute — it lies in the things themselves (but not in virtue of what they are).

‘Nature* then is what has been stated. Things ‘have a nature* which have a principle of this kind. Each of them is a substance ; for it is a subject, 1 and nature always implies a subject in which it inheres.

The term ‘according to nature* is applied to all these 35 things and also to the attributes which belong to them in virtue of what they are, for instance the property of fire to be carried upwards — which is not a ‘ nature * nor ‘ has a nature* but is ‘ by nature * or ‘ according to nature *.

What t nature is, then, and the meaning of the terms 193 ‘by nature* and ‘according to nature*, has been stated. That nature exists, it would be absurd to try to prove ; for it is obvious that there are many things of this kind, and to prove what is obvious by what is not is the mark of 5 a man who is unable to distinguish what is self-evident from what is not. (This state of mind is clearly possible.

A man blind from birth might reason about colours. Presumably therefore such persons must be talking about words without any thought to correspond.)

Some identify the nature or substance of a natural object with that immediate constituent of it which taken by itself 10 is without arrangement, e. g. the wood is the ‘nature* of the bed, and the bronze the ‘ nature* of the statue.

As an indication of this Antiphon points out that if you planted a bed and the rotting wood acquired the power of sending up a shoot, it would not be a bed that would come up, but wood 2 — which shows that the arrangement in accordance with the rules of the art is merely an incidental 15 attribute, whereas the real nature is the other, which, further, persists continuously through the process of making.

But if the material of each of these objects has itself

1 Placing a comma after n in 1 . 34.

1 Cf. Antiphon, fr. 15 Diels.

I 93 a the same relation to something else, say bronze (or gold) ao to water, bones (or wood) to earth and so on, that (they say) would be their nature and essence. Consequently some assert earth, others fire or air or water or some or all of these, to be the nature of the things that are. For whatever any one of them supposed to have this character — whether one thing or more than one thing — this or these 25 he declared to be the whole of substance, all else being its affections, states, or dispositions. Every such thing they held to be eternal (for it could not pass into anything else), but other things to come into being and cease to be times without number.

This then is one account of ‘ nature ', namely that it is the immediate material substratum of things which have in themselves a principle of motion or change.

30 Another account is that ‘ nature * is the shape or form which is specified in the definition of the thing.

For the word ‘ nature * is applied to what is according to nature and the natural in the same way as ‘ art ’ is applied to what is artistic or a work of art. We should not say in the latter case that there is anything artistic about a thing, if it is a bed only potentially, not yet having the form of a bed ; 35 nor should we call it a work of art. The same is true of natural compounds. What is potentially flesh or bone has not yet its own 4 nature and does not exist ‘ by nature i93 b until it receives the form specified in the definition, which we name in defining what flesh or bone is. Thus in the second sense of ‘ nature * it would be the shape or form (not separable except in statement) of things which have 5 in themselves a source of motion. (The combination of the two, e. g. man, is not * nature ’ but 1 by nature 1 or 4 natural \)

The form indeed is ‘ nature ’ rather than the matter ; for a thing is more properly said to be what it is when it has attained to fulfilment than when it exists potentially. Again man is bom from man, but not bed from bed. That is why people say that the figure is not the nature of a bed, 10 but the wood is — if the bed sprouted not a bed but wood would come up. But even if the figure is art, then on the i93 b same principle the shape of man is his nature. For man is born from man.

We also speak of a thing s nature as being exhibited in the process of growth 1 by which its nature is attained. The ‘nature' in this sense is not like ‘doctoring', which leads not to the art of doctoring but to health. Doctoring 15 must start from the art, not lead to it. But it is not in this way that nature (in the one sense) is related to nature (in the other). What grows qua growing 2 grows from something into something. Into what then does it grow? Not into that from which it arose but into that to which it tends. The shape then is nature.

‘Shape’ and ‘nature’, it should be added, are used in two senses. For the privation too is in a way form. But 20 whether in unqualified coming to be there is privation, i.e. a contrary to what comes to be, we must consider later. 3

2 We have distinguished, then, the different ways in which the term ‘ nature ' is used.

The next point to consider is how the mathematician differs from the physicist. 4 Obviously physical bodies contain surfaces and volumes, lines and points, and these are the subject-matter of mathematics.

Further, is astronomy 5 different from physics or a depart- 35 ment of it? It seems absurd that the physicist should be supposed to know the nature of sun or moon, but not to know any of their essential attributes, particularly as the writers on physics obviously do discuss their shape also and whether the earth and the world are spherical or not. 30

Now the mathematician, though he too treats of these things, 6 nevertheless docs not treat of them as the limits of a physical body ; nor does he consider the attributes indicated as the attributes of such bodies. That is why he separates them ; for in thought they are separable from motion, and it makes no difference, nor does any falsity

1 Cf. Metaphysics , ioi4 b 16. ‘“The coming to be of growing things”, as if the v in were long ' (as it is in <f>vofuu ).

8 De Gen . et Carr. i. 3. 4 Or student of nature (<£i><ri*or).

35 result, if they are separated. The holders of the theory of Forms do the same, though they are not aware of it ; for they separate the objects of physics, which are less separable i94 a than those of mathematics. This becomes plain if one tries to state in each of the two cases the definitions of the things and of their attributes. 4 Odd * and 4 even \ 4 straight ’ and 'curved’, and likewise ‘number’, ‘line’, and ‘figure’, 5 do not involve motion ; not so ‘ flesh ’ and * bone ’ and ‘ man ’ — these are defined like 4 snub nose *, not like 4 curved \

Similar evidence is supplied by the more physical of the branches of mathematics, such as optics, harmonics, and astronomy. These are in a way the converse of geometry. While 1 geometry investigates physical lines io but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical.

Since 4 nature ’ has two senses, the form and the matter, we must investigate its objects as we would the essence of snubness. That is, such things are neither independent of matter nor can be defined in terms of matter only. 15 Here too indeed one might raise a difficulty. 2 Since there are two natures, with which is the physicist concerned ? Or should he investigate the combination of the two ? 3 But if the combination of the two, then also each severally. Does it belong then to the same or to different sciences to know each severally ?

If we look at the ancients, physics would seem to be ao concerned with the matter . (It was only very slightly that Empedocles and Democritus touched on the forms and the essence.)

But if on the other hand art imitates nature, and it is the part of the same discipline to know the form and the matter up to a point (e. g. the doctor has a knowledge of health and also of bile and phlegm, in which health is realized, and the builder both of the form of the house and 35 of the matter, namely that it is bricks and beams, and so

2 Omitting in 1 . 15, with E 1 Them. Phil. Simp.

5 Putting a full-stop after (pvmKov in 1 . 16, and a mark of interrogation after the first aptj>oiv in 1. 17.

forth) : if this is so, it would be the part of physics also to know nature in both its senses.

Again, ‘ that for the sake of which ’, or the end, belongs to the same department of knowledge as the means. But the nature is the end or * that for the sake of which \

For if a thing undergoes a continuous change and there is a stage which is last, this stage is the end 1 or 1 that for the sake of which \ (That is why the poet 2 was carried 3° away into making an absurd statement when he said ‘ he has the end 3 for the sake of which he was born ’. For not every stage that is last claims to be an end, but only that which is best.)

For 4 the arts make their material (some simply ‘make' if, others make it serviceable), and we use everything as if it was there for our sake. (We also are in a sense 35 an end. ‘That for the sake of which * has two senses: the distinction is made in our work On Philosophy P)

The arts, therefore, which govern the matter and have knowledge are two, namely the art which uses the i94 b product and the art which directs the production of it.

That is why the using art also is in a sense directive ; but it differs in that it knows the form, 7 whereas the art which is directive as being concerned with production knows the matter. For the helmsman knows and prescribes what 5 sort of form a helm should have, the other from what wood it should be made and by means of what operations.

In the products of art, however, we make the material with a view to the function, whereas in the products of nature the matter is there all along.

Again, matter is a relative term : to each form there corresponds a special matter. How far then must the physicist know the form or essence? Up to a point, j 0 perhaps, as the doctor must know sinew or the smith

8 An unidentified comic poet (Kock, Com . Att. Fr. iii, p. 493).

* i. e. death.

* Placing a full stop before in 1. 33.

6 i. e. in the dialogue De Philosophic

* Reading in 1 . 1 kcu yv<opt(ovaai, with F and Phil.

I94 b bronze (i. e. until he understands the purpose of each) : and 1 the physicist is concerned only with things whose forms are separable indeed, but do not exist apart from matter. Man is begotten by man and by the sun as well. The mode of existence and essence of the separable it is 15 the business of the primary type of philosophy 2 to define.

Now that we have established these distinctions, we must proceed to consider causes, their character and number. Knowledge is the object of our inquiry, and men do not think they know a thing till they have grasped the ao ‘ why 1 of it (which is to grasp its primary cause ). 3 So clearly we 4 * too must do this as regards both coming to be and passing away and every kind of physical change, in order that, knowing their principles, we may try to refer to these principles each of our problems.

In 6 7 one sense, then, (1) that out of which a thing comes to be and which persists, is called ‘cause’, e.g. the bronze 35 of the statue, the silver of the bowl, and the genera of which the bronze and the silver are species.

In another sense (2) the form or the archetype, i. e. the statement of the essence, and its genera, are called ‘ causes * (e.g. of the octave the relation of 2:1, and generally number ), 6 and the parts in the definition.

Again (3) the primary source of the change or coming 30 to rest ; e.g. the man who gave advice is a cause, the father is cause of the child, and generally what makes of what is made and what causes change of what is changed.

Again (4) in the sense of end or ‘ that for the sake of which’ a thing is done, e.g. health is the cause of walking about. (‘ Why is he walking about ? * we say. 7 4 To be healthy \ and, having said that, we think we have assigned

a i.e. not of natural philosophy, but of metaphysics. Cf. Met.z.

* The proximate cause, which is primarily responsible for an event.

4 i. e. natural philosophers.

6 I94 b 23-19^ 21 is repeated almost verbatim in Met . A. 2.

7 Placing a full stop after fyapkv in 1 . 34.

the cause.) The same is true also of all the intermediate 35 steps which are brought about through the action of something else as means towards the end, e g. reduction * of flesh, purging, drugs, or surgical instruments are means towards health. All these things are ‘ for the sake of’ the 195® end, though they differ from one another in that some are activities, others instruments.

This then perhaps exhausts the number of ways in which the term 4 cause ’ is used.

As the word has several senses, it follows that there are several causes of the same thing (not merely in virtue of a concomitant attribute), e.g. both the art of the sculptor 5 and the bronze are causes of the statue. These are causes of the statue qua statue, not in virtue of anything else that it may be — only not in the same way, the one being the material cause, the other the cause whence the motion comes. Some things cause each other reciprocally, e.g. hard work causes fitness and vice versa , but again not in 10 the same way, but the one as end, the other as the origin of change. Further the same thing is the cause of contrary results. For that which by its presence brings about one result is sometimes blamed for bringing about the contrary by its absence. Thus we ascribe the wreck of a ship to the absence of the pilot whose presence was the cause of its safety.

All the causes now mentioned fall into four familiar 15 divisions. 1 The letters are the causes of syllables, the material of artificial products, fire, &c., of bodies, the parts of the whole, and the premisses of the conclusion, in the sense of * that from which ’. Of these pairs the one set are causes in the sense of substratum, e.g. the parts, the other 30 set in the sense of essence — the whole and the combination and the form. But the seed and the doctor and the adviser, and generally the maker, are all sources whence the change or stationariness originates, 2 while the others are causes in the sense of the end or the good of the rest ; for * that for the sake of which ’ means what is best and

1 Reading in 1 . 15 rpckrov?. Bekker’s rfaovs is a misprint.

9 Omitting in 1 . 23 rj with E and Met. ioi3 b 25.

25 the end of the things that lead up to it. (Whether we say the 'good itself’ or the ‘apparent good* makes no difference.)

Such then is the number and nature of the kinds of cause.

Now the modes of causation are many, though when brought under heads they too can be reduced in number. For ‘ cause ’ is used in many senses and even within the 33 same kind one may be prior to another (e.g. the doctor and the expert are causes of health, the relation 2 : 1 and number of the octave), and always what is inclusive to what is particular. Another mode of causation is the incidental and its genera, e.g. in one way ‘Polyclitus’, in another ‘ sculptor ’ is the cause of a statue, because ‘ being 35 Polyclitus ’ and ‘ sculptor ’ are incidentally conjoined. Also the classes in which .the incidental attribute is included ; thus ‘ a man ’ could be said to be the cause of a statue or, I 95 b generally, ‘a living creature’. An incidental attribute too may be more or less remote, e. g. suppose that ‘ a pale man * or ‘ a musical man ’ were said to be the cause of the statue.

All causes, both proper and incidental, may be spoken 5 of either as potential or as actual ; e. g. the cause of a house being built is either ‘house-builder’ or ‘house-builder building

Similar distinctions can be made in the things of which the causes are causes, e.g. of ‘ this statue ’ or of ‘ statue 1 or of ‘ image * generally, of ‘ this bronze ’ or of ‘ bronze ’ or of * material 1 generally. So too with the incidental attributes. 10 Again we may use a complex expression for either and say, e.g., neither ‘ Polyclitus ’ nor ‘ sculptor * but ‘ Polyclitus, sculptor \

All these various uses, however, come to six in number, under each of which again the usage is twofold. Cause means either what is particular or a genus, or an 15 incidental attribute or a genus of that, and these either as a complex or each by itself ; and all six either as actual or as potential. The difference is this much, that causes which are actually at work and particular exist and cease b to exist simultaneously with their effect, e.g. this healing person with this being-healed person and that housebuilding man with that being-built house ; but this is not always true of potential causes — the house and the housebuilder ao do not pass away simultaneously.

In investigating the cause of each thing it is always necessary to seek what is most precise (as also in other things) : thus man builds because he is a builder, and a builder builds in virtue of his art of building. This last cause then is prior : and so generally.

Further, generic effects should be assigned to generic *5 causes, particular effects to particular causes, e.g. statue to sculptor, this statue to this sculptor ; and powers are relative to possible effects, actually operating causes to things which are actually being effected.

This must suffice for our account of the number of causes and the modes of causation. 30

4 But chance also and spontaneity are reckoned among causes: many things are said both to be and to come to be as a result of chance and spontaneity. We must inquire therefore in what manner chance and spontaneity are present among the causes enumerated, and whether they are the same or different, and generally what chance and 35 spontaneity are.

Some people 1 even question whether they are real or not. They say that nothing happens by chance, but that 196* everything which we ascribe to chance or spontaneity has some definite cause, e.g. coming ‘by chance * into the market and finding there a man whom one wanted but did not expect to meet is due to one's wish to go and buy in the market. Similarly in other cases of chance 2 it is 5 always possible, they maintain, to find something which is the cause ; but not chance, for if chance were real, it would seem strange indeed, and the question might be raised, why on earth none of the wise men of old in speaking of the causes of generation and decay took account of chance ;

1 Apparently Democritus is meant. Cf. Diels, Vors* ii. 29. 3-11.

2 Omitting Xcyopimv in 1. 6 with E l , io whence it would seem that they too did not believe that anything is by chance. But there is a further circumstance that is surprising. Many things both come to be and are by chance and spontaneity, and although all know that each of them can be ascribed to some cause (as the old 15 argument 1 said which denied chance), nevertheless they speak of some of these things as happening by chance and others not. For this reason also they ought to have at least referred to the matter in some way or other.

Certainly the early physicists found no place for chance among the causes which they recognized — love, strife, mind, fire, or the like. This is strange, whether they supposed that there is no such thing as chance or whether 20 they thought there is but omitted to mention it — and that too when they sometimes used it, as Empedocles does when he says that the air is not always separated into the highest region, but ‘as it may chance \ At any rate he says in his cosmogony that ‘ it happened to run that way at that time, but it often ran otherwise/ 2 He tells us also that most of the parts of animals came to be by chance.

25 There are some 3 too who ascribe this heavenly sphere and all the worlds 4 to spontaneity. They say that the vortex arose spontaneously, i.e. the motion that separated and arranged in its present order all that exists. This statement might well cause surprise. For they are asserting that chance is not responsible for the existence or generation 30 of animals and plants, nature or mind or something of the kind being the cause of them (for it is not any chance thing that comes from a given seed but an olive from one kind and a man from another) ; and yet at the same time they assert that the heavenly sphere and the divinest of visible things arose spontaneously, having no such cause as 35 is assigned to animals and plants. Yet if this is so, it is a fact which deserves to be dwelt upon, and something ig6 b might well have been said about it. For besides the other absurdities of the statement, it is the more absurd that

* Apparently Democritus is meant. Cf. Simplicius 331. 1 6.

I96 b people should make it when they see nothing coming to be spontaneously in the heavens, but much happening by chance among the things which as they say are not due to chance ; whereas we should have expected exactly the opposite.

Others 1 there are who, indeed, believe that chance is 5 a cause, but that it is inscrutable to human intelligence, as being a divine thing and full of mystery.

Thus we must inquire what chance and spontaneity are, whether they are the same or different, and how they fit into our division of causes.

5 First then we observe that some things always come to 10 pass in the same way, and others for the most part . 2 It is clearly of neither of these that chance is said to be the cause , 3 nor can the ‘ effect of chance * be identified with any of the things that come to pass by necessity and always, or for the most part . 2 But as there is a third class of events besides these two — events which all say arc ‘ by chance ' — it is plain that there is such a thing as chance and spontaneity ; for we know that things of this kind are due 15 to chance and that things due to chance are of this kind.

But, secondly, some events are for the sake of something, others not. Again, some of the former class are in accordance with deliberate intention, others not, but both are in the class of things which are for the sake of something. Hence it is clear that even among the things which are ao outside the necessary and the normal, 2 there are some in connexion with which the phrase ‘ for the sake of something ’ is applicable. (Events 4 5 that are for the sake of something include whatever may be done as a result of thought or of nature.) Things of this kind, then, when they come to pass incidentally are said to be 4 by chance'. For just as a thing is something either in virtue of itself or incidentally, 6 35

3 Putting a comma after Xcycrm, not after tvxv, in 1 . 12.

5 A may ‘be’ B t either because it is A or because A is casually conjoined with some other attribute of the subject which is />.

so may it be a cause. For instance, the housebuilding faculty is in virtue of itself the cause of a house, whereas the pale or the musical 1 is the incidental cause. That which is per se cause of the effect is determinate, but the incidental cause is indeterminable, for the possible attributes of an individual are innumerable. To resume then; when 30 a thing of this kind comes to pass among events which are for the sake of something, it is said to be spontaneous or by chance. (The distinction between the two must be made later 2 — for the present it is sufficient if it is plain that both are in the sphere of things done for the sake of something.)

Example; A man is engaged in collecting 3 subscriptions for a feast. He would have gone to such and such a place for the purpose of getting the money, if he had known. He 35 actually went there for another purpose, and it was only incidentally that he got his money by going there 4 ; and this was not due to the fact that he went there as a rule or i97 a necessarily, nor is the end effected (getting the money) a cause present in himself — it belongs to the class of things that are intentional and the result of intelligent deliberation. It is when these conditions are satisfied that the man is said to have gone ‘ by chance \ If he had gone of deliberate purpose and for the sake of this — if he always or normally went there when he was collecting payments — he would not be said to have gone ‘ by chance \

5 It 5 is clear then that chance is an incidental cause in the sphere of those actions for the sake of something which involve purpose. Intelligent reflection, then, and chance are in the same sphere, for purpose implies intelligent reflection.

It is necessary, no doubt, that the causes of what comes to pass by chance be indefinite ; and that is why chance is supposed to belong to the class of the indefinite and to be 10 inscrutable to man, and why it might be thought that, in a way, nothing occurs by chance. For all these statements

1 Incidental attributes of the housebuilder. * In ch. 6.

BOOK II. 5 197* are correct, because they are well grounded. Things do, in a way, occur by chance, for they occur incidentally and chance is an incidental cause . But strictly it is not the cause— without qualification — of anything ; for instance, a housebuilder is the cause of a house ; incidentally, a fluteplayer may be so.

And the causes of the man’s coming and getting the 15 money (when he did not come for the sake of that) are innumerable. He may have wished to see somebody or been following somebody or avoiding somebody, or may have gone to see a spectacle . 1 Thus to say that chance is a thing contrary to rule is correct. For 1 rule ’ applies to what is always true or true for the most part, whereas chance belongs to a third type of event. Hence, to conclude, since 30 causes of this kind 2 are indefinite, chance too is indefinite.

(Yet in some cases one might raise the question whether any incidental fact might be the cause of the chance occurrence, e. g. of health the fresh air or the sun’s heat 3 may be the cause, but having had one’s hair cut cannot \ for some incidental causes are more relevant to the effect than others.)

Chance 4 * or fortune is called 1 good ’ when the result is 25 good, ‘ evil * when it is evil. The terms ‘ good fortune ’ and ‘ ill fortune ’ are used when either result is of considerable magnitude. Thus one who comes within an ace of some great evil or great good is said to be fortunate or unfortunate . 6 The mind affirms the presence of the attribute, ignoring the hair’s breadth of difference. Further, it is with 3 ° reason that good fortune is regarded as unstable ; for chance is unstable, as none of the things which result from it can be invariable or normal.

Both are then, as I have said, incidental causes— -both chance and spontaneity — in the sphere of things which are capable of coming to pass not necessarily, nor normally,

2 i. e. incidental causes.

8 Reading in 1 . 28 ff (VTvx*iy fj arv^tiv, with E and Simp.

35 and with reference to such of these as might come to pass for the sake of something.

They differ in that * spontaneity * is the wider term. 6 Every result of chance is from what is spontaneous, but not everything that is from what is spontaneous is from chance.

197 Chance and what results from chance are appropriate to agents that arc capable of good fortune and of moral action generally. Therefore necessarily chance is in the sphere of moral actions. This is indicated by the fact that good fortune is thought to be the same, or nearly the same, as happiness, and happiness to be a kind of moral action,

5 since it is well-doing. Hence what is not capable of moral action cannot do anything by chance. Thus an inanimate thing or a lower animal or a child cannot do anything by chance, because it is incapable of deliberate intention ; nor can 4 good fortune 1 or ‘ill fortune’ be ascribed to them, except metaphorically, as Protarchus, 1 for example, said that the stones of which altars are made are fortunate to because they are held in honour, while their fellows are trodden under foot. Even these things, however, can in a way be affected by chance, when one who is dealing with them does something to them by chance, but not otherwise.

The spontaneous on the other hand is found both in the 15 lower animals and in many inanimate objects. We say, for example, that the horse came ‘spontaneously \ because, though his coming saved him, he did not come for the sake of safety. Again, the tripod fell 2 ‘of itself’, because, though when it fell it stood on its feet so as to serve for a seat, it did not fall for the sake of that.

Hence it is clear that events which (1) belong to the general class of things that may come to pass for the sake of something, (2) do not come to pass for the sake of what actually results, and (3) have an external cause, may be 30 described by the phrase ‘ from spontaneity \ These 4 spontaneous ’ events are said to be ‘ from chance * if they have the further characteristics of being the objects of deliberate

1 Probably the reference is to the Protarchus described as a pupil of Gorgias in Plat. Phil, 58 A. Cf. Zeller, Phil . d. Gr .. i.« 1323, n. 4.

2 i.e. on its feet 09 * i97 b intention and due to agents capable of that mode of action.

This is indicated by the phrase 4 in vain’, which is used when A , which is for the sake of B , does not result in B.

For instance, taking a walk is for the sake of evacuation of the bowels ; if this does not follow after walking, we say that we have walked 4 in vain ’ and that the walking was 4 vain \ This implies that what is naturally the means to 25 an end is 4 in vain \ when it does not effect the end towards which it was the natural means — for it would be absurd for a man to say that he had bathed in vain because the sun was not eclipsed, since the one was not done with a view to the other. Thus the spontaneous is even according to its derivation the case in which the thing itself happens in vain. 1 The stone that struck the man did not fall for 30 the purpose of striking him ; therefore it fell spontaneously, because it might have fallen by the action of an agent and for the purpose of striking. The difference between spontaneity and what results by chance 2 3 4 is greatest in things that come to be by nature ; for when anything comes to be contrary to nature, we do not say that it came to be by chance, but by spontaneity. Yet strictly this too is differ- 35 ent from the spontaneous proper ; for the cause of the latter is external, that of the former internal.

We have now explained what chance is and what spon- 198® taneity is, and in what they differ from each other. Both belong to the mode of causation 3 4 source of change \ for either some natural or some intelligent agent is always the cause ; but in this sort of causation the number of possible causes is infinite.

Spontaneity 4 and chance are causes of effects which, 5 though they might result from intelligence or nature, have in fact been caused by something incidentally . Now since nothing which is incidental is prior to what is per se, it is clear that no incidental cause can be prior to a cause perse . Spontaneity and chance, therefore, are posterior to

1 There is no parallel in English for this false derivation.

* Reading in 1. 33 rov, with E and Phil.

3 Reading in 1 . 2 rijp b’ alrtas ra>v Tpoflw, with E.

I98 a jo intelligence and nature. Hence, however true it may be that the heavens are due to spontaneity, it will still be true that intelligence and nature will be prior causes 1 of this All 2 and of many things in it besides.

It is clear then that there are causes, and that the ^ 15 number of them is what we have stated. The number is the same as that of the things comprehended under the question ‘why ’. The ‘why’ is referred ultimately either (1), in things which do not involve motion, e. g. in mathematics, to the ‘ what* (to the definition of ‘straight line' or ‘commensurable’, &c.), or (2) to what initiated a motion, e.g. ‘why did they go to war? — because there had been 20 a raid * ; or (3) we are inquiring ‘ for the sake of what ? * — ‘that they may rule’; or (4), in the case of things that come into being, we are looking for the matter. The causes, therefore, are these and so many in number.

Now, the causes being four, it is the business of the physicist to know about them all, and if he refers his problems back to all of them, he will assign the 4 why ’ in the way proper to his science— the matter, the form, the 35 move, ‘i ‘ that for the sake of which \ The last three often coincide 3 ; for the ‘ what ’ and 4 that for the sake of which * are one, while the primary source of motion is the same in species as these 4 (for man generates man), and so too, in general, are all things which cause movement by being themselves moved ; and such as are not of this kind are no longer inside the province of physics, for they cause motion not by possessing motion or a source of motion in themselves, but being themselves incapable of motion. Hence there 30 are three branches of study, one of things which are incapable of motion, 5 the second of things in motion, but indestructible, 6 the third of destructible things. 7

* Reading in 1 . 12 vovu dlnov udi <j>umv nvm with FI Simp.

Reading in 1 . 13 rov ttmtos, with FI Them. Phil. Simp.

They are different individuals .

6 Reading in 1. 30 with E and Phil.

(2) and (3) belong to physics, (1) to physics only in so far as such things are the cause of motion.

The question ‘ why \ then, is answered by reference to the matter, to the form, and to the primary moving cause.

For in respect of coming to be it is mostly in this last way that causes are investigated — * what comes to be after what ? what was the primary agent or patient ? * and so at each step of the series.

Now the principles which cause motion in a physical 35 way are two, of which one is not physical, as it has no principle of motion 1 in itself. Of this kind is whatever i9® b causes movement, not being itself moved, such as (1) that which is completely unchangeable, the primary reality, and (2) the essence of that which is coming to be, i. e. the form ; for this is the end or ‘ that for the sake of which \ Hence since nature is for the sake of something, we must know this cause also. We must explain the * why * in all the senses of 5 the term, namely, (1) that from this that will necessarily result (‘ from this * either without qualification or in most cases) ; (2)’ that * this must be so if that is to be so * (as the conclusion presupposes the premisses) 2 ; (3) that this was the essence of the thing ; and (4) because it is better thus (not without qualification, but with reference to the essential nature in each case).

g We must explain then (1) that Nature belongs to the 10 class of causes which act for the sake of something; (2) about the necessary and its place in physical problems, for all writers ascribe things to this cause, arguing that since the hot and the cold, &c., are of such and such a kind, therefore certain things necessarily are and come to be — and if they mention any other cause (one 3 his 4 friendship 15 and strife \ another 4 his ‘ mind ’), it is only to touch on it, and then good-bye to it.

A difficulty presents itself : why should not nature work, not for the sake of something, nor because it is better so, but just as the sky rains, not in order to make the corn grow, but of necessity? What is drawn up must cool, and

1 i. e. no capacity of being itself moved.

9 i.e. the material cause or the condicio sine qua non ; cf. 195*

* Empedocles.

4 Anaxagoras.

ig8 b

20 what has been cooled must become water and descend, the result of this being that the corn grows. Similarly if a man's crop is spoiled on the threshing-floor, the rain did not fall for the sake of this— in order that the crop might be spoiled — but that result just followed. Why then should it not be the same with the parts in nature, e. g. that our teeth should come up of necessity — the front teeth sharp, 75 fitted for tearing, the molars broad and useful for grinding down the food — since they did not arise for this end, but it was merely a coincident result ; and so with all other parts in which we suppose that there is purpose ? Wherever then all the parts came about just what they would have 30 been if they had come to be for an end, such things survived, being organized spontaneously in a fitting way ; whereas those which grew otherwise perished and continue to perish, as Empedocles says his ‘man-faced oxprogeny 'did . 1

Such are the arguments (and others of the kind) which may cause difficulty on this point. Yet it is impossible that this should be the true view. For teeth and all other 35 natural things either invariably or normally come about in a given way ; but of not one of the results of chance or spontaneity is this true. We do not ascribe to chance or i99 a mere coincidence the frequency of rain in winter, but frequent rain in summer we do; nor heat in the dog-days, but only if we have it in winter. If then, it is agreed that things are either the result of coincidence or for an end, and these cannot be the result of coincidence or spontaneity, 5 it follows that they must be for an end ; and that such things are all due to nature even the champions of the theory which is before us would agree. Therefore action for an end is present in things which come to be and are by nature.

Further, where a series has a completion, all the preceding steps are for the sake of that. Now surely as in 10 intelligent action, so in nature ; and as in nature, so it is in each action, if nothing interferes . 2 Now intelligent action

x 99 a is for the sake of an end ; therefore the nature of things also is so. 1 Thus if a house* e.g., had been a thing made by nature, it would have been made in the same way as it is now by art ; and if things made by nature were made also by art, they would come to be in the same way as by nature. Each step then in the series is for the sake of the 15 next ; and generally art partly completes what nature cannot bring to a finish, and partly imitates her. If, therefore, artificial products are for the sake of an end, so clearly also are natural products. The relation of the later to the earlier terms of the series is the same in both.

This is most obvious in the animals other than man : 20 they make things neither by art nor after inquiry or deliberation. Wherefore people discuss whether it is by intelligence or by some other faculty that these creatures work,

— spiders, ants, and the like. By gradual advance in this direction we come to see clearly that in plants too that is produced which is conducive to the end — leaves, e. g. grow 25 to provide shade for the fruit. If then it is both by nature and for an end that the swallow makes its nest and the spider its web, and plants grow leaves for the sake of the fruit and send their roots down (not up) for the sake of nourishment, it is plain that this kind of cause is operative in things which come to be and are by nature. And since 3°

* nature ’ means two things, the matter and the form, of which the latter is the end, and since all the rest is for the sake of the end, the form must be the cause in the sense of 4 that for the sake of which \

Now mistakes come to pass even in the operations of art : the grammarian makes a mistake in writing and the doctor pours out the wrong dose. Hence clearly mistakes are 35 possible in the operations of nature also. If then in art i99 b there are cases in which what is rightly produced serves a purpose, and if where mistakes occur there was a purpose in what was attempted, only it was not attained, so must it be also in natural products, and monstrosities will be failures in the purposive effort. Thus in the original com- 5 binations 2 the 4 ox-progeny * if they failed to reach a deter- 1 Reading in 1 . 11 Xpa tpeted rov, with Phil. Simp. 1 Cf. 198** 3a.

I 99 b minate end must have arisen through the corruption of some principle corresponding to what is now the seed.

Further, seed must have come into being first, and not straightway the animals: the words ‘ whole-natured first . . -* 1 must have meant seed.

Again, in plants too we find the relation of means to end, io though the degree of organization is less. Were there then in plants also 1 olive-headed vine-progeny \ like the ‘ manheaded ox-progeny or not ? An absurd suggestion ; yet there must have been, if there were such things among animals.

Moreover, among the seeds anything must have come to be at random. But the person who asserts this entirely 15 does away with * nature , and what exists ‘ by nature \ For those things are natural which, by a continuous movement originated from an internal principle, arrive at some completion : the same completion is not reached from every principle ; nor any chance completion, but always the tendency in each is towards the same end, if there is no impediment.

The end and the means towards it may come about by ao chance. We say, for instance, that a stranger has come by chance, paid the ransom, 2 and gone away, when he does so as if he had come for that purpose, though it was not for that that he came. This is incidental, for chance is an incidental cause, as I remarked before. 3 But when an event takes place always or for the most part, it is not incidental 35 or by chance. In natural products the sequence is invariable, if there is no impediment.

It is absurd to suppose that purpose is not present because we do not observe the agent deliberating. Art does not deliberate. If the ship-building art were in the wood, it would produce the same results by nature . If, therefore, purpose is present in art, it is present also in

2 Reading in 1 . 20 Xvad^vot (yp. I, yp. Phil.). There is probably a reference to Plato’s imprisonment in Aegina and to his being ransomed by Anniceris, who had accidentally arrived there (Z>. L . in. 20; Lucian, Dem . Enc. 23 ; Aelian, Var. Hist . ii. 27).

* l 96 b 23 - 7 * nature. The best illustration is a doctor doctoring him- 3° self : nature is like that

It is plain then that nature is a cause, a cause that operates for a purpose.

9 As regards what is ‘ of necessity *, we must ask whether the necessity is ‘hypothetical \ or ‘simple ' as well. The 35 current view places what is of necessity in the process of production, just as if one were to suppose that the wall of 200 a a house necessarily comes to be because what is heavy is naturally carried downwards and what is light to the top, wherefore the stones and foundations take the lowest place, with earth 1 * above because it is lighter, and wood at the lop of all as being the lightest. Whereas, though the wall 5 does not come to be without these, it is not due to these, except as its material cause : it comes to be for the sake of sheltering and guarding certain things. Similarly in all other things which involve production for an end ; the product cannot come to be without things which have a necessary nature, but it is not due to these (except as its material) ; it comes to be for an end. For instance, why 10 is a saw such as it is? To effect so-and-so and for the sake of so-and-so. This end, however, cannot be realized unless the saw is made of iron. It is, therefore, necessary for it to be of iron, if we are to have a saw and perform the operation of sawing. What is necessary then, is necessary on a hypothesis ; it is not a result necessarily determined by antecedents. Necessity is in the matter, while ‘ that for the sake of which ’ is in the definition.

Necessity in mathematics is in a way similar to necessity 15 in things which come to be through the operation of nature. Since a straight line is what it is, 3 it is necessary that the angles of a triangle should equal two right angles.

But not conversely ; though if the angles are not equal to two right angles, then the straight line is not what it is either. But in things which come to be for an end, the

1 i. e. baked earth, bricks.

8 i. e. since it is such that one line standing on another makes with it angles «■ 2 right angles.

E reverse is true. If the end is to exist or does exist, that ao also which precedes it will exist or does exist ; otherwise just as there, if the conclusion is not true, the premfss will not be true, so here the end or ‘ that for the sake of which ' will not exist. For this too is itself a starting-point, but of the reasoning, not of the action ; while in mathematics the starting-poirjt is the starting-point of the reasoning only, as there is no action. If then there is to be a house, such- 35 and-such things must be made or be there already or exist, or generally the matter relative to the end, bricks and stones if it is a house. But the end is not due to these except as the matter, nor will it come to exist because of them. Yet if they do not exist at all, neither will the house, or the saw— the former in the absence of stones, the latter in the absence of iron — just as in the other case the premisses will not be true, if the angles of the triangle are not equal to two right angles.

30 The necessary in nature, then, is plainly what we call by the name of matter, and the changes in it. Both causes must be stated by the physicist, but especially the end ; 1 for that is the cause of the matter, not vice versa ; and the end is * that for the sake of which and the beginning starts from the 35 definition or essence; as in artificial products, since a house 200 b is of such-and-such a kind, certain things must necessarily come to be or be there already, or since health is this, these things must necessarily come to be or be there already. Similarly if man is this, then these ; if these, then those. 2 Perhaps the necessary is present also in the defini- 5 tion. For if one defines the operation of sawing as being a certain kind of dividing, then this cannot come about unless the saw has teeth of a certain kind ; and these cannot be unless it is of.iron. For in the definition too there are some parts that are, as it were, its matter.

2 i. e. what i these ' presuppose.

2QO b

I Nature has been defined as a ‘principle of motion and change’, and it is the subject of our inquiry. We must therefore see that we understand the meaning of ‘ motion * ; for if it were unknown, the meaning of ‘ nature ’ too would be unknown.

When we have determined the nature of motion, our 15 next task will be to attack in the same way the terms which are involved in it. Now motion is supposed to belong to the class o( things which are continuous ; and the infinite presents -itself first in the continuous — that is how it comes about that ‘infinite* is often used in definitions of the continuous (‘ what is infinitely divisible is continuous ’). Besides these, place , void, and time are thought to be 20 necessary conditions of motion.

Clearly, then, for these reasons and also because the attributes mentioned are common to, and coextensive with, all the objects of our science, we must first take each of them in hand and discuss it. For the investigation of special attributes comes after that of the common attributes . 1

To begin then, as we said, with motion. 25

We 2 may start by distinguishing 3 (1) what exists in a state of fulfilment only, (2) what exists as potential, (3) what exists as potential 4 and also in fulfilment — one being a ‘ this *, another ‘ so much *, a third ‘ such *, and similarly in each of the other modes of the predication of being.

Further, the word ‘ relative ' is used with reference to (1) excess and defect, (2) agent and patient and generally 3 °

1 The subject of Physics ((pvo-ucrj) is natural bodies and their properties. Their common properties are the subject of the present treatise.

* Omitingj n in 1 . 26, with Phil, and Met.

»OO b what can move and what can be moved, 1 For ‘what can cause movement ’ is relative to ‘ what can be moved \ and vice versa.

Again, 2 there is no such thing as motion over and above the things. It is always with respect to substance or to quantity or to quality or to place that what changes changes. But it is impossible, as we assert, to find any-

35 thing common to these which is neither ‘ this ’ nor quantum »oi a nor quale nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them.

Now each of these belongs to all its subjects in either of two ways : namely (i) substance — the one is positive form, 5 the other privation ; (2) in quality, white and black ; (3) in quantity, complete and incomplete ; (4) in respect of locomotion, 3 upwards and downwards or light and heavy. Hence there are as many types of motion or change as there are meanings of the word ‘ is \ 4

We have now before us the distinctions in the various classes of being between what is fully real and what is potential.

10 Def. The fulfilment of what exists potentially , in so far as it exists potentially , is motion — namely, of what is alterable qua alterable, alteration : of what can be increased and its opposite what can be decreased (there is no common name), increase and decrease : of what can come to be and can pass away, coming to be and passing away : of what can be carried along, locomotion .

15 Examples will elucidate this definition of motion. When the buildable, in so far as it is just that, is fully real, it is being - built , and this is build ing* Similarly, learning, doctoring, rolling, leaping, ripening, ageing.

1 The former pair denote a special kind of the latter, namely change of quality (‘ such-ness ’) or alteration.

8 ** (faopa, ‘ being carried *, translation In the Categories (c. 14) this kind of ‘motion 1 is simply called pcra&oKr) Kara tottqv.

4 While the wider term perafioXr) (change) is used in all the categories, Kivrjcrts (motion) holds only in Quality, Quantity, and Place.

The same thing, if it is of a certain kind, can be both potential and fully real, not indeed at the same time or not 20 in the same respect, but e. g. potentially hot and actually cold. Hence at once such things will act and be acted on by one another in many ways : each of them will be capable at the same time of causing alteration and of being altered. Hence, too, what effects motion as a physical agent can be moved : when a thing of this kind causes motion, it is itself also moved. This, indeed, has led some people to 35 suppose that every mover is moved. But this question depends on another set of arguments, and the truth will be made clear later. 1 It is possible for a thing to cause motion, though it is itself incapable of being moved.

It 2 * is the fulfilment of what is potential when it is already fully real and operates not as itself but as 7 novable? that is motion. What I mean by ‘as * is this : Bronze is potentially a statue. But it is not the fulfilment of bronze 30 as bronze which is motion. For ‘to be bronze* and ‘ to be a certain potentiality* 4 are not the same. If they were identical without qualification, i. e. in definition , 5 the fulfilment of bronze as bronze would have been motion. But they are not the same, as has been said. (This is obvious in contraries. 1 To be capable of health * and ‘ to be capable 35 of illness 1 are not the same, for if they were there would 201 be no difference between being ill and being well. Yet the subject both of health and of sickness — whether it is humour cf blood — is one and the same.)

We can distinguish, then, between the two — just as, to give another example, 4 colour * and ‘ visible * are different — and clearly it is the fulfilment of what is potential as potential that is motion. So this, precisely, is motion. 5

Further 0 it is evident that motion is an attribute of

* Reading in 1 . 28 ivtpyfi ov% avro dXX* jj Ktvrjrov, with yp. I Asp.

Them.

4 Omitting tuvijru in 1 . 32, with Simp, and Met. io65 b 26.

5 When A and B are identical in definition (or intension), it is also true that whatever is A is also B. But even when they are different in definition, we can still say that 'A is B\ if a subject which has the attribute A has also the attribute B .

aoi b a thing just when it is fully real in this way, and neither before nor after. For each thing of this kind 1 is capable of being at one time actual, at another not. Take for instance the buildable as buildable. 2 The actuality of the io buildable as buildable is the process of building. For the actuality of the buildable must be either this or the house. But when there is a house, the buildable is no longer buildable. On the other hand, it is the buildable which is being built. The process then of being built must be the kind of actuality required. But building is a kind of motion, and the same account will apply to the other 15 kinds also.

The soundness of this definition is evident both when we 2 consider the accounts of motion that the others have given, and also from the difficulty of defining it otherwise.

One could not easily put motion and change in another genus — this is plain if we consider Where some people put 30 it ; they identify motion with ‘difference’ or 4 inequality * 3 or ‘not being’ ; but such things are not necessarily moved, whether they are 4 different ’ or ‘ unequal ’ or ‘ non-existent ’ ; Nor is change either to or from these rather than to or from their opposites.

The reason why they put motion into these genera is 35 that it is thought to be something indefinite, 4 and the principles in the second column are indefinite because they are privative : none of them is either ‘this* or ‘such’ or 5 comes under any of the other modes of predication. The reason in turn why motion is thought to be indefinite is that it cannot be classed simply as a potentiality or as an actuality — a thing that is merely capable of having a certain 30 size is not undergoing change, nor yet a thing that is

1 i. e. all things which are tyvm ku <rwpara.

2 Reading in 1. 8 to oiKodofxyrop fj oltcodofxrjTop with Met . io66 a 2, Simp., Them., and inserting a comma thereafter.

3 Plato in the Timaeus (52 E, 57 E, 58 a) makes motion depend on inequality.

4 In the Pythagorean columns of opposites (e.g. Arist. Met . 986 a 25), r)p€povv and kivov^vov are placed under 7 rtpas and Hn eipov respectively.

8 Omitting on in 1 . 27, with Met . io66 a 16, Them., and Bonitz.

aoi b actually of a certain size, and motion is thought to be a sort of actuality , but incomplete, the reason for this view being that the potential whose actuality it is is incomplete. This is why it is hard to grasp what motion is.

It is necessary to class it with privation or with potentiality or with sheer actuality, yet none of these seems possible. There remains then the suggested mode of definition, 35 namely that it is a sort of actuality, or actuality of the 202 a kind described, hard to grasp, but not incapable of existing.

The mover too is moved, as has been said — every mover, that is, which is capable of motion, and whose immobility is rest — when a thing is subject to motion its immobility is rest. 1 2 * For to act on the movable as such is just to move 5 it. But this it does by contact , so that at the same time it is also acted on. Hence we can define motion as the fulfilment of the movable qua movable , the cause of the attribute being contact ivith what can move? so that the mover is also acted on. The mover or agent will always be the vehicle of a form, either a ‘ this 'ora' such V* which, when 10 it acts, will be the source and cause of the change, e. g. the full-formed man begets man from what is potentially man.

3 The 4 solution of the difficulty that is raised about the motion— whether it is in the movable — is plain. It is the fulfilment of this potentiality, and by the action of that which has the power of causing motion ; and the actuality of that which has the power of causing motion is not other than the actuality of the movable, for it must be the fulfil- *5 ment of both. A thing is capable of causing motion because it can do this, it is a mover because it actually does it. But

1 rjptfxui is the firivatto , not the contradictory (ajupipr/u), of Kivr)<ris y i. e. it can be predicated only of a thing which is capable of motion.

2 1 move’ in the sense of cause motion. This seems to be intended to be the complete or real definition of the attribute * motion \ i. e. the definition which embodies the cause of the attribute. Cf. Post . An.

4 All the manuscripts except E addin 1 . 10 rjTaoovbc. It seems better to omit these words, as Aristotle is thinking mainly of the generation of substance, and of alteration of quality — the cases in which form is most obviously transferred .

it is on the movable that it is capable of acting. Hence there is a single actuality of both alike, just as one to two and two to one are the same interval, and the steep ascent ao and the steep descent are one— for these are one and the same, although they can be described in different ways. So it is with the mover and the moved.

This view has a dialectical difficulty. Perhaps it is necessary that the actuality of the agent and that of the patient should not be the same. The one is 4 agency ’ and the other ‘patiency*; and the outcome and completion of the one is an ‘ action \ that of the other a ‘ passion 35 Since then they are both motions, we may ask : in what are they, if they are different? Either (a) bot. are in what is acted on and moved, or ( b ) the agency is in the agent and the patiency in the patient. 2 (If we ought to call the latter also ‘ agency the word would be used in two senses.)

Now, in alternative (< b ), the motion will be in the mover, for the same statement will hold of ‘ mover' and 'moved \ s 30 Hence either every mover will be moved, or, though having motion, it will not be moved.

If on the other hand (a) both are in what is moved and acted on — both the agency and the patiency (e.g. both teaching and learning, though they are two y in the learner ), then, first, the actuality of each will not be present in each, and, a second absurdity, a thing will have two motions at 35 the same time. How will there be two alterations of quality 4 in one subject towards one definite quality? The thing is impossible : the actualization will be one. ao2 b ® ut ( some one will say) it is contrary to reason to suppose that there should be one identical actualization of two things which are different in kind. Yet there will be, if teaching and learning are the same, and agency and

1 ndOor =- affection, modification, change caused in a thing ab extra .

2 Aristotle omits the two other possibilities as they obviously lead to absurdity.

8 i. e. we can substitute 'mover' and ‘moved’ for ‘agent’ and ‘ patient ’ in the formulation of the hypothesis.

4 Alterations of quality = dXXo««cr€ir. Aristotle sometimes tends to think of tcipriM as primarily change of quality, rather than as change of position.

patiency. To teach will be the same as to learn, and to act the same as to be acted on — the teacher will necessarily be learning everything that he teaches, and the agent will be acted on.

One may reply : 5

(i) It is not absurd that the actualization of one thing should be in another. Teaching is the activity of a person who can teach, yet the operation is performed on some patient — it is not cut adrift from a subject, but is of A on B .

(a) There is nothing to prevent two things having one and the same actualization, 1 provided the actualizations are not described in the same way, but are related as what can act to what is acting. 2

(3) Nor is it necessary that the teacher should learn, 10 even if to act and to be acted on are one and the same, provided they are not the same in definition (as * raiment * and ‘ dress '), but are the same merely in the sense in which the road from Thebes to Athens and the road from Athens to Thebes are the same, as has been explained above. 3 For it is not things which are in a way the same that have all their attributes the same, but only such as 15 have the same definition. But indeed it by no means follows from the fact that teaching is the same as learning, that to learn is the same as to teach, any more than it follows from the fact that there is one distance between two things which are at a distance from each other, that the two vectors AB and -BA are one and the same. To generalize, teaching is not the same as learning, or agency as patiency, in the full sense, though they belong to the ao same subject , the motion ; for the ‘ actualization of X in Y * and the ‘ actualization of Y through the action of X' differ in definition .

What then Motion is, has been stated both generally and particularly. It is not difficult to see how each of

1 Reading in 1 . 8 with FI and Simp. Ktikvti 0 v6*v ri)v avrqv dvat for avrqp eivai kq>\vu.

2 What can act and what is acting are idem subjecto , but not idem definitione . Read hwd^pov in 1. 10, with E.

8 Cf. *18-20.

aoa b

35 its types will be defined— alteration is the fulfilment of the alterable qua alterable (or, more scientifically, the fulfilment of what can act and what can be acted on, as such) — generally and again in each particular case, building, healing, &c. A similar definition will apply to each of the other kinds of motion.

30 The science of nature is concerned with spatial magni- 4 tudes and motion and time, and each of these at least is necessarily infinite or finite, even if some things dealt with by the science are not, e. g. a quality or a point — it is not necessary perhaps that such things should be put under either head. Hence it is incumbent on the person who 35 specializes in physics to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, iv hat it is.

The appropriateness to the science of this problem is 203 a clearly indicated. All who have touched on this kind of science in a way worth considering have formulated views about the infinite, and indeed, to a man, make it a principle of things.

(1) Some, as the Pythagoreans and Plato, make the 5 infinite a principle in the sense of a self-subsistent substance, and not as a mere attribute of some other thing. Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these), and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the Forms are not outside, because they are nowhere), yet that the infinite is present not only in the objects of sense but in the Forms also.

10 further, the Pythagoreans identify the infinite with the even. For this, they say, when it is cut off and shut in by the odd, provides things with the element of infinity. An indication of this is what happens with numbers. If the gnomons are placed round the one, and without the one , 1

1 TTfptTiBffifpwv yap rav yvapovav ntpi r6 tv kq! *&)/;/*. No thoroughly satisfactory explanation of icai xupts has been given. But Aristotle’s general meaning is fairly plain. He is describing two constructions : in the one odd gnomons are placed round the one, in the other even in the one construction the figure that results is always different, in the other it is always the same. But Plato 15 has two infinites, the Great and the Small.

The physicists, on the other hand, all of them, always regard the infinite as an attribute of a substance which is different from it a d belongs to the class of the so-called elements 1 — water or air or what is intermediate between them. Those who make them limited in number never make them infinite in amount. But those who make the elements infinite in number, as Anaxagoras and Democritus do, say ao that the infinite is continuous by contact — compounded of the homogeneous parts according to the one, of the seedmass of the atomic shapes according to the other.

Further, Anaxagoras held that any part is a mixture in the same way as the All, on the ground of the observed fact that anything comes out of anything. For it is probably for this reason that he maintains that once upon a time all things were together. (This flesh and this bone 25 were together, and so of any thing: therefore all things: and at the same time too.) For there is a beginning of separation, not only for each thing, but for all. Each thing that comes to be comes to be from a similar body, and there is a coming to be of all things, though not, it is true, at the same time. Hence there must also be an origin of 30 coming to be. One such source there is which he calls Mind, and Mind begins its work of thinking from some starting-point. So necessarily all things must have been together at a certain time, and must have begun to be moved at a certain time.

Democritus, for his part, asserts the contrary, namely that no element arises from another element. Nevertheless for him 2 the common body is a source of all things, differ- s*03 b ing from part to part in size and in shape.

It is clear then from these considerations that the inquiry concerns the physicist. Nor is it without reason that they gnomons are placed round the two . The translation follows Milhaud (P hilosofihes-gdomUres , p. 115)* See also Burnet, Early Greek Philosophy*, p. 103, n. 2.

1 Aristotle does not regard them as elements.

* Reading in 1. 34 cii/ra>, with Phil, and Bonitz.

all make it a principle or source. We cannot say that the 5 infinite has no effect, and the only effectiveness which we can ascribe to it is that of a principle. Everything is either a source or derived from a source. But there cannot be a source of the infinite or limitless, for that would be a limit of it. Further, as it is a beginning, it is both uncreatable and indestructible. For there must be a point at which what has come to be reaches completion, and also a termiio nation of all passing away. That is why, as we say, there is no principle of this , but it is this which is held to be the principle of other things, and to encompass all and to steer all, as those assert who do not recognize, alongside the infinite, other causes, such as Mind or Friendship. Further they identify it with the Divine, for it is 4 deathless and imperishable ' as Anaximander says, with the majority of the physicists.

T 5 Belief in the existence of the infinite comes mainly from five considerations :

(1) From the nature of time — for it is infinite.

(2) From the division of magnitudes — for the mathematicians also use the notion of the infinite.

(3) If comingto be and passing away do not give out, it is only because that from which things come to be is infinite.

20 (4) Because the limited always finds its limit in something, so that there must be no limit, if everything is always limited by something different from itself.

(5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody — not only number but also mathematical magnitudes and what is outside the heaven are supposed to be infinite because they never give out in our thought .

2 - The last fact (that what is outside is infinite) leads people to suppose that body also is infinite, and that there is an infinite number of worlds. Why should there be body in one part of the void rather than in another ? Grant only that mass is anywhere and it follows that it must be everywhere. Also, if void and place are infinite, there must be

BOOK III. 4 ao 3 b infinite body too, for in the case of eternal things what may be must be.

But the problem of the infinite is difficult : many contra- 30 dictions result whether we suppose it to exist or not to exist. If it exists, we have still to ask how it exists ; as a substance or as the essential attribute of some entity?

Or in neither way, yet none the less is there something which is infinite or some things which are infinitely many ?

The problem, however, which specially belongs to the 204® physicist is to investigate whether there is a sensible magnitude which is infinite.

We must begin by distinguishing the various senses in which the term ‘ infinite ’ is used.

(1) 1 What is incapable of being gone through, because it is not its nature to be gone through (the sense in which the voice is ‘ invisible ’).

(2) What admits of being gone through, the process however having no termination, or (3) what scarcely admits of being gone through. 5

(4) What naturally admits of being gone through, but is not actually gone through or does not actually reach an end.

Further, everything that is infinite may be so in respect of addition or division or both.

5 Now it is impossible that the infinite should be a thing which is itself infinite, separable from sensible objects. If the infinite is neither a magnitude nor an aggregate, but is 10 itself a substance and not an attribute, it will be indivisible ; for the divisible must be either a magnitude or an aggregate. But if indivisible, then not infinite, except in the sense ( 1 ) in which the voice is ‘ invisible \ But this is not the sense in which it is used by those who say that the infinite exists, nor that in which we are investigating it, namely as (2), ‘that which cannot be gone through’. But 2 if the infinite exists as an attribute, it would not be, qua infinite, 15 an element in substances, any more than the invisible would be an element of speech, though the voice is invisible.

Further, 1 how can the infinite be itself any thing, unless both number and magnitude, of which -it is an essential attribute, exist in that way? If they are not substances, a fortiori the infinite is not.

20 It 2 is plain, too, that the infinite cannot be an actual thing and a substance and principle. For any part of it that is taken will be infinite, if it has parts : for ‘ to be infinite ’ and 4 the infinite * are the same, if it is a substance and not predicated of a subject. Hence it will be either 25 indivisible or divisible into infinites. Put the same thing cannot be many infinites. (Yet just as part of air is air, so a part of the infinite would be infinite, if it is supposed to be a substance and principle.) Therefore the infinite must be without parts and indivisible. But this cannot be true of what is infinite in full completion: for it must be a definite quantity.

Suppose then that infinity belongs to substance as an 30 attribute. But, if so, it cannot, as we have said, be described as a principle, but rather that of which it is an attribute — the air or the even number.

Thus the view of those who speak after the manner of the Pythagoreans is absurd. With the same breath they treat the infinite as substance, and divide it into parts.

This 3 discussion, however, involves the more general 35 question whether the infinite can be present in mathematical objects and things which are intelligible aind do not 204 b have extension, as well as among sensible objects. Our inquiry (as physicists) is limited to its special subject-matter, the objects of sense, and we have to ask whether there is or is not among them a body which is infinite in the direction of 4 increase.

We may begin with a dialectical argument and show as follows that there is no such thing.

5 If ‘ bounded by a surface ’ is the definition of body there cannot be an infinite , body either intelligible or sensible.

4 Reading in 1 . 4 ini Bekker’s n<pi is a misprint.

ao4 b

Nor can number taken in abstraction be infinite, for number or that which has number is numerable. If then the numerable can be numbered, it would also be possible to go through the infinite.

If, 1 2 on the other hand, we investigate the question more 10 in accordance with principles appropriate to physics, we are led as follows to the same result.

The infinite body must be either (i) compound, or ( 2 ) simple ; yet neither alternative is possible.

(1) Compound the infinite body will not be, if the elements are finite in number. For they must be more than one, and the contraries must always balance, and no one of them can be infinite. If one of the bodies falls in any degree short of the other in potency — suppose fire is 15 finite in amount while air is infinite and a given quantity of fire exceeds in power the same amount of air in any ratio provided it is numerically definite — the infinite body will obviously prevail over and annihilate the finite body. On the other hand, it is impossible that each should be infinite. ‘Body’ is what has extension in all directions and the ao infinite is what is boundlessly extended, so that the infinite body would be extended in all directions ad infinitum?

Nor (2) can the infinite body be one and simple, whether it is, as some 3 hold, a thing over and above the elements (from which they generate the elements) or is not thus qualified.

(a) We must consider the former alternative ; for there are some people who make this the infinite, and not air or water, in order that 4 the other elements may not be annihilated by the element which is infinite. They have contrariety with each other — air is cold, water moist, fire hot ; if one were infinite, the others by now would have ceased to be. As it is, they say, the infinite is different from them and is their source.

It is impossible, however, that there should be such a body ; not because it is infinite — on that point a general 30

2 There could not be two such bodies.

8 The reference is probably to Anaximander.

proof can be given which applies equally to all, air, water, or anything else — but 1 simply because there is, as a matter of fact, no such sensible body, alongside the so-called elements. Everything can be resolved into the elements of which it is composed. Hence the body in question would have been present in our world here, alongside air and fire and earth and water: but nothing of the kind is observed.

35 ( b ) Nor can fire or any other of the elements be infinite.

205 a For generally, and apart from the question how any of them could be infinite, the All, even if it were limited, cannot either be or become one of them, as Heraclitus says that at some time all things become fire. (The same argu- 5 ment applies also to the one which the physicists suppose to exist alongside the elements : for everything changes from contrary to contrary, e.g. from hot to cold).

The preceding consideration of the various cases serves to show us whether it is or is not possible that there should be an infinite sensible body. The following arguments give a general demonstration that it is not possible.

io It 2 is the nature of every kind of sensible body to be somewhere, and there is a place appropriate to each, the same for the part and for the whole, e.g. for the whole earth and for a single clod, and for fire and for a spark.

Suppose (a) that the infinite sensible body is homogeneous. Then each part will be either immovable or always being carried along. Yet neither is possible. For why downwards rather than upwards or in any other direction? I mean, e.g., if you take a clod, where will it be 15 moved or where will it be at rest ? For ex hypo the si the place of the body akin to it is infinite. Will it occupy the whole place, then ? And how ? What then will be the nature of its rest and of its movement, or where will they be ? It will either be at home everywhere — then it will not

BOOK III. 5 a °5 a be moved ; or it will be moved everywhere — then it will not come to rest. 1

But if (6) the All has dissimilar parts, the proper places of the parts will be dissimilar also, and the body of the All ?o will have no unity except that of contact. Then, further, the parts will be either finite or infinite in variety of kind.

(i) Finite they cannot be, for if the All is to be infinite, some of them would have to be infinite, while the others were not, e. g. fire or water will be infinite. But, as we have seen before, such an element would destroy what is contrary to it. (This indeed is the reason why none of the 15 physicists made fire or earth the one infinite body, but either water or air or what is intermediate between them, because the abode of each of the two was plainly determinate, while the others have an ambiguous place between up and down.) 2

But 3 (ii) if the parts are infinite in number and simple, their proper places too will be infinite in number, and the same will be true of the elements themselves. If that is 30 impossible, and the places are finite, the whole too must be finite ; for the place and the body cannot but fit each other. Neither is the whole place larger than what can be filled by the body 4 (and then the body would no longer 5 be infinite), nor is the body larger than the place ; for 35 either there would be an empty space or a body whose nature it is to be nowhere.

Anaxagoras gives an absurd account of why the infinite ao5 b is at rest. He says that the infinite itself is the cause of its being fixed. This because it is in itself, since nothing else contains it — on the assumption that wherever anything is, it is there by its own nature. But this is not true : 5 a thing could be somewhere by compulsion, and not where it is its nature to be.

1 Reading in 11. 18-19 h n&vraxov ptvfl — ov KivijGrjertrai a pa • fj navraxov Kivr)$i\atTai — ovk a pa arrjatrai .

* This sentence should probably come, as Pacius suggests, after thai in b i.

4 Omitting the first &pa in 1 . 34, with E Them. Phil.

• Reading in I. 35 armpa he ovre, with E and Phil;

Even if it is true as true can be that the whole is not moved (for what is fixed by itself and is in itself must be immovable), yet we must explain why it is not its nature to be moved. It is not enough just to make this statement and then decamp. Anything else might be in a io state of rest, but there is no reason why it should not be its nature to be moved. The earth is not carried along, and would not be carried along if it were infinite, provided it is held together by 1 the centre. Rut it would not be because there was no other region in which it could be carried along that it would remain at the centre, but because this is its nature . 2 Yet in this case also we may say that it fixes itself.. If then in the case of the earth, supposed to be 15 infinite, it is at rest, not because it is infinite, but because it has weight and what is heavy rests at the centre and the earth is at the centre, similarly the infinite also would rest in itself, not because it is infinite and fixes itself, but owing to some other cause.

Another difficulty emerges at the same time. Any part of the infinite body ought to remain at rest. Just as the infinite remains at rest in itself because it fixes itself, so 20 too any part of it you may take will remain in itself. The appropriate places of the whole and of the part are alike, e.g. of the whole earth and of a clod the appropriate place is the lower region ; of fire as a whole and of a spark, the upper region. If, therefore, to be in itself is the place of the infinite, that also will be appropriate to the part. Therefore it will remain in itself.

In 3 general, the view that there is an infinite body is 25 plainly incompatible with the doctrine that there is necessarily a proper place for each kind of body, if every sensible body has either weight or lightness, and if a body has a natural locomotion towards the centre if it is heavy, and upwards if it is light. This would need to be true of the infinite also. But neither character can belong to it : it cannot be either as a whole, nor can it be half the one and

1 Reading in 1. 11 xm 6 , with Simp. Phil, and Bonitz.

2 Omitting ol in 1. 13 with E and Them.

half the other. For how should you divide it ? or how can 30 the infinite have the one part up and the other down, or an extremity and 1 a centre ?

Further, every sensible body is in place, and the kinds or differences of place are up-down, before-behind, right-left ; and these distinctions hold not only in relation to us and by arbitrary agreement, but also in the whole itself. But in 35 the infinite body they cannot exist. In general, if it is impossible that there should be an infinite place, and if every body is in place, there cannot be an infinite body. ao6 a

Surely what is in a special place is in place, and what is in place is in a special place. Just, then, as the infinite cannot be quantity— that would imply that it has a particular quantity/ 2 e. g. two or three cubits ; quantity just means these — so a things being in place means that it is 5 some where, and that is either up or down or in some other of the six differences of position : but each of these is a limit.

It is plain from these arguments that there is no body which is actually infinite.

5 But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and an end of 10 time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in ; and clearly there is a sense in which the infinite exists and another in which it does not.

We must keep in mind that the word ‘is’ means either what potentially is or what fully is.

Further, a thing is infinite either by addition or by 15 division. 3

Now, as we have seen, magnitude is not actually infinite.

But by division it is infinite. (There is no difficulty in refuting the theory of indivisible lines. 4 ) The alternative then remains that the infinite has a potential existence.

2 Reading in 1. 3 nocrov yap n, with Bonitz.

* Cf. Bk. vi and De Lineis Insecabilibus.

But the phrase * potential existence * is ambiguous. When we speak of the potential existence of a statue we mean that 30 there will be an actual statue. It is not so with the infinite. There will not be an actual infinite. The word ‘ is * has many senses, and we say that the infinite ‘ is * in the sense in which we say ‘ it is day ' or * it is the games because one thing after another is always coming into existence. For of these things too the distinction between potential and actual existence holds. We say that there are Olympic games, both in the sense that they may occur and that they are actually occurring.

35 The infinite exhibits itself in different ways — in time, in the generations of man, and in the division of magnitudes. For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different. Again, 30 'being’ has more than one sense, 1 * so that we must not regard the infinite as a * this \ % such as a man or a horse, but must suppose it to exist in the sense in which we speak of the day or the games as existing — things whose being has not come to them like that of a substance, but consists in a process of coming to be or passing away ; definite if you like at each stage, yet always different. ao6 b But when this takes place in spatial magnitudes, what is taken persists, while in the succession of time and of men it takes place by the passing away of these in such a way that the source of supply never gives out

In a way the infinite by addition is the same thing as the infinite by division. In a finite magnitude, the infinite by addition comes about in a way inverse to that of the other. 5 For in proportion as we see division going on, in the same proportion we see addition being made to what is already marked off. For if we take a determinate part of a finite magnitude and add another part determined by thi same ratio (not taking in the same amount of the original whole), 3

1 Inserting in 1 . 29 m (oti E) rb ripcu rr\€OPa\m Xtytrai, with E Phil. Simp.

9 A fully existent individual. .

1 Reading in 1 . 8 ti rov oXov piycGo?, with F and Simp.

ao6 b and so on, we shall not traverse the given magnitude. But 10 if we increase the ratio of the part, so as always to take in the same amount, we shall traverse the magnitude, for every 1 finite magnitude is exhausted by means of any determinate quantity however small.

The infinite, then, exists in no other way, but in this way it does exist, potentially and by reduction. It exists fully in the sense in which we say ‘ it is day ' or 4 it is the games ' ; and potentially as matter exists, not independently as what 15 is finite does.

By addition then, also, there is potentially an infinite, namely, what we have described as being in a sense the same as the infinite in respect of division. For it will always be possible to take something ab extra. Yet the sum of the parts taken will not exceed every determinate magnitude,just as in the direction of division every determinate magnitude is surpassed in smallness and there will be a smaller part

But in respect of addition there cannot be an infinite 20 which even potentially exceeds every assignable magnitude, unless it has the attribute of being actually infinite, as the physicists hold to be true of the body which is outside the world, whose essential nature is air or something of the kind. But if there cannot be in this way a sensible body which is infinite in the full sense, evidently there 35 can no more be a body which is potentially infinite in respect of addition, except as the inverse of the infinite by division, as we have said. It is for this reason that Plato also made the infinites two in number, because it is supposed to be possible to exceed all limits and to proceed ad infinitum in the direction both of increase and of reduction. Yet though he makes the infinites two, he does not use them.

For in the numbers the infinite in the direction of reduction 3* is not present, as the monad is the smallest ; nor is the infinite in the direction of increase, for the parts number only up to the decad.

The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, J107* but what always has something outside it. This is indicated 1 Omitting the second t 6 in 1 . 1 1, with E F.

by the fact that rings also that have no bezel are described as ‘endless’, 1 because it is always possible to take a part which is outside a given part. The description depends on a certain similarity, but it is not true in the full sense of the 5 word. This condition alone is not sufficient : it is necessary also that the next part which is taken should never be the same. In the circle, the latter condition is not satisfied : it is only the adjacent part from which the new part is different.

Our definition then is as follows :

A quantity is infinite if it is such that we can always take a part outside what has been already taken. On the other hand, what has nothing outside it is complete and whole. For thus we define the whole — that from which 10 nothing is wanting, as a whole man or a whole box. What is true of each particular is true of the whole as such — the whole is that of which nothing is outside. On the other hand that from which something ‘is absent and outside, however small that may be, is not * all \ ‘ Whole ’ and

‘complete’ are either quite identical or closely akin. Nothing is complete (re'Aeioi/) which has no end (rAoy) ; and the end is a limit.

*5 Hence Parmenides must be thought to have spoken better than Melissus. The latter says that the whole is infinite, 2 but the former describes it as limited, ‘ equally balanced from the middle’. 3 For to connect the infinite with the all and the whole is not like joining two pieces of string ; 4 for it is from this they get the dignity they ascribe 2o to the infinite — its containing 5 all things and holding 0 the all in itself — from its having a certain similarity to the whole. It is in fact the matter of the completeness which belongs to size, and what is potentially a whole, though not in the full sense. It is divisible both in the direction of reduction and of the inverse addition. It is a whole and limited ; not,

1 an€ipot.

4 A proverbial example of combining things which are homogeneous.

5 Reading in 1 . 19 ntpiixtiv, with E and Them.

however, in virtue of its own nature, but in virtue of what is other than it. It does not contain, but, in so far as it is infinite, is contained. Consequently, also, it is unknowable, 25 qua infinite ; for the matter has no form. (Hence it is plain that the infinite stands in the relation of part rather than of whole. For the matter is part of the whole, as the bronze is of the bronze statue.) If it contains in the case of sensible things, 1 in the case of intelligible things the great and the small ought to contain them. But it is absurd 30 and impossible to suppose that the unknowable and indeterminate should contain and determine.

7 It is reasonable that there should not be held to be an infinite in respect of addition such as to surpass every magnitude, but that there should be thought to be such an infinite in the direction of division. For the matter 2 and 35 the infinite arc contained inside what contains them, while it is the form which contains. It is natural too to suppose that 207* in number there is a limit in the direction of the minimum, and that in the other direction every assigned number is surpassed. In magnitude, on the contrary, every assigned magnitude is surpassed in the direction of smallness, while in the other direction there is no infinite magnitude. The 5 reason is that what is one is indivisible whatever it may be, e. g. a man is one man, not many. Number on the other hand is a plurality of * ones * and a certain quantity of them. Hence number must stop at the indivisible : for ‘two ’ and ‘ three 1 are merely derivative terms, and so with each of the other numbers. But in the direction of largeness it is 10 always possible to think of a larger number : for the number of times a magnitude can be bisected is infinite. Hence this infinite is potential, never actual : the number of parts that can be taken always surpasses any assigned number.

But this number is not separable from the process of bisection, and its infinity is not a permanent actuality but consists in a process of coming to be, like time and the number of time.

8 Omitting in 1. 35, with E and Simp.

15 With magnitudes the o&trary holds. What is continuous is divided ad infinitum , but there is no infinite in the direction of increase. For the size which it can potentially be, it can also actually be . 1 Hence since no sensible magnitude is infinite, it is impossible to exceed every assigned magni- 20 tude ; for if it were possible there would be something bigger than the heavens.

The infinite 2 is not the same in magnitude and movement and time, in the sense of a single nature, but its secondary sense depends on its primary sense, i. e. movement is called infinite in virtue of the magnitude covered by the movement (or alteration or growth), and time because of the 35 movement. (I use these terms for the moment. Later I shall explain what each of them means, and also why every magnitude is divisible into magnitudes.)

Our account does not rob the mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untraversable. In point of fact they do not need the infinite and do not 30 use it. They postulate only that the finite straight line may be produced as far as they wish. It is possible to have divided in the same ratio as the largest quantity another magnitude of any size you like. Hence, for the purposes of proof, it will make no difference to them to have such an infinite instead, while its existence will be in the sphere of real magnitudes.

35 In the four-fold scheme of causes, it is plain that the infinite is a cause in the sense of matter, and that its essence ao8 a is privation, the subject as such being what is continuous and sensible. All the other thinkers, too, evidently treat the infinite as matter — that is why it is inconsistent in them to make it what contains, and not what is contained.

5 It remains to dispose of the arguments 3 which are sup- 8 posed to support the view that the infinite exists not only

1 Otherwise the potentiality would be unintelligible.

ao8* potentially but as a separate thing. Some have no cogency ; others can be met by fresh objections that are valid.

(i) In order that coming to be should not fail, it is not necessary that there should be a sensible body which is actually infinite. The passing away of one thing may be the coming to be of another, the All being limited. 10

{%) There is a difference between touching and being limited. The former is relative to something and is the touching of something (for everything that touches touches something), and further is an attribute of some one of the things which are limited. On the other hand, what is limited is not limited in relation to anything. Again, contact is not necessarily possible between any two things taken at random.

(3) To rely on mere thinking is absurd, for then the excess 15 or defect is not in the thing but in the thought. One might think that one of us is bigger than he is and magnify him ad infinitum . But it does not follow that he is bigger 1 than the size we are, just because some one thinks he is, but only because he is the size he is. The thought is an accident.

(a) Time indeed and movement are infinite, and also 20 thinking, in the sense that each part that is taken passes in succession out of existence.

(b) Magnitude is not infinite either in the way of reduction or of magnification in thought.

This concludes my account of the way in which the infinite exists, and of the way in which it does not exist, and of what it is.

1 Omitting rovaanos and fj in l, 18, with yp. Phil, and Diels.

The physicist must have a knowledge of Place, too, as i well as of the infinite — namely, whether there is such a thing or not, and the manner of its existence and what it 30 is — both because all suppose that things which exist are somewhere (the non-existent is nowhere — where is the goat-stag or the sphinx?), and because ‘motion’ in its most general and primary sense is change of place, which we call ‘ locomotion \

The question, what is place ? presents many difficulties. An examination of all the relevant facts seems to lead 35 to divergent conclusions. Moreover, we have inherited nothing from previous thinkers, whether in the way of a statement of difficulties or of a solution. ao8 b The existence of place is held to be obvious from the fact of mutual replacement. Where water now is, there in turn, when the water has gone out as from a vessel, air is present. When therefore another body occupies this same place,

5 the place is thought to be different from all the bodies which come to be in it and replace one another. What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both.

Further, the typical locomotions of the elementary natural bodies — namely, fire, earth, and the like— show not only that 10 place is something, but also that it exerts a certain influence. Each is carried to its own place, if it is not hindered, the one up, the other down. Now these are regions or kinds of place— up and down and the rest of the six directions. Nor do such distinctions (up and down and right and left,

15 & c *) h°ld only in relation to us. To us they are not always the same but change with the direction in which we are turned : that is why the same thing may be both right and left, up and down, before and behind. But in nature each is distinct, taken apart by itself. It is not every ao8 b chance direction which is 1 up \ but where fire and what is light are carried ; similarly, too, ‘ down ’ is not any chance 20 direction but where what has weight and what is made of earth are carried— the implication being that these places do not differ merely in relative position, but also as possessing distinct potencies. This is made plain also by the objects studied by mathematics. Though they have no real place, they nevertheless, in respect of their position relatively to us, have a right and left as attributes ascribed to them only in consequence of their relative position, not having by nature these various characteristics 1 . Again, the theory that the void exists involves the existence 25 of place : for one would define void as place bereft of body.

These considerations then would lead us to suppose that place is something distinct from bodies, and that every sensible body is in place. Hesiod too might be held to have given a correct account of it when he made chaos first. At least he says : 3°

First of all things came chaos to being, then broadbreasted earth, 2 implying that things need to have space first, because he thought, with most people, that everything is somewhere and in place. If this is its nature, the potency of place must be a marvellous thing, and take precedence of all other things. For that without which nothing else can 35 exist, while it can exist without the others, must needs be first ; for place does not pass out of existence when the 209* things in it are annihilated.

True, but even if we suppose its existence settled, the question of its nature presents difficulty — whether it is some sort of 1 bulk * of body or some entity other than that, for we must first determine its genus.

(1) Now it has three dimensions, length, breadth, depth, 5 the dimensions by which all body also is bounded. But

1 Reading in 1 . 24 wf pW v Xryop-va hia Sttriu, ovk c x°vra tyvcrti, with Laas (tot r« fxovov kt\. Simp.). The readings of the MSS. are due to a conjecture by Alexander.

the place cannot be body; for if it were there would be two bodies in the same place.

(2) Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply to them : where the bounding

10 planes of the water were, there in turn will be those of the air. But when we come to a point we cannot make a distinction between it and its place. Hence if the place Of a point is not different from the point, no rfiore will that of any of the others be different, and place will not be something different from each of them.

(3) What in the world then are we to suppose place to be ? If it has the sort of nature described, it cannot be an element

15 or composed of elements, whether these be corporeal or incorporeal : for while it has size, it has not body. But the elements of sensible bodies are bodies, while nothing that, has size results from a combination of intelligible elements.

(4) Also we may ask : of what in things is space the cause ? None of the four modes of causation can be

20 ascribed to it. It is neither cause in the sense of the matter of existents (for nothing is composed of it), nor as the form and definition of things, nor as end, nor does it move existents.

(5) Further, too, if it is itself an existent, where will it be ? Zeno's difficulty 1 demands an explanation : for if

25 everything that exists has a place, place too will have a place, and so on ad infinitum .

(6) Again, just as every body is in place, so, too, every place has a body in it. What then shall we say about growing things ? It follows from these premisses that their place must grow with them, if their place is neither less nor greater than they are.

By asking these questions, then, we must raise the whole

30 problem about place — not only as to what it is, but even whether there is such a thing.

We may distinguish generally between predicating B of a A because it (A) is itself, and because it is something else ;

and particularly between place which is common and in which all bodies are, and the special place occupied primarily by each. I mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens ; and you are in the air because you are on the earth ; and similarly on the earth because you are in this 35 place which contains no more than you.

Now 1 if place is what primarily contains each body, it 309 b would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined : for this is the limit of each body.

If, then, we look at the question in this way the place of 5 a thing is its form. But, if we regard the place as the extension of the magnitude, it is the matter. For this is different from the magnitude: it is what is contained and defined by the form, as by a bounding plane. Matter or the indeterminate is of this nature ; when the boundary and attributes of a sphere are taken away, nothing but the 10 matter is left.

This is why Plato in the Timaeus 2 says that matter and space are the same ; for the * participant * and space are identical. (It is true, indeed, that the account he gives there of the ‘ participant 1 is different from what he says in his so-called ‘unwritten teaching ’. 3 Nevertheless, he did 15 identify place and space.) I mention Plato because, while all hold place to be something, he alone tried to say what it is.

In view of these facts we should naturally expect to find difficulty in determining what place is, if indeed it is one of these two things, matter or form. They demand a very 30 close scrutiny, especially as it is not easy to recognize them apart.

But it is at any rate not difficult to see that place cannot be either of them. The form and the matter are not

1 X«y« . . . <rc a 33- b i is parenthetical, and there should be a comma before « in b i (so Bonitz).

# where he apparently identified < the participant * with 1 the great and the small * ; cf. 1. 35.

separate from the thing, whereas the place can be separated. As we pointed out , 1 where air was, water in turn comes to 35 be, the one replacing the other ; and similarly with other bodies. Hence the place of a thing is neither a part nor a state of it, but is separable from it. For place is supposed to be something like a vessel — the vessel being a transportable place. But the vessel is no part of the thing.

30 In so far then as it is separable from the thing, it is not the form : qua containing, it is different from the matter.

Also it is held that what is anywhere is both itself something and that there is a different thing outside it . 2 (Plato of course, if we may digress, ought to tell us why the form 35 and the numbers are not in place, if ‘ what participates * is place — whether what participates is the Great and the Small 2io a or the matter, as he called it in writing in the Timaeus .) 3

Further, how could a body be carried to its own place, if place was the matter or the form ? It is impossible that what has no reference to motion or the distinction of up and down can be place. So place must be looked for among things which have these characteristics.

5 If the place is in the thing 4 (it must be if it is either shape or matter) place will have a place : for both the form and the indeterminate undergo change and motion along with the thing, and are not always in the same place, but are where the thing is. Hence the place will have a place.

Further, when water is produced from air, the place has 10 been destroyed, for the resulting body is not in the same place . 6 What sort of destruction then is that ?

This concludes my statement of the reasons why space must be something, and again of the difficulties that may be raised about its essential nature.

The next step we must take is to see in how many 3 senses one thing is said to be 4 in ’ another.

4 Reading avru in 1 . 5, with the MSS.

B The place of the air is part of the substance air.

BOOK IV. 3 aio a

(i) As the finger is ‘ in ' the hand and generally the part 15 * in ’ the whole.

(а) As the whole is * in ’ the parts : for there is no whole over and above the parts.

(3) As man is 4 in * animal and generally species 4 in > genus.

(4) As the genus is 4 in ’ the species and generally the part of the specific form ‘in’ the definition of the specific form.

(5) As health is 4 in ' the hot and the cold and generally a° the form 1 in ’ the matter.

(б) As the affairs of Greece centre ‘ in * the king, and generally events centre 4 in * their primary motive agent.

(7) As the existence of a thing centres 1 in 9 its good and generally 4 in 1 its end, i. e. in ‘that for the sake of which ’ it exists.

(8) In the strictest sense of all, as a thing is 1 in' a vessel, and generally 4 in 9 place.

One might raise the question whether a thing can be in 35 itself, or whether nothing can be in itself— everything being either wwhere or in something else .

The question is ambiguous ; we may mean the thing qua itself or qua something else.

When there are parts of a whole — the one that in which a thing is, the other the thing which is in it — the whole will be described as being in itself. For a thing is described in terms of its parts, as well as in terms of the thing as a whole, e. g. a man is said to be white because the visible surface of him is white, or to be scientific because his thinking faculty has been trained. The jar then will not 30 be in itself and the wine will not be in itself. But the jar of wine will : for the contents and the container are both parts of the same whole.

In this sense then, but not primarily, a thing can be in itself, namely, as 4 white * is in body (for the visible surface is in body), and science is in the mind. 1

1 Because the faculty of reasoning is in the mind, fj €m<f)dvua . . . <rd>naTi (*34- b i) is parenthetical.

aio b

It is from these, which are ‘ parts * (in the sense at least of being ‘in’ the man), that the man is called white, &c. But the jar and the wine in separation are not parts of a whole, though together they are. So when there are parts, a thing will be in itself, as 4 white ’ is in man because it is in body, and in body because it resides in the visible 5 surface. We cannot go further and say that it is in surface in virtue of something other than itself. (Yet it is not in itself : though these are in a way the same thing,) they differ in essence, each having a special nature and capacity, * surface * and 4 white ’.

Thus if we look at the matter inductively we do not find anything to be 4 in* itself in any of the senses that have been distinguished ; and it can be seen by argument that it to is impossible. For each of two things will have to be both, e. g. the jar will have to be both vessel and wine, and the wine both wine and jar, if it is possible for a thing to be in itself ; so that, however true it might be that they were in each other, the jar will receive the wine in virtue not of its 1 5 being wine but of the wine’s being wine, and the wine will be in the jar in virtue not of its being a jar but of the jar’s being a jar. Now that they are different in respect of their essence is evident ; for ‘ that in which something is ’ and ‘ that which is in it ’ would be differently defined.

Nor is it possible for a thing to be in itself even incidentally : for two things would be at the same time in the jo same thing. The jar would be in itself — if a thing whose nature it is to receive can be in itself ; 1 and that which it receives, namely (if wine) wine, will be in it.

Obviously then a thing cannot be in itself primarily .

Zenos problem 2 — that if Place is something it must be in something 3 — is not difficult to solve. There is nothing to prevent the first place from being i in ’ something else — a 5 not indeed in that as 1 in ’ place, but as health is ‘ in * the

1 Reading a comma after tlvai in 1 . 20.

8 Reading tv nvt in 1 . 23, with Them. Phil. Simp.

2IO b hot as a positive determination of it or as the hot is ‘ in * body as an affection. So we escape the infinite regress.

Another thing is plain: since the vessel is no part of what is in it 1 (what contains in the strict sense is different from what is contained), place could not be either the matter or the form of the thing contained, but must be different — for the latter, both the matter and the shape, 3° are parts of what is contained.

This then may serve as a critical statement of the difficulties involved.

4 What then after all is place? The answer to this question may be elucidated as follows.

Let us take for granted about it the various characteristics which are supposed correctly to belong to it essentially . 2 We assume then —

(1) Place is what contains that of which it is the place.

(a) Place is no part of the thing. 2ii a

(3) The immediate place of a thing is neither less nor greater than the thing.

(4) Place can be left behind by the thing and is separable.

In addition :

(5) All place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes 5 the place either up or down.

Having laid these foundations, we must complete the theory. We ought to try to make our investigation such as will render an account of place, and will not only solve the difficulties connected with it, but will also show that the attributes supposed to belong to it do really belong to it, and further will make clear the cause of the trouble and 10 of the difficulties about it. Such is the most satisfactory kind of exposition.

First then we must understand that place would not

1 Reading avry in L 28, with Simp, and Bonitz.

2II a have been thought of, if there had not been a special kind of motion, namely that with respect to place. It is chiefly for this reason that we suppose the heaven also to be in place, because it is in constant movement. Of this kind of change there are two species — locomotion on the 15 one hand and, on the other, increase and diminution. For these too involve variation of place : what was then in this place has now in turn changed to what is larger or smaller.

Again, when we say a thing is ‘ moved the predicate either (1) belongs to it actually, in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter case it may be either (a) something which by its own ao nature is capable of being moved, e. g. the parts of the body or the nail in the ship, or (b) something which is not in itself capable of being moved, but is ahvays moved through its conjunction with something else, as 4 whiteness ’ or 4 science \ These have changed their place only because the subjects to which they belong do so.

We say that a thing is in the world, in the sense of in 35 place, because it is in the air, and the air is in the world ; and when we say it is in the air, we do not mean it is in every part of the air, but that it is in the air because of the outer surface of the air which surrounds it ; for if all the air were its place, the place of a thing would not be equal to the thing — which it is supposed to be, and which the primary place in which a thing is actually is. 1

When what surrounds, then, is not separate from the 30 thing, but is in continuity with it, the thing is said to be in what surrounds it, not in the sense of in place, but as a part in a whole. But when the thing is separate and in contact, it is immediately 4 in ’ the inner surface of the surrounding body, and this surface is neither a part of what is in it nor yet greater than its extension, but equal to it ; for the extremities of things which touch are coincident.

Further, if one body is in continuity with another, it is 35 not moved in that but with that. On the other hand it is

1 As Bonitz pointed out, u . . . tariv ( 11 . 27-9) is parenthetical, and there should be a comma after tlvai (1. 28), and a colon after the parenthesis.

2II a moved in that if it is separate. It makes no difference whether what contains is moved or not.

Again, when it is not separate it is described as a part in 2ii b a whole, as the pupil in the eye or the hand in the body : when it is separate, as the water in the cask or the wine in the jar. For the hand is moved with 1 the body and the water in the cask.

It will now be plain from these considerations what place 5 is. There are just four things of which place must be one — the shape, or the matter, or some sort of extension between the bounding surfaces of the containing body, or this boundary itself if it contains no extension over and above the bulk of the body which comes to be in it.

Three of these it obviously cannot be :

(1) The shape is supposed to be place because it sur- jo rounds, for the extremities of what contains and of what is contained are coincident. Both the shape and the place, it is true, are boundaries. But not of the same thing: the form is the boundary of the thing, the place is the boundary of the body which contains it.

(2) The extension between the extremities is thought to be something, because what is contained and separate may often be changed while the container remains the same (as 1 water may be poured from a vessel) — the assumption being that the extension is something over and above the body displaced. But there is no such extension. One of the bodies which change places and are naturally capable of being in contact with the container falls in — whichever it may chance to be.

If there were an extension which were such as to exist independently and be permanent, there would be an infinity ac of places in the same thing. 2 For when the water and the air change places, all the portions of the two together will play the same part in the whole which was previously played by all the water in the vessel ; at the same time

1 Reading /lira in I. 4 ; Bekker’s Kara is a misprint.

(Laas) Ka\ fjitvop, tv t£ avrdd dnttpot ktX. (F Phil. Simp., except that Simp, has the comma after avry).

the place too will be undergoing change; so that there will be another place which is the place of the place, and 35 many places will be coincident. There is not a different place of the part, in which it is moved, when the whole vessel changes its place : it is always the same : for it is in the (proximate) place where they are that the air and the water (or the parts of the water) succeed each other, not in that place in which they come to be, which is part of the place which is the place of the whole world.

50 (3) The matter, too, might seem to be place, at least if we consider it in what is at rest and is thus separate but in continuity. For just as in change of quality there is something which was formerly black and is now white, or formerly soft and now hard — this is just why we say that the matter exists — so place, because it presents a similar 35 phenomenon, is thought to exist — only in the one case we say so because what was air is now water, in the other because where air formerly was there is now water. But 212* the matter, as we said before, 1 is neither separable from the thing nor contains it,- whereas place has both characteristics.

Well, then, if place is none of the three — neither the form nor the matter nor an extension which is always there, different from, and over and above, the extension of the 5 thing which is displaced — place necessarily is the one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. 2 (By the contained body is meant what can be moved by way of locomotion.)

Place is thought to be something important and hard to grasp, both because the matter and the shape present themselves along with it, and because the displacement of the body that is moved takes place in a stationary container, 10 for it seems possible that there should be an interval which is other than the bodies which are moved. The air, too, which is thought to be incorporeal, contributes something to

* Reading in 1. 6 c rwparos Kaff 6 ovmrrrci rw Trrpic^o/xcVo), with Them. Phil. Simp.

the belief: it is not only the boundaries of the vessel which seem to be place, but also what is between them, regarded as empty. Just, in fact, as the vessel is transportable place, so place is a non-portable vessel. So when what is within 15 a thing which is moved, is moved 1 and changes its place, as a boat on a river, what contains plays the part of a vessel rather than that of place. Place on the other hand is rather what is motionless : so it is rather the whole river that is place, because as a whole it is motionless.

Hence we conclude that the innermost motionless boun - 20 dary of what contains is place .

This explains why the middle of the heaven and the surface which faces us of the rotating system are held to be ‘ up ' and ‘ down ’ in the strict and fullest sense for all men : for the one is always at rest, while the inner side of the rotating body 2 remains always coincident with itself. Hence since the light is what is naturally carried up, and 25 the heavy what is carried down, the boundary which contains in the direction of the middle of the universe, and the middle itself, are down, and that which contains in the direction of the outermost part of the universe, and the outermost part itself, are up.

For this reason, too, place is thought to be a kind of surface, and as it were a vessel, i. e. a container of the thing.

Further, place is coincident with the thing, for bound- 30 aries are coincident with the bounded.

5 If then a body has another body outside it and containing it, it is in place, and if not, not. That is why, even if there were to be water which had not a container, the parts" of it, on the one hand, will be moved (for one part is contained in another), while, on the other hand, the whole will be moved in one sense, but not in another. For as a whole 35 it does not simultaneously change its place, though it will be moved in a circle : for this place is the place of its 2ia b parts. (Some things are moved, not up and down, but in

1 Omitting ti in 1 . 16 with EFG.

aia b a circle ; others up and down, such things namely as admit of condensation and rarefaction.)

As was explained , 1 some things are potentially in place, others actually. So, when you have a homogeneous sub- 5 stance which is continuous, the parts are potentially in place : when the parts are separated, but in contact, like a heap, they are actually in place.

Again, (i) some things are per se in place, namely every body which is movable either by way of locomotion or by way of increase is per se somewhere, but the heaven, as has been said , 2 is not anywhere as a whole, nor in any place, if 10 at least, as we must suppose, no body contains it. On the line on which it is moved, its parts have place 3 ; for each is contiguous to the next.

But (2) other things arc in place indirectly, through something conjoined with them, as the soul and the heaven. The latter is, in a way, in place, for all its parts are : for on the orb one part contains another. That is why the upper part is moved in a circle, while the All is not anywhere. 15 For what is somewhere is itself something, and there must be alongside it some other thing wherein it is and which contains it. But alongside the All or the Whole there is nothing outside the All, and for this reason all things are in the heaven ; for the heaven, we may say, is the All. Yet their place is not the same as the heaven. It is part of it, the innermost part of it, which is in contact 20 with the movable body ; 4 and for this reason the earth is in water, and this in the air, and the air in the aether, and the aether in heaven, but we cannot go on and say that the heaven is in anything else.

It is clear, too, from these considerations that all the problems which were raised 5 about place will be solved when it is explained in this way ;

(1) There is no necessity that the place should grow with the body in it,

8 It is only in reference to its parts that it can be said to be moved,

4 Omitting ncpas Tjpfpovv in 1 . 19, with E Them. Simp.

(2) Nor that a point should have a place,

(3) Nor that two bodies should be in the same place, 25

(4) Nor that place should be a corporeal interval: for what is between the boundaries of the place is any body which may chance to be there, not an interval in body.

Further, (5) place is also somewhere, not in the sense of being in a place, but as the limit is in the limited ; for not everything that is is in place, but only movable body.

Also (6) it is reasqnable that each kind of body should be carried to its own place. For a body which is next in 30 the series and in contact (not by compulsion) is akin, and bodies which are united do not affect each other, while those which are in contact interact on each other. 1

Nor (7) is it without reason that each 2 should remain naturally in its proper place. For this part has the same relation to its place, 3 as a separable part to its whole, as 35 when one moves a part of water or air : so, too, air is 213* related to water, for the one is like matter, the other form — water is the matter of air, air as it were the actuality of water, for water is potentially air, while air is potentially water, though in another way.

These distinctions will be drawn more carefully later. 4 On the present occasion it was necessary to refer to them : 5 what has now been stated obscurely will then be made more clear. If the matter and the fulfilment are the same thing (for water is both, the one potentially, the other completely), water will be related to air in a way as part

1 The scheme suggested is

Fire J Air | Water J

Earth j

Dry Hot Hot ' Wet. Wet ' Coldx Cold' Dry

2 Omitting in 1 . 33 otaorov, with FG.

4 De Gen . et Corr, i. 3.

2I3 a to whole. That 5 s why these have contact : it is organic union when both become actually one. jo This concludes my account of place — both of its existence and of its nature.

The investigation of similar questions about the void, 6 also, must be held to belong to the physicist— namely whether it exists or not, and how it exists or what it is — just as about place. The views taken of it involve arguments both for and against, in much the same sort of way.

15 For those who hold that the void exists regard it as a sort of place or vessel which is supposed to be ‘ full ’ when it holds the bulk which it is capable of containing, ‘ void ’ when it is deprived of that — as if ‘ void ’ and 1 full ’ and * place ’ denoted the same thing, though the essence of the three is different.

20 We must begin the inquiry by putting down the account given by those who say that it exists, then the account of those who say that it does not exist, and third the current view on these questions.

Those who try to show that the void does. not exist do not disprove what people really mean by it, but only their erroneous way of speaking ;* this is true of Anaxagoras and of those who refute the existence of the void in this way.

35 They merely give an ingenious demonstration that air is something — by straining wine-skins and showing the resistance of the air, and by cutting it off in clepsydras. But people really mean that there is an empty interval in which there is no sensible body. They hold that everything 30 which is is body and say that what has nothing in it at all is void (so what is full of air is void). It is not then the existence of air that needs to be proved, but the non-existence of an interval, different from the bodies, either separable or actual — an interval which divides the whole body so as to break its continuity, as Democritus and Leucippus s*i3 b hold, and many other physicists — or even perhaps as some-

1 Reading in 1 . 24 a\\* t dpaprivount, with Them. Phil. Simp, and Pacius.

2I3 b thing which is outside the whole body, which remains continuous.

These people, then, have not reached even the threshold of the problem, but rather those who say that the void exists.

(1) They argue, for one thing, that change in place (i. e. locomotion and increase) would not be. For it is main- 5 tained that motion would seem not to exist, if there were no void, since what is full cannot contain anything more.

If it could, and there were two bodies in the same place, it would also be true that any number of bodies could be together; for it is impossible to draw a line of division beyond which the statement would become untrue. If this were possible, it would follow also that the smallest body would contain the greatest ; for ‘ many a little makes 10 a mickle’: thus if many equal bodies can be together, so also can many unequal bodies.

Melissus, 1 indeed, infers from these considerations that the All is immovable ; for if it were moved there must, he says, be void, but void is not among the things that exist.

This argument, then, is one way in which they show that there is a void.

(2) They reason from the fact that some things are 15 observed to contract and be compressed, as people say that a cask will hold the wine which formerly filled it, along with the skins into which the wine has been decanted, 2 which implies that the compressed body contracts into the voids present in it.

Again (3) increase, too, is thought to take place always by means of void, for nutriment is body, and it is impos- 20 sible for two bodies to be together. A proof of this they find also in what happens to ashes, which absorb as much water as the empty vessel.

The Pythagoreans, 3 too, (4) held that void exists and that it enters the heaven itself, 4 which as it were inhales it, from the infinite air. Further it is the void which distin-

4 Reading in 1. 23 with G.

3 5 guishes the natures of things, as if it were like what separates and distinguishes 1 the terms of a series. This holds primarily in the numbers, for the void distinguishes their nature.

These, then, and so many, are the main grounds on which people have argued for and against the existence of the void.

30 As a step towards settling which view is true, we must 7 determine the meaning of the name.

The void is thought to be place with nothing in it. The reason for this is that people take what exists to be body, and hold that while every body is in place, void is place in which there is no body, so that where there is no body, there must be void.

2i4 a Every body, again, they suppose to be tangible ; and of this nature is whatever has weight or lightness.

Hence, by a syllogism, what has nothing heavy or light in it, is void.

This result, then, as I have said, is reached by syllogism.

5 It would be absurd to suppose that the point is void ; for the void must be place which has in it an interval in tangible body.

But at all events we observe then that in one way the void is described as what is not full of body perceptible to touch ; and what has heaviness and lightness is perceptible to touch. So we would raise the question : what would they say of an interval that has colour or sound — is it void io or not? Clearly they would reply that if it could receive what is tangible it was void, and if not, not.

In another way void is that in which there is no 4 this ' or corporeal substance. So some say that the void is the matter of the body (they identify the place, too, with this), and in this 2 they speak incorrectly ; for the matter is not 15 separable from the things, but they are inquiring about the void as about something separable.

Since we have determined the nature of place, 3 and void

2 Placing the comma after to alro in 1 . 14.

8 ch. 4.

s«4 a must, if it exists, 1 be place deprived of body, and we have stated both in what sense place exists and in what sense it does not, it is plain that on this showing void does not exist, either unseparated or separated ; for the void is meant to be, not body but rather an interval in body. 20 This is why the void is thought to be something, viz. because place is, and for the same reasons. For the fact of motion in respect of place comes to the aid both of those who maintain that place is something over and above the bodies that come to occupy it, and of those who maintain that the void is something. They state that the void is the condition of movement in the sense of that in which movement takes place ; and this would be the kind of thing 25 that some say place is.

But there is no necessity for there being a void if there is movement. It is not in the least needed as a condition of movement in general, for a reason which, 2 * incidentally, escaped Melissus ; viz. that the full can suffer qualitative change.

But not even movement in respect of place involves a void ; for bodies may simultaneously make room for one another, though there is no interval separate and apart from the ;,o bodies that are in movement. And this is plain even in the rotation of continuous things, as in that of liquids.

And things can also be compressed not into a void but because they squeeze out what is contained in them (as, for instance, when water is compressed the air within it is squeezed out) ; and things can increase in size not only by 214* the entrance of something but also by qualitative change ; e, g. if water were to be transformed into air.

In general, both the argument about increase of oize u and that about the water poured on to the ashes 4 get in their own way. For either not any and every part of the body 5 is increased, or bodies may be increased otherwise than by the addition of body, or there may be two bodies in the same place (in which case they are claiming to solve a quite

1 Reading commas before and after tl t<mv in 1 . 17.

2I4 b general difficulty, but are not proving the existence of void), or the whole body must be void, if it is increased in every part and is increased by means of void. The same argument applies to the ashes, ro It is evident, then, that it is easy to refute the arguments by which they prove the existence of the void.

Let us explain again that there is no void existing 8 separately, as some maintain. If each of the simple bodies has a natural locomotion, e. g. fire upward and earth downx 5 ward and towards the middle of the universe, it is clear that it cannot be the void that is the condition of locomotion. What, then, will the void be the condition of ? It is thought to be the condition of movement in respect of place, and it is not the condition of this.

Again, if void is a sort of place deprived of body, when there is a void where will a body placed in it move to ?

It certainly cannot move into the whole of the void. The 20 same argument applies as against those who think that place is something separate, into which things are carried ; viz. how will what is placed in it move, or rest? Much the same argument will apply to the void as to the \ up* and ‘ down 1 in place, as is natural enough since those who maintain the existence of the void make it a place.

And in what way will things be present either in place 25 or in the void ? For the expected 1 result does not take place when a body 2 is placed as a whole in a place conceived of as separate and permanent ; for a part of it, unless it be placed apart, will not be in a place but in the whole. Further, if separate place does not exist, neither will void.

If people say that the void must exist, as being necessary if there is to be movement, what rather turns out to be 30 the case, if one studies the matter, is the opposite, that not a single thing can be moved if there is a void ; for as with those who for a like reason say the earth is at rest, so, too,

1 Expected by those who believe in a separately existing place or void.

* Reading in k 26 aS>fxa n, with Phil’s and Simp.’s paraphrase.

2I4 b in the void things must be at rest ; for there is no place to which things can move more or less than to another ; since the void in so far as it is void admits no difference.

The second reason is this 1 : all movement is either com- 215® pulsory or according to nature, and if there is compulsory movement there must also be natural (for compulsory movement is contrary to nature, and movement contrary to nature is posterior to that according to nature, so that if each of the natural bodies has not a natural movement, none of the other movements can exist) ; but how can there 5 be natural movement if there is no difference throughout the void or the infinite ? For in so far as it is infinite, there will be no up or down or middle, and in so far as it is a void, up differs no whit from down ; for as there is no difference in what is nothing, there is none in the void (for 10 the void 2 seems to be a non-existent and a privation of being), but natural locomotion seems to be differentiated, so that the things that exist by nature must be differentiated. Either, then, nothing has a natural locomotion, or else there is no void.

Further, in point of fact things that are thrown move though that which gave them their impulse is not touching them, either by reason of mutual replacement, as some 15 maintain, or because the air that has been pushed pushes them with a movement quicker than the natural locomotion of the projectile wherewith it moves to its proper place. 3 But in a void none of these things can take place, nor can anything be moved save as that which is carried is moved.

Further, no one could say why a thing once set in motion should stop anywhere ; for why should it stop here rather 20 than here ? So that a thing will either be at rest or must be moved ad infinitum , unless something more powerful get in its way.

Further, things are now thought to move into the void because it yields ; but in a void this quality is present equally everywhere, so that things should move in all directions.

1 Reading iflf 1. 1 hrttO* on, with I Them. Simp.

2 Reading in 1. 10 *at roO k*vov : to yap kwov, with H Them. Simp.

3 i. e. downwards.

Further, the truth of what we assert is plain from the 35 following considerations. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, as between water, air, and earth, or because, other things being equal, the moving body differs from the other owing to excess of weight or of lightness.

Now the medium causes a difference because it impedes the moving thing, most of all if it is moving in the opposite 30 direction, but in a secondary degree even if it is at rest ; and especially a medium that is not easily divided, i. e. a medium that is somewhat dense.

2i5 b A, then, will move through B in time F, and through A, which is thinner, 1 in time E (if the length ofB is equal to A), in proportion to the density of the hindering body. For let B be water and A air ; then by so much as air is thinner 5 and more incorporeal than water, A will move through A faster than through B. Let the speed have the same ratio to the speed, then, that air has to water. Then if air is twice as thin, the body will traverse B in twice the time that it does A, and the time F will be twice the time E. 10 And always, by so much as the medium is more incorporeal and less resistant and more easily divided, the faster will be the movement.

Now there is no ratio in which the void is exceeded by body, as there is no ratio of o to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more 15 than it exceeds 2, still there is no ratio by which it exceeds o; for that which exceeds must be divisible into the excess + that which is exceeded, so that 4 will be what it exceeds o by + o. For this reason, too, a line does not exceed a point — unless it is composed of points ! Similarly 20 the void can bear no ratio to the full, and therefore neither can movement through the one to movement through the other, but if a thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio. 2 For let

1 Reading in 1 . 2 Xcirrorcpov, with E G Them. Simp.

2 Placing the comma in 1 . 22 before dta tov kcvov.

Z be void, equal in magnitude to B and to A. Then if A is to traverse and move through it in a certain time, H, a time less than E, however, the void will bear this ratio 35 to the full. But in a time equal to H, A will traverse the part 0 of A. And it will surely also traverse in that time any substance Z which exceeds air in thickness in the ratio which the time E bears to the time H. For if the body Z 30 be as much thinner than A as E exceeds H, A, if it moves through Z, will traverse it in a time inverse to the speed of the movement, i. e. in a time equal to H. If, then, there is ai6 a 7/0 body in Z, A will traverse Z still more quickly. But we supposed that its traverse of Z when Z was void occupied the time H. So that it will traverse Z in an equal time whether Z be full or void. But this is impossible. It is plain, then, that if there is a time in which it will move through any part of the void, this impossible result will follow : it will be found to traverse a certain 5 distance, whether this be full or void, in an equal time ; for there will be some body which is in the same ratio to the other body as the time is to the time.

To sum the matter up, the cause of this result is obvious, viz. that between any two movements there is a ratio (for they occupy time, and there is a ratio between any two times, so io long as both are finite), but there is no ratio of void to full.

These are the consequences that result from a difference in the media ; the following depend upon an excess of one moving body over another. We see that bodies which have a greater impulse either of weight or of lightness, if they are alike in other respects, 1 move faster over an J5 equal space, and in the ratio which their magnitudes bear to each other. Therefore they will also move through the void with this ratio of speed. But that is impossible ; for why should one move faster ? (In moving through plena it must be so ; for the greater divides them faster by its force.

For a moving thing cleaves the medium either by its shape, or by the impulse which the body that is carried along or is projected possesses.) Therefore all will possess equal ao velocity. But this is impossible.

1 Omitting rot* crxwaai in 1 . 14, as Simplicius may have done.

It is evident from what has been said, then, that, if there is a void, a result follows which is the very opposite of the reason for which those who believe in a void set it up. They think that if movement in respect of place is to exist, the void cannot exist, separated all 1 by itself ; but this is *5 the same as to say that place is a separate cavity ; and this has already been stated to be impossible . 2

But even if we consider it on its own merits the so-called vacuum will be found to be really vacuous. For as, if one puts a cube in water, an amount of water equal to the cube will be displaced ; so too in air ; but the effect is imperceptible to sense. And indeed always, in the case of any 30 body that can be displaced, it must, if it is not compressed, be displaced in the direction in which it is its nature to be displaced — always either down, if its locomotion is downwards as in the case of earth, or up, if it is fire, or in both directions-— whatever 3 be the nature of the inserted body. Now in the void this is impossible ; for it is not body ; the void must have penetrated 4 the cube to a distance equal to 35 that which this portion of void formerly occupied in the ai6 b void, just as if the water or air had not been displaced by the wooden cube, but had penetrated right 6 through it.

But the cube also has a magnitude equal to that occupied by the void ; a magnitude which, if it is also hot or cold,

5 or heavy or light, is none the less different in essence from all its attributes, even if it is not separable from them ;

I mean the volume of the wooden cube. So that even if it were separated from everything else and were neither heavy nor light, it will occupy an equal amount of void, and fill the same place, as the part of place or of the void equal to itself. How then will the body of the cube differ from the 10 void or place that is equal to it? And if there can be two such things, why cannot there be any number coinciding? This, then, is one absurd and impossible implication of the

* Omitting the second in 1 . 33, with Prantl, and apparently with Simp.

4 Omitting in 1. 35, with E.

ai6 b theory. It is also evident that the cube will have this same volume even if it is displaced, which is an attribute possessed by all other bodies also. Therefore if this differs in no respect from its place, 1 why need we assume a place for bodies over and above the volume of each, if their volume be conceived of as free from attributes? It contributes nothing 15 to the situation if there is an equal interval attached to it as well. [Further, it ought to be clear by the study of moving things what sort of thing void is. But in fact it is found nowhere in the world. For air is something, though it does not seem to be so — nor, for that matter, would water, if fishes were made of iron; for the discrimination of the tangible is by touch. 2 ]

It is clear, then, from these considerations that there is no 20 separate void.

9 There are some who think that the existence of rarity and density shows that there is a void. If rarity and density do not exist, they say, neither can things contract and be compressed. But if this were not to take place, either there would be no movement at all, or the universe 3 5 would bulge, as Xuthus 3 said, or air and water must 4 * always change into equal amounts (e. g. if air has been made out of a cupful of water, at the same time out of an equal amount of air a cupful of water must have been made), or void must necessarily exist ; for compression and expansion 6 cannot take place otherwise.

Now, if they mean by the rare that which has many 30 voids existing separately, it is plain that if void cannot exist separate any more than a place can exist with an extension all to itself, neither can the rare exist in this sense. But if they mean that there is void, not separately existent, but still present in the rare, this is less impossible, yet, first, the void turns out not to be a condition of all

1 Reading rov ronov in 1 . 14 ; Bekker’s tovt6 ttqv is a misprint.

* The words in brackets are unknown to the Greek commentators and probably spurious.

* A Pythagorean of Croton ; cf. Diels, Vers? i. 284. 22-5,

4 Inserting dti after act in 1 . 26, with Bonitz.

1 Reading in 1 . 29 firffcrctWlat, with E and apparently Simp.

35 movement, but only of movement upwards (for the rare is » I 7 a Hght, which is the reason why they say fire is rare) ; second, the void turns out to be a condition of movement not as that in which it takes place, but in that the void carries things up as skins by being carried up themselves carry up what is continuous with them. Yet how can void have a local movement or a place ? For thus that into which void moves is till then void of a void.

5 Again, how will they explain, in the case of what is heavy, its movement downwards ? And it is plain that if the rarer and more void a thing is the quicker it will move upwards, if it were completely void it would move with a maximum speed ! But perhaps even this is impossible, that it should move at all 1 ; the same reason which showed that in the void all things are incapable of moving shows that the void cannot move, viz., the fact that the speeds are incomparable.

IO Since we deny that a void exists, but for the rest the problem has been truly stated , 2 that either there will be no movement, if there is not to be condensation and rarefaction, or the universe will bulge, or a transformation of water into air will always be balanced by an equal transformation of air into water (for it is clear that the air pro-

15 duced from water is bulkier than the water) 3 : it is necessary therefore, if compression does not exist, either that the next portion will be pushed outwards and make the outermost part bulge, or that somewhere else there must be an equal amount of water produced out of air, so that the entire bulk of the whole may be equal, or that nothing moves. For when anything is displaced this will always happen, unless it comes round in a circle ; but locomotion is not always circular, but sometimes in a straight line.

30 These then are the reasons for which they might say that there is a void ; our statement is based on the assumption that there is a single matter for contraries, hot and cold and the other natural contrarieties, and that what exists actually is produced from a potential existent, and

9 Putting a colon before amyicy in 1 . 15, with Bonitz.

that matter is not separable from the contraries but its being 1 is different, and that a single matter may serve for 35 colour and heat and cold.

The same matter also serves for both a large and a small body. This is evident ; for when air is produced from water, the same matter has become something different, not by acquiring an addition to it, but has become actually what it was potentially, and, again, water is produced from air in the same way, the change being sometimes from 30 smallness to greatness, and sometimes from greatness to smallness. Similarly, therefore, if air which is large in extent comes to have a smaller volume, or becomes greater from being smaller, 'it is the matter which is potentially both that comes to be 2 each of the two.

For as the same matter becomes hot from being cold, and cold from being hot, because it was potentially both, so too from hot it can become more hot, though nothing in 2i7 b the matter has become hot that was not hot when the thing was less hot ; just as, if the arc or curve of a greater circle becomes that of a smaller, whether it remains the same or becomes a different curve, convexity has not come to exist in anything that was not convex but straight (for 5 differences of degree do not depend on an intermission of the quality) ; nor can we get any portion of a flame, in which both heat and whiteness are not present. So too, then, is the earlier heat related to the later . 3 So that the greatness and smallness, also, of the sensible volume are extended, not by the matter's acquiring anything new, but because the matter is potentially matter 4 for both states ; so that the same thing is dense and rare, and the two 10 qualities have one matter.

The dense is heavy, and the rare is light. [Again, as the arc of a circle when contracted into a smaller space does not acquire a new part which is convex, but what was there has been contracted ; and as any part of fire that one takes will be hot ; so, too, it is all a question of contraction and 15

8 Reading in 1, 8 npos rrjp v<rr<pov (so perhaps Simp.).

4 Omitting q in 1. 10, with E.

2I7 b expansion 1 of the same matter. 2 ] There are two types in each case, both in the dense and in the rare ; for both the heavy and the hard are thought to be dense, and contrariwise both the light and the soft are rare ; and weight and hardness fail to coincide in the case of lead and iron.

20 From what has been said it is evident, then, that void does not exist either separate (either absolutely separate or as a separate element in the rare) or potentially, unless one is willing to call the condition of movement void, whatever it may be. At that rate the matter of the heavy and the light, qua matter of them, would be the void ; for the dense and the rare are productive of locomotion in virtue of 3 5 this contrariety, and in virtue of their hardness and softness productive of passivity and impassivity, i. e. not of locomotion but rather of qualitative change.

So much, then, for the discussion of the void, and of the sense in which it exists and the sense in which it does not exist.

Next for discussion after the subjects mentioned is Time, io 30 The best plan will be to begin by working out the difficulties connected with it, making use of the current arguments. First, does it belong to the class of things that exist or to that of things that do not exist ? Then secondly, what is its nature? To start, then: the following considerations would make one suspect that it either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and ai8 a is not yet. Yet time — both infinite time and any time you like to take — is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality.

Further, if a divisible thing is to exist, it is necessary that, when it exists, all or some of its parts must exist.

5 But of time some parts have been, while others have to be, and no part of it is, though it is divisible. For what is

* The words in brackets appear to be an alternative version of 11, 2-1 1 ; they are not in place here.

ai8*

‘now’ is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of * nows \

Again, the ‘now' which seems to bound the past and the future— does it always remain one and the same or is it always other and other? It is hard to say. 10

(i) If it is always different and different, and if none of the parts in time which are other and other are simultaneous (unless the one contains and the other is contained, as the shorter time is by the longer), and if the ‘now 1 which is not, but formerly was, must have ceased-to-be at some time, the 'nows' too cannot be simultaneous with 15 one another, but the prior ‘ now ' must always have ceasedto-be. But the prior ‘ now ' cannot have ceased-to-be in 1 itself (since it then existed) ; yet it cannot have ceased-tobe in another ‘ now ’. For we may lay it down that one ‘ now ' cannot be next to another, any more than point to point. 2 If then it did not cease-to-be in the next ‘now’ but in another, it would exist simultaneously with the 20 innumerable ‘nows 'between the two 3 — which is impossible.

Yes, but (a) neither is it possible for the * now ’ to remain always the same. No determinate divisible thing has a single termination, whether it is continuously extended in one or in more than one dimension: but the ‘now' is a termination, and it is possible to cut off a determinate time. Further, if coincidence in time (i. e. being neither 25 prior nor posterior) means to be ‘in one and the same “ now ” ', 4 then, if both what is before and what is after are in this same 4 now ’, things which happened ten thousand years ago would be simultaneous with what has happened to-day, and nothing would be before or after anything else.

This may serve as a statement of the difficulties about 3 <> the attributes of time.

1 The argument would be clearer if we could say ‘ during * itself*"

If the existent perished ‘ in * itself, it would never exist without perishing.

8 Omitting roh vvv in 1. 21, as Phil, apparently does.

PHY.SICA ai8 a

As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through.

Some assert that it is (i) the movement of the whole, 2i8 b others that it is (2) the sphere itself. 1

(1) Yet part, too, of the revolution is a time, but it certainly is not a revolution : for what is taken is part of a revolution, not a revolution. Besides, if there were more heavens than one, the movement of any of them equally would be time, so that there would be many times at the same time.

5 (2) Those who said that time is the sphere of the whole thought so, no doubt, on the ground that all things are in time and all things are in the sphere of the whole. The view is too naive for it to be worth while to consider the impossibilities implied in it.

But as time is most usually supposed to be (3) motion and a kind of change, we must consider this view.

10 Now (a) the change or movement of each thing is only in the thing which changes or where the thing itself which moves or changes may chance to be. But time is present equally everywhere and with all things.

Again, ( b ) change is always faster or slower, whereas 15 time is not: for ‘fast* and ‘slow ' are defined by time —

‘ fast * is what moves much in a short time, ‘ slow ' what moves little in a long time ; but time is not defined by time, by being either a certain amount or a certain kind of it.

Clearly then it is not movement. (We need not dis- 2otinguish at present between ‘movement’ and ‘ change

But neither does time exist without change ; for when H the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed, any more than those who are fabled to sleep 2 5 among the heroes in Sardinia 2 do when they are awakened ; for they connect the earlier ‘now ’ with the later and make

1 Aristotle is probably referring to Plato and the Pythagoreans respectively. Cf. Diels, Vors . 3 i. 355. 6.

2 For the fable cf. Rohde, Rhein . Mus. xxxv. 1 57 flf.

them one* cutting out the interval because of their failure to notice it. So, just as, if the 1 now 1 were not different but one and the same, there would not have been time, so too when its difference escapes our notice the interval does not seem to be time. If, then, the non-realization of the existence of time happens to us when we do not distinguish 30 any change, but the soul seems to stay in one indivisible state, and when we perceive and distinguish we say time has elapsed, evidently time is* not independent of movement and change. It is evident, then, that time is neither 219 movement nor independent of movement.

We must take this as our starting-point and try to discover — since we wish to know what time is — what exactly it has to do with movement.

Now we perceive movement and time together : for even when it is dark and we are net being affected through the body, if any movement takes place in the 5 mind we at once suppose that some time also has elapsed ; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other.

But what is moved 1 is moved from something to something, and all magnitude is continuous. Therefore the movement goes with the magnitude. Because the magnitude is continuous, the movement too must be continuous, and if the movement, then the time ; for the time that has passed is always thought to be in proportion to the movement.

The distinction of * before * and ‘ after * holds primarily, then, 2 in place ; and there in virtue of relative position. Since then ‘ before 1 and * after * hold in magnitude, they must hold also in movement, these corresponding to those. But also in time the distinction of * before * and ‘ after J must hold, for time and movement always correspond with each other. The * before ' and ‘ after ' 3 in motion identical in

1 Kiurjcrts here must be restricted to that Kara rbv tSttov.

2 Omitting de in 1 . 14, with EH Them. Al.

8 Omitting avra>u in 1. 20, with H Them. Phil. Simp.

ao substratum with motion yet differs from it in definition, and is not identical with motion.

But we apprehend time only when we have marked motion, marking it by 1 * before ’ and * after ’ ; and it is only when we have perceived ‘ before 9 and ‘ after ’ in motion that 35 we say that time has elapsed. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the * nows ’ are two, one before and one after, it is then that we say that there is time, and this that*we say is time. For what is bounded by the 1 now ’ is thought to be time — we may assume this.

30 When, therefore, we perceive the ‘ now ’ as one, and neither as before and after in a motion nor as an identity but in relation to a 4 * before 1 and an ‘ after \ no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do perceive a ‘ before * 2i9 b and an * after ', then we say that there is time. For time is just this — number of motion in respect of ‘before' and * after \

Hence time is not movement, but only movement in so far as it admits of enumeration. A proof of this: we discriminate the more or the less by number, but more or less movement by time. Time then is a kind of number. 5 (Number, we must note, is used in two senses — both of what is counted or the countable and also of that with which we count. Time obviously 2 is what is counted, not that with which we count: these are different kinds of thing.)

Just as motion is a perpetual succession, so also is time. 10 But every simultaneous time is self-identical ; for the ‘ now * as a subject is an identity, but it accepts different attributes. 3

* E. g. if you come in when I go out, the time of your coming in is in fact the time of my going out, though for it to be the one and to be the other are different things.

ai9 b

The ‘now' measures time, in so far as time involves the * before and after’.

The ‘ now * in one sense is the same, in another it is not the same. In so far as it is in succession, it is different (which is just what its being now 1 was supposed to mean), but its substratum 2 is an identity : for motion, as was said, 5 * *5 goes with magnitude , 4 and time, as we maintain, with motion. Similarly, then, there corresponds to the point 6 the body which is carried along, and by which we are aware of the motion and of the ‘ before and after ’ involved in it. This is an identical substratum (whether a point or a stone or something else of the kind), but it has different attributes — as the sophists assume that Coriscus’ being in ao the Lyceum is a different thing from Coriscus’ being in the market-place . 6 And the body which is carried along is different, in so far as it is at one time here and at another there. But the ‘now’ corresponds to the body that is carried along, as time corresponds to the motion. For it is by means of the body that is carried along that we become aware of the ‘ before and after ’ in the motion, and 35 if we regard these as countable we get the ‘ now ’. Hence in these also the ‘ now ’ as substratum 7 remains the same (for it is what is before 8 and after in movement), but what is predicated of it is different ; for it is in so far as the ‘ before and after ’ is numerable that we get the 4 now ’. This is what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is carried. For what is carried is a real thing, 30 the movement is not. Thus what is called 4 now ’ in one sense is always the same ; in another it is not the same : for this is true also of what is carried.

Clearly, too, if there were no time, there would be no 4 now and vice versa. Just as the moving body and its loco- aao*

1 Reading in 1 . 14 to vvp uvai , with Phil, and Bonitz.

2 Reading B Bt 1 ror«, with H and Simp. s Ml.

4 i. e. with the path traversed. 8 i. e. in the path.

8 sc. to prove that Coriscus is different from himself. I.e.j they assume that a difference in the attribute means a difference m the substratum.

* Reading rb npbrtpop in 1 . 26, with EH I Phil.

motion involve each other mutually, so too do the number of the moving body and the number of its locomotion. For the number of the locomotion is time, while the ‘ now ’ corresponds to the moving body, and is like the unit of number.

Time, then, also is both made continuous by the ‘ now ' 5 and divided at it. For here too there is a correspondence with the locomotion and the moving body. For the motion or locomotion is made one by the thing which is moved, because it is one — not because it is one in its own nature (for there might be pauses in the movement of such a thing) — but because it is one in definition 1 : for this determines the movement as 4 before’ and 'after*. Here, too, there is a correio spondence with the point ; for the point also both connects and terminates the length — it is the beginning of one and the end of another. But when you take it in this way, using the one point as two, a pause is necessary, if the same point is to be the beginning and the end. The ‘ now ’ on the other hand, since the body carried is moving, is always different.

Hence time is not number in the sense in which there is ‘ number ’ of the same point because it is beginning and end, 15 but rather as the extremities of a line 2 form a number, and not as the parts of the line do so, both for the reason given (for we can use the middle point as two, so that on that analogy time might stand still), and further because obviously the 'now* is no * part of time nor the section any part of the movement, any more than the points are parts 20 of the line — for it is two lines that are parts of one line.

In so far then as the 4 now ' is a boundary, it is not time, but an attribute of it ; in so far as it numbers, it is number; for boundaries belong only to that which they bound, but number (e. g. ten) is the number of these 4 horses, and belongs also elsewhere.

It is clear, then, that time is ‘ number of movement in 25 respect of the before and after and is continuous since it is an attribute of what is continuous.

1 i. e. as moved .

* Reading in I. 16 rrjr ypa^rjs paWov, with Phil. Simp.

Reading ohbiv in 1. 19, with EG Al. Asp. Simp.

* Reading apiBfxbs rwfc in 1 . 23, with E Phil. Simp.

aao tt

12 The smallest number, in the strict sense of the word 1 number is two . 1 But of number as concrete, sometimes there is a minimum, sometimes not: e. g. of a ‘line’, the smallest in respect of multiplicity is two (or, if you like, one), but in respect of size there is no minimum ; for every line 3° is divided ad infinitum. Hence it is so with time. In respect of number the minimum is one (or two) ; in point of extent there is no minimum.

It is clear, too, that time is not described as fast or slow, but as many or few 2 and as long or short. For as continuous aao b it is long or short and as a number many or few, but it is not fast or slow — any more than any number with which we number is fast or slow.

Further, there is the same time everywhere at once, but 5 not the same time before and after, for while the present change is one, the change which has happened and that which will happen are different. Time is not number with which we count, but the number of things which are counted, and this according as it occurs before or after is always different, for the ‘ nows ’ are different. And the 10 number of a hundred horses and a hundred men is the same, but the things numbered are different — the horses from the men. Further, as a movement can be one and the same again and again, so too can time, e. g. a year or a spring or an autumn.

Not only do we measure the movement by the time, but *5 also the time by the movement, because they define each other. The time marks the movement, since it is its number, and the movement the time. We describe the time as much or little, measuring it by the movement, just as we know the number by what is numbered, e. g. the number of the horses by one horse as the unit. For we 20 know how many horses there are by the use of the number ; and again by using the one horse as unit we know the number of the horses itself. So it is with the time and the movement ; for we measure the movement by the time and vice versa. It is natural that this should happen ;

3 e. g. * many years \

35 for the movement goes with the distance and the time with the movement, because they are quanta and continuous and divisible. The movement has these attributes because the distance is of this nature, and the time has them because of the movement. And we measure both the distance by the movement and the movement by the distance ; for we say that the road is long, if the journey 30 is long, and that this is long, if the road is long — the time, too, if the movement, and the movement, if the time. aai a Time is a measure of motion and of being moved, and it measures the motion by determining a motion which will measure exactly the whole motion, as the cubit does the length by determining 1 an amount which will measure out the whole. Further ‘to be in time' means, for movement, that both it and its essence are measured by time 5 (for simultaneously it measures both the movement and its essence, and this is what being in time means for it, that its essence should be measured).

Clearly then 2 ‘to be in time’ has the same meaning for other things also, namely, that their being should be measured by time. ‘ To be in time* is one of. two things : lo (x) to exist when time exists, (2) as we say of some things that they are 1 in number \ The latter means either what is a part or mode of number — in general, something which belongs to number — or that things have a number.

Now, since time is number, the * now ’ and the * before' 15 and the like are in time, just as ‘ unit ’ and c odd ' and ‘ even ' are in number, i. e. in the sense that the one set belongs to number, the other to time. But things are in time as they are in number. If this is so, they are contained by time as things in place are contained by place.

Plainly, too, to be in time does not mean to coexist with 30 time, any more than to be in motion or in place means to coexist with motion or place. For if ‘ to be in something ' is to mean this, then all things will be in anything, and the heaven will be in a grain ; for when the grain is, then also is the heaven. But this is a merely incidental conjunction,

* Reading in 11. 5-7 (Sput . . • own), brjkov on, with Al. Simp.

whereas the other is necessarily involved : that which is in time necessarily involves that there is time when it is, and 25 that which is in motion that there is motion when it is.

Since what is * in time ' is so in the same sense as what is in number is so, a time greater than everything in time can be found. So it is necessary that all the things in time should be contained by time, just like other things also which are ‘ in anything \ e. g. the things * in place * by place.

A thing, then, will be affected by time, just as we are 3 ° accustomed to say that time wastes things away, and that all things grow old through time, and that there is oblivion owing to the lapse of time, but we do not say the same of getting to know or of becoming young or fair. For time aai b is by its nature the cause rather of decay, since it is the number of change, and change removes what is.

Hence, plainly, things which are always are not, as such, in time, for they are not contained by time, nor is their being measured by time. A proof of this is that none of 5 them is affected by time, which indicates that they are not in time.

Since time is the measure of motion, it will be the measure of rest too — indirectly. For all rest i$ in time.

For it does not follow that what is in time is moved, though what is in motion is necessarily moved. For time is not motion, but ‘ number of motion ’ : and what is at rest, also, can be in the number of motion. Not everything that is not in motion can be said to be * at rest '--but only that which can be moved, though it actually is not moved, as was said above . 1

‘ To be in number ’ means that there is a number of the thing, and that its being is measured by the number in 15 which it is. Hence if a thing is *«n time' it will be measured by time. But time will measure what is moved and what is at rest, the one qua moved, the other qua at rest; for it will measure their motion and rest respectively.

Hence what is moved will not be measurable by the time simply in so far as it has quantity, but in so far as

3o its motion has quantity. Thus none of the things which are neither moved nor at rest are in time : for 4 to be in time * is ‘to be measured by time', while time is the measure of motion and rest.

Plainly, then, neither will everything that does not exist be in time, i. e. those non-existent things that cannot exist, as the diagonal cannot be commensurate with the side.

3 5 Generally, if time is directly the measure of motion and indirectly of other things, it is clear that a thing whose existence is measured by it will have its existence in rest or motion. Those things therefore which are subject to perishing and becoming — generally, those which at one time exist,

30 at another do not — are necessarily in time: for there is a greater time which will extend both beyond their existence and beyond the time which measures their existence.

Of things which do not exist but are contained by time 222 a some were, e. g. Homer once was, some will be, e.g. a future event ; this depends on the direction in which time contains them ; if on both, they have both modes of existence. 1 As to such things as it does not contain in any way, they neither were nor are nor will be. These are those non-existents whose opposites always are, as the 5 incommensurability of the diagonal always is — and this will not be in time. Nor will the commensurability, therefore ; hence this eternally is not, because it is contrary to what eternally is. A thing whose contraiy is not eternal can be and not be, and it is of such things that there is coming to be and passing away.

10 The ‘ now 1 is the link of time, as has been said 2 (for it 13 connects past and future time), and it is a limit 3 of time (for it is the beginning of the one and the end of the other). But this is not obvious as it is with the point, which is fixed. It divides potentially, and in so far as it is dividing 15 the ‘now 1 is always different, but in so far as it connects it is always the same, as it is with mathematical lines.

1 Putting a comma after apforcpa in 1 . 2.

8 Omitting oXeor in I. 11, with F. and Simp.

For the intellect it is not always one and the same point, since it is other and other 1 when one divides the line ; but in so far as it is one, it is the same in every respect.

So the ‘now’ also is in one way a potential dividing of time, in another the termination of both parts, and their unity.

And the dividing and the uniting are the same thing and in the same reference, but in essence they are not the same.

So 2 one kind of ‘ now ’ is described in this way : another 20 is when the time is near this kind of ‘now*. 4 He will come now’ because he will come to-day; ‘he has come now ’ because he came to-day. But the things in the Iliad have not happened 1 now nor is 3 the flood ‘ now ’ — not that the time 4 from now to them is not continuous, but because they are not near.

‘At some time' means a time determined in relation to the first of the two types of ‘now’, 5 e.g. ‘at some time’ 25 Troy was taken, and ‘ at some time ’ there will be a flood ; for it must be determined with reference to the ‘ now ’. There will thus be a determinate time from this ‘ now ’ to that, 6 and there was such in reference to the past event.

But if there be no time which is not ‘sometime', every time will be determined.

Will time then fail ? Surely not, if motion always exists.

Is time then always different or does the same time recur? 30 Clearly time is, in the same way as motion is. For if one and the same motion sometimes recurs, it will be one and the same time, and if not, not.

Since the ‘ now ’ is an end and a beginning of time, not 222 b of the same time however, but the end of that which is past and the beginning of that which is to come, it follows that, as the circle has its convexity and its concavity, in a sense, in the same thing, so time is always at a beginning and at an end. And for this reason it seems to be always different ; for the 4 now ’ is not the beginning and the end 5 of the same thing ; if it were, it would be at the same time

1 Reading in 1. 17 aWrj Kai aWrj, with F Them. Phil.

2 Reading in 1. 20 pivovv ovra> : with GHI Them. Simp.

8 Omitting ytyov « in 1. 23, with Them.

8 Cf. 11. 20 f. • Omitting Kai before tk in 1. 28, with GH Phil.

aaa b and in the same respect two opposites . 1 And time will not fail ; for it is always at a beginning.

‘Presently* or ‘just* refers to the part of future time 10 which is near the indivisible present ‘now* (‘ When do you walk ? * * Presently*, because the time in which he is going to do so is near), and to the part of past time which is not far from the ‘now* (‘When do you walk?* ‘I have just been walking*). But to say that Troy has just been taken — we do not say that, because it is too far from the 1 now *. ‘ Lately too, refers to the part of past time which is near 2 the present ‘now*. ‘When did you go?* ‘Lately*, if the time is near the existing now. ‘ Long ago * refers to the distant past.

15 ‘Suddenly* refers to what has departed from its former condition in a time imperceptible because of its smallness ; but it is the nature of all change to alter things from their former condition. In time all things come into being and pass away ; for which reason some called it the wisest of all things, but the Pythagorean Paron 3 called it the most stupid, because in it we also forget ; and his was the truer view. It is clear then that it must be in itself, as we said 30 before, 4 the condition of destruction rather than of coming into being (for change, in itself, makes things depart from their former condition), and only incidentally of coming into being, and of being. A sufficient evidence of this is that nothing comes into being without itself moving somehow and acting, but a thing can be destroyed even if it does not move at all. And this is what, as a rule, we chiefly 35 mean by a thing *s being destroyed by time. Still, time does not work even this change ; even this sort of change takes place incidentally in time.

We: have stated, then, that time exists and what it is, and in how many senses we speak of the * now *, and what ‘ at some time * f ‘ lately *, ‘ presently * or 1 just *, ‘ long ago *, and * suddenly * mean.

1 Putting a full stop after uj \ in 1 . 6, with Bonitz.

8 Nothing further is known of Paron. 4 22i b 1.

BOOK IV. 14 aaa b

14. These distinctions having been drawn, 1 it is evident that 3° every change and everything that moves is in time ; for the distinction of faster and slower exists in reference to all change, since it is found in every instance. In the phrase 1 moving faster' I refer to that which changes before another into the condition in question, when it moves over 223* the same interval and with a regular movement; e.g. in the case of locomotion, if both things move along the circumference of a circle, or both along a straight line ; and similarly in all other cases. But what is before is in time ; for we say 1 before * and ‘ after ' with reference to the 5 distance from the 1 now and the ‘ now ' is the boundary of the past and the future ; so that since ‘ nows ' are in time, the before and the after will be in time too ; for in that in which the 'now' is, the distance from the 'now' will also be. But ‘ before ' is used contrariwise with reference to past and to future time ; for in the past we call ‘ before ' 10 what is farther from the * now and * after' what is nearer, but in the future we call the nearer 1 before ' and the farther ‘ after \ So that since the ‘ before ' is in time, and every movement involves a ‘ before evidently every change and 15 every movement is in time.

It is also worth considering how time can be related to the soul ; and why time is thought to be in everything, both in earth and in sea and in heaven. Is it because it is an attribute, or state, of movement (since it is the number of movement) 2 and all these things are movable (for they are all in place), and time and movement are together, both *o in respect of potentiality and in respect of actuality ?

Whether if soul did not exist time would exist or not, is a question that, may fairly be asked ; for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can be, counted.

But if nothing but soul, or in soul reason, is qualified to 25 count, there would not be time unless there were soul, but

#40. IH only that of which time is an attribute, i.e. if movement can exist without soul, and the before and after are attributes of movement, and time is these qua numerable.

One might also raise the question what sort of movement 30 time is the number of. Must we not say 4 of any kind’? For things both come into being in time and pass away, and grow, and are altered in time, and are moved locally ; thus it is of each movement qua movement that time is the number. And so it is simply the number of continuous movement, not of any particular kind of it.

223 b But other things as well may have been moved now, and there would be a number of each of the two movements. Is there another time, then, and will there be two equal times at once ? Surely not. For a time that is both equal and simultaneous is one and the same time, 1 and even those that are not simultaneous are one in kind ; for 5 if there were dogs, and horses, and seven of each, it would be the same number. So, too, movements that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration ; still the time of the two changes is the same if their number also is equal and simultaneous ; 10 and for this reason, while the movements are different and separate, the time is everywhere the same, because the number of equal and simultaneous movements is everywhere one and the same.

Now there is such a thing as locomotion, and in locomotion there is included circular movement, and everything is measured by some one thing homogeneous with it, units by a unit, horses by a horse, and similarly 15 times by some definite time, and, as we said, 2 time is measured by motion as well as motion by time (this being so because by a motion definite in time the quantity both of the motion and of the time is measured) ; 3 if, then, what

f Placing a comma after topurpdvy in 1 . 15 and a semicolon before tl in 1. 18, and treating roOro . . . xpovou in 11 . 16-18 as parenthetical, with Bonitz.

is first is the measure of everything homogeneous with it, regular circular motion is above all else the measure, because the number of this is the best known. Now neither 20 alteration nor increase nor coming into being can be regular, but locomotion can be. This also is why time is thought to be the movement of the sphere, viz. because the other movements are measured by this, and time by this movement.

This also explains the common saying that human affairs form a circle, and that there is a circle in all other things 25 that have a natural movement and coming into being and passing away. This is because all other things are discriminated by time, and end and begin as though conforming to a cycle ; for even time itself is thought to be a circle.

And this opinion again is held because time is the measure 30 of this kind of locomotion and is itself measured by such. So that to say that the things that come into being form a circle is to say that there is a circle of time ; and this is to say that it is measured by the circular movement ; for apart from the measure nothing else to be measured is observed; the whole is just a plurality of 224* measures.

It is said rightly, too, that the number of the sheep and of the dogs is the same number if the two numbers are equal, but not the same decad or the same ten ; just as the equilateral and the scalene are not the same triangle , yet they 5 are the same figure , because they are both triangles. For things are called the same so-and-so if they do not differ by a differentia of that thing, but not if they do; e. g. triangle differs from triangle by a differentia of triangle, 1 therefore they are different triangles ; but they do not differ by a differentia of figure, but are in one and the same division of it. For a figure of one kind is a circle and a figure of another kind a triangle, and a triangle of 10 one kind is equilateral and a triangle of another kind scalene. They are the same figure, then, and that, triangle,

1 Reading in 1 . 7 rplyuvop rpiywov rptywvov , with Torstrik and perhaps with Simplicius.

but not the same triangle . 1 Therefore the number of two groups also is the same number 2 (for their number does not differ by a differentia of number), but it is not the same decad ; for the things of which it is asserted differ ; one group are dogs, and the other horses.

15 We have now discussed time — both time itself and the matters appropriate to the consideration of it.

I Everything 1 which changes does so in one of three a»4* senses. It may change (i) accidentally, as for instance when we say that something musical walks, that which walks being something in which aptitude for music is an accident. Again (3) a thing is said without qualification to change because something belonging to it changes, i. e. in statements which refer to part of the thing in question : thus the body 25 is restored to health because the eye or the chest, that is to say a part of the whole body, is restored to health.

And above all there is (3) the case of a thing which is in motion neither accidentally nor in respect of something else belonging to it, but in virtue of being itself directly in motion. Here we have a thing which is essentially movable : and that which is so is a different thing according to the particular variety of motion : for instance it may be a thing capable of alteration : and within the sphere of alteration it is again a different thing according as it is capable of being restored to health or capable of being heated. And 30 there aie the same distinctions in the case of the mover:

(x) one thing causes motion accidentally, (a) another partially (because something belonging to it causes motion),

(3) another of itself directly, as, for instance, the physician heals, the hand strikes. We have, then, 2 the following factors: (a) on the one hand that which directly causes motion, and (b) on the other hand that which is in motion : further, we have (c) that in which motion takes place, 35 namely time, and (distinct from these three) (d) that from which and (e) that to which it proceeds : for every motion a#4 b proceeds from something and to something, that which is directly in motion being distinct from that to which it is in motion and that from which it is in motion : for instance,

1 With 1. ai- b i cf. Met. 1-9.

we may take the three things ‘ wood 4 hot \ and 4 cold \ of which the first is that which is in motion, the second is that to which the motion proceeds, and the third is that from which it proceeds. This being so, it is clear that the motion is in 5 the wood, not in its form : for the motion is neither caused nor experienced by the form or the place or the quantity. So we are left with a mover, a moved, and a goal of motion. I do not include the starting-point of motion : for it is the goal rather than the starting-point of motion that gives its name to a particular process of change. Thus * perishing * is change to not-being , though it is also true that that which perishes changes from being : and ‘becoming' is change to being , though it is also change from not -being. io Now a definition of motion has been given above, 3 from 2 which it will be seen that every goal of motion, whether it be a form, an affection, or a place, is immovable, as, for instance, knowledge and heat. Here, however, a difficulty may be raised. Affections, it may be said, are motions, and whiteness is an affection : thus there may be change to j 5 a motion. 3 To this we may reply that it is not whiteness but whitening that is a motion. Here also the same distinctions are to be observed : a goal of motion may be so accidentally, or partially and with reference to something other than itself, or directly and with no reference to anything else : 4 for instance, a thing which is becoming white changes accidentally to an object of thought, the colour 2 o being only accidentally the object of thought ; it changes to colour, 5 because white is a part of colour, or to Europe, because Athens is a part of Europe ; but it changes essentially to white colour. It is now clear in what sense a thing is in motion essentially, accidentally, or in respect of something other than itself, and in what sense the phrase

1 201* io.

3 i.e. there may be motion not only in to kivov^vov but also in

TO tlf t KlVtlTlll.

4 Omitting in 1 . 17 to before both nar <?XXo and pfj mt «\Xo, which are intended merely to amplify Kara pipos and npurm respectively : there are only three distinct senses, as may be seen from the opening words of the book.

6 Here mra pipes must be supplied in sense, if not in the text.

1 itself directly ’ is used 1 in the case both of the mover and of the moved : and it is also clear that the motion is notin a 5 the form but in that which is in motion, that is to say ‘ the movable in activity’. Now accidental change we may leave out of account : for it is to be found in everything, at any time, and in any respect. Change 2 which is not accidental on the other hand is not to be found in everything, but only in contraries, in things intermediate between contraries, and in contradictories, as may be proved by indue- 30 tion. An intermediate may be a starting-point of change, since for the purposes of the change it serves as contrary to either of two contraries : for the intermediate is in a sense the extremes. Hence we speak of the intermediate as in a sense a contrary relatively to the extremes and of either extreme as a contrary relatively to the intermediate : for instance, the central note is low relatively to the highest and high relatively to the lowest, and grey is light relatively to black and dark relatively to white . 3

And since every change is from something to something 35 — as the word itself (ptra/ 3 oA/j) indicates, implying some- 225* thing ‘after’ (pera) something else, that is to say something earlier and something later — that which changes must change in one of four ways : from 4 subject to subject, from subject to non-subject, from non-subject to subject, 5 or from non-subject to non-subject, where by ‘subject’

I mean what is affirmatively expressed. So it follows necessarily from what has been said above 5 that there are

1 It seems possible to keep (with Bekker) the words Ka\ 7ra>r to airro npwrov, regarding avro npurov as a phrase quoted from above. Argyropylus, however, renders ‘ et quomodo idem primum sit which seems pointless. Others regard the words as a mere repetition of the preceding irm k a3' avrb kmitcu — though in order to do so they have to emend to to r<p — and therefore bracket them as an interpolation.

8 It seems necessary to use four terms in English, though two are sufficient in Greek, since both ptXav and \cvk6v are more elastic in meaning than the English ‘black’ and ‘white’, which, however, must be used here to translate to pt\av and to Xev* 6v } the two extremes.

8 224 b 28, 29. Or (k T&v tiprjfitv ov might mean ‘ of the four conceivable kinds of change just mentioned ’ : but Aristotelian usage seems in favour of the rendering adopted in the text, which gives just as good sense.

only three kinds of change, that from subject to subject, that from subject to non-subject, and that from non-subject to io subject : for the fourth conceivable kind, that from nonsubject to non-subject, is not change, as in that case there is no opposition either of contraries or of contradictories.

Now change from non-subject to subject, the relation being that of contradiction, is ‘ coming to be * — 1 unqualified coming to be * when the change takes place in an unqualified way, c particular coming to be ' when the change is change in a particular character : for instance, a change from notwhite to white is a coming to be of the particular thing, white, 15 while change from unqualified not-being to being is coming to be in an unqualified way, in respect of which we say that a thing ‘ comes to be * without qualification, not that it * comes to be * some particular thing. Change from subject to non-subject is 1 perishing' — * unqualified perishing * when the change is from being to not-being, ‘ particular perishing ' when the change is to the opposite negation, the distinction being the same as that made in the case of coming to be.

30 Now 1 the expression 1 not-being' is used in several senses : and there can be motion neither of that which ‘ is not ' in respect of the affirmation or negation of a predicate, 2 * nor of that which ‘ is not ’ in the sense that it only potentially : is ’, that is to say the opposite of that which actually ‘ is ' in an unqualified sense : for although that which is ‘ not-white ' or * not-good 9 may nevertheless be in motion accidentally (for example that which is * not-white ' might be a man), yet that which is without qualification 4 * not-so-and-so ’ cannot in any sense 25 be in motion : therefore it is impossible for that which is not to be in motion. This being so, it follows that ‘becoming ' cannot be a motion : for it is that which ‘ is not ' that ‘ becomes For however true it may be that it accidentally

1 The following sentences are very loosely joined together, but the sequence of thought is fairly clear. The apodosis to the «t-clause must be found in the words a 6 v varov r 6 prj tv kivuo&cu, 1. 25, where yap must be omitted, with Themistius and with some MSS. in Met. 1067*30.

2 Lit. ‘in respect of conjunction or separation * : i.e. in false judged ments, which ‘join together' things which ought not to be joined together, e.g. ‘man has wings or ‘separate ’ things which ought not to be separated, e. g. 1 man has not arms \

BOOK V. i M 5 a

* becomes 7 it is nevertheless correct to say that it is that which 4 is not ’ that in an unqualified sense ( becomes '. And similarly it is impossible for that which * is not ' to be at rest.

There are these difficulties, then, in the way of the 3° assumption that that which ‘ is not * can be in motion : and it may be further objected that, whereas everything which is in motion is in space, that which 4 is not ' is not in space : for then it would be somewhere .

So, too, * perishing ' is not a motion : for a motion has for its contrary either another motion or rest, whereas ‘ perishing * is the contrary of 4 becoming \

Since, then, every motion is a kind of change, and there are only the three kinds of change mentioned above ; 2 and 35 since of these three those which take the form of 4 becoming' and ‘perishing', that is to say those which imply a aa 5 b relation of contradiction, are not motions : it necessarily follows that only change from subject to subject is motion.

And every such subject is either a contrary or an intermediate (for 3 a privation may be allowed to rank as a contrary) and can be affirmatively expressed, as naked, toothless, 4 or black. If, then, the categories are severally 5 distinguished as Being, Quality, Place, Time, Relation, Quantity, and Activity or Passivity, it necessarily follows that there are three kinds of motion — qualitative, quantitative, and local.

a In respect of Substance there is no motion, because Sub- io stance has no contrary among things that are. Nor is there motion in respect of Relation : 6 for it may happen that when one correlative changes, the other, although this does not itself change, is no longer® applicable, so that in these cases the motion is accidental. Nor is there motion

1 i. e. 4 that it is something in which to pq By is an accident that becomes, and not rd pq By itself 1 . * 1. 7.

8 The connexion of thought is : * the fact that there are motions fK crreprjartM r or «!$ <r rcprpnv does not affect the validity of the assertion that the \moK*ip(va 01 motion are q cmvrin q p*ra£v : for a crrtpqcnt which is a viroKuptvov of motion (sc. of niyqais as distinct from y tvt<m) is after all in a sense tvavrtov and (like other tVama) dqXovrai Karaffmcrt 1/

• Reading in 1 . 11 rov npfc n, with the MS. A b in Met 1068* II.

as5 b in respect of Agent and Patient — in fact there can never be motion of mover and moved, because there cannot be 15 motion of motion or becoming of becoming or in general change of change.

For in the first place there are two senses in which motion of motion is conceivable. (1) The motion of which there is motion might be conceived as subject ; e. g. a man is in motion because he changes from fair to dark. Can it be that in this sense motion grows hot or cold, or changes place, or increases or decreases ? Impossible : for change is not a subject. Or ( 2 ) can there be motion of motion in the sense that some other subject changes from a change to another mode of being, as e. g. a man changes from falling ill to getting well ? Even this is possible only in an accidental sense. For, whatever the subject may be , 1 movement is change from one form to another. (And the same holds 2 5 good of becoming and perishing, except that in these processes we have a change to a particular 2 kind of opposite, while the other, motion, is a change to a different 3 kind .) 4 So, if there is to be motion of motion, that which is changing from health to sickness must simultaneously be changing from this very change to another. It is clear, then , 5 that by the time that it has become sick, it must also have changed to whatever may be the other change concerned (for that it should be at rest, though logically possible, is excluded by the theory). Moreover this other can never be any casual change, but must be a change from some- 30 thing definite to some other definite thing. So in this case it must be the opposite change, viz. convalescence. It is only accidentally that there can be change of change, e. g. there is a change from remembering to forgetting only because the subject of this change changes at one time to knowledge, at another to ignorance . 6 *

1 Reading in l. 23 Hrracri for avrrj , with MS. A b in Met. io68 a 23.

2 sc. a contradictory. 8 sc. a contrary.

Simplicius and with the MS. A b in Met . 1068*25.

6 Reading in I. 28 dq, with E H I.

6 Reading in 1 . 33 ayvotav, with (apparently) Philoponus and

Simplicius.

In the second place, if there is to be change of change and becoming of becoming, we shall have an infinite regress. Thus if one of a series of changes is to be a change 35 of change, the preceding change must also be so : e. g. if 2a6 a simple becoming was ever in process of becoming, then that which was becoming simple becoming was also in process of becoming, so that we should not yet have arrived at what was in process of simple becoming but only at what was already in process of becoming in process of becoming. 1 And this again was sometime in process of becoming, so that even then we should not have arrived at what was in process of simple becoming. And since in an infinite series there is no first term, here there will be no first stage and therefore no following stage either. On this hypo- 5 thesis, then, nothing can become or be moved or change.

Thirdly, if a thing is capable of any particular motion, it is also capable of the corresponding contrary motion or the corresponding coming to rest, and a thing that is capable of becoming is also capable of perishing: consequently, if there be becoming of becoming, that which is in process of becoming is in process of perishing at the very moment when it has 2 reached the stage of becoming: since it cannot be in process of perishing when it is just beginning to become or after it has ceased to become : for that which is in process of perishing must be in existence.

Fourthly, there must be a substrate underlying all pro- »o cesses of becoming and changing. What can this be in the present case? It is either the body or the soul that undergoes alteration : what 3 is it that correspondingly becomes motion or becoming ? And again what 4 is the goal of their motion ? It must be the motion or becoming of something from something to something else . 6 But in what sense can this be so ? For the becoming of learning cannot be 15 learning: so neither can the becoming of becoming be

2 Reading in 1. 8 ycvijrat, with EF.

* Reading in l. 12 ovtm tl to yivofitvov, with F Simp, and some MSS. in Met. io68 b 12.

becoming, nor can the becoming of any process be that process.

Finally, since there are three kinds of motion, the substratum and the goal of motion must be one or other of these, e. g. locomotion will have to be altered or to be locally moved.

To sum up, then, since everything that is moved is moved in one of three ways, either accidentally, or partially, 20 or essentially, change can change only accidentally, as e.g. when a man who is being restored to health runs or learns : arid accidental change we have long ago 1 decided to leave out of account.

Since, 2 then, motion can belong neither to Being nor to Relation nor to Agent and Patient, it remains that there can be motion only in respect of Quality, Quantity, and 25 Place: for with each of these we have a pair of contraries. Motion in respect of Quality let us call alteration, a general designation that is used to include both contraries : and by Quality I do not here mean a property of substance (in that sense that which constitutes a specific distinction is a quality) but a passive quality in virtue of which a thing is said to be acted on or to be incapable of being acted on. 3 ° Motion in respect of Quantity has no name that includes both contraries, but it is called increase or decrease according as one or the other is designated : that is to say motion in the direction of complete magnitude is increase, motion in the contrary direction is decrease. Motion in respect of Place has no name either general or particular : but we may designate it by the general name of locomotion, though strictly the term ‘ locomotion ’ is applicable to things that change their place only when they have not the power to 35 come to a stand, and to things that do not move themselves locally.

a»6 b Change within the same kind from a lesser to a greater or from a greater to a lesser degree is alteration : for it is motion either from a contrary or to a contrary, 3 whether in an unqualified or in a qualified sense : for change to a lesser

8 Reading in 1 . 2 JJ yap cVamov fj (MS. E) eh iVamoy.

degree of a quality will be called change to the contrary of that quality, and change to a greater degree of a quality 5 will be regarded as change from the contrary of that quality to the quality itself. 1 It makes no difference whether the change be qualified or unqualified, except that in the former case the contraries will have to be contrary to one another only in a qualified sense : and a thing’s possessing a quality in a greater or in a lesser degree means the presence 2 or absence in it of more or less of the opposite quality. It is now clear, then, that there are only these three kinds of motion.

The 3 term ‘ immovable ’ we apply in the first place to that io which is absolutely incapable of being moved (just as we correspondingly apply the term invisible to sound) ; in the second place to that which is moved with difficulty after a long time or whose movement is slow at the start — in fact, what we describe as hard to move ; and in the third place to that which is naturally designed for and capable of motion, but is not in motion when, where, and as it naturally would be so. This last is the only kind of immovable thing of which I use the term ‘ being at rest * : for rest is contrary to motion, so that rest will be negation 15 of motion in that which is capable of admitting motion.

The foregoing remarks are sufficient to explain the essential nature of motion and rest, the number of kinds of change, and the different varieties of motion.

3 Let us now proceed to define the terms 4 together 9 and ‘ apart ’, * in contact ’, 1 between ‘ in succession ‘ contiguous’, and ‘continuous’, and to show in what circumstances 20 each of these terms is naturally applicable.

Things 4 are said to be together in place when they are in one place (in the strictest sense of the word ' place ’) and to be apart when they are in different places.

Things are said to be in contact when their extremities are together.

2 Reading in 1. 8 ro ttXcov, with E.

as6 b

That which a changing thing, if it changes continuously 25 in a natural manner, naturally reaches 1 before it reaches that to which it changes last, is between. Thus * between ’ implies the presence bf at least three things : for in a process of change it is the contrary that is * last ’ : and a thing is moved continuously if it leaves no gap or only the smallest possible 2 gap in the material — not in the time (for a gap in the time does not prevent things having a ‘ between \ while, on the other hand, there is nothing to prevent the highest 30 note sounding immediately after the lowest) but in the material in which the motion takes place. This is manifestly true not only in local changes but in every other kind 227* 7 as well. (Now 3 every change implies a pair of opposites, and opposites may be either contraries or contradictories ; since then contradiction admits of no mean term, it is obvious that ‘ between ’ must imply a pair of contraries.)

226 b 32 That 4 is locally contrary which is most distant in a straight line: for the shortest line is definitely limited, and that which is definitely limited constitutes a measure. 5

A thing is 1 in succession ’ when it is after the beginning 6 35 in position or in form 7 or in some other respect in which it 227* is definitely so regarded, and when further there is nothing of the same kind as itself between it and that to which it is in succession, e. g. a line or lines if it is a line, a unit or units if it is a unit, a house if it is a house (there is nothing to prevent something of a different kind being between). For that which is in succession is in succession to a particular thing, and is something posterior : for one is not ‘ in 5 succession ’ to two, nor is the first day of the month to the second : in each case the latter is ‘ in succession * to the former.

A thing that is in succession and touches is ‘ contiguous \ 10 The * continuous * is a subdivision of the contiguous :

9 Sense seems to require this transposition : v, Prantl, ad loc ., and cf. Themistius.

6 sc. for to irk<i<rTov. 6 Omitting in 1 . 35 povov, with E.

7 Reading in 1 . 35 fidu for with EH.

things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that 15 which holds them together is one, so too will the whole be one, e. g. by a rivet or glue or contact or organic union.

It is obvious that of these terms 4 in succession 1 is first in order of analysis : for that which touches is necessarily in succession, but not everything that is in succession touches : and so succession is a property of things prior in definition, e. g. numbers, while contact is not. And if there 20 is continuity there is necessarily contact, but if there is contact, that alone does not imply continuity: for the extremities of things may be ‘ together 9 without necessarily being one : but they cannot be one without being necessarily together. So natural junction is last in coming to be: for the extremities must necessarily come into contact if they are to be naturally joined : but things that are in contact 25 are not all naturally joined, while where there is no contact clearly there is no natural junction either. Hence, if as some say 4 point * and 4 unit * have an independent existence of their own, it is impossible for the two to be identical : for points can touch while units can only be in succession. Moreover, there can always be something 30 between points (for all lines are intermediate between points 1 ), whereas it is not necessary that there should possibly be anything between units : for there can be nothing between the numbers one and two.

We have now defined what is meant by ‘ together 1 and ‘apart’, ‘contact*, ‘between* and ‘in succession*, ‘ con- as*7 b tiguous * and ‘ continuous * : and we have shown in what circumstances each of these terms is applicable.

4 There are many senses in which motion is said to be ‘ one * : for we use the term ‘ one ’ in many senses.

Motion is on t genetically according to the different cate-

1 Cf. 231*9.

5 gories to which it may be assigned : thus any locomotion is one generically with any other locomotion, whereas alteration is different generically from locomotion.

Motion is one specifically when besides being one generically it also takes place in a species incapable of subdivision: e. g. colour has specific differences: therefore blackening and whitening differ specifically ; but at all events 1 every whitening will be specifically the same with every other whitening and every blackening with every 10 other blackening. But whiteness is not further subdivided by specific differences : hence any whitening is specifically one with any other whitening. Where it happens that the genus is at the same time a species, it is clear that the motion will then in a sense 2 be one specifically though not in an unqualified sense: learning is an example of this, knowledge being on the one hand a species of apprehension and on the other hand a genus including the various knowledges. A difficulty, however, may be raised as to whether 15 a motion is specifically one when the same thing changes from the same to the same, e. g. when one point changes again and again from a particular place to a particular place: if this motion is specifically one, circular motion will be the same as rectilinear motion, and rolling the same as walking. But is not this difficulty removed by the principle already laid down that if that in which the motion takes place is specifically different (as in the present instance the circular path is specifically different from the ao straight) the motion itself is also different ? We have explained, then, what is meant by saying that motion is one generically or one specifically.

Motion is one in an unqualified sense when it is one essentially or numerically : and the following distinctions will make clear what this kind of motion is. There are three classes of things in connexion with which we speak of motion, the * that which \ the * that in which and the ‘ that during which \ I mean that 3 there must be some-

1 Reading in 1. 9 b' obv, with EH.

8 Omitting in 1. 24 o, with EF.

BOOK V. 4 a*7 b thing that is in motion, e.g. a man or gold, and it must be 35 in motion in something, e. g. a place or an affection, and during something, for all motion takes place during a time.

Of these three it is the thing in which the motion takes place that makes it one generically or specifically, 1 it is the thing moved that makes the motion one in subject, and it is the time that makes it consecutive : but it is the three together that make it one without qualification : to effect this, that in which the motion takes place (the species) must 30 be one and incapable of subdivision, that during which it takes place (the time) must be one and unintermittent, and that which is in motion must be one — not in an accidental sense (i. e. it must be one as the white that blackens is one or Coriscus who walks is one, not in the accidental sense in which Coriscus and white may be one), nor 228® merely in virtue of community of nature (for there might be a case of two men being restored to health at the same time in the same way, e.g. from inflammation of the eye, yet this motion is not really one, but only specifically one).

Suppose, however, that Socrates undergoes an alteration specifically the same but at one time and again at another : in this case if it is possible for that which ceased to be again to come into being and remain numerically the same, then this motion too will be one: otherwise it will be the 5 same but not one. And akin to this difficulty there is another ; viz. is health one ? and generally are the states and affections in bodies severally one in essence although (as is clear) the things that contain them are obviously in motion and in flux ? Thus if a person’s health at daybreak and at the present moment is one and the same, why should not 10 this health be numerically one with that which he recovers after an interval ? The same argument applies in each case.* There is, however, we may answer, this difference : that if

1 The text seems faulty, though Simplicius read the same. The translation follows the suggestion of Bonitz in inserting, after tavurai in 1. 28, to rcj> vTTOKfififvtp plav iv rtp npaypari & Kivdrai. But the next clause is, in view of 228*26-31, best emended by reading to & tXopivrfv iv r<j) Xp<foq>.

* sc. the case of c£tts and the case of tuvrja-as .

aa8 a the states are two then it follows simply from this fact 1 that the activities must also in point of number be two (for only that which is numerically one can give rise to an 15 activity that is numerically one), but if the state is one, this is not in itself enough to make us regard the activity also as one : for when a man ceases walking, the walking no longer is, but it will again be if he begins to walk again. But, be this as it may, if in the above instance the health is one and the same, then it must be possible for that which is one and the same to come to be and to cease to be many times. However, 2 these difficulties lie outside our present inquiry.

20 Since every motion is continuous, a motion that is one in an unqualified sense must (since every motion is divisible) be continuous, and a continuous motion 3 must be one. There will not be continuity between any motion and any other indiscriminately any more than there is between any two things chosen at random in any other sphere : there can be continuity only when the extremities of the two things are one. Now some 4 things have no extremities at all ; and the extremities of others differ specifically although 35 we give them the same name of ‘ end ' : how should e. g. the ‘ end 1 of a line and the * end * of walking touch or come to be one ? Motions that are not the same either specifically or generically may, it is true, be consecutive (e. g. a man may run and then at once fall ill of a fever), and again, in the torch-race we have consecutive but not continuous locomotion : for according to our definition there can be continuity only when the ends of the two things are one. 30 Hence motions may be consecutive 5 or successive in virtue of the time being continuous, but there can be continuity only in virtue of the motions themselves being continuous, that is when the end of each is one with the end of the aa8 b other. Motion, therefore, that is in an unqualified sense continuous and one must be specifically the same, of one

2 Reading in L 19 pip ovp, with FHI.

8 Reading in 1 . 22 p lav, with Them, and Bonitz. 4 sc. indivisibles.

thing, and in one time. Unity is required in respect of time in order that there may be no interval of immobility, for where there is intermission of motion there must be rest, and a motion that includes intervals of rest will be not one but many, so that a motion that is interrupted by stationary- 5 ness is not one or continuous, and it is so interrupted if there is an interval of time. And though of a motion that is not specifically one (even if the time is unintermittent) the time 1 is one, the motion is specifically different, and so cannot really be one, for motion that is one must be specifically one, though motion that is specifically one is not jo necessarily one in an unqualified sense. We have now explained what we mean when we call a motion one without qualification.

Further, a motion is also said to be one generically, specifically, or essentially when it is complete, just as in other cases completeness and wholeness are characteristics of what is one : and sometimes a motion even if incomplete is said to be one, provided only that it is continuous.

And besides the cases already mentioned there is another 15 in which a motion is said to be one, viz. when it is regular : for in a sense a motion that is irregular is not regarded as one, that title belonging rather to that which is regular, as a straight line is regular, 2 the irregular being as such 3 divisible. But the difference would seem to be one of degree. 4 In every kind of motion we may have regularity or irregularity: thus there may be regular alteration, and locomotion 20 in a regular path, e. g. in a circle or on a straight line, and it is the same with regard to increase and decrease. The difference that makes a motion irregular 5 * is sometimes to be found in its path : thus a motion cannot be regular if its path is an irregular magnitude, e. g. a broken

1 Omitting in 1. 8 ov, with E, and reading 6 xpo vos, 6 pcV xpoyor, with Bonitz.

■ 6fjta\r}s (® 6fioiofi(pr)s of mathematical writers), regular in the sense that any part applied to any other part can coincide with it.

* e. g. a line partly straight and partly curved (and the motion along it) may be divided accordingly.

4 i. e. regularity and irregularity do not constitute distinct species of motion : they occur in every kind of motion, making it more or less what it is. 8 Reading in 1. 21 awpaXia, with E Them.

aa8 b line , 1 a spiral , 2 or any other magnitude that is not such that any part of it taken at random fits on to any other 35 that may be chosen. Sometimes it is found neither in the place nor in the time nor in the goal but in the manner of the motion: for in some cases the motion is differentiated by quickness and slowness: thus if its velocity is uniform a motion is regular, if not it is irregular. So quickness and slowness are not species of motion nor do they constitute specific differences of motion, because this distinction occurs in connexion with all the distinct species 30 of motion. The same is true of heaviness and lightness 3 when they refer to the same thing : e. g. they do not specifically distinguish earth from itself or fire from itself.

229 11 Irregular motion, therefore, while in virtue of being continuous it is one, is so in a lesser degree, as is the case with locomotion in a broken line : and a lesser degree of something always means an admixture of its contrary. And since every motion that is one can be both regular and irregular, motions that are consecutive but not specifically 5 the same cannot be one 4 and continuous : for how should a motion composed of alteration and locomotion be regular ?

If a motion is to be regular its parts ought to fit one another.

We have further to determine what motions are contrary 5 to each other, and to determine similarly how it is with rest. And we have first to decide whether contrary motions are motions respectively from and to the same thing, e. g.

10 a motion from health and a motion to health (where the opposition, it would seem, is of the same kind as that between coming to be and ceasing to be) ; or motions respectively from contraries, e. g. a motion from health and a motion from disease ; or motions respectively to contraries, e. g. a motion to health and a motion to disease ; or motions respectively from a contrary and to the opposite contrary, e. g. a motion from health and a motion to disease ;

1 i. e. as we should say, (wo lines meeting in an angular point.

2 One spiral — the cylindrical helix — is regular : but this property was first proved for it by Apollonius.

8 Which cause quick and slow motion.

or motions respectively from a contrary to the opposite contrary and from the latter to the former, e. g. a motion from health to disease and a motion from disease to health : for motions must be contrary to one another in one or 15 more of these ways, as there is no other way in which they can be opposed.

Now motions respectively from a contrary and to the opposite contrary, c. g. a motion from health and a motion to disease, are not contrary motions : for they are one and the same. (Yet their essence is not the same, just as changing from health is different from changing to disease.)

Nor are motions respectively from a contrary and from the 20 opposite contrary contrary motions, for a motion from a contrary is at the same time a motion to a contrary or to an intermediate (of this, however, we shall speak later), 1 but changing to a contrary rather than changing from a contrary would seem to be the cause of the contrariety of motions, the latter being the loss, the former the gain, of contrariness. Moreover, each several motion takes its 25 name rather from the goal than from the starting-point of change, e. g. motion to health we call convalescence, motion to disease sickening. Thus we are left with motions respectively to contraries, and motions respectively to contraries from the opposite contraries. Now it would seem that motions to contraries are at the same time motions from contraries (though their essence may not be the same ;

‘to health’ is distinct, I mean, from ‘from disease’, and * from health 9 from ‘to disease ’).

Since then change differs from motion (motion being 30 change from a particular subject to a particular subject), it follows that contrary motions are motions respectively from a contrary to the opposite contrary and from the latter to the former, e, g. a motion from health to disease 229 b and a motion from disease to health. Moreover, the consideration of particular examples will also show what kinds of processes are generally recognized as contrary : thus falling ill is regarded as contrary to recovering ones health, these processes having contrary goals, and being taught as 5

contrary to being led into error by another, it being possible to acquire error, like knowledge, either by one's own agency or by that of another. Similarly we have upward locomotion and downward locomotion, which are contrary lengthwise, 1 locomotion to the right and locomotion to the left, which are contrary breadthwise, and forward locomotion and backward locomotion, which too are contraries.

10 On the other hand, a process simply to a contrary, e.g. that denoted by the expression ‘ becoming white', where no starting-point is specified, is a change but not a motion. And in all cases of a thing that has no contrary we have as contraries change from and change to the same thing. Thus coming to be is contrary to ceasing to be, and losing to gaining. But these are changes and not motions. And 15 wherever a pair of contraries admit of an intermediate, motions to that intermediate must be held to be in a sense motions to one or other of the contraries : for the intermediate serves as a contrary for the purposes of the motion, in whichever direction the change may be, e. g. grey in a motion from grey to white takes the place of black as starting-point, in a motion from white to grey it takes the place of black as goal, and in a motion from black to grey it takes the place of white as goal : for the middle is opposed 20 in a sense to either of the extremes, as has been said above. 2 Thus we see that two motions are contrary to each other only when one is a motion from a contrary to the opposite contrary and the other is a motion from the latter to the former.

But since a motion appears to have contrary to it not 6 only, another motion but also a state of rest, we must determine how this is so. A motion has for its contrary in the strict sense of the term another motion, but it also has for an opposite a state of rest (for rest is the privation of 25 motion and the privation of anything may be called its

* 224k 32 sqq. There is no need to insert cvavrlov (with Prantl) after pccrov in 1. 19.

a»9 b contrary), and motion of one kind 1 has for its opposite rest of that kind, e. g. local motion has local rest. This statement, however, needs further qualification : there remains the question, is the opposite of remaining at a particular place motion from or motion to that place ? It is surely clear that since there are two subjects between which motion takes place, motion from one of these (A) to its contrary 30 (B) has for its opposite remaining in A , while the reverse motion has for its opposite remaining in B . At the same time these two are also contrary to each other : for it would be absurd to suppose that there are contrary motions and not opposite states of rest. States of rest in contraries are 23°* opposed. To take an example, a state of rest in health is (1) contrary to a state of rest in disease, and (2) the motion to which it is contrary is that from health to disease. For (2) it would be absurd that its contrary motion should be that from disease to health, since motion to that in which a thing is at rest is rather a coming to rest, the coming to rest 5 being found to come into being simultaneously with the motion ; and one of these two motions it must be. And (1) rest in whiteness is of course not contrary to rest in health.

Of all things that have no contraries there are opposite changes (viz. change from the thing and change to the thing, e. g. change from being and change to being), but no motion.

So, too, of such things there is no remaining though there is absence of change. Should there be a particular subject, 10 absence of change in its being will be contrary to absence of change in its not-being. And here a difficulty may be raised : if not-being is not a particular something, what is it, it may be asked, that is contrary to absence of change in a thing’s being ? and is this absence of change a state of rest ? If it is, then either it is not true that every state of rest is contrary to a motion or else coming to be and ceasing to be are motion. It is clear then that, since we 15 exclude these from among motions, we must not say that this absence of change is a state of rest : we must say that it is similar to a state of rest and call it absence of change.

1 Reading in 1. 26 *roia noi a, with Phil.

And it will have for its contrary 1 either nothing or absence of change in the thing’s not-being, or the ceasing to be of the thing : for such ceasing to be is change from it and the thing’s coming to be is change to it.

Again, a further difficulty may be raised. How is it, it may be asked, that whereas in local change both remaining ao and moving may be natural or unnatural, in the other changes this is not so ? e. g. alteration is not now natural and now unnatural, for convalescence is no more natural or unnatural than falling ill, whitening no more natural or unnatural Jthan blackening ; so, too, with increase and decrease : these are not contrary to each other in the sense that either of 35 them is natural while the other is unnatural, nor is one increase contrary to another in this sense ; and the same account may be given of becoming and perishing : it is not true that becoming is natural and perishing unnatural (for growing old 2 is natural), nor do we observe one becoming to be natural and another unnatural. We answer that if 30 what happens under violence is unnatural, then violent perishing is unnatural and as such contrary to natural perishing. Are there then also some becomings that are violent and not the result of natural necessity, and are therefore contrary to natural becomings, and violent ina30 b creases and decreases, e. g. the rapid growth to maturity of profligates and the rapid ripening of seeds even when not packed close in the earth ? And how is it with alterations ? Surely just the same : we may say that some alterations are violent while others are natural, e.g. patients alter naturally 5 or unnaturally according as they throw off fevers on the critical daysor not. But, it maybe objected, then we shall have perishings contrary to one another, not to becoming . 3 Certainly : and why should not this in a sense be so ? 4 Thus it is so if one perishing is pleasant and another painfuh and so one perishing will be contrary to another not in an

1 If there is no ov to be contrary to the ov, then dpfTuPXrjata in the 5v will have no contrary : if there is, it will have for contraries (a) the dp*Ta&\r)aia in the M ov and (b) the (pBopd which « ptrafioXi) dp*rafi\r}(rias tov Svtos (tts dp*raft\r]ariav rov pi) ovros).

2 Reading in 1. 28 rj yap yrjpavcris , with EH.

8 Reading in 1. 7 y*vtcrci (Bekker’s yevtarus is a misprint).

unqualified sense, but in so far as one has this quality and the other that.

Now motions and states of rest universally 1 exhibit 10 contrariety in the manner described above , 2 e.g. upward motion and rest above are respectively contrary to downward motion and rest below, these being instances of local contrariety ; and upward locomotion belongs naturally to fire and downward to earth, i.e. the locomotions of the two are contrary to each other. And again, fire moves up naturally and down unnaturally : and its natural motion is certainly contrary to its unnatural motion. Similarly with 15 remaining : remaining above is contrary to motion from above downwards, and to earth this remaining comes unnaturally, this motion naturally. So the unnatural remaining of a thing is contrary to its natural motion, just as we find a similar contrariety in the motion of the same thing : one 20 of its motions, the upward or the downward, will be natural, the other unnatural.

Here, however, the question arises, has every state of rest that is not permanent a becoming, and is this becoming a coming to a standstill? If so, there must be a becoming of that which is at rest unnaturally, e. g. of earth at rest above : and therefore this earth during the time that it was being carried Violently upward was coming to a standstill. But whereas the velocity of that which comes to a standstill seems always to increase, the velocity of that which is carried violently seems always to decrease : so it will be in 25 a state of rest without having become so. Moreover ‘ coming to a standstill * is generally recognized to be identical or at least concomitant with the locomotion of a thing to its proper place . 3

There is also another difficulty involved in the view that remaining in a particular place is contrary to motion from that place. For when a thing is moving from or discarding something, it still appears to have that which is being discarded, so that if a state of rest is itself contrary to the 3 °

1 i.e. the contrariety of natural )( violent is no exception.

8 we must not use the term Zor aa$ai to describe the process that ends in unnatural rest.

motion from the state of rest to its contrary, the contraries rest and motion will be simultaneously predicable of the same thing. May we not say, however, that in so far as the thing is still stationary it is in a state of rest in a qualified sense ? For, 1 in fact, whenever a thing is in motion, part of it is at the starting-point while part is at the goal 23 1 * to which it is changing : and consequently a motion finds its true contrary rather in another motion than in a state 2 of rest.

With regard to motion and rest, then, we have now explained in what sense each of them is one and under what conditions they exhibit contrariety.

5 3 [With regard to coming to a standstill the question may be raised whether there is an opposite state of rest to unnatural as well as to natural motions. It would be absurd if this were not the case: for a thing may remain still merely under violence: thus we shall have a thing being in a non-permanent state of rest without having become so. But it is clear that it must be the case : for just as there is unnatural motion, so, too, a thing may be in an unnatural state of rest. Further, some things have a natural and an unnatural motion, e. g. fire has a natural upward motion and an unnatural downward motion : is it, then, this unnatural downward motion or is it the natural downward motion of earth that is contrary to the natural upward motion ? Surely it is clear that both are contrary to it though not in the same sense : the natural motion of earth is contrary inasmuch as the motion of fire is also natural, 15 whereas the upward 4 motion of fire as being natural is contrary to the downward motion of fire as being unnatural. The same is true of the corresponding cases of remaining. But there would seem to be a sense in which a state of rest and a motion are opposites.]

2 T)pctxT}<ns seems to be used for rjptpia. Cf. 25 i a 26.

8 This confused paragraph following what should be the final sentence of the book is omitted by six MSS., ignored by Themistius, and considered superfluous by Simplicius.

I Now if the terms ‘ continuous *, ‘ in contact *, and ‘ in succession ’ are understood as defined above 1 — things being ‘continuous* if their extremities are one, ‘in contact * if their extremities are together, and ‘ in succession* if there is nothing of their own kind intermediate between them — nothing that is continuous can be composed of indivisibles : e. g. a line cannot be composed of points, the line being 25 continuous and the point indivisible. For the extremities of two points can neither be one (since of an indivisible there can be no extremity as distinct from some other part) nor together (since that which has no parts can have no extremity, the extremity and the thing of which it is the extremity being distinct).

Moreover, if that which is continuous is composed of ' points, these points must be either continuous or in contact 3° with one another : and the same reasoning applies in the case of all indivisibles. Now for the reason given above 23i b they cannot be continuous : and one thing can be in contact with another only if whole is in contact with whole or part with part or part with whole. But since indivisibles have no parts, they must be in contact with one another as whole with whole. And if they are in contact with one another as whole with whole, they will not be continuous: for that which is continuous has distinct parts : and these parts into which 5 it is divisible are different in this way, i.e. spatially separate.

Nor, again, can a point be in succession to a point or a moment to a moment in such a way that length can be composed of points or time of moments: for things are in succession if there is nothing of their own kind intermediate between them, whereas that which is intermediate between points is always a 2 line and that which is intermediate between moments is always a period of time.

Again, if length and time could thus be composed of 10

2 i, e. if we take any two points (moments) A and JB, jsince they cannot touch there is a line (time) between them : and on this line (in

J*3i b indivisibles, they could be divided into indivisibles, since each is divisible into the parts of which it is composed. But, as we saw, no continuous thing is divisible into things without parts. Nor can there be anything of any other kind intermediate between the parts or between the moments : for if there could be any such thing it is clear that it must be either indivisible or divisible, and if it is divisible, it must be divisible either into indivisibles or into divisibles that are infinitely divisible, in which case it is continuous.

15 Moreover, it is plain that everything continuous is divisible into divisibles that are infinitely divisible : for if it were divisible into indivisibles, we should have an indivisible in contact with an indivisible, since the extremities of things that are continuous with one another are one and 3 arc in contact.

The same reasoning applies equally to magnitude, to time, and to motion: either all of these are composed of indivisibles and are divisible into indivisibles, or none.

20 This may be made clear as follows. If a magnitude is composed of indivisibles, the motion over that magnitude must be composed of corresponding indivisible motions : e. g. if the magnitude ABr is composed of the indivisibles A, B, T, each corresponding part of the motion AEZ of 12

25 over ABr is indivisible. Therefore, 2 since where there is motion there must be something that is in motion, and where there is something in motion there must be motion, therefore the being-moved will also be composed of indivisibles. So 12 traversed A when its motion was A, B when its motion was E, and T similarly when its motion was Z. Now 3 a thing that is in motion from one place to another cannot at the moment when it was in motion both be in motion and at the same time have completed its motion at the place to which it was in motion : e. g. if a man is walking to Thebes, he cannot be walking to Thebes and at this time) we can always take another point (moment) r. A and B have between them another thing of the same kind, and so are not €<t>c£r}S.

1 Omitting the comma in 1. 18. 8 L 25 reading &J, with EH IK.

* There is a slight anacoluthon, the virtual apodosis being intro* duced by ©or* (232“ 2).

the same time have completed his walk to Thebes : and, as 30 we saw, f 2 traverse3 the partless section A in virtue of the 232® presence of the motion A. Consequently, if f2 actually passed through A after being in process of passing through, the motion must be divisible : for at the time when 12 was passing through, it neither was at rest nor had completed its passage but was in an intermediate state: while if it is passing through and has completed its passage at the same moment , then that which is walking 1 will at the moment 5 when it is walking have completed its walk and will be in the place to which it is walking ; that is to say, it will have completed its motion at the place to which it is in motion . 2 And if a thing is in motion over the whole ABr and its motion is the three A, E, and Z, and if it is not in motion at all over the partless section A but has completed its motion over it, then the motion will consist not of motions but of starts, and will take place by 3 a things having completed a motion without being in motion : for on this assumption it has completed its passage through A without passing through it. So it will be possible for a thing to 10 have completed a walk without ever walking : for on this assumption it has completed a walk over a particular distance without walking over that distance. Since, then, everything must be either at rest or in motion, ’and 12 is therefore at rest in each of the sections A, B, and F, it follows that a thing can be continuously at rest and at the same time in motion : for, as we saw, £2 is in motion over the whole ABr and at rest in any part (and consequently in the whole) of it. Moreover, if the indivisibles composing '5 AEZ are motions, it would be possible for a thing in spite of the presence in it of motion to be not in motion but at rest, while if they are not motions, it would be possible for motion to be composed of something other than motions.

And if length and motion are thus indivisible, it is neither more nor less necessary that time also be similarly indivisible, that is to say be composed of indivisible moments :

1 Reading commas before and after to 8a8t(ov in 1. 4.

1 Which is ex hypotkesi impossible (231** 28-30).

ao for if the whole distance is divisible and an equal velocity will cause a thing to pass through less of it in less time, the time must also be divisible, and conversely, if the time in which a thing is carried over the section A is divisible, this section A must also be divisible.

And since every magnitude is divisible into magnitudes — a for we have shown that it is impossible for anything continuous to be composed of indivisible parts, and every 35 magnitude is continuous — it necessarily follows that the quicker of two things traverses a greater magnitude in an equal time, an equal magnitude in less time, and a greater magnitude in less time, in conformity with the definition sometimes given of ‘ the quicker*. Suppose that A is quicker than B. Now since of two things that which changes sooner, is quicker, in the time ZH, in which A has 30 changed from T to A, B will not yet have arrived at A but will be short of it: so that in an equal time the quicker will pass over a greater magnitude. More than this, it will pass over a greater magnitude in less time : for in the time in which A has arrived at A, B being the slower has arrived, let us say, at E. Then since A has occupied the whole 232 b time ZH in arriving at A, it will have arrived at 0 in less time than this, say ZK. Now the magnitude T 0 1 that A has passed over is greater than the magnitude TE, and the time ZK is less than the whole time ZH : so that the quicker will pass over a greater magnitude in less time.

5 And from this it is also clear that the quicker will pass over an equal magnitude in less time than the slower. For since it passes over the greater magnitude in less time than the slower, and (regarded by itself) passes over AM the greater in more time than AS the lesser, the time IIP in which it passes over AM will be more than the time 112 10 in which it passes over AS: so that, the time IIP being less than the time FIX in which the slower passes over A 2 , the time n 2 will also be less than the time BIX : for it is less than the time IIP, and that which is less than some-

J_J r E © A. Bekker’s TA in 1. 3 is a misprint.

thing else that is less than a thing is also itself less than that thing. Hence it follows that the quicker will traverse an equal magnitude in less time than the slower. Again, since the motion of anything must always occupy either 15 an equal time or less or more time in comparison with that of another thing, and since, whereas a thing is slower if its motion occupies more time and of equal velocity if its motion occupies an equal time, the quicker is neither of equal velocity nor slower, it follows that the motion of the quicker can occupy neither an equal time nor more time.

It can only be, then, that it occupies less time, and thus we get the necessary consequence that the quicker will pass over an equal magnitude (as well as a greater) in less time than the slower. ao

And since every motion is in time and a motion may occupy any time, and the motion of everything that is in motion may be either quicker or slower, both quicker motion and slower motion may occupy any time : and this being so, it necessarily follows that time also is continuous.

By continuous I mean that which is divisible into divisibles that are infinitely divisible : and if we take this as the deft- 25 nition of continuous, it follows necessarily that time is continuous. For since it has been shown that the quicker will pass over an equal magnitude in less time than the slower, suppose that A is quicker and B slower, and that the slower has traversed the magnitude TA in the time ZH. Now it is 30 clear that the quicker will traverse the same magnitude in less time than this : let us say in the time Z0. Again, since the quicker has passed over the whole FA in the time Z 0 , the slower will in the same time pass over TK, say, 1 which is less than TA. And since B, the slower, has passed 233* over TK in the time Z 0 , the quicker will pass over it in less time : so that the time Z0 will again be divided. And if this is divided the magnitude TK will also be divided just as TA was : and again, if the magnitude is divided, the time will also be divided. And we can carry on this process for 5 ever, taking the slower after the quicker and the quicker after the slower alternately, and using what has been 1 1 . 33 reading ?<ttw, with E Them. Simp.

PHYSIC A a 33* demonstrated at each stage as a new point of departure : for the quicker will divide the time and the slower will divide the length. If, then, this alternation always holds good, and at every turn involves a division, it is evident io that all time must be continuous. And at the same time it is clear that all magnitude is also continuous ; for the divisions of which time and magnitude respectively are susceptible are the same and equal.

Moreover, the current popular arguments make it plain that, if time is continuous, magnitude is continuous also, inasmuch as a thing passes over half a given magnitude in 15 half the time taken to cover the whole: in fact without qualification it passes over a less magnitude in less time ; for the divisions of time and of magnitude will be the same. And if either is infinite, so is the other, and the one is so in the same way as the other ; i. e. if time is infinite in respect of its extremities, 1 length is also infinite in respect of its extremities: if time is infinite in respect of divisibility, ao length is also infinite in respect of divisibility : and if time is infinite in both respects, magnitude is also infinite in both respects.

Hence Zeno’s argument 2 makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called ‘ infinite ’ : 35 they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility : for in this sense the time itself is also infinite : and so we find that the time occupied by the passage over 30 the infinite is not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in number.

1 i. e. extends infinitely in both directions.

2 i. e. one of his arguments for the impossibility of motion, which ran as follows : if motion is possible, a thing can in a finite time pass over infinite things touching each of them ; but this is impossible : therefore motion is impossible, Cf. 239 b 9~i4, Top. i6o b 7.

The passage over the infinite, 1 then, cannot occupy a finite time, and the passage over the finite cannot occupy an infinite time: if the time is infinite the magnitude must be infinite also, and if the magnitude is infinite, so also is the time. This may be shown as follows. Let AB be a finite magnitude, and let us suppose that it is traversed in infinite time T, and let a finite period TA of the time be 35 taken. Now in this period the thing in motion will pass a 38 b over a certain segment of the magnitude : let BE be the segment that it has thus passed over. (This will be either an exact measure of AB or less 2 or greater than an exact measure: it makes no difference which it is.) Then, since a magnitude equal to BE will always be passed over in an equal time, and BE measures the whole magnitude, the 5 whole time occupied in passing over AB will be finite: for it will be divisible into periods equal in number to the segments into which 3 the magnitude is divisible. Moreover, if it: is the case that infinite time is not occupied in passing over every magnitude, but it is possible to pass over some magnitude, say BE, in a finite time, and if this BE measures the whole of which it is a part, and if an equal io magnitude is passed over in an equal time, then it follows that the time like the magnitude is finite. That infinite time will not be occupied in passing over BE is evident if the time be taken as limited in one direction 4 : for as the part will be passed over in less time than the whole, the time occupied in traversing this part must be finite, the limit in one direction being given. The same reasoning will also show the falsity of the assumption that infinite length can be traversed in a finite time. It is evident, then, from what 15

1 i. e. in the strict sense, viz. extending infinitely in both directions.

a i.e. the nearest multiple of BE to AB will be less or greater than AB : e. g. 4 feet Karapfrpci 16 feet (16 being an exact multiple of 4), ^

^ feet cAXccim (the nearest multiple being 15, i.e. less than 16), 6 feet * vnipfidWn (the nearest multiple being 18, i.e. greater than 16). Obviously, since the amount by which BE AAcum or \mep 8 dWti is always less than BE, it makes no difference to the argument whether BE is an exact measure or not.

1 1 . 7 omit with E, and the comma.

4 i. e. the point B at which the motion begins is fixed, and the moment at which the motion begins must similarly be regarded as fixed.

etf.is L has been said that neither a line nor a surface nor in fact anything continuous can be indivisible.

This conclusion follows not only from the present argument but from the consideration that the opposite assumption implies the divisibility of the indivisible. For since the distinction of quicker and slower may apply to motions ao occupying any period of time and in an equal time the quicker passes over a greater length, it *may happen that it will pass over a length twice, or one and a half times, as great as that passed over by the slower : for their respective velocities may stand to one another in this proportion. Suppose, then, that the quicker has in the same time been carried over a length one and a half times as great as that traversed by the slower, and that the respective magnitudes are divided, that 1 of the quicker, the magnitude ARTA, 2 into three indivisibles, and that 3 of the slower into the two 35 indivisibles EZ, ZH. Then the time may also be divided into three indivisibles, for an equal magnitude will be passed over in an equal time. Suppose then that it is thus divided into KA, AM, MN. Again, since in the same time the slower has been carried over EZ, ZH, the time may also be similarly divided into two. Thus the indivisible will be divisi- 30 ble, and that which has no parts will be passed over not in an indivisible but in a greater time. 4 It is evident, therefore, that nothing continuous is without parts.

The present also is necessarily indivisible — the present, 3 that is, not in the sense in which the word is applied to one thing in virtue of another, 6 but in its proper and primary 35 sense ; in which sense it is inherent in all time. For the 234* present is something that is an extremity of the past (no part of the future being on this side of it) and also of the future (no part of the past being on the other side of it) : it is, as we have said, 6 a limit of both. And if it is once shown

4 The slower will traverse EZ in a greater time than the indivisible time in which the quicker traverses KA.

6 i. e. in which it means a period of time including the present proper.

that it is essentially of this character and one and the same, it will at once be evident also that it is indivisible.

Now the present that is the extremity of both times 5 must be one and the same : for if each extremity were different, the one could not be in succession to the other, because nothing continuous can be composed of things having no parts: and if the one is apart from the other, there will be time intermediate between them, because everything continuous is such that that there is something intermediate between its limits and described by the same name as itself. But if the intermediate thing is time, it will be divisible : for all time has been shown 1 to be divisible. 10 Thus on this assumption the present is divisible. But if the present is divisible, there will be part of the past in the future and part of the future in the past : for past time will be marked off from future time at the actual point of division. Also the present will be a present not in the , proper sense but in virtue of something else : for the division *5 which yields it will not be a division proper. 2 Furthermore, there will be a part of the present that is past and a part that is future, and it will not always be the same part that is past or future : in fact one and the same present will not be simultaneous 3 : for the time maybe divided at many points. 4 If, therefore, the present cannot possibly have these characteristics, it follows that it must be the same present that belongs to each of the two times. 5 But if this is so it ao is evident that the present is also indivisible : for if it is divisible it will be involved in the same implications as before.

It is clear, then, from what has been said that time contains something indivisible, and this is what we call a present.

We will now show that nothing can be in motion in a present. For if this is possible, 6 there can be both quicker 25 and slower motion in the present. Suppose then that in

1 Chapter 2.

2 i. e. it will not be a point of division but merely something intermediate between past and future.

8 234* 18 reading ri> avro apa, with E.

4 i. e. the present, being a period of time, can itself be divided into a number of presents.

* i. e. that ends one period of time and begins the next.

a 34 a the present N the quicker has traversed the distance AB. That beingso, the slower will in the same present traverse a distance less than AB, say AT. But since the slower will have occupied the whole present in traversing AT, the 30 quicker will occupy less than this in traversing it. Thus we shall have a division of the present, whereas we found it to be indivisible. It is impossible, therefore, for anything to be in motion in a present.

Nor can anything be at rest in a present : for, as we were saying , 1 that only can be at rest which is naturally designed to be in motion but is not in motion when, where, or as it would naturally be so : since, therefore, nothing is naturally designed to be in motion in a present, it is clear that nothing can be at rest in a present either.

Moreover, inasmuch as it is the same present that belongs 35 to both the times , 2 and it is possible for a thing to be in motion throughout one time and to be at rest throughout 234 b the other, and that which is in motion or at rest for the whole of a time will be in motion or at rest as the case may be in any part of it in which it is naturally designed to be in motion or at rest : this being so, the assumption that there can be motion or rest in a present will carry with it the implication that the same thing can at the same time be at rest and in motion : for both the times have the same extremity, viz. the present.

5 Again, when we say that a thing is at rest, we imply that its condition in whole and in part is at the time of speaking uniform with what it was previously : but the present contains no ‘previously’ : consequently, there can be no rest in it.

It follows then that the motion of that which is in motion and the rest of that which is at rest must occupy time.

10 Further, everything that changes must be divisible. For 4 since every change is from something to something, and when a thing is at the goal of its change it is no longer changing, and when both it itself and all its parts are at the starting-point of its change 3 it is not changing (for that

Kat avro , . . iravra, ov (xtTaftak'Xu, which is in whole and in part in an unvarying condition is not in a state of change) ; it follows, therefore, 1 that part of 15 that which is changing must be at the starting-point and part at the goal : for as a whole it cannot be in both or in neither. (Here by ‘goal of change' I mean that which comes first in the process of change : e. g. in a process of change from white the goal in question will be grey, not black: for it is not necessary that that which is changing should be at either of the extremes.) It is evident, there- jo fore, that everything that changes must be divisible.

Now motion is divisible in two senses. In the first place it is divisible in virtue of the time that it occupies. In the second place it is divisible according to the motions of the several parts of that which is in motion : e. g. if the whole A F is in motion, there will be a motion of AB and a motion of Br. That being so, let AE be the motion of the part AB and EZ the motion of the part Br. Then the whole AZ 2 must 25 be the motion of AT : for AZ must constitute the motion of AT inasmuch as AEand EZ severally constitute the motions of each of its parts. But the motion of a thing can never be constituted by the motion of something else: consequently the whole motion is the motion of the whole magnitude.

Again, since every motion is a motion of something, and the whole motion AZ is not the motion of either of the parts (for each of the parts AE, EZ is the motion of one of the parts AB, Br) or ol anything else (for, the whole motion 3° being the motion of a whole, the parts of the motion are the motions of the parts of that whole : and the parts of AZ are the motions of AB, Br 3 and of nothing else: for, as we saw, 4 a motion that is one cannot be the motion of more things than one) : since this is so, the whole motion will be the motion of the magnitude ABB.

Again, if there is a motion of the whole other than AZ, say © 1 , the motion of each of the parts may be subtracted from it : and these motions will be equal to AE, EZ 35 respectively : for the motion of that which is one must be 235*

1 Placing a colon before avdyicrj in 1 . 15.

* Omitting f) in 1 . 25, with E.

1 Reading in 1 . 32 AB BP with Them. Simp. 4 223 b 1 sqq.

a 35* one. So if the whole motion 01 may be divided into the motions of the parts, 01 will be equal to AZ: if on the other hand there is any remainder, say KI, this will be a 5 motion of nothing : for it can be the motion neither of the whole nor of the parts (as the motion of that which is one must be one) nor of anything else : for a motion that is continuous must be the motion of things that are continuous. And the same result follows if the division of 01 reveals a surplus on the side of the motions of the parts. 1 Consequently, if this is impossible, the whole motion must be the same as and equal to AZ.

This then is what is meant by the division of motion according to the motions of the parts: and it must be applicable to everything that is divisible into parts, io Motion is also susceptible of another kind of division, that according to time. For since all motion is in time and all time is divisible, and in less time the motion is less, it follows that every motion must be divisible according to time. And since everything that is in motion is in motion in a certain sphere and for a certain time and has a motion 15 belonging to it, it follows that the time, the motion, the being-in-motion, the thing that is in motion, and the sphere of the motion must all be susceptible of the same divisions (though spheres of motion are not all divisible in a like manner: thus quantity is essentially, quality accidentally divisible). For suppose that A is the time occupied by the ao motion B. Then if all the time has been occupied by the whole motion, it will take less of the motion to occupy half the time, less again to occupy a further subdivision of the time, and so on to infinity. Again, the time will be divisible similarly to the motion : for if the whole motion occupies all the time half the motion will occupy half the time, 2 and less of the motion again will occupy less of the time.

*5 In the same way the being-in-motion will also be divisible. For let T be the whole being-in-motion. Then the being-in-

1 i. e. of what can this surplus motion be the motion ?

2 i. e. if the motion is regular.

motion that corresponds to half the motion 1 will be less than the whole being-in-motion, that which corresponds to a quarter of the motion will be less again, and so on to infinity. Moreover by setting out successively the beingin-motion corresponding to each of the two motions AT (say) and TE, we may argue that the whole being-in-motion will correspond to the whole motion (for if it were some - 3 ° other being-in-motion that corresponded to the whole motion, there would be more than one bcing-in-motion corresponding to the same motion), the argument being the same as that whereby we showed 2 that the motion of a thing is divisible into the motions of the parts of the thing : for if we take separately the being-in-motion corresponding to each of the two motions, we shall see that the whole bcing-in-motion is continuous. 3

The same reasoning will show the divisibility of the length, and in fact of everything that forms a sphere of change (though 4 some of these are only accidentally 35 divisible because that which changes is so) : for the division of one term will involve the division of all. So, too, in the matter of their being finite or infinite, they will all alike be either the one or the other. And we now see that in most 235** cases the fact that all the terms are divisible or infinite is a direct consequence of the fact that the thing that changes is divisible or infinite: for the attributes ‘divisible’ and ‘infinite’ belong in the first instance to the thing that changes. That divisibility does so we have already 0 shown ; 5 that infinity does so will be made clear in what follows. 7

5 Since everything that changes changes from something to something, that which has changed must at the moment

1 i. e. in which half the motion is realized, to KivtiaOai being the state of the klv(w^(pqp in so far as it actually exhibits Kivrjais.

5 Cf. 235*6: Kivyris being continuous, tuvuaQm is so also.

4 The accepted punctuation seems wrong : the sentence has yap . . . diaipf&riatrai serves to justify not the reservation introduced by n\rjp but the general conclusion as to the divisibility of the terms involved in motion,

5 An exception would be the divisibility of which would follow from that of kIp^is rather than from that of Kivovptpov.

when it has first changed be in that to which it has changed. For that which changes retires from or leaves that from which it changes : and leaving, if not identical with changing, 10 is at any rate a consequence of it. And if leaving is a consequence of changing, having left is a consequence of having changed: for there is a like relation between the two in each case.

One kind of change, then, being change in a relation of contradiction, where a thing has changed from not-being 15 to being it has left not-being. Therefore it will be in being: for everything must either be or not be. It is evident, then, that in contradictory change that which has changed must be in that to which it has changed. And if this is true in this kind of change, it will be true in all other kinds as well : for in this matter what holds good in the case of one will hold good likewise in the case of the rest.

Moreover, if we take each kind of change separately, the truth of our conclusion will be equally evident, on the ground that that which has changed must be somewhere 20 or in something. For, since it has left that from which it has changed and must be somewhere, it must be either in that to which it has changed or in something else. If, then, that which has changed to B is in something other than B, say T, it must again be changing from F to B : for it cannot be assumed that there is no interval 1 between F 35 and B, since change is continuous. Thus we have the result that the thing that has changed, at the moment when it has changed, is changing to that to which it has changed, which is impossible: that which has changed, therefore, must be in that to which it has changed. So it is evident likewise that that which has come to be, at the moment when it has come to be, will be , and that which

Cf. the definition of c^ofxtvov as o au ?</>*£*/$■ op affTTirat (227*6}. The exact connexion of thought is a little obscure: but the argument seems to be this : since the change is continuous, the changing thing, if it has not yet reached the state B, must be in process of reaching it, for there must be a gap between B and any intermediate state V which is different from B, and this gap can be bridged only by a process of change : the change being continuous, the changing thing when it reaches r must be in process of change towards B. Read r« B in 1 . 24 with Hayduck.

has ceased to be will uot-be: for what we have said applies universally to every kind of change, and its truth is most obvious in the case of contradictory change. It is clear, 30 then, that that which has changed, at the moment when it has first changed, is in that to which it has changed.

We will now show that the ‘ primary when ’ in which that which has changed effected the completion of its change must be indivisible, where by ‘ primary* I mean possessing the characteristics in question of itself and not in virtue of the. possession of them by something else belonging to it. For let A F be divisible, and let it be divided at B. If then the completion of change has been 35 effected in AB or again in BP, Ar cannot be the primary thing in which the completion of change has been effected.

If, on the other hand, it has been changing in both AB and BP (for it must either have changed or be changing in each of them), it must have been changing in the whole Ar : 236 11 but our assumption was that AT contains only the completion of the change. It is equally impossible to suppose that one part of AP contains the process and the other the completion of the change : for then we shall have something prior to what is primary . 1 So that in which the completion of change has been effected must be indivisible.

It is also evident, therefore, that that in which that which 5 has ceased to be has ceased to be and that in which that which has come to be has come to be are indivisible.

But there are two senses of the expression ' the primary when in which something has changed On the one hand it may mean the primary when containing the completion of the process of change — the moment when it is correct to say ‘it has changed': on the other hand it may mean the primary when containing the beginning of the process of change. Now the primary when that has reference to 10 the end of the change is something really existent : for a change may really be completed, and there is such a thing as an end of change, which we have in fact shown to be indivisible because it is a limit. But that which has

1 sc. Bl' will have more right than AT to be regarded as that in which the change has been completed.

reference to the beginning is not existent at all : for there is no such thing as a beginning of a process of change , 1 and the time occupied by the change does not contain 15 any primary when in which the change began. For suppose that AA is such a primary when. Then it cannot be indivisible: for, if it were, the moment immediately preceding the change and the moment in which the change begins would be consecutive (and moments cannot be consecutive). Again, if the changing thing is at rest in the whole preceding time TA 2 (for we may suppose that it is at rest), it is at rest in A also 3 : so if AA is without parts, it will simultaneously be at rest and have changed : for it is 20 at rest in A and has changed in A . 4 Since then AA is not without parts, it must be divisible, and the changing thing must have changed in every part of it (for if it has changed in neither of the two parts into which A A is divided, it has not changed in the whole either : if, on the other hand, it is in process of change in both parts, it is likewise in process of change in the whole : and if, again, it has changed in one of the two parts, the whole is not the primary when in 25 which it has changed : it must therefore have changed in every part). It is evident, then, that with reference to the beginning of change there is no primary when in which change has been effected : for the divisions are infinite.

So, too, of that which has changed there is no primary part that has changed. For suppose that of AE the primary part that has changed is AZ (everything that 30 changes having been shown 5 to be divisible): and let 01

1 i. e. no part of the process can be called absolutely first, because that part may be divided again, thus reaching a prior ‘first ’, and so on to infinity. Similarly of course no part of the process can strictly be called the end : but the limit (iripas) exists as such, because it is not a part of the process but an indivisible something marking the fact that the process is concluded. In the same sense there is an dpxhi but it is not strictly speaking an apxn pcTafio\rjs t because as yet the process has not begun ; so it remains true that there is no such thing as t 6 iv $ npArco rjp^nro p era/3d\\fiv.

2 i e. if the two moments mentioned above are assumed to be really only one (A).

8 It would be more correct to say ‘ is not in motion in A *, for in a moment nothing can be either at rest or in motion (234* 24 sqq.).

4 sc. because AA being indivisible is the same as A.

be the time in which AZ has changed. If, then, in the whole time AZ has changed, in half the time there will be a part 1 that has changed, less than and therefore prior to AZ : and again there will be another part prior to this, and yet another, and so on to infinity. Thus of that which changes there cannot be any primary part that has changed.

It is evident, then, from what has been said, that neither 35 of that which changes nor of the time in which it changes is there any primary part.

With regard, however, to the actual subject of change 2 — that is to say that in respect of which a thing changes — there is a difference to be observed. For in a process of change we may distinguish three terms — that which changes, that in which it changes, and the actual subject of change , 3 e. g. the man, the time, and the fair complexion^

Of these the man and the time are divisible: but with the 5 fair complexion it is otherwise (though they are all divisible accidentally, for that in which the fair complexion or any other quality is an accident is divisible). For 4 of actual subjects of change it will be seen that those which are classed as essentially, not accidentally, divisible have no primary part. Take the case of magnitudes: let AB be 10 a magnitude, and suppose that it has moved from B to a primary ‘ where * F. Then if BF is taken to be indivisible, two things without parts will have to be contiguous (which is impossible): if on the other hand it is taken to be divisible, there will be something prior to T to which the magnitude has changed, and something else again prior to that, and so on to infinity, because the process of division may be continued without end. Thus there can be no 15

1 1 . 32 reading torm rt, with Simp.

3 Keeping in 1. 1 the reading of all the MSS. — aiVo Se & ^er«&iXX«t (‘ the actual tiling that changes’ in the particular ptraSaWov, e. g. its place, its quantity, its quality), explained immediately as k<i 8 * 6 lAtrafidWft,

8 Reading in 1 . 3 with four MSS. km 6 tura&dWn, to be explained as above.

4 The generally accepted punctuation can hardly be right, as the cntt clause contains no sort of justification of the immediately preceding statement : it connects rather with the sentence ending ovk( 0 ' 6 polm *£«* (236^ 1), the intervening sentence being of a parenthetical character.

primary * where ’ to which a thing has changed. And if we take the case of quantitative change, we shall get a like result, for here too the change is in something continuous.

It is evident, then, that only in qualitative motion can there be anything essentially indivisible.

20 Now everything that changes changes in time, and that 6 in two senses: for the time in which a thing is said to change may be the primary time, or on the other hand it may have an extended reference, as e. g. when we say that a thing changes in a particular year because it changes in a particular day. That being so, that which changes must be changing in any part of the primary time in which it changes. This is clear from our definition of 1 * * primary V in which the word is said to express just this: it may also, however, be made evident by the following argument. a5 Let XP be the primary time in which that which is in motion is in motion: and (as all time is divisible) let it be divided at K. Now in the time XK it either is in motion or is not in motion, and the same is likewise true of the time KP. Then if it is in motion in neither of the two parts, it will be at rest in the whole : for it is impossible that it should be in motion in a time in no part of which 30 it is in motion. If on the other hand it is in motion in only one of the two parts of the time, XP cannot be the primary time in which it is in motion : for its motion will have reference to a time other than XP. It must, then, have been in motion in any part of XP.

And now that this has been proved, it is evident that everything that is in motion must have been in motion before. For if that which is in motion has traversed the 35 distance KA in the primary time XP, in half the time a thing that is in motion with equal velocity and began its motion at the same time will have traversed half the distance. But if this second thing whose velocity is equal a 37 has traversed a certain distance in a certain time, the

1 2 35 b 33* The 4 primary time 9 is the irreducible minimum : thus the very terms of the definition make it clear that a thing must be changing in the whole of the * primary time * in which it changes.

original thing that is in motion must have traversed the same distance in the same time. Hence that which is in motion must have been in motion before.

Again, if by taking the extreme moment of the time — for it is the moment that defines the time, and time is that 5 which is intermediate between moments — we are enabled to say that motion has taken place in the whole time XP or in fact in any period 1 of it, motion may likewise be said to have taken place in every other such period. But half the time finds an extreme in the point of division. Therefore motion will have taken place in half the time and in fact in any part of it : for as soon as any division is made there is always a time defined by moments. If, then, all time is divisible, and that which is intermediate between 10 moments is time, everything that is changing must have completed an infinite number of changes.

Again, since a thing that changes continuously and has not perished or ceased from its change must either be changing or have changed in any part of the time of its change, and since it cannot be changing in a moment, it follows that it must have changed at every moment in the time: consequently, since the moments are infinite in 15 number, everything that is changing must have completed an infinite number of changes.

And not only must that which is changing have changed, but that which has changed must also previously have been changing, since everything that has changed from something to something has changed in a period of time. For 30 suppose that a thing has changed from A to B in a moment. Now the moment in which it has changed cannot be the same as that in which it is at A (since in that case it would be in A and B at once) : for we have shown above 2 * that that which has changed, when it has changed, is not in

1 Reading in 1. 4 rj oAa>r lv otmovv xp° p< P' The insertion of a second rj after 5 \<os seems to make oA pointless, rw iravr\ xp having preceded : and cf. below oAo>r h qt&ovv t&v /ufpwv (23 7* 8). If the text is otherwise right, xp™*? here must mean 4 period of the whole time ’ :

otherwise no sense can be given to roh oXXot* : but one would like to read something like cV 6 t<$ovv xP& vt P rovrov), r<j> A afaiv kt A.

that from which it has changed. If, on the other hand, it isa different moment, there will be a period of time intermediate between the two: for, as we saw, 1 moments are 25 not consecutive. Since, then, it has changed in a period of time, and all time is divisible, in half the time it will have completed another 2 change, in a quarter another, and so on to infinity: consequently when it has changed, it must have previously been changing.

Moreover, the truth of what has been said is more evident in the case of magnitude, because the magnitude 30 over which what is changing changes is continuous. For suppose that a thing 3 has changed from T to A. Then if TA is indivisible, two things without parts will be consecutive. But since this is impossible, that which is intermediate between them must be a magnitude and divisible into an infinite number of segments : consequently, before the change is completed, the thing changes to those segments. Everything that has changed, therefore, must previously 35 have been changing : for the same proof also holds good *S 1 h of change with respect to what is not continuous, changes, that is to say, between contraries and between contradictories. In such cases we have only to take the time in which a thing has changed and again apply the same reasoning. So that which has changed must have been changing and that which is changing must have changed, and a process of change is preceded by a completion of 5 change and a completion by a process : and we can never take any stage and say that it is absolutely the first. The reason of this is that no two things without parts can be contiguous, and therefore in change the process of division is infinite, 4 just as lines may be infinitely divided so that one part is continually increasing and the other continually decreasing. 5

1 231*6 sqq. : where it is shown that moments cannot be of which fvou is a subdivision (V. 3. 227*6).

2 i. e. different from the whole change.

3 1 . 30 reading yap n, with F.

6 i. e. you may begin by cutting off half the line, then half of what remains, and so on, the part cut off thus continuously increasing and the part remaining continually decreasing.

So it is evident also that that which has become must *o previously have been in process of becoming, and that which is in process of becoming must previously have become everything (that is) that is divisible and continuous : though it is not always the actual thing that is in process of becoming of which this is true: sometimes it is something else, that is to say, some part of the thing in question, e. g. the foundation-stone of a house. 1 So, too, in the case of that which is perishing and that which has perished : for that which becomes and that which perishes must contain an element of infiniteness as an immediate consequence of the fact that they are continuous things 2 : and 15 so a thing cannot be in process of becoming without having become or have become without having been in process of becoming. So, too, in the case of perishing and having perished : perishing must be preceded by having perished, and having perished must be preceded by perishing. It is evident, then, that that which has become must previously have been in process of becoming, and that which is in process of becoming must previously have become: for all 20 magnitudes and all periods of time are infinitely divisible.

Consequently no absolutely first stage of change can be represented by any particular part of space or time which the changing thing may occupy.

7 Now since the motion of everything that is in motion occupies a period of time, and a greater magnitude is traversed in a longer time, it is impossible that a thing should undergo a finite motion in an infinite time, if this is 35 understood to mean not that the same motion or a part of it is continually repeated, 3 but that the whole infinite time is occupied by the whole finite motion. In all cases where a thing is in motion with uniform velocity it is clear that the finite magnitude is traversed in a finite time. For if

1 i. e. the ‘ having become ’ (completion) of a house must be preceded by its ‘ becoming ’ : for when a foundation-stone is being laid, the process is to be regarded not merely as the laying of the foundation-stone but also as the building of the house, of which it is a part.

1 i. e. they are which being crvvtxfj are therefore cis antipuv

&iaip€TCl.

8 as e.g. in the case of rotation or the swing of a pendulum.

U37 b we take a part of the motion which shall be a measure of the whole, the whole motion is completed in as many equal 1 30 periods of the time as there are parts of the motion. Consequently, since these parts are finite, both in size individually and in number collectively, the whole time must also be finite : for it will be a multiple of the portion, equal to the time occupied in completing the aforesaid part multiplied by the number of the parts.

But it makes no difference even if the velocity is not uniform. For let us suppose that the line AB 2 repre- 35 sents a finite stretch over which a thing has been moved in the given time, and let TA be the infinite time.

238* Now if one part of the stretch must have been traversed before another part (this is clear, that in the earlier and in the later part of the time a different part of the stretch has been traversed : for as the time lengthens a different part of the motion will always be completed in it, whether the 5 thing in motion changes with uniform velocity or not : and whether the rate of motion increases or diminishes or remains stationary this is none the less so), :t let us then take AE a part of the whole stretch of motion AB which shall be a measure of AB. Now this part of the motion occupies a certain period of the infinite time: it cannot itself occupy an infinite time, for we are assuming that that is occupied by the whole AB. And if again I take another 10 part equal to AE, that also must occupy a finite time in consequence of the same assumption. And if I go on taking parts in this way, on the one hand there is no part which will be a measure of the infinite time (for the infinite cannot be composed of finite parts whether equal or unequal, because there must be some unity which will be a measure 15 of things finite in multitude or in magnitude, which, whether they are equal or unequal, are none the less limited in magnitude) ; while on the other hand the finite stretch of motion AB is a certain multiple of AE : consequently the motion AB must be accomplished in a finite time. More-

* Reading in 1 . 35 rb AB, with Simp, and Bonitz.

* Reading a comma after »)ttov in 1. 6, with Bonitz.

over it is the same with coming to rest as with motion . 1 And so it is impossible for one and the same thing to be infinitely in process of becoming or of perishing . 2

The same reasoning will prove that in a finite time there 20 cannot be an infinite extent of motion or of coming to rest, whether the motion is regular or irregular. For if wc take a part which shall be a measure of the whole time, in this part a certain fraction, not the whole, of the magnitude will be traversed, because we assume that the traversing of the whole occupies all the time. Again, in another equal part of the time another part of the magnitude will be traversed : and similarly in each part of the time that we 35 take, whether equal or unequal to the part originally taken.

It makes no difference whether the parts are equal or not, if only each is fin'te : for it is clear that while the time is exhausted by the subtraction of its parts, the infinite magnitude will not be thus exhausted, since the process of subtraction is finite both in respect of the quantity subtracted and of the number of times a subtraction is made. Consequently the infinite magnitude will not be traversed in a finite time : and it makes no difference whether the 30 magnitude is infinite in only one direction or in both : for the same reasoning will hold good.

This having been proved, it is evident that neither can a finite magnitude traverse ar infinite magnitude in a finite time, the reason being the same as that given above : in part of the time it will traverse a finite magnitude and in 35 each several part likewise, so that in the whole time it will traverse a finite magnitude.

And since a finite magnitude will not traverse an infinite in a finite time, it is clear that neither will an infinite »38 b traverse a finite in a finite time. For if the infinite could traverse the finite, the finite could traverse the infinite ; for it makes no difference which of the two is the thing in motion: either case involves the traversing of the infinite

1 viz. a finite process of coming to rest (completion of motion) cannot occupy an infinite time.

8 A thing that is TO avrb Ka\ #V is TMTtpaaniPOv : its ycmris or $0opd is therefore also irtntpaa-pivrj and cannot be awei'p^ ( t0 which du is here equivalent),

'UJ5.J6 M

5 by the finite. For when the infinite magnitude A is in motion a part of it, say FA, will occupy the finite B , 1 atid then another, and then another, and so on to infinity. Thus the two results will coincide : the infinite will have completed a motion over the finite and the finite will have traversed the infinite : for it would seem to be impossible io for the motion of the infinite over the finite to occur in any way other than by the finite traversing the infinite either by locomotion over it or by measuring it . 2 Therefore, since this is impossible, the infinite cannot traverse the finite.

Nor again will the infinite traverse the infinite in a finite 15 time. Otherwise it would also traverse the finite, for the infinite includes the finite. We can further prove this in the same way by taking the time as our starting-point . 3

Since, then, it is established that in a finite time neither will the finite traverse the infinite, nor the infinite the finite, nor the infinite the infinite , 4 it is evident also that in 20 a finite time there cannot be infinite motion : for what difference does it make whether we take the motion or the magnitude to be infinite? If either of the two is infinite, the other must be so likewise: for all locomotion is in space . 6

Since everything to which motion or rest is natural is in 8 motion or at rest in the natural time, place, and manner, that which is coming to a stand, when it is coming to 35 a stand, must be in motion : for if it is not in motion it must be at rest : but that which is at rest cannot be coming to rest . 6 From this it evidently follows that coming to a stand must occupy a period of time : for the motion of that which is in motion occupies a period of time, and that

1 Reading in 1 . 6 to B to irarepaapuop, with E.

2 i. e. the finite must either travel from end to end of the infinite (if the infinite could have ends) or be itself traversed by the infinite, thus * measuring up ' the infinite with itself as the measure.

8 viz. by dividing up the ir rn tpaa pivot \P l in the way described above (238*22 sqq.) instead of the mntpaapivov piytSot.

4 Reading in 1 . 18 rb iinetpov to arrtipnv, with FHI 2 K.

• And therefore infinity in any of the terms must imply spatial infinity of st>rae sort. v

• In tljis connexion ripcptfaBui is identical in meaning with imaotai.

which is coming to a stand has been shown to be in motion : consequently coming to a stand must occupy a period of time.

Again, since the terms 'quicker* and ‘slower* are used only of that which occupies a period of time, and the process 30 of coming to a stand may be quicker or slower, the same conclusion follows.

And 1 that which is coming to a stand must be coming to a stand in any part of the primary time in which it is coming to a stand. For if it is coming to a stand in neither of two parts into which the time may be divided, it cannot be coming to a stand in the whole time, with the result that that which is coming to a stand will not be coming to a stand. If on the other hand it is coming to a stand in only one of the two parts of the time, the whole cannot be the primary time in which it is coming to a stand: for it 33 is coming to a stand in the whole time not primarily but in virtue of something distinct from itself, 2 the argument being the same as that which we used above about things in motion. 3

And just as there is no primary time in which that which is in motion is in motion, so too there is no primary time 239 11 in which that which is coming to a stand is coming to a stand, there being no primary stage either of being in motion or of coming to a stand. For let AB be the primary time in which a thing is coming to a stand. Now AB cannot be without parts : for there cannot be motion in that which is without parts, because the moving thing would necessarily have been already moved for part o' the time of its movement : 4 and that which is coming to 5 a stand nas been shown to be in motion. But since AB is therefore divisible, the thing is coming to a stand in every one of the parts of AB: for we have shown above 6 that it

1 A new point is here introduced. It is not the apodosis to the previous sentence cri 3* «t *tX., which serves only to substantiate the conclusion already reached : the apodosis is not expressed, but is easily supplied.

B 238 b 3£ sqq.

is coming to a stand in every one of the parts in which it is primarily coming to a stand. Since, then, that in which primarily a thing is coming to a stand must be a period of time and not something indivisible, and since all time is infinitely divisible, there cannot be anything in which primarily it is coming to a stand, io Nor again can there be a primary time at which the being at rest of that which is at rest occurred : for it cannot have occurred in that which has no parts, because there cannot be motion in that which is indivisible, and that in which rest takes place is the same as that in which motion takes place : for we defined 1 a state of rest to be the state of a thing to which motion is natural but which is not in motion when (that is to say in that 2 in which) motion would be natural to it. Again, our use of the phrase ‘being at 15 rest* also implies that the previous state of a thing is still unaltered, not one point only but two at least being thus needed to determine its presence : consequently that in which a thing is at rest cannot be without parts. Since, then, it is divisible, it must be a period of time, and the thing must be at rest in every one of its parts, as may be shown by the same method as that used above in similar demonstrations.

20 So there can be no primary part of the time : and the reason is that rest and motion are always in a period of time, and a period of time has no primary part any more than a magnitude or in fact anything continuous : for everything continuous is divisible into an infinite number of parts.

And since everything that is in motion is in motion in a period of time and changes from something to something, when its motion is comprised within a particular period of time essentially — that is to say when it fills the whole and 35 not merely a part of the time in question 3 — it is impossible

2 sc. time. *ai lv Z (which is here equivalent to orf) is added simply for the sake of introducing the exact expression used immediately before.

a 1. 24. It is hard to get any sense out of Bekker's reading — r&v iv tKfivov n vL The reading of EH I Simp, rut tWyov rm will give the that in that time that which is in motion should be over against some particular thing primarily. 1 For if a thing — itself and each of its parts — occupies the same space for a definite period of time, it is at rest : for it is in just these circumstances that we use the term ‘ being at rest ' — when at one moment after another it can be said with truth that a thing, itself and its parts, occupies the same space. So if this is being at rest it is impossible for that which is ?,o changing to be as a whole, at the time when it is primarily changing, over against any particular thing (for the whole period of time is divisible), so that in one part of it after another it will be true to say that the thing, itself and its parts, occupies the same space. If this is not so and the aforesaid proposition is true only at a single moment, then the thing will be over against a particular thing not for any period of time but only at a moment that limits the time.

It is true that at any moment it is always over against 35 something stationary : but it is not at rest : for at a moment 239 b it is not possible for anything to be either in motion or at rest. So while it is true to say that that which is in motion is at a moment not in motion and is opposite some particular thing, it cannot in a period of time be over against that which is at rest : for that would involve the conclusion that that which is in locomotion is at rest.

9 Zeno's reasoning, however, is fallacious, when he says that 5 if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. 2 This is false, for time is not composed of required sense, as also would rw cV row ckcivov tl pi, which I would suggest as best accounting for the variants.

* i.e. a space only just large enough to contain it, not a larger space of which only part is occupied.

2 Zeno’s argument apparently does not prove that the arrow is at rest because it is not in motion, ad fjptfxtiirav t) kivutm is therefore not used as a premise, and the best way of emending the passage is (with Zeller) to treat fj tavurai as a gloss introduced through the influence of such passages as 23*> b 23. tan 1. 6 can in the context stand for c<m Kara t6 "<rop t but possibly we should insert Kara to taov after vvv 1 . 7, with Zeller and some MS. support.

indivisible moments any more than any other magnitude is composed of indivisibles.

io Zeno's arguments 1 about motion, which cause so much disquietude to those who try to solve the problems that they present, are four in number. The first asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal . 8 This we have discussed above . 3

The second is the so-called ‘ Achilles’, and it amounts 15 to this, that in a race the quickest runner can never overtake the slowest 4 , since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. This argument is the same in principle as that which depends on bisection , 6 though it differs from it in that the spaces with which we successively have to 20 deal are not divided into halves. The result of the argument is that the slower is not overtaken : but it proceeds along the same lines as the bisection-argument (for in both a division of the space in a certain way leads to the result that the goal is not reached, though the 4 Achilles 9 goes further in that it affirms that even the quickest runner 6 in legendary tradition must fail in his 35 pursuit of the slowest 7 ), so that the solution must be the same. And the axiom that that which holds a lead is never overtaken is false: it is not overtaken, it is true, while it holds a lead : but it is overtaken nevertheless if it is granted that it traverses the finite distance prescribed. These then are two of his arguments.

30 The third is that already given above, to the effect that

1 On the arguments generally see Noel in the Revue de M/taphysique et de Morale , vol. i, pp. 107 sqq., and Russell, Principles of Mathematics , vol. i, chs. 42, 43. Further references to the literature of the subject are given in Zeller, i. 6 755 n., and in Heath, Gk. Mathematics ■, i. 279, 280 n, 1, 283 n. 2. The first two arguments are addressed to those who assert, the second two to those who deny the infinite divisibility of space and time.

2 The remaining half being again divisible into two, and so on to infinity.

4 Reading ml. 15 fipa&vTarov, with E, Themistius, and Simplicius.

6 viz. the first argument given above, 11. 11-14.

6 sc. Achilles as described by Homer — rro^as wkvs

7 sc. the tortoise, proverbial for slowness : cf. Plut. Mor. 1082 E.

the flying arrow is at rest, which result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow.

The fourth argument 1 is that concerning the two rows of

1 Zeno’s fourth argument may be represented thus : —

Let C 1 have reached B* at the moment M in the time T,

Then at the same moment M—

(1) Since B x and C l are travelling with equal velocity, B 3 i must have reached C 8 (= A 8 ) and must have occupied the same time as CK Therefore B l 's time == T.

(2) C l must have travelled a distance equal to A l -A s t since (a) it has passed all the B* s, (j3) each B = each A, (y) spaces of equal size must be traversed in equal times if the speed be equal. B\ however, has only travelled the distance A 5 - A 8 . Therefore B\ having travelled only half the distance, can have occupied only half the time that has

T been occupied by C\ Therefore B v s time = — .

( 3 ) C 1 must have completed the course, since having started at the middle point of the course it has travelled a distance equal to A l * -A 8

(«= half the course). Therefore B l must also have completed the course. But for this to have happened (that is to say, for all the B’s to have passed all the C’s) twice as much time must have elapsed as bodies, each row being composed of an equal number of bodies of equal size, passing each other on a race-coursc as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that 35 between the middle point and the starting-post. This, he thinks, involves the conclusion that half a given time is 240* equal to double that time. The fallacy of the reasoning lies in the assumption that a body occupies an equal time in passing with equal velocity a body that is in motion and a body of equal size that is at rest ; which is false.' For instance (so runs the argument), let A, A . . . be the 5 stationary bodies of equal size, B, B . . . the bodies, equal in number and in size to A, A . . originally occupying the half of the course from the starting-post to the middle of the As, and T, T . . . those originally occupying the other half from the goal to the middle of the A's, equal in number, size, and velocity to B, B . . . . Then three consequences follow :

First, as the B’s and the Fs pass one another, the first B reaches the last F at the same moment as the first F io reaches the last B. Secondly, 1 at this moment the first F has passed all the A’s, 2 whereas the first B :J has passed was necessary to enable C 1 to reach IP. But the time occupied by C 1 in reaching IP — T . Therefore B lt s time — 2 T.

Thus at the same moment M the time occupied since the start by T

P l is both — and 2 T. Consequently, if motion is possible, half a given time is equal to double that time, which is absurd. Therefore motion is impossible. Q.E.D.

As the argument is intended for those who attempt to evade the first two by denying the infinite divisibility of space and time, and to refute scientific theories as to the structure of matter that involve the view that matter' is divisible ultimately into units {oyKOi) occupying a certain amount of space and yet not themselves divisible, the assumption that Aristotle stigmatizes as false is not an arbitrary assumption of Zeno’s own but a deduction from the view criticized.

For a further discussion of the passage and justification of the rendering given above, see an article by R. K. Gaye in the Journal of Philology , xxxi. 95 sqq.

1 Reading cn/fiftaivu Si, with ETHK, Alex.

4 Reading iravra to. A, with FKE 2 and Simplicius.

3 Reading ri> Si B, with E and Simplicius.

only half the A’s, and has consequently occupied only half the time occupied by the first F, since each of the two occupies an equal time in passing each A. Thirdly, at the same moment all the B’s have passed all the T’s : for the first T and the first B will simultaneously reach the opposite ends of the course, since (so says Zeno) the time occupied 15 by the first T in passing each of the B’s is equal to that occupied by it in passing each of the A’s, because an equal time is occupied by both the first B and the first F in passing all the A’s. This is the argument, but it presupposed the aforesaid fallacious assumption.

Nor in reference to contradictory change shall vve find anything unanswerable in the argument that if a thing is 20 changing from not-white, say, to white, and is in neither condition, then it will be neither white nor not-white: for the fact that it is not 7 cholly in cither condition will not preclude us from calling it white or not-white. We call a thing white or not-white not necessarily because it is wholly either one or the other, but because most of its parts or the most essential parts 1 of it are so: not being in a certain 25 condition is different from not being wholly in that condition.

So, too, in the case of being and not-being and all other conditions which stand in a contradictory relation : while the changing thing must of necessity be in one of the two opposites, it is never wholly in either.

Again, in the case of circles and spheres and everything whose motion is confined within the space that it occupies, it is not true to say that the motion can be nothing but 30 rest, on the ground that such things in mot ion, themselves and their parts, will occupy the same position for a period of time, and that therefore they will be at once at rest and in motion.

For in the first place the parts do not occupy the same position for any period of time : and in the second place the whole also is always changing to a different position : for if we take the orbit as described from a point A on a 240**

1 i. e. the parts (not necessarily a majority of the whole) the whiteness of which more especially justifies us in calling the whole thing white : e.g. we may speak of the sea being white if the crests of the waves are white.

circumference, it will not be the same as the orbit as described from B or T or any other point on the same circumference except in an accidental sense, the sense that is to say in which a musical man is the same as a man. 1

5 Thus one orbit is always changing into another, and the thing will never be at rest. And it is the same with the sphere and everything else whose motion is confined within the space that it occupies.

Our next point is that that which is without parts cannot IO be in motion except accidentally: i.e. it can be in motion only in so far as the body or the magnitude is in motion io and the partless is in motion by inclusion therein, 2 just as that which is in a boat may be in motion in consequence of the locomotion of the boat, or a part may be in motion in virtue of the motion of the whole. (It must be remembered, however, that by ‘ that which is without parts' I mean that which is quantitatively indivisible (and that the case of the motion of a part is not exactly parallel ) 3 : for parts have motions belonging essentially and severally to themselves 15 distinct from the motion of the whole. The distinction may be seen most clearly in the case of a revolving sphere, in which the velocities of the parts near the centre and of those on the surface are 4 different from one another and from that of the whole ; this implies that there is not one motion but many.) As we have said, then, that which is without parts can be in motion in the sense in which a man sitting in a boat is in motion when the boat is travelling,

30 but it cannot be in motion of itself. For suppose that it is

1 i.e. the one orbit is the same as the other only in the sense that they both belong to or are * accidents ’ of ((rvfifteftqtcf) the same portion of space, just as the attributes pova-iKos and «i/<9/>(«>7ror may belong to the same individual.

8 The point is that to apfptf can have no motion of its own just because it is dfirpts, whereas fupiy, not being < l/uepf /, may have motions of their own as well as accidental motions. It is only in so far as the ptpos is in motion merely in virtue of the motion of the oAov that its motion is comparable with that of the dpipts.

changing from AB to Br — either from one magnitude to another, 1 or from one form to another, 2 or from some state to its contradictory — and let A be the primary time in which it undergoes the change. Then in the time in which it is changing it must be either in AB or in Br or partly in one and partly in the other : for this, as we saw, 3 is true of as everything that is changing. Now it cannot be partly in each of the two: for then it would be divisible into parts. Nor again can it be in Br : for then it will have completed the change, whereas the assumption is that the change is in process. It remains, then, that in the time in which it is changing, it is in AB. That being so, it will be at rest : for, as we saw, 4 to be in the same condition for a period of time is to be at rest. So it is not possible for 30 that which has no parts to be in motion or to change in any way: for only one condition could have made it possible for it to have motion, viz. that time shpuld be composed ofmoments, in which case at any moment it would have completed a motion or a change, so that it would never be 241® in motion, but would always have been in motion. But this we have already shown above 5 to be impossible: time is not composed of moments, just as a line is not composed of points, and motion is not composed of starts : for this theory simply makes motion consist of indivisibles in exactly 5 the same way as time is made to consist of moments or a length 6 of points.

Again, it may be shown in the following way that there can be no motion of a point or of any other indivisible. That which is in motion can never traverse a space greater than itself without first traversing a space equal to or less than itself. That being so, it is evident that the point also must first traverse a space equal to or less than itself. But 10 since it is indivisible, there can be no space less than itself

1 SC. either Kara t6ttov or Kara noaov.

8 234 b io sqq., where, however, it is pointed out that only the third alternative here mentioned is really possible (234 b 15) : the other two are included here only for the sake of completeness.

for it to traverse first : so it will have to traverse a distance equal to itself. Thus the line will be composed of points, for the point, as it continually traverses a distance equal to itself, will be a measure of the whole line. But since this is impossible, it is likewise impossible for the indivisible to be in motion.

Again, since motion is always in a period of time and never in a moment, and all time is divisible, for everything that is in motion there must be a time less than that 1 in which it traverses a distance as great as itself. For that in which it is in motion will be a time, because all motion is in a period of time ; and all time has been shown above 2 * to be divisible. Therefore;* if a point is in motion, there must be a time less than that 4 in which it has itself traversed 20 any distance. 5 But this is impossible, for in less time it must traverse less distance, and thus the indivisible will be divisible into something less than itself, just as the time is so divisible : the fact being that the only condition under which that which is without parts and indivisible could be in motion would have been the possibility of the infinitely 25 small being in motion in a moment : for in the two questions— that of motion in a moment and that of motion of something indivisible — the same principle is involved.

Our next point is that no process of change is infinite t for every change, whether between contradictories or between contraries, is a change from something to something. Thus in contradictory changes the positive or the negative, as the case may be, is the limit, e. g. being is the limit of coming to be and not-being is the limit of ceasing, to be : and in contrary changes the particular contraries 30 are the limits, since these are the extreme points of any such process of change, and consequently of every process

2 f, e A d ' ng in *• *7 ( with F - and apparently Simplicius) f, ,V <S.

Omitting S’ in 1. 19, with FHK.

‘ sc. a distance equal to itself, which ‘is the least it can travel (211* 1 ‘K , If would be easler lf we could read oow mV/, 0 r urop mV,/ with(apparently) Philoponus and Themistius. ' * 1 of alteration : for alteration is always dependent upon 1 some contraries. Similarly contraries are the extreme points of processes of increase and decrease : the limit of increase is to be found in the complete magnitude proper to the peculiar nature of the thing that is increasing, while »4i b the limit of decrease is the complete loss of such magnitude. Locomotion, it is true, we cannot show to be finite in this way, since it is not always between contraries. But since that which cannot be cut (in the sense that it is inconceivable that it should be cut, the term ‘cannot' being used in several senses 2 ) — since it is inconceivable that that 5 which in this sense cannot be cut should be in process of being cut, and generally that that which cannot come to be should be in process of coming to be, it follows that it is inconceivable that that which cannot complete a change 3 should be in process of changing to that to which it cannot complete a change. 3 If, then, it is to be assumed that that which is in locomotion is in process of changing, it must be capable of completing the change. 3 Consequently its motion is not infinite, and it will not be in locomotion over an infinite distance, for it cannot traverse such a 10 distance.

It is evident, then, that a process of change cannot be infinite in the sense that it is not defined by limits. But it remains to be considered whether it is possible in the sense that one and the same process of change may be infinite in respect of the time which it occupies. Jf it is not one process, it would seem that there is nothing to prevent its being infinite in this sense; e. g. if a process 15 of locomotion be succeeded by a process of alteration and that by a process of increase and that again by a process

1 That this is the meaning of *£ here seems clear. It is unlikely that the starting-point of the change should be insisted upon rather than the final limit; cf. 241*29, 30 above. Aristotle means that the existence of dWoitotns always implies the existence of a pair of contraries.

2 For the different senses of dbvvarov see Metaph . A. ioi9 l> 19 sqq.

8 Reading in 11 . 7 (after to), 8, and 9 (with one MS.) /if raftaXtiv, the aorist being necessary to denote the act as opposed to the process of change ; cf. Tfv ffipat )( TtfivtaOcu above. Simplicius apparently had fjLfTaftaktiv.

24I b of coming to be : in this way there may be motion for ever so far as the time is concerned, but it will not be one motion, because all these motions do not compose one. If it is to be one process, no motion can be infinite in respect of the time that it occupies, with the single excep- 20 tion of rotatory locomotion.

24I b i Everything that is in motion must be moved by something. For if it has not the source of its motion in itself 25 it is evident that it is moved by something other than itself, for there must be something else that moves it. If on the other hand it has the source of its motion in itself, let AB be taken to represent that which is in motion essentially of itself and not in virtue of the fact that something belonging to it is in motion. Now in the first place to assume that AB, because it is in motion as a whole and is not moved 30 by anything external to itself, is therefore moved by itself — this is just as if, supposing that KA is moving AM and is also itself in motion, we were to deny 1 2 that KM is moved by anything on the ground that it is not evident which is the part that is moving it and which the part that is moved.

In the second place that which is in motion without being moved by anything does not necessarily cease from its motion because something else is at rest, but a thing must 342® be moved by something if the fact of something else having ceased from its motion causes it to be at rest. Thus, 3 if this is accepted, everything that is in motion must be moved by something. For AB, which has been taken to 5 represent that which is in motion, must be divisible, since everything that is in motion is divisible. Let it be divided, then, at T. Now if TB is not in motion, then AB will not be in motion : for if it is, it is clear that Ar would be in motion while BF is at rest, and thus AB cannot be in 10

1 On the text of this book, see Shute, Anecdota Oxoniensia , Classical Series, vol. i, part 3. For the purposes of this translation the Teubner text of Prantl has been taken as the standard for chapters I to 3.

2 It will make no difference to the translation whether cl is repeated before w <f>a(ncot or not. In view of the intervening clause the repetition does not seem impossible.

8 The use of yap implies a slight ellipse : * (I make this point) for . . .* a4« a motion essentially and primarily. But ex hypotkcsi AB is in motion essentially and primarily. Therefore if TB is not in motion AB will be at rest. But we have agreed that that which is at rest if something else is not in motion must be moved by something. Consequently, everything that is in motion must be moved by something : for that 15 which is in motion will always be divisible, and if a part of it is not in motion the whole must be at rest.

Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved 1 2 by something else that is in motion, and that by something else, and so on con- 20 tinually : then the series cannot go on to infinity, but there must be some first movent. For let us suppose that this is not so and take the series to be infinite. Let A then be moved by B, B by F, F by A, and so on, each member of the series being moved by that which comes next to it. Then since ex hypothesi the movent while causing motion is also itself in motion, and the motion of the moved and the motion of the movent must proceed simultaneously (for the movent is causing motion 3 and 35 the moved is being moved simultaneously) it is evident that the respective motions of A, B, I', and each of the other moved movents are simultaneous. Let us take the motion of each separately and let E be the motion of A, Z of B, and H and 0 respectively the motions of T and A: for though they are all moved severally one by another, yet we may still take the motion of each as numerically 30 one, since every motion is from something to something and is not infinite in respect of its extreme points. By a motion that is numerically one I mean a motion that proceeds from something numerically one and the same to something numerically one and the same in a period of time numerically one and the same : for a motion may be 35 the same generically, specifically, or numerically : it is

generically the same if it belongs to the same category, e. g. substance or quality: it is specifically the same if it proceeds from something specifically the same to something specifically the same, e. g. from white to black or from good to bad, which is not of a kind specifically distinct : 1 it is numerically the same if it proceeds from something 242 b numerically one to something numerically one in the same period of time, e g. from a particular white to a particular black, or from a particular place to a particular place, in a particular period of time: for if the period of time were not one and the same, the motion would no longer be numerically one though it would still be specifically one.

We have dealt with this question above . 2 Now let us * further take the time in which A has completed its motion, and let it be represented by K. Then since the motion of A J is finite the time will also be finite. But since the movents and the things moved arc infinite, the motion EZ 1 I 0 , i. e. the motion that is composed of all the individual motions, must be infinite. For the motions of 15 A, B, and the others may be equal, or the motions of the others may be greater : but assuming what is conceivable , 4 we find that whether they are equal 5 or some are greater, in both cases the whole motion is infinite. And since the motion of A and that of each of the others are simultaneous, the whole motion must occupy the same time as the motion of A: but the time occupied by the motion of A is finite: consequently the motion will be infinite in a finite time, which is impossible . 6

It might be thought that what we set out to prove 7 has

1 i. e. ayaSd and Katca themselves admit of further differences tear cifiop. Read in 1 . 37 us kkikov ndu'upnpov } with the MSS.

3 Reading in l.,io rrjs nw A, with the MSS.

4 i.e. certain conceivable cases: it will not do to assume the other possible case, viz. that in which, as we proceed backwards along the series of motions, they become less : for if Z were less than E, H than Z, and so on to infinity, tj 0X17 Klvrjmr would not be anupos,

8 Reading in 1 . 17 ft re ttrnt, with Simp.

8 i. e. it is impossible in such cases as we are considering, though the present case has not as yet been shown to be one of such cases : cf. the immediate sequel.

7 sc. that there is a irparov kivovv.

20 thus been shown, but our argument so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition : for in a finite time there may be an infinite motion, though not of one thing, but of many : and in the case that we are considering this is so: for each thing accomplishes its own motion, and there is no impossibility in many things being in motion simultaneously. But if (as we see to be universally the case) that which primarily is moved locally and corasporeally 1 must be either in contact with or continuous with that which moves it, the things moved and the movents must be continuous or in contact with one another, so that together they all form a single unity: whether this unity is finite or infinite makes no difference to our present argument ; for in any case since the things in motion are infinite in number the whole motion will be infinite, if, as is theoretically possible, each motion is either equal to or greater than that which follows it in the series : for we shall take as actual that which is theoretically possible. 30 If, then, A, B, T, A form an infinite magnitude 2 that passes through the motion EZH 0 in the finite time K, this involves the conclusion that an infinite motion is passed through in a finite time : and whether the magnitude in question is finite or infinite this is in either case impossible. Therefore the series must come to an end, and there must be a first movent and a first moved : 3 for the »43 a fact that this impossibility results only from the assumption of a particular case 4 is immaterial, since the case assumed is theoretically possible, and the assumption of a theoretically possible case ought not to give rise to any impossible result.

1 Locomotion caused by something acting on the body is here opposed to locomotion caused by something acting cn the mind, e. g.

r6 (ptHTTOV,

2 Reading in I. 31 (with the MSS.) dimp 6 p n. There is no need to alter (with Prantl) dnupop to rm> a7rfi'pa>v, as it is easy to take the words fj to ircncpacrjjicpov rj to aimpov at the end of the sentence as an afterthought added for the sake of completeness.

8 For Kivovptvov we should rather expect pf) Ktpovptpov (not moved by anything else), and this is what Simplicius seems to have read.

4 sc. the case in which each motion is either equal to or greater than the motion that follows it in the series.

2 That which is the first movent of a thing — in the sense that it supplies not ‘that for the sake of which * but the source of the motion — is always together with that which is moved by it (by ‘together' I mean that there is nothing intermediate between them). This is universally true 5 wherever one thing is moved by another. And since there are three kinds of motion, local, qualitative, and quantitative, there must also be three kinds of movent, that 10 which causes locomotion, that which causes alteration, and that which causes increase or decrease.

Let us begin with locomotion, for this is the primary motion. Everything that is in locomotion is moved either by itself or by something else. In the case of things that are moved by themselves it is evident that the moved and the movent are together : for they contain within themselves their first movent, so that there is nothing in between. The motion of things that are moved by some- 15 thing else must proceed in one of four ways : for there are four kinds of locomotion caused by something other than that which is in motion, viz. pulling, pushing, carrying, and twirling. All forms of locomotion are reducible to these.

Thus pushing on is a form of pushing in which that which is causing motion away from itself 1 follows up that which it pushes and continues to push it : pushing off occurs when the movent does not follow up the thing that it has moved : throwing when the movent causes a motion 20 away from itself 1 more violent than the natural locomotion 243*’ of the thing moved, which continues its course so long as it is controlled by the motion imparted to it. Again, pushing apart and pushing together are forms respectively of pushing oflf and pulling : pushing apart is pushing oflT, which may be a motion either away from the pusher or away from something else, while pushing together is pulling, 5 which may be a motion towards something else as well as towards the puller. We may similarly classify all the varieties of these last two, e. g. packing and combing: the former is a form of pushing together, the latter a form of pushing apart. The same is true of the other processes

1 Reading in ft 19, b 1, a(f> uvtov.

of combination and separation (they will all be found to be forms of pushing apart or of pushing together), 1 except such as are involved in the processes of becoming and io perishing. (At the same time it is evident that there is no other kind of motion but 2 combination and separation: for they may all be apportioned to one or other of those already mentioned.) Again, inhaling is a form of pulling, exhaling a form of pushing : and the same is true of spitting and of all other motions that proceed through the body, whether secretive or assimilative, the assimilative being forms of 15 pulling, the secretive of pushing off. All other kinds of locomotion must be similarly reduced, for they all fall under one or other of our four heads. And again, of these four, carrying and twirling are reducible to pulling and pushing. For carrying always follows one of the other three methods, for that which is carried is in motion accidentally, because it is in or upon something that is in 20 motion, and that which carries it is in doing so being either 244* pulled or pushed or twirled ; 3 thus carrying belongs to all the other three kinds of motion in common. And twirling is a compound of pulling and pushing, for that which is twirling a thing must be pulling one part of the thing and pushing another part, since it impels one part away from itself and another part towards itself. If, therefore, it can be shown that that which is pushing and that which is pulling are adjacent respectively to that which is being 5 pushed and that which is being pulled, it will be evident that in all locomotion there is nothing intermediate between

3 Reading in 1 . 11 (with the MSS. and Bekker) t) avyKpiaiu Prantl alters ff to 17 : the meaning would then be 1 combination and separation do not constitute a kind of motion distinct from those enumerated \ But this would be in part a repetition, and in part (so far as ytWtr and (f> 6 opd are concerned) a contradiction, of the preceding sentence. The reading of the MSS. is defensible if we regard &pn di . . . ttpr^pivwv as a parenthesis, the sense being that from another point of view we may reduce all kinds of motion to crvyicpuru and btaKpum, which are coextensive with wrtf and cXftr.

• i.e. unless to o^oiV happens to be a living being, but that case need not be considered, as Aristotle’s object is to prove that t 6 np&rov Ktpov v Kivovptvy *<m, which has already been proved in the case of things that avrd v<p avrtop wmrai, among which ffxyjrvxa are of course included. Cf. 243* 13 above.

moved and movent. But the former fact is clear even from the definitions of pushing and pulling, for pushing is motion to something else from oneself or from something else, and pulling is motion from something else to oneself or to something else, when the motion of that which is pulling is quicker 1 than the motion that would separate 2 io from one another the two things that are continuous: 3 for it is this that causes one thing to be pulled on along with the other. (It might indeed be thought that there is a form of pulling that arises in another way : that wood, e. g. pulls fire in a manner different from that described above. But it makes no difference whether that which pulls is in motion or is stationary when it is pulling: in the latter case it pulls to the place where it is, while in the former it pulls to the place where it was.) Now it is impossible to move anything either from oneself to something else 15 or from something else to oneself without being in contact with it : it is evident, therefore, that in all locomotion there 244* is nothing intermediate between moved and movent.

Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be proved by induction : for in every case we find that the respective extremities of that which causes and that which undergoes alteration are adjacent. For 4 our assumption is that things that are undergoing alteration are altered in virtue of their being affected in respect of their so-called

1 Reading in 1 . 9 Odrrwv, with Simp.

2 Reading in 1 . 10 (\kovtov rrj s xwpifoi'aqr, with Par. 1859 and Simp.

3 i. e. the thing pulling and the thing pulled. The second motion is the natural resistance of the thing pulled, which seeks to disconnect itself from that which is pulling it.

4 Reading in 1. 4 to nptbrop dWoiovpfPop. viroKtirai yap r}p.ip rb ra ti\\oiovp.€va Kara ras miBrjTucivt \cyopcpaf trotoT^rar i racr^opra dXXoiowr&n* to yap nou'ip dXXoiovTat rw aicr&r)rbp ( lvai‘ aiV^ra 5* /artV, otr $ia<£«poi/<ri to trdifxara dXX>)X«i>j'* anav yap <ra>pa ctoparos rots alaBrjTots rj irXfioo-iv rj Aarrocriv q r V f*<*X\oy teal Jjttov rots avroie' aXXa prjv kui dWoiovrat to d\\oiovfi(vop vird tS>p ilpr}p(p<ap* It seems clear that in the text as given by Bekker something imust have dropped out between dWaiovptpop and M tS>p tlprpitpup : and Prantl would restore it as above, partly from Simplicius and partly from the second text as given in six MSS. Even so the connexion of thought is not quite clear. For the term iraBrjrtKat TrouSnjm cf. Cat . viii. 9*28 sqq.

affective qualities, since that which is of a certain quality is altered in so far as it is sensible, and the characteristics in which bodies differ from one another are sensible characteristics ; for every body differs from another in possessing a greater or lesser number of sensible characteristics or in possessing the same sensible characteristics in a greater or lesser degree. But the alteration of that which undergoes alteration is also caused by the above-mentioned charac- 5 teristics, which are affections of some particular underlying quality, 1 Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white : and we make these assertions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts that have no power of senseio perception and of the senses themselves. For in a way even the senses undergo alteration, since the active sense is a motion through the body in the course of which the sense 2 * is affected in a certain way. We see, then, that the animate is capable of every kind of alteration of which the inanimate is capable : but the inanimate is not capable of every kind of alteration of which the animate is capable, since it is not capable of alteration in respect of the senses : 15 moreover the inanimate is unconscious of being affected by 245® alteration, whereas the animate is conscious of it, though there is nothing to prevent the animate also being unconscious of it when the process of the alteration does not concern the senses. Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration it is evident that the respective extremities of that which causes and that which 5 undergoes alteration are adjacent. Thus the air is continuous with that which causes the alteration, 11 and the body that undergoes alteration is continuous with the air. Again, the colour is continuous with the light and the light

1 Reading in 1 . 6 (with the MSS. and Bekker) rrjs wrojcetpcVipr not6njTos,

* nta-drjatf in this passage is used in such a way as to include the meanings of 4 sense- percept ion ’ and of 4 sense-organ \ s i. e. in cases of ci (f>fj such as Geppavcrtf, a 45 a with the sight. 1 And the same is true of hearing and smelling : for the primary movent in respect to the moved is the air. Similarly, in the case of tasting, the flavour is adjacent to the sense of taste. And it is just the same in the io case of things that are inanimate and incapable of sense-perception. Thus there can be nothing intermediate between that which undergoes and that which causes alteration.

Nor, again, can there be anything intermediate between that which suffers and that which causes increase : for the part of the latter that starts the increase does so by becoming attached in such a way to the former that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of the thing becoming detached. So that which causes increase and that which 15 causes decrease must be continuous with that which suffers increase and that which suffers decrease respectively : and if two things are continuous with one another there can be nothing intermediate between them.

It is evident, therefore, that between the extremities of the moved and the movent that are respectively first and last 245* in reference to the moved there is nothing intermediate.

3 Everything, we say, that undergoes alteration is altered by sensible causes, and there is alteration only in things that are said to be essentially affected by sensible things.

The truth of this is to be seen from the following con- 5 siderations. Of all other things it would be most natural to suppose that there is alteration in figures and shapes, and in acquired states and in the processes of acquiring and losing these: but as a matter of fact in neither of these two classes 2 of things is there alteration.

In the first place, when a particular formation 3 * 5 of a thing is completed, we do not call it by the name of its 10 material : e. g. we do not call the statue ‘ bronze * or the

1 Terms are used somewhat loosely all through this passage, cf.

alcr6r)<ns above. Here xP**P a ls coloured surface, <pm the illuminated air, and fyt? the organ of sight.

* tT\r)\iaTa and popfai make up one class as against Qus : hence

Ovfi(T€pOlS.

s»45 b pyramid 1 4 wax * or the bed * wood but we use a derived expression and call them 1 of bronze 1 waxen, 1 and ‘ wooden 1 respectively. But when a thing has been affected and altered in any way we still call it by the original name : thus we speak of the bronze or the wax being dry or fluid or hard or hot. 2 * i 5 And not only so: we also speak of the particular fluid or hot substance as being bronze, giving the material the same name as that which we use to describe the affection. 8

246® Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a things affections or alterations we still call it by the name of its material, it is evident that becomings of the former kind cannot be alterations.

Moreover it would seem absurd even to speak in this way, 5 to speak, that is to say, of a man or house or anything else that has come into existence as having been altered. Though it may be true that every such becoming is necessarily the result of something’s being altered, the result, e. g. of the material’s being condensed or rarefied or heated or cooled, nevertheless it is not the things that are coming into existence that are altered, and their becoming is not an alteration. I0 Again, acquired states, whether of the body or of the soul, are not alterations. For some are excellences and others are defects, and neither excellence nor defect is an alteration: excellence is a perfection (for when anything acquires its proper excellence we call it perfect, since it is then if ever 15 that we have a thing in its natural state : e. g. we have a perfect circle when we have one as good as possible), 4 while defect is a perishing of or departure from this condition. So just as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose. that the coping or the tiling is an alteration or

1 sc. candle.

2 Reading in 1. 13 (with four MSS.) fapov yap k ai vypou teat <TKkr)pov tca'i Btppov.

5 i. e. that which is lypav or 8 «pp 6 u (has the iruBot of vypurrjs or 8 pporijs) we may denote by the expression ru Btppov or to i>yp 6 v.

BOOK VII. 3 246* that in receiving its coping or its tiling a house is altered ao and not perfected), the same also holds good in the case of excellences and defects and of the persons or things that possess or acquire them : for excellences are perfections 246 b of a thing’s nature and defects are departures from it : consequently they arc not alterations.

Further, we say that all excellences depend upon particular relations. Thus bodily excellences such as health and a good state of body we regard as consisting in a 5 blending of hot -and cold elements within the body in due proportion, in relation either to one another or to the surrounding atmosphere : and in like manner we regard beauty, strength, and all the other bodily excellences and defects.

Kach of them exists in virtue of a particular relation and puts that which possesses it in a good or bad condition with regard to its proper affections, where by ‘proper’ affections I mean those influences that from the natural constitution of a thing tend to promote or destroy its existence. Since, then, relatives are neither themselves 10 alterations nor the subjects of alteration or of becoming or in fact of any change whatever, it is evident that neither states nor the processes of losing and acquiring states are alterations, though it may be true that their becoming or perishing is necessarily, like the becoming or perishing of 15 a specific character or form, the result of the alteration of certain other things, e. g. hot and cold or dry and wet elements or the elements, whatever they may be, on which the states primarily depend. For each several bodily defect or excellence involves a relation with those things from which the possessor of the defect or excellence is naturally subject to alteration : thus excellence disposes its possessor to be unaffected by these influences or to be affected by those of them that ought to be admitted, 1 while defect disposes its possessor to be affected by them or to be unaffected by those of them that ought to be admitted.

And the case is similar in regard to the states of the ao soul, all of which (like those of body) exist in virtue of 247®

1 The alternative is added because, while some would use nuSrj only in a bad sense, others would recognize both good and bad miBi}.

particular relations, the excellences being perfections of nature and the defects departures from it : moreover, excellence puts its possessor in good condition, while defect puts its possessor in a bad condition, to meet his proper affections. Consequently these cannot any more than the 5 bodily states be alterations, nor can the processes of losing and acquiring them be so, though their becoming is necessarily the result of an alteration of the sensitive part of the soul, and this is altered by sensible objects : for all moral excellence is concerned with bodily pleasures and pains, which again depend either upon acting or upon remembering or upon anticipating. Now those that depend upon io action are determined by sense-perception, i. e. they are stimulated by something sensible : and those that depend upon memory or anticipation are likewise to be traced to sense-perception, for in these cases pleasure is felt either in remembering what one has experienced or in anticipating what one is going to experience. Thus all pleasure of this kind 1 must be produced by sensible things : and since the presence 2 in any one of moral defect or excellence involves 15 the presence 2 in him of pleasure or pain (with which moral excellence and defect are always concerned), and these pleasures and pains are alterations of the sensitive part, 3 it is evident that the loss and acquisition of these states no less than the loss and acquisition of the states of the body must be the result of the alteration of something else. Consequently, though their becoming is accompanied by an alteration, they are not themselves alterations.

»47 b Again, the states of the intellectual part of the soul are not alterations, nor is there any becoming of them. In the first place it is much more 4 true of the possession of knowledge that it depends upon a particular relation. And further, it is evident that there is no becoming of these states. For that which is potentially possessed of know-

1 sc. of the sensitive part of the soul.

* It is hardly possible without awkwardness to give the full force of «VytW0ai here in English. It means strictly i to come to be present in \

8 Aristotle really means * arise from the alteration of the sensitive part ' : but his mode of expression is as often somewhat loose.

4 Reading in 1. 2 ^aXXov, with (apparently) Simp.

ledge becomes actually possessed of it not by being set in motion at all itself but by reason of the presence 1 of some- 5 thing else : i. e. it is when it meets with the particular object that it knows in a manner 2 the particular through its knowledge of the universal. (Again, there is no becoming of the actual use and activity of these states, unless it is thought that there is a becoming of vision and touching and that the activity in question is similar to these.) And the original acquisition of knowledge is not a becoming or an alteration 3 : for the terms ‘knowing' and ‘understandmg' imply that the intellect has reached a state of rest and come to a standstill . 4 * and there is no becoming that leads to a state of rest, since, as we have said above , 6 no change at all can have a becoming. Moreover, just as to say, when any one has passed from a state of intoxication or sleep or disease to the contrary state, that he has become possessed of knowledge again is incorrect in spite of the 15 fact that he was previously incapable of using his knowledge, so, too, when any one originally acquires the state, it is incorrect to say that he becomes possessed of knowledge : for the possession of understanding and knowledge is produced by the soul’s settling down 0 out of the restlessness natural to it. Hence, too, in learning and in forming judgements on matters relating to their sense-perceptions children are inferior to adults owing to the great amount 248* of restlessness and motion in their souls. Nature itself causes the soul to settle down and come to a state of rest for the performance of some of its functions, while for the

1 No one English word will quite give the force of vrrapfm here : it implies that something objective ‘appears on the scene’, 4 comes into existence in relation to to *Vi<7r>)poi> \ a The qualification is added because knowledge {fmar^rj) in the strict sense is concerned not with the particular but with the universal.

The point here is that knowledge of the universal includes a sort of knowledge of the particular, out of which it was originally built up.

4 The etymological connexion between imarfjfifj and cm/vai, can hardly be adequately given in translation. Read X tyofitda in 1. 11, with Par. 1859.

* The same etymological connexion is here present to Aristotle’s mind as that noted above.

performance of others other things 1 do so: but in either case the result is brought about through the alteration of something in the body, as we see in the case of the use 2 3 5 and activity of the intellect arising from a man’s becoming sober or being awakened. It is evident, then, from the preceding argument that alteration and being altered occur in sensible things and in the sensitive part of the soul and, except accidentally, in nothing else.

ro . A difficulty may be raised as to whether every motion 4 is commensurable with every other or not. Now if they are all commensurable and if two things to have the same velocity must accomplish an equal motion in an equal time, then we may have a circumference equal to a straight line, or, of course, the one may be greater or less than the other. Further, if one thing alters and another accomplishes a locomotion in an equal time, we may have an

15 alteration and a locomotion equal to one another: thus an affection will be equal to a length, which is impossible. But is it not y only when an equal motion is accomplished by two things in an equal time that the velocities of the two are equal ? Now an affection cannot be equal to a length. Therefore there cannot be an alteration equal to or less than a locomotion : and consequently it is not the case that every motion is commensurable with every other.

But how will our conclusion work out in the case of the circle and the straight line ? It would be absurd to suppose

20 that the motion of one thing in a circle and of another in a straight line cannot be similar, but that the one must inevitably move more quickly or more slowly than the other, just as if the course of one were downhill and of the other uphill. Moreover it does not as a matter of fact make any difference to the argument to say that the one motion must inevitably be quicker or slower than the other :

1 e. g. education, experience, etc.

2 Reading in 1. 5 xp f ) <**«>* with several MSS. This gives a much better balance to the sentence than fyc/><rfa>f which Bekker and Prantl adopt : becoming sober and being awakened lead to the recovery of the use and the activity of the intellect.

for then the circumference can be greater or less than the straight line ; and if so it is possible for the two to be equal. For if in the time A the quicker (B) passes over 35 the distance B' and the slower (r) passes over the distance F', B' will be greater than F': for this is what we 1 took 248 b ‘quicker* to mean: and so quicker motion also implies that one thing traverses an equal distance in less time than another : consequently there will be a part of A in which B will pass over a part of the circle equal to F', while F will occupy the whole of A in passing over F'. None the less, if the two motions 2 are commensurable, we are confronted 5 with the consequence stated above, viz. that there may be a straight line equal to a circle. But these are not commensurable : and so the corresponding motions are not commensurable either.

But may we say that things are always commensurable if the same terms are applied to them without equivocation? e. g. a pen, a wine, and the highest note in a scale are not commensurable: we cannot say whether any one of them is sharper than any other : and why is this ? they are incommensurable because it is only equivocally that the same term ‘sharp* is applied to them: whereas the highest note in a scale is commensurable with the leadingnote, because the term 4 sharp * has the same meaning as applied to both. Can it be, then, that the term ‘ quick * has 10 not the same meaning as applied to straight motion and to circular motion respectively ? If so, far less will it have the same meaning as applied to alteration and to locomotion.

Or shall we in the first place deny that things are always commensurable if the same terms are applied to them without equivocation? For the term ‘much* has the same meaning whether applied to water or to air, yet water and air are not commensurable in respect of it: 3 or, if this

2 The sense is improved by taking the first {n^X^ra to refer to the motions and the second to the straight line and the circle. The awkwardness of expression is not un-Aristotelian. The objector is supposed to maintain (248* 19) that the two motions must surely be commensurable. Nevertheless, says A., this would imply etc. . . .

8 i. c. a body of water will have more bwayus though it may have the same 3 y#eos as a body of air.

illustration is not considered satisfactory, ‘double' at any rate would seem to have the same meaning as applied to each (denoting in each case the proportion of two to one), yet water and air are not commensurable in respect of it. 1 15 But here again may we not take up the same position and say that the term ‘ much ’ is equivocal ? In fact there are some terms of which even the definitions are equivocal ; e. g. if ‘much* were defined as ‘so much and more’, ‘so much ' would mean something different in different cases : 2 ‘ equal ’ is similarly equivocal ; and ‘ one ’ again is perhaps 20 inevitably an equivocal term; and if ‘one* is equivocal, so is ‘ two Otherwise why is it that some things 3 are commensurable while others 4 are not, if the nature of the attribute in the two cases is really one and the same?

Can it be that the incommensurability of two things in respect of any attribute is due to a difference in that which is primarily capable of carrying the attribute ? Thus horse and dog are so commensurable that we may say which is the whiter, since that which primarily contains the whiteness is the same in both, viz. the surface: and similarly they are commensurable in respect of size. But water and speech are not commensurable in respect of clearness, 6 since that which primarily contains the attribute is different 35 in the two cases. It would seem, however, that we must reject this solution, since clearly we could thus make all equivocal attributes univocal and say merely that that which contains each of them is different in different cases: s*49 a thus * equality \ ‘ sweetness,’ and ‘ whiteness ’ will severally always be the same, though that which contains them is different in different cases. Moreover, it is not any casual thing that is capable of carrying any attribute : each single

1 e. g. two cubic feet of air will have twice the Kvafus of one cubic foot of air but not twice the bvvapis of one cubic foot of water.

3 Reading in 1 . 18 a comma after <n (cf. Met. 102 i a 6),

8 e. g. two cubic feet of air and one cubic foot of air.

4 e. g. two cubic feet of air and one cubic foot of water ; the doubleness in the two cases is not identical. Cf. above.

5 The attribute ^question is still \eW>r>jf, which can be applied in Greek not only to innot and kvu>v but also to vdap and <f>u>vr) : but a change of word is necessary in English.

BOOK VII. 4 * 49 * attribute can be carried primarily only by one single thing.

Must we then say that, if two things are to be commensurable in respect of any attribute, not only must the attribute in question be applicable to both without equivocation, but there must also be no specific differences either in the attribute itself or in that which contains the attribute — that these, I mean, must not be divisible in the way in 5 which colour is divided into kinds ? Thus in this respect one thing will not be commensurable with another, i. e. we cannot say that one is more coloured than the other where only colour in general and not any particular colour is meant ; but they are commensurable in respect of whiteness.

Similarly in the case of motion : two things are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion. Suppose, then, that in a certain time an alteration is undergone by one half 1 of a body’s length and a locomotion is accomplished by the other half: can we say that in this case the alteration is io equal to the locomotion and of the same velocity ? That would be absurd, and the reason is that there are different species of motion. And if in consequence of this we must say that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference. 2 What, then, is the reason of this? Is it that locomotion is a genus or that line is a genus? (We may 15 leave the time out of account, since that is one and the same.) If the lines are specifically different, the locomotions also differ specifically from one another: 3 for locomotion is specifically differentiated according to the

1 The argument clearly requires that the two parts represented by to ptv and ro St should be equal : cf. l<rov rnarovSL above.

* This ?eetns to be the general sense of the sentence w<rr* <1 . . . nfpifaprjt. But the connexion of thought is so obscure that I am inclined to suspect a lacuna, e. g. u>crrt to twro tlSos mvijcre btt nvai heart po>, tt i<roTa\r} c<rr«i. aXX’ tl #crX.

8 Reading in 1 . 1 5 (with Simplicius) xpovos 6 aiVoj * Av St r<p tTSti *) aXXa, tent ttettva tiSti Bia<f>tp(i . The ordinary reading of the MSS. and of Bekker is said by Simplicius to have been introduced from the second text.

fl 49 a specific differentiation of that over which it takes place. (It is also similarly differentiated, it would seem, accordingly as the instrument of the locomotion is different: thus if feet are the instrument, it is walking, if wings it is flying ; but perhaps we should rather say that this is not so, and that in this case the differences in the locomotion are merely differences of posture in that which is in motion. 1 ) We may say, therefore, that things are of equal velocity 20 if in an equal time they traverse the same magnitude :■ and when I call it ‘ the same ’ I mean that it contains no specific difference and therefore no difference in the motion that takes place over it. So we have now to consider how motion is differentiated : and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that in the case of equivocal terms sometimes the different senses in which they are used are far removed from one another, while sometimes there is a certain likeness between them, and sometimes again they are nearly related cither generically or analogically, with the result that they seem not to be equivocal though they really are.

2 5 When, then, is there a difference of species? Is an attribute specifically different if the subject is different while the attribute is the same, or must the attribute itsell be different as well ? And how are we to define the limits of a species ? What will enable us to decide that particular instances of whiteness or sweetness are the same or different ? Is it enough that it appears different in one subject from what it appears in another? Or must there be no sameness at all ? And further, where alteration is in question, how is one alteration to be of equal velocity with another? One person may be cured quickly and another slowly, and 3o cures may also be simultaneous : so that, recovery of health being an alteration, we have here alterations of equal 249 b velocity, since each alteration occupies an equal time. But what 2 alteration? We cannot here speak of an ‘equal’

* i. e. what (qualification are we to introduce into our definition of ro l(rorax*s in aWolaais corresponding to loop or mbrov piytQo* (249* 19) in the case of <j>opu ? Thus r « will be accusative.

a 49 b alteration : what corresponds in the category of quality to equality in the category of quantity is 1 likeness \ However, let us say that there is equal velocity where the same change is accomplished in an equal time. Are we, then, to find 5 the commensurability in the subject of the affection or in the affection itself? In the case that we have just been considering it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that both are alike. If on the other hand the affection is different in the two cases, e. g. when the alterations take the form of becoming white and becoming healthy respectively, here there is no sameness or equality or likeness inasmuch as the difference in the affections 1 at once makes the alterations specifically different, and there is no unity 10 of alteration any more than there would be unity of locomotion under like conditions . 2 So we must find out how many species there are of alteration and of locomotion respectively. Now if the things that are in motion — that is to say, the things to which the motions belong essentially and not accidentally — differ specifically, then their respective motions will also differ specifically : if on the other hand they differ generically or numerically, the motions also will differ generically or numerically as the case may be. But there still remains the question whether, supposing I5 that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the affections, or in the things altered, to see e. g. whether a certain quantity of each has become white. Or ought we not rather to look for it in both ? That is to say, the alterations are the same or different according as the affections are the same or different , 3 while they are equal or unequal according as the things altered are equal or unequal . 3

And now we must consider the same question in the case of becoming and perishing : how is one becoming of 30 equal velocity with another ? They are of equal velocity

1 ravra ; SC. ro \tvKaiv6jnvov and rb vyia(6fj,(vov.

3 sc. if there are two locomotions of different species.

8 Reading in 1 . 18 ro avro ft an to avro (to avro avro E), and in 1 . IQ

o if in an equal lime there are produced two things that are the same 1 2 * and specifically inseparable, e. g. two men (not merely generically inseparable as e. g. two animals). Similarly one is quicker than the other if in an equal time the product is different in the two cases. I state it thus because we have no pair of terms that will convey this * difference * in the way in which unlikeness is conveyed. 1 If we adopt the theory that it is number that constitutes being, we may indeed speak of a ‘greater number' and a ‘lesser number' 4 within the same species, but there is no common term that will include both relations, 5 nor are 25 there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of an affection by ‘ more of a quantity by ‘ greater \

Now since wherever there is a movent, its motion 5 always acts upon something, is always in something, and always extends to something (by ‘ is always in something’

I mean that it occupies a time : and by ‘extends to something* I mean that it involves the traversing of a certain amount of distance: for at any moment when a thing is causing motion, it also has caused motion, so that there must always be a certain amount of distance that has been traversed and a certain amount of time that has been 30 occupied). 6 If, then, A the movent have moved B a 250 a distance T in a time A, then in the same time the same force A will move |B twice the distance T, and in \ A it will move -|B the whole distance 1 ": for thus the rules of proportion will be observed. Again if a given force move 5 a given weight a certain distance in a certain time and

1 i. e. in the matter of completeness of development : there is no sufficiently specialized term for Aristotle to use. Cf. the sequel.

2 sc. use these general terms to nuro and crept)?.

5 i. e. a\h)to)(r€is are 1 tvp&XqTai in respect of 6 pouW^ and avofwidrrjs : and the relation of dvopoioTrjs is indicated by the use of the two terms puXXo v and rjrr ov,

4 i. e. instead of merely using the single term crepov.

5 Aristotle has as a matter of fact just used < report for this, but he feels that this is really too wide a term.

• Reading \«ya> L 2 8 ... novy 1. 30 as a parenthesis, followed by a comma (so Bonitz).

half the distance in half the time, 1 2 * half the motive power will move half the weight the same distance in the same time. Let E represent half the motive power A and Z half the weight B : then the ratio between the motive power and the weight in the one case is similar and proportionate to the ratio in the other, so that each force will cause the same distance to be traversed in the same time.

But if E move Z a distance F in a time A, it does not 10 necessarily follow that E can move twice Z half the distance F in the same time. If, then, A move B a distance F in a time A, it does not follow that E, being half of A, will in the time A or in any fraction of it cause B 2 to traverse a part of T the ratio between which and the whole of F is proportionate to that between A and E (whatever fraction of A E may be) : :i in fact it might well be that it will 15 cause no motion at all ; for it does not follow that, if a given motive power causes a certain .amount of motion, half that power will cause motion either of any particular amount or in any length of time : otherwise one man might move a ship, since both the motive power of the shiphaulers and the distance that they all cause the ship to traverse are divisible into as many parts as there are men. Hence Zeno’s reasoning is false when he argues that there 2 o is no part of the millet that does not make a sound : for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. 4 In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially.

If on the other hand we have two forces each of which 25 separately moves one of two weights a given distance in a given time, then the forces in combination will move the combined weights an equal distance in an equal time : for in this case the rules of proportion apply.

1 Reading in 1 . 5 a comma after r//u<m and not after mwi (so Bonitz).

2 Omitting in 11 . 12, 13, with Simp., and reading in 1 . 12 otn;, with EHK.

8 Both the text and the exact sense of this sentence are somewhat doubtful. In 1 . 14 I read (ti) rrjs, with Prantl, and omit rj , with EFK.

Then does this hold good of alteration and of increase also ? Surely it does, for in any given case we have a 30 definite thing that causes increase and a definite thing that suffers increase, and the one causes and the other suffers a certain amount of increase in a certain amount of time. Similarly we have a definite thing that causes alteration and a definite thing that undergoes alteration, and a certain amount, or rather degree, 1 of alteration is complete^ in 350 to a certain amount of time : thus in twice as much time twice as much alteration will be completed and conversely twice as much alteration will occupy twice as much time: and the alteration of half of its object will occupy half as much time and in half as much time half of the object will be altered : or again, in the same amount of time it will be altered twice as much.

On the other hand if that which causes alteration or increase causes a certain amount of increase or alteration 5 respectively in a certain amount of time, it does not necessarily follow that half the force will occupy twice the time in altering or increasing the object, or that in twice the time the alteration or increase will be completed by it: 2 it may happen that there will be no alteration or increase at all, the case being the same as with the weight.

1 lit . 'a certain amount in respect of more or less’ : the qualification is added because dAAo/axm is not measured by quantity in the strict sense like (j>opd but by degree : in this case we say paWov or rjrrov where in the other case we say txu(ov or i\ arrov. Cf. above 249 b 26.

2 It seems necessary to read in 1 , 5 r<> rjpiarv iv dirrAatrio) *nl «V Stir\a<rl<p rjfxiarv. Only so will the point made correspond to that made about weight in *12-19.

1 It remains to consider the following question. Was there ever a becoming of motion before which it had no being, and is it perishing again so as to leave nothing in motion ?

Or are we to say that it never had any becoming and is not perishing, but always was and always will be ? Is it in fact an immortal never-failing property of things that are, a sort of life as it were to all naturally constituted things ?

Now the existetice of motion is asserted by all who have 15 anything to say about nature, because they all 1 concern themselves with the construction of the world and study the question of becoming and perishing, which processes could not come about without the existence of motion. But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in process of perishing, assert that there is always 20 motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, 2 make corresponding assumptions in regard to motion. If then it is possible that at any time nothing should be in motion, this must come about in one of two ways : either in the manner described by Anaxagoras, who says that all things were together and at rest for an infinite 25 period of time, and that then Mind introduced motion and separated them ; or in the manner described by Empedocles, according to whom the universe is alternately in motion and at rest — in motion, when Love is making the one out of many, or Strife is making many out of one, and at rest

1 Reading in 1. *7 na<nv, Bekker’s nacrav is a misprint.

2 tvu tf pi ) dtt in 1 . 22 is difficult As Simplicius says, the words really stand for mi *al del rov avrov § tvn piv % 01 * del Be. We should probably read ewi (>} del) n p) do', with (apparently) Themistius.

in the intermediate periods of time— -his account being as follows :

3 ° ‘ Since 1 One hath learned to spring from Manifold,

And One disjoined makes Manifold arise,

251 Thus they Become, nor stable is their life:

But since their motion must alternate be,

Thus have they ever Rest upon their round ’ :

for we must suppose that he means by this that they 5 alternate from the one motion to the other . 2 We must consider, then, how this matter stands, for the discovery of the truth about it is of importance, not only for the study of nature, but also for the investigation of the First Principle.

Let us take our start from what we have already 3 laid down in our course on Physics . 4 Motion, we say, is the io fulfilment of the movable in so far as it is movable. Each kind of motion, therefore, necessarily involves the presence of the things that are capable of that motion. In fact, even apart from the definition of motion, every one would admit that in each kind of motion it is that which is capable of that motion that is in motion : thus it is that which is capable of alteration that is altered, and that which is 15 capable of local change that is in locomotion : and so there must be something capable of being burned before there can be a process of being burned, and something capable of burning before there can be a process of burning. Moreover, these things also must either have a beginning before

2 i. e. from motion towards <v to motion towards no \\d and vice versa. But the last two lines quoted from Empedocles do not naturally bear this meaning : he seems to be insisting first on the rotation and then on the permanence of the rotation ; he does not here say anything about the piragv in which occurs that foe pin which as

Aristotle says makes k'ivtjctis to cease altogether. — Reading in 1. 4 ro yap fl di rud aWdacrovra' ivOci'fti (Kuorc Xcyuv uiriv vnoXqnrtov, with FHI.

8 iii. I.

4 The title of the whole eight books of this treatise (or, rather course of lectures) is <I>uri-ur) 'A Kpoamt. When Aristotle refers to ra <f>voriKa or ra n epi (f)va€w he usually means the first four books only ; books V, VI, and VIII are referred to as ra ntpi tuviprew. Cf. 267^21.

which they had no being, or they must be eternal. Now if there was a becoming of every movable thing, it follows that before the motion in question another change or motion must have taken place in which that which was capable of being moved or of causing motion had its becoming. To suppose, on the other hand, that these 20 things were in being throughout all previous time without there being any motion appears unreasonable on a moment's thought, and still more unreasonable, wc shall find, on further consideration. For if we arc to’ say that, while there are on the one hand things that are movable, and on the other hand things that arc motive, there is a time when there is a first movent and a first moved, and another time when there is no such thing but only something that is at rest, then this thing that is at rest must 25 previously have been in process of change : for there must have been some cause of its rest, rest 1 being the privation of motion. Therefore, before this first change there will be a previous change. For some things cause motion in only one way, while others can produce cither of two contrary motions : thus fire causes heating but not cooling, whereas 30 it would seem that knowledge may be directed to two contrary ends while remaining one and the same. Even in the former class, however, there seems to be something similar, for a cold thing in a sense causes heating by turning away and retiring, just as one possessed of knowledge voluntarily makes an error when he uses his knowledge in the reverse way. 2 But at any rate all things that are 251** capable respectively of affecting and being affected, or of causing motion and being moved, are capable of it not under all conditions, but only when they are in a particular condition and approach one another : so it is on the approach of one thing to another that the one causes

1 Simplicius in his commentary has Tjpepla here though we cannot be sure that he is quoting verbally from Aristotle. But A. uses r)ptpr)ois to mean not only ‘ coming to rest ’ but also ‘ being at rest *, which must be the meaning here as we are professedly only dealing with a state of rest. Cf. v. 6. 231*2.

2 i. e. by means of his knowledge he can be sure of giving a wrong opinion and thus deceiving some one.

PHVSICA

25i b motion and the other is moved, and when they are present under such conditions as rendered the one motive and the 5 other movable. So if the motion was not always in process, it is clear that they must have been in a condition not such as to render them capable 1 respectively of being moved and of causing motion, and one or other of them must have been in process of change : for in what is relative this is a necessary consequence: e. g. if one thing is double another when before it was not so, one or other of them, if not both, must have been in process of change. It follows, then, that there will be a process of change previous to the first, io (Further, how can there be any ‘before’ and ‘after’ without the existence of time ? Or how can there be any time without the existence of motion ? If, then, time is the number of motion or itself a kind of motion, it follows that, if there is always time, motion must also be eternal. But so far as time is concerned we see that all with one exception are in agreement in saying that it is uncreated : 15 in fact, it is just this 2 that enables Democritus to show that all things cannot have had a becoming : for time, he says, is uncreated. Plato alone asserts the creation of time, saying 3 that it had a becoming together with the universe, the universe according to him having had a becoming. Now since time cannot exist and is unthinkable apart from 20 the moment, and the moment is a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time : for the extremity of the last period of time that we take must be found in some moment, since time contains no point of contact 4 for 25 us except the. moment. Therefore, since the moment is both a beginning and an end, there must always be time on both sides of it. But if this is true of time, it is evident

1 Reading in 1 . 4 cos rjv f and in 1 . 6 cos fjv dvpaptva, with E, Cf. Met . 1048*6.

2 Reading in 1 . 16 rouror, with EH.

8 Aristotle is thinking of a passage in the Timaeus (38 B).

4 It is difficult to give the exact force of Xn/ 3 etv. Aristotle means that we can only ‘ lay hold of * or ‘ have at command * the present moment, since all the rest of time is either no longer or not yet in existence.

BOOK VIII. i 251* that it must also be true of motion, time being a kind of affection of motion.)

The same reasoning will also serve to show the imperishability of motion : just as a becoming of motion would involve, as we saw, the existence of a process of 30 change previous to the first, in the same way a perishing of motion would involve the existence of a process of change subsequent to the last : for when a thing ceases to be moved, it does not therefore at the same time cease to be movable — e. g. the cessation of the process of being burned does not involve the cessation of the capacity of being burned, since a thing may be capable of being burned without being in process of being burned — nor, when a thing ceases to be movent, does it therefore at the same time cease to be motive. Again, the destructive agent will 252* have to be destroyed, after what it destroys has been destroyed, 1 and then that which has the capacity of destroying it will have to be destroyed afterwards, (so that there will be a process of change subsequent to the last,) for being destroyed also is a kind of change. If, then, the view which we are criticizing involves these impossible consequences, it is clear that motion is eternal and cannot have existed at one time and not at another : in fact, such a view can hardly be described as anything else than fantastic.

And much the same may be said of the view that such 5 is the ordinance of nature and that this must be regarded as a principle, as would seem to be the view of Empedocles when he. says that the constitution of the world is of necessity such that Love and Strife alternately predominate and cause motion, while in the intermediate period of time there is a state of rest. Probably also those who, like 10 Anaxagoras, assert a single principle (of motion 2 ) would hold this view. But that which is produced or directed by nature can never be anything disorderly : for nature is

2 It is necessary to insert these words, as Anaxagoras is of course a pluralist, and Aristotle is only thinking of the place assigned to vow in his system as the sole cause of motion in contradistinction to the two causes (< piKla and vtb cos) asserted by Empedocles.

everywhere the cause of order. Moreover, there is no ratio in the relation of the infinite to the infinite, whereas order always means ratio. But if we say that there is first a state of rest for an infinite time, and then motion is 15 started at some moment, and that the fact that it is this rather than a previous moment is of no importance, and involves no order, then we can no longer say that it is nature's work : for if anything is of a certain character naturally , it either 1 is so invariably and is not sometimes of this and sometimes of another character (e. g. fire, which travels upwards naturally, does not sometimes do so and sometimes not) or there is a ratio in the variation. It 20 would be better, therefore, to say with Empedocles and any one else who may have maintained such a theory as his that the universe is alternately at rest and in motion : for in a system of this kind we have at once a certain order. But even here the holder of the theory ought not only to assert the fact : he ought also to explain the cause of it : i. e. he should not make any mere assumption or lay down any gratuitous axiom, but should employ either 25 inductive or demonstrative reasoning. The Love and Strife postulated by Empedocles are not in themselves causes of the fact in question, nor is it of the essence of either that it should be so, the essential function of the former being to unite, of the latter to separate. If he is to go on to explain this alternate predominance, he should adduce cases where such a state of things exists, as he points to the fact that among mankind we have something that unites men, namely Love, while on the other hand 30 enemies avoid one another: thus from the observed fact that this occurs in certain cases comes the assumption that it occurs also in the universe. Then, again, some argument is needed to explain why the predominance of each of the two forces lasts for an equal period of time. But it is a wrong assumption to suppose universally that we have an adequate first principle in virtue of the fact that something always is so or always happens so. Thus Democritus reduces the causes that explain nature to the fact that 1 Reading in 1. 17 rj.

things happened in the past in the same way as they happen now: but he does not think fit to seek for a first 35 principle to explain this 4 always ' : so, while his theory is 252 b right in so far as it is applied to certain individual cases, he is wrong in making it of universal application. Thus, a triangle always has its angles equal to two right angles, but there is nevertheless an ulterior cause of the eternity of this truth, whereas first principles are eternal and have no ulterior cause. Let this conclude what we have to say 5 in support of our contention that there never was a time when there was not motion, and never will be a time when there will not be motion.

2 The arguments that may be advanced against this position arc not difficult to dispose of. The chief considerations that might be thought to indicate that motion may exist though at one time it had not existed at all arc the following:

First, it may be said that no process of change is eternal : for the nature of all change is such that it proceeds jo from something to something, so that every process of change must be bounded by the contraries that mark its course, and no motion can go on to infinity.

Secondly, we see that a thing that neither is in motion nor contains any motion within itself can be set in motion ; e. g, inanimate things that arc (whether the whole or some part is in question) not in motion but at rest, are at some moment set in motion: whereas, if motion cannot have 15 a becoming before which it had no being, these things ought to be either always or never in motion.

Thirdly, the fact 1 is evident above all in the case of animate beings: for it sometimes happens that there is no motion in us and we are quite still, and that nevertheless we are then at some moment set in motion, that is to say it sometimes happens that we produce a beginning of motion in ourselves spontaneously without anything having 20 set us in motion from without. We see nothing like this in the case of inanimate things, which are always set in

1 SC. to tdvrjmu timi it ore fr) avernv* motion by something else from without: the animal, on the other hand, we say, moves itself: therefore, if an animal is ever in a state of absolute rest, we have a motionless thing in which motion can be produced from the thing itself, and not from without. Now if this can occur in an 35 animal, why should not the same be true also of the universe as a whole? If it can occur in a small world 1 it could also occur in a great one : and if it can occur in the world, it could also occur in the infinite; that is, if the infinite could as a whole possibly be in motion or at rest.

Of these objections, then, the first-mentioned — that 30 motion to opposites is not always the same and numerically one — is a correct statement ; in fact, this may be said to be a necessary conclusion, provided that it is possible for the motion of that which is one and the same to be not always one and the same. (I mean that e. g. we may question whether the note given by a single string is one and the same, or is different each time the string is struck, although the string is in the same condition and is moved 35 in the same way.) But still, however this may be, there is nothing to prevent there being a motion that is the same 253 11 in virtue of being continuous and eternal : we shall have something to say later 2 that will make this point clearer.

As regards the second objection, no absurdity is involved in the fact 3 that something not in motion may be set in motion, that which caused the motion from without being at one time present, and at another absent. Nevertheless, how this can be so remains matter fur inquiry; how it comes about, I mean, that the same motive force at one time causes a thing to be in motion, and at another does 5 not do so : for the difficulty raised by our objector really amounts to this — why is it that some things are not always £t rest, and the rest always in motion ?

The third objection may be thought to present more difficulty than the others, namely, that which alleges that motion arises in things*in which it did not exist before, and

1 i. e. this fact does not prove the theory of m'Sio? *lvr}<ris to be absurd.

adduces in proof the case of animate things: thus an animal is first at rest and afterwards walks, not having , 0 been set in motion apparently by anything from without. This, however, is false: for we observe that there is always some part of the animal’s organism in motion, and the cause of the motion of this part is not the animal itself, but, it may be, its environment. Moreover, we say that the animal itself originates not all of its motions but its locomotion. So it may well be the case — or rather we may 15 perhaps say that it must necessarily be the case — that many motions are produced in the body by its environment, and some of these set in motion the intellect or the appetite, and this again then sets the whole animal in motion: this is what happens when animals are asleep : though there is then no perceptive motion in them, there is some motion that causes them to wake up again. But we will leave ao this point also to be elucidated at a later 1 stage in our discussion.

3 Our enquiry will resolve itself at the outset into a consideration of the above-mentioned problem — what can be the reason why some things in the world at one time are in motion and at another are at rest again? Now one of three things must be true: either all things are always at rest, or all things are always in motion, or some things are J5 in motion and others at rest : and in this last case again either the things that are in motion are always in motion and the things that are at rest are always at rest, or they are all constituted so as to be capable alike of motion and of rest ; or there is yet a third possibility remaining — it may be that some things in the world are always motionless, others always in motion, while others again admit of both conditions. This last is the account of the matter that we 30 must give : for herein lies the solution of all the difficulties raised and the conclusion of the investigation upon which we are engaged.

1 Chapter 6.

To maintain that all things are at rest , 1 and to disregard sense-perception in an attempt to show the theory to be reasonable , 2 would be an instance of intellectual weakness : it would call in question a whole system, not a particular 35 detail : moreover, it would be an attack not only on the physicist but on almost all sciences and all received 253 b opinions, since motion plays a part in all of them. Further, just as in arguments about mathematics objections that involve first principles do not affect the mathematician — and the other sciences are in similar case — so, too, objections involving the point that we have just raised do not 5 affect the physicist : for it is a fundamental assumption with him that motion is ultimately referable to nature herself . 3

The assertion that all things are in motion we may fairly regard as equally false, though it is less subversive of physical science : 4 * for though in our course on physics 6 it was laid down that rest no less than motion is ultimately referable to nature herself, nevertheless 6 motion is the characteristic fact of nature : moreover, the view is actually io held by some that not merely some things but all things in the world are in motion and always in motion, though we cannot apprehend the fact by sense-perception. Although the supporters of this theory do not state clearly what kind of motion they mean, or whether they mean all kinds, it is no hard matter to reply to them: thus we may point

1 The Greek as it stands is not quite logical : the Suivoias appcaaria is not t6 7 rdpr’ rjpffiiiv but to tuivt rjptptlv \tyav. Some such word as \iyeiv must be supplied from (tjtciv following.

* The words Cyruv \ 6 yov mean to seek an explanation t>r rationale of the theory, to give a rational account of it.

8 lit. ‘nature is the original cause of motion’; i. e. motion is an ultimate fact in the constitution of the world. See i. 2. 184**25 sqq.

4 lit . ‘ less contrary to the investigation ’, sc. physical investigation.

* Reading in 1 . 9 o/xu>?. It is impossible to get any sense out of 6poi<os y the reading of all the MSS. The two words are often confused : moreover Pad us has opw and mentions no other reading. Even so the sense given to (pvaucbv is somewhat strained : it must mean that whereas rjpepla is a mere crrlpTjans of motion, klvtjctis is a positive fact in nature, being conceived of as emphatically a process. We might perhaps get this sense more easily by reading o\>x opolm : ‘motion is natural in a different sense i. e. in a more special sense.

out that there cannot be a continuous process either of increase or of decrease : that which comes between the two has to be included . 1 The theory resembles that about the 15 stone being worn away by the drop of water or split by plants growing out of if: if so much has been extruded or removed by the drop, it does not follow that half the amount has previously been extruded or removed in half the time : the case of the hauled ship is exactly comparable : here we have so many drops setting so much in motion, but a part of them will not set as much in motion in any period of time. The amount removed is, it is true, divisible into a number of parts, but no one of these was set in 20 motion separately : they were all set in motion together.

It is evident, then, that from the fact that the decrease is divisible into an infinite number of parts it does not follow that some part must always be passing away: it all passes away at a particular moment. Similarly, too, in the case of any alteration whatever if that which suffers alteration is infinitely divisible it does not follow from this that the same is true of the alteration itself, which often occurs all 25 at once, as in freezing. Again, when any one has fallen ill, there must follow a period of time in which his restoration to health is in the future: the process of change cannot take place in an instant : yet the change cannot be a change to anything else but health.- The assertion, therefore, that alteration is continuous is an extravagant calling into question of the obvious : for alteration is a change from 3° one contrary to another. Moreover, we notice that a stone becomes neither harder nor softer. 3 Again, in the matter of locomotion, it would be a strange thing if a stone could be falling or resting on the ground without our being able to perceive the fact. Further, it is a law of nature that earth and all other bodies should remain in their proper

1 i.e. a thing cannot go on increasing or decreasing to infinity: there comes a time when it either remains constant or changes to the contrary process, and the two processes must be separated by at least a moment of rjpffiia {rb pter ov).

a Thus vy Inverts, a particular form of eXWoiwerts, is not crvvtxTjs.

3 An argument from ordinary experience : a stone retains the same degree of hardness at least for a very long period : it cannot therefore be always changing in this respect.

PI-IYSICA

35 places and be moved from them only by violence : from the fact then that some of them are in their proper places it follows that in respect of place also all things cannot be 254 a in motion. These and other similar arguments, then, should convince us that it is impossible either that all things are always in motion or that all things are always at rest.

Nor again can it be that some things are always at rest, others always in motion, and nothing sometimes at rest and 5 sometimes in motion. This theory must be pronounced impossible on the same grounds as those previously mentioned : viz. that we see the above-mentioned changes occurring in the case of the same things . 1 We may further point out that the defender of this position is fighting against the obvious, for on this theory there can be no such thing as increase : nor can there be any such thing as compulsory motion, if it is impossible that a thing can be at io rest before being set in motion unnaturally . 2 This theory, then, does away with 3 becoming and perishing. Moreover, motion, it would seem, is generally thought to be a sort of becoming and perishing, for that to which a thing changes comes to be , 4 or occupancy of it comes to be , 5 and that from which a thing changes ceases to be, or there ceases to be occupancy of it. It is clear, therefore, that there are cases of occasional motion and occasional rest.

15 We have now to take the assertion that all things are sometimes at rest and sometimes in motion and to confront it with the arguments previously advanced. We must take our start as before from the possibilities that we distinguished just above. Either all things are at rest, or all things are in motion, or some things are at rest and others in motion. And if some things are at rest and i.e. we make the same appeal to sense-perception: we observe the same thing to be now in motion, now at rest (e. g. a falling stone) and vice versa. '

1 The clause tl pfj ... rrporcpou refers only to piai or Kiprjatt. The reason why the theory does away with aufaa is is not stated, because what has been said above (253* 13), that atfo ns cannot be applies here too. A ' 9 sc. because neither yivtats nor <j)0opd can be cvwxrjs.

4 sc. in ytvtats proper and d\AoW<s.

others in motion, then it must be that either all things are ao sometimes at rest and sometimes in motion, or some things are always at rest and the remainder always in motion, 1 or some of the things are always at rest and others always in motion while others again are sometimes at rest and sometimes in motion. Now we have said before that it is impossible that all things should be at rest : nevertheless we may now repeat that assertion. We may point out that, even if it is really the case, as certain persons assert, 2 2 5 that the existent is infinite and motionless, it certainly does not appear to be so if we follow sense-perception: many things that exist appear to be in motion. Now if there is such a thing as false opinion or opinion at all, there is also motion : and similarly if there is such a thing as imagination, or if it is the case that anything seems to be different at different times : for imagination and opinion are thought to be motions of a kind. 3 But to investigate this question 30 at all-— to seek a reasoned justification of a belief with regard to which we are too well off to require reasoned justification — implies bad judgement of what is better and what is worse, what commends itself to belief and what does not, what is ultimate and what is not. It is likewise impossible that all things should be in motion or that some things should be always in motion and the remainder always at rest. We have sufficient ground for rejecting 35 all these theories in the single fact that we see some things that are sometimes in motion and sometimes at rest. It is 254* evident, therefore, that it is no less impossible that some things should be always in motion and the remainder always at rest than that all things should be at rest or that all things should be in motion continuously. It remains, then, to consider whether all things are so constituted as to be capable both of being in motion and of being at rest, or whether, while some things are so constituted, some are 5

1 Repeating in I, 22 ff to, ph net ra 6 * cut KtptTcrOm before avr&>t>y a simple and easy correction, to make the enumeration complete. Prantl inserts the words after aur&v, but the other position seems slightly better and palaeographically easier.

2 Melissus is meant ; cf. 185*32.

always at rest and some are always in motion : for it is this last view that we have to show to be true.

Now of things that cause motion or suffer motion, to 4 some the motion is accidental, to others essential : thus it is accidental to what merely belongs to or contains as a part a thing that causes motion or suffers motion,

10 essential to a thing that causes motion or suffers motion not merely by belonging to such a thing or containing it as a part.

Of things to which the motion is essential some derive their motion from themselves, others from something else : and in some cases their motion is natural, in others violent and unnatural. Thus in things that derive their motion 15 from themselves, e. g. all animals, the motion is natural (for when an animal is in motion its motion is derived from itself) : and whenever the source of the motion of a thing is in the thing itself we say that the motion of that thing is natural. Therefore the animal as a whole moves itself naturally : but the body of the animal may be in motion unnaturally as well as naturally : it depends upon the kind 1 of motion that it may chance to be suffering and the kind of 20 element 2 of which it is composed. And the motion of things that derive their motion from something else is in some cases natural, in others unnatural : e. g. upward motion of earthy things and downward motion of fire are unnatural. Moreover the parts of animals are often in motion in an unnatural way, their positions 3 and the character of the motion 4 being abnormal. The fact that a thing that is in 25 motion derives its motion from something is most evident in things that are in motion unnaturally, because in such cases it is clear that the motion is derived from something other than the thing itself. Next to things that are in motion unnaturally those whose motion while natural is

1 e.g. the motion of jumping natural to the animal as a whole is unnatural to the body qua body, which is ycripov and naturally has a downward tendency.

2 . i. e. the material of which a body is composed may be so light as naturally to have an upward tendency.

8 e. g. a man may walk on his hands.

4 e. g. a man may roll along the ground instead of walking.

derived from themselves — e.g. animals — make this fact clear : for here the uncertainty is not as to whether the motion is derived .from something but as to how we ought to distinguish in the thing between the movent and the moved. It would seem that in animals, just as in ships 30 and things not naturally organized, that which causes motion is separate from that which suffers motion, and that it is only in this sense that the animal as a whole causes its own motion.

The greatest difficulty, however, is presented by the remaining case of those that we last distinguished. Where things derive their motion from something else we distinguished the cases in which the motion is unnatural : we 35 are left with those that are to be contrasted with the othcis by reason of the fact that the motion is natural. It is in 255 s1 these cases that difficulty would be experienced in deciding whence the motion is derived, e.g. in the case of light and heavy things. When these things arc in motion to positions the reverse of those they would properly occupy, their motion is violent : when they are in motion to their proper positions — the light thing up and the heavy thing down — their motion is natural ; but in this latter case it is no longer evident, as it is when the motion is unnatural, whence their motion is derived. It is impossible to say 5 that their motion is derived from themselves: this is a characteristic of life and peculiar to living things. Further, if it were, it would have been in their power to stop themselves (I mean that if e.g. a thing can cause itself to walk it can also cause itself not to walk), and so, since on this supposition fire itself possesses the power of upward locomotion, it is clear that it should also possess the power of downward locomotion. Moreover if things 10 move themselves, it would be unreasonable to suppose that in only one kind of motion is their motion derived from themselves. Again, how can anything of continuous and naturally connected substance move itself? In so far as a thing is one and continuous not merely in virtue of contact, it is impassive : it is only in so far as a thing is divided that one part of it is by nature active and another

15 passive. Therefore none of the things 1 that we are now considering move themselves (for they are of naturally connected substance), nor does anything else that is continuous : in each case the movent must be separate from the moved, as we see to be the case with inanimate things when an animate thing moves them. It is the fact that these things 2 also always derive their motion from something : what it is would become evident if we were to distinguish the different kinds of cause.

10 The above-mentioned distinctions can also be made in the case of things that cause motion : some of them .are capable of causing motion unnaturally (e. g. the lever is not naturally capable of moving the weight), others naturally (e. g. what is actually hot is naturally capable of moving 3 what is potentially hot) : and similarly in the case of all other things of this kind.

In the same way, too, what is potentially of a certain quality or of a certain quantity or in a certain place is 35 naturally movable when it contains the corresponding principle in itself and not accidentally (for the same thing may be both of a certain quality and of a certain quantity, but the one is an accidental, not an essential property of the other 4 ). So when fire or earth is moved by something the motion is violent when it is unnatural, and natural when it brings to actuality the proper activities 5 that so they potentially possess. But the fact that the term ‘ potentially 1 is used in more than one sense is the reason why it is not evident whence such motions as the upward motion of fire and the downward motion of earth are derived. One who is learning a science potentially knows it in a different sense from one who while already possessing the knowledge is not actually exercising it. Wherever we have something capable of acting and something

1 SC. rrvp and the like (ra Kara (fivcriv Kivovpeva)*

8 i. e. causing to become hot.

4 i.e. a thing may, in the process of becoming irorfv, incidentally become ito*t6p 9 and vice versa: but the becoming rrocrov is irrelevant to the change or motion from not 6v to noiov or from irov to irotJ.

• sc. upward motion and downward motion respectively.

capable of being correspondingly acted on, in the event of any such pair being in contact what is potential becomes 35 at times actual: 1 e.g. the learner becomes from one poten- 2 55 b tial something another potential something : for one who possesses knowledge of a science but is not actually exercising it knows the science potentially in a sense, though not in the same sense as he knew it potentially before he learnt it. And when he is in this condition, if something does not prevent him, he actively exercises his knowledge: otherwise he would be in the contradictory state of not knowing. In regard to natural bodies also the case is similar. 5 Thus what is cold is potentially hot : then a change takes place and it is fire, and it burns, unless something prevents and hinders it. So, too, with heavy and light : light is generated from heavy, e. g. air from water (for water is the first thing that is potentially light), and air is actually light, and 10 will at once realize its proper activity as such unless something prevents it. The activity of lightness consists in the light thing being in a certain situation, namely high up : 8 when it is in the contrary situation, it is being prevented from rising. The case is similar also in regard to quantity and quality. But, be it noted, this is the question we are trying to answer — how can we account for the motion of light things and heavy things to their proper situations?

The reason for it is that they have a natural tendency 15 respectively towards a certain position : and this constitutes the essence of lightness and heaviness, the former being determined by an upward, the latter by a downward, tendency. As we have said, a thing may be potentially light or heavy in more senses than one. Thus not only when a thing is water is it in a sense potentially light, but when it has become air it may be still potentially light : for

1 The sentence is awkwardly expressed, del and cWor# seeming to contradict one another, but I do not think any alteration in the text is necessary. Certainly it will not do to omit mar*, without which the statement would not be true : e. g. to produce something more than the mere contact of the teacher's mind with the learner's mind is needed. 1 take dd to mean that there is no exceptional c/ass of noirjTKtov and naBrjriK6v that as such does not conform to the rule : tfVtdrc virtually means in ‘ favourable circumstances \

2 i. e. above anything that is heavier.

it may be that through some hindrance it does not occupy 20 an upper position, whereas, if what hinders it is removed, it realizes its activity and continues to rise higher. The process whereby what is of a certain quality changes to a condition of active existence is similar : thus the exercise of knowledge follows at once upon the possession of it unless something prevents it. So, too, what is of a certain quantity extends itself over a certain space unless something prevents it. 1 The thing in a sense is and in a sense is not moved by one who moves what is obstructing and 25 preventing its motion (e. g. one who pulls away a pillar from under a roof or one who removes a stone from a wineskin in the water is the accidental cause of motion : 2 and in the same way the real cause of the motion of a ball rebounding from a wall is not the wall but the thrower.'* So it is clear that in all these cases the thing does not 30 move itself, but it contains within itself the source of motion — not of moving something or of causing motion, but of suffering it. 4

If then the motion of all things that are in motion is either natural or unnatural and violent, and all things whose motion is violent and unnatural are moved by something, and something other than themselves, and again all things whose motion is natural are moved by something — both those that are moved by themselves and those that 35 are not moved by themselves (e. g. light things and heavy 256® things, which are moved either by that which brought the thing into existence as such and made it light and heavy, or by that which released what was hindering and preventing it) ; then all things that are in motion must be moved by something.

Now this may come about in either of two ways. Either 5 the movent is not itself responsible for the motion, which

1 i.e. it may be possibly compressed so that it does not occupy the amount of space that such a nocrov would normally occupy : in that case it is bvpapu irocrop in the second sense.

* The real cause here is the upward or downward tendency.

3 In this case the wall is an instance of a Kara (rvuftcftriKos kip ovv.

4 i. e. the quality of being affected by or responsive to the activity of

TO KIPQVP, is to be referred to something else which moves the movent, or the movent is itself responsible for the motion. 5 Further, in the latter case, either the movent immediately precedes the last thing in the series , 1 or there may be one or more intermediate links : e. g. the stick moves the stone and is moved by the hand, which again is moved by the man ; in the man, however, we have reached a movent that is not so in virtue of being moved by something else. Now we say that the thing is moved both by the last and by the first movent in the series, but more strictly by the first, sinc^ the first movent moves the last, » whereas the last does not move the first, and the first will move the thing without the last, but the last will not move it without the first : e. g. the stick will not move anything unless it is itself moved by the man. If then everything that is in motion must be moved by something, and the movent must either itself be moved by something else or not, and in the former case there must be i some first movent that is not itself moved by anything else, while in the case of the immediate movent being of this kind there is no need of an intermediate movent that is also moved 2 (for it is impossible that there should be an infinite series of movents, each of which is itself moved by something elsc, :i since in an infinite series there is no first term) — if then everything that is in motion is moved by something, and the first movent is moved but a not by anything else, it must be moved by itself.

This same argument may also be stated in another way as follows. Every movent moves something and moves it with something, either with itself or with something else: e. g. a man moves a thing either himself or with a stick,

1 i. e. the thing that is moved.

2 The argument is stated so concisely that it is perhaps hardly clear : but the reasoning appears to be as follows. Z (to foxarov, the thing whose motion is to be accounted for) must be moved directly either by X (a kivoG* vn uXAou Kivovfxwop) or by Y (a kipovv hr* u\\ov KLvovfitvov). Now Y implies an ultimate X, though Y\ Y" may intervene : but X does not necessarily imply Y in order to move Z : otherwise if Y is necessary in order to enable X to move Z, Y will be necessary to enable it to move Y } and so on ad infinitum.

2S6 a and a thing is knocked down either by the wind itself or by 3 5 a stone propelled by the wind. But it is impossible for that with which a thing is moved to move it without being moved by that which imparts motion by its own agency : 1 on the other hand, if a thing imparts motion by its own agency, it is not necessary that there should be anything else with which it imparts motion, whereas if there is a different thing with which it imparts motion, there must be something that imparts motion not with something else but with itself, or else there will be an infinite series. If, then, anything is a movent while being itself moved, 30 the series must stop somewhere and not be infinite. Thus, if the stick moves something in virtue of being moved by the hand, the hand moves the stick : and if something else moves with the hand> the hand also is moved by something different from itself. So when motion by means of an instrument is at each stage caused by something different from the instrument, this must always be preceded by something else 2 which imparts motion with itself. Therefore, if this last movent is in motion and there is nothing 2 56 b else that moves it, it must move itself. So this reasoning also shows that, when a thing is moved, if it is not moved immediately by something that moves itself, the series brings us at some time or other to a movent of this kind.

And if we consider the matter in yet a third way we shall get this same result as follows. If everything that is 5 in motion is moved by something that is in motion, either this being in motion is an accidental attribute of the movents in question, so that each of them moves something while being itself in motion, but not always because it is itself in motion, or it is not an accidental but an essential attribute. Let us consider the former alternative. If then it is an accidental attribute, it is not necessary that that which is in motion should be in motion ; and if this is so it is clear that there may be a time when nothing that exists is in motion, since the accidental is not necessary

1 alrro is written in 1. 25 for avrov to avoid the possible misinterpretation of rov avrov. Cf. 13, 27, 258 b 23, 259* I,

BOOK VIII. 5 25 6 b but contingent. Now if we assume the existence of a possi- 10 bility, any conclusion that we thereby reach will not be an impossibility, though it may be contrary to fact. But the non-existence of motion is an impossibility : for we have shown above 1 that there must always be motion.

Moreover, the conclusion to which we have been led is a reasonable one. For there must be three things — the moved, the movent, and the instrument of motion. Now 15 the moved must be in motion, but it need not move anything else: the instrument of motion must both move something else and be itself in motion (for it changes together with the moved, with which it is in contact and continuous, as is clear in the case of things that move other things locally, in which case the two things must up to a certain point 2 be in contact) : and the movent — that is to say, that which causes motion in such a manner that it is not merely the instrument of motion — must be unmoved. Now we have visual experience of the 20 last term in this series, namely that which has the capacity of being in motion, but does not contain a motive principle, and also of that which is in motion but is moved by itself and not by anything else 3 : it is reasonable, therefore, not to say necessary, to suppose the existence of the third term also, that which causes motion but is itself unmoved.

So, too, Anaxagoras is right when he says that Mind is 25

2 i. e. not necessarily continuously : e. g. a thing thrown continues its course after contact with the thrower has ceased.

3 I am convinced that Bekker’s reading (which is that of two MSS. including the best) is right— b Kivelrai ptv, ov\ vn dX'hov fic dXX’ v(p* civtov. Prantl reads h kiv€i pev, bit dXXov fie (kiv€itcu) dXX* o\>x b<p> airrov. For the transposition of ov* there is MS. authority : but the substitution of Kivd for icivelrai and the insertion of Kivfrrai later are alterations of Brand's own, based as it seems to me on a complete misunderstanding of Aristotle’s meaning. Apparently he would equate the middle term here with the $ctKTi)pia of the previous illustration. But there is no essential difference between the Xi3os and the fiaKTTjpta as regards their motion, and we have no right at all to infer from their existence the existence of a kivovv okIvtjtov : the most that we could infer tvXoyas would be the existence of an avroKivrjrov. As I read the passage, from the admitted existence of what is avroKtvtjrov (e. g. a stone) and of what is both kivovv and mvovptvov (e. g. an animal, which as moving itself shows the amalgamation of both principles) Aristotle infers by dmXoyia that presumably what is kivovv only also exists.

impassive and unmixed, since he makes it the principle of motion : for it could cause motion in this sense 1 only by being itself unmoved, and have supreme control only by being unmixed.

We will now take the second alternative. If the movent is not accidentally but necessarily in motion — so that, if it were not in motion, it would not move anything — then the movent, in so far as it is in motion, must be in 30 motion in one of two ways : it is moved either as that is which is moved 2 with the same kind of motion, or with a different kind — either that which is heating, I mean, is itself in process of becoming hot, that which is making healthy in process of becoming healthy, and that which is causing locomotion in process of locomotion, or else that which is making healthy is, let us say, in process of locomotion, and that which is causing locomotion in process of, say, increase. But it is evident that this is impossible. For if we adopt the first assumption we have to make it apply within each of the very lowest species into which 2 57 a motion can be divided : e. g. we must say that if someone 3 is teaching some lesson in geometry, he is also in process of being taught that same lesson in geometry, and that if he is throwing he is in process of being thrown in just the same manner. Or if we reject this assumption we must say that one kind of motion is derived from another; e. g. that that which is causing locomotion is in process of 5 increase, that which is causing this increase is in process of being altered by something else, and that which is causing this alteration is in process of suffering some different kind of motion. But the series must stop somewhere, since the kinds of motion are limited ; and if we say that the process is reversible, and that that which is causing alteration is in process of locomotion, we do no more than if we had said at the outset that that which is causing locomotion is in process of locomotion, and that 10 one who is teaching is in process of being taught : for it is

1 SC. as apxh *tyijtr€a>r.

2 Reading in 1. 30 cot to (axm to E).

5 The neuter would sound absurd here in English.

clear that everything that is moved is moved by the movent that is further back in the series as well as by that which immediately moves it : in fact the earlier movent is that which more strictly moves it. But this is of course impossible : for it involves the consequence that one who is teaching is in process of learning what he is teaching, whereas teaching necessarily implies possessing knowledge, and learning not possessing it. Still more unreasonable is the consequence involved that, since everything that is 15 moved is moved by something that is itself moved by something else, 1 everything that has a capacity for causing motion has as such a corresponding capacity for being moved : i. e. it will have a capacity for being moved in the sense in which one might say that everything that has a capacity for making healthy, and exercises that capacity, 2 * has as such a capacity for being made healthy, and that which has a capacity for building has as such a capacity for being built. It will have the capacity for being thus moved either immediately or through one or more links (as it will if, while everything that has a capacity for causing motion has as such a capacity for being moved by something else, the motion that it has the capacity for suffering 20 is not that with which it affects what is next to it, but a motion cf a different kind ; e. g. that which has a capacity for making healthy might as such have a capacity for learning : the series, however, could be traced back, as we said before, until at some time or other we arrived at the same kind of motion). Now the first alternative is impossible, and the second is fantastic : 4 it is absurd that that

1 It is necessary to insert ‘by something else' in view of the possibility admitted below (257*27) that to kivov^vov nf/utrov ulro tavTo Kivrjaet,

2 The words kq\ vyi d(ov in 1 . 17 seem pointless and irrelevant, and there is no trace of them in Simplicius.

5 Reading in 1 . 21 (with three MSS. including the best) natfrjruor'.

* Alexander (quoted by Simplicius) interpreted this to mean that while both alternatives are impossible, the second has the additional characteristic of being n-Xacr nar&fas. Simplicius himself, however, considers that the second alternative, while certainly *rXu<r/Lt«ra>dfy, is not logically impossible, since it might be denied that Kivyrtit are irrtrcpacriiiviu or that a thing KtvttTai paXXov into rov 7r pnttpov ran* KipowTuv. If Simplicius is right, the connexion is very loose, since the which has a capacity for causing alteration should as such *5 necessarily have a capacity, let us say, for increase. It is not necessary, therefore, that that which is moved should always be moved by something else that is itself moved by something else : so there will be an end to the series. Consequently the first thing that is in motion will derive its motion either from something that is at rest or from itself. But if there were any need to consider which of the two, that which moves itself or that which is moved by something else, is the cause and principle of motion, 30 every one would decide for the former : for that which is itself independently a cause is always prior as a cause 1 to that which is so only in virtue of being itself dependent upon something else that makes it so.

We must therefore make a fresh start and consider the question ; if a thing moves itself, in what sense and in what manner does it do so ? Now everything that is in motion must be infinitely divisible, for it has been shown already 2 257 b in our general course on Physics , 3 that everything that is essentially in motion is continuous. Now it is impossible that that which moves itself should in its entirety move itself : for then, while being specifically one and indivisible, it would as a whole both undergo and cause the same locomotion or alteration : thus it would at the same time 5 be both teaching and being taught (the same thing), or both restoring to and being restored to the same health. Moreover, we have 4 established the fact that it is the movable that is moved ; and this is potentially, not actually, in motion, but the potential is in process to actuality, and motion is an incomplete actuality of the movable. The movent on the other hand is already in activity : e. g. it is that which is hot that produces heat : in fact, that which second alternative has just been distinctly declared to be only a special case of the first.

1 This must be the sense, whether we read with Bekker in 1 . 30 alrtov ad irp6r*pov or with EK del nparfpou aluop : in either case alnop is wanted both as subject and as predicate.

2 The reference is apparently to vi. 4. 234 b 10 sqq.

# See note on 251*9.

BOOK VIII. 5 257 b produces the form 1 is always something that possesses it Consequently (if a thing can move itself as a whole), the io same thing in respect of the same thing 2 may be at the same time both hot and not hot. So, too, in every other case where the movent must be described by the same name in the same sense as the moved . 3 Therefore when a thing moves itself 4 it is one part of it that is the movent and another part that is moved. But it is not self-moving 6 in the sense that each of the two parts is moved by the other part : the following considerations make this evident. In the first place, if each of the two parts is to i 5 move the other, there will be no first movent. If a thing is moved by a series of movents, that which is earlier in the series is more the cause of its being moved than that which comes next, and will be more truly the movent : for we found that there are two kinds of movent, that which is itself moved by something else and that which derives its motion from itself: and that which is further from the thing that is moved is nearer to the principle of motion than that which is intermediate.” In the second place, 20 there is no necessity for the movent part to be moved by anything but itself: so it can only be accidentally that the other part moves it in return. I take then the possible case of its not moving it : then there will be a part that is moved and a part that is an unmoved movent. In the third place, there is no necessity for the movent to be moved in return: on the contrary the necessity that there should always be motion makes it necessary that there should be some movent that is either unmoved or moved by itself. In the fourth place we should then have a thing 35 undergoing the same motion that it is causing — that which is producing heat, therefore, being heated. But as a matter

1 i. e. any particular characteristic such as heat.

3 i. e. the whole of itself : there is no question of one part of a thing heating another part.

8 i. e, in respect of the imparted characteristic : thus to foppalvov and to 6 (ppaip 6 fifvov both have the predicative &*pp 6 v applied to them in the same sense (avwpvpw).

8 Reading in 1 . 14 kipovp, with EK Simp.

8 sc. between t 6 iroppwrtpop and to Ktvovptvov, of fact that which primarily moves itself 1 cannot contain either a single part that moves itself or a number of parts each of which moves itself. For, if the whole is moved by itself, it must be moved either by some part of itself or as 30 a whole by itself as a whole. If, then, it is moved in virtue of some part of it being moved by that part itself, it is this part that will be the primary self-movent, since, if this part is separated from the whole, the part will still move itself, but the whole will do so no longer. If on the other hand the whole is moved by itself as a whole, it must be accidentally that the parts move themselves: and therefore, their self-motion not being necessary, we may take the case 258® of their not being moved by themselves. Therefore in the whole of the thing we may distinguish that which imparts motion without itself being moved and that which is moved : for only in this way is it possible for a thing to be selfmoved. Further, if the whole moves itself wc may distinguish in it that which imparts the motion and that which is moved : so while we say that AB is moved by itself, we 5 may also say that it is moved by A. And since that which imparts motion may be cither a thing that is moved by something else or a thing that is unmoved, and that which is moved may be cither a thing that imparts motion to something else or a thing that docs not, that which moves itself must be composed of something that is unmoved but imparts motion and also of something that is moved but does not necessarily impart motion but may or may not do so. Thus let A be something that imparts motion but is unmoved, B something that is moved by A and moves F, 10 r something that is moved by B but moves nothing (granted that we eventually arrive at F we may take it that there is only one intermediate term, though there may be more). Then the whole ABr moves itself. But if I take away F, AB will move itself, A imparting motion and B being moved, whereas T will not move itself or in fact be moved 15 at all. Nor again will Br move itself apart from A : for B imparts motion only through being moved by something else, not through being moved by any part of itself. So 1 Cf. 256*35 n.

BOOK VIII. 5 258* only AB moves itself. That which moves itself, therefore, must comprise something that imparts motion but is unmoved and something that is moved but does not necessarily move anything else : and each of these two things, 20 or at any rate one of them, 1 must be in contact with the other. If, then, that which imparts motion is a continuous substance — that which is moved must of course be so — it is clear that it is not through some part of the whole being of such a nature as to be capable of moving itself that the whole moves itself : it moves itself as a whole, both being moved and imparting motion through containing a part that imparts motion and a part that is moved. It does 25 not impart motion as a whole nor is it moved as a whole : it is A alone that imparts motion and B alone that is moved. It is not true, further, that T is moved by A, which is impossible. 2

Here a difficulty arises : if something is taken away from A (supposing that that which imparts motion but is unmoved is a continuous substance), or from B the part that is moved, will the remainder of A continue to impart motion or the remainder of B continue to be moved ? If 3 ° so, it will not be AB primarily that is moved by itself, since, when something is taken away from AB, the remainder of AB will still continue to move itself. Perhaps we may state the case thus : there is nothing to prevent each 258 b of the two parts, or at any rate one of them, that which is moved, being divisible though actually undivided, so that if it is divided it will not continue in the possession of the same capacity: and so there is nothing to prevent self-

1 If both are corporeal, the two things will be mutually in contact : but if one is incorporeal and the other not, the first may be said to be in contact with (cbnrar&u) the second, but not vice versa. So here the kipovv thcivrjTop may be said drrTtaOai rov Kipovjji'pov, but to Kipovfifpop cannot be said &rrrc<r()ai tov kivovptos cuuvrjTov hi. See de Gen. et Corr. i. 6. 323® 25 sqq.

2 This sentence comes in awkwardly here, and I am inclined to think that it should be omitted. It was not known to Alexander, nor did it occur in most of the MSS. known to Simplicius. The best of our MSS. omits it. The point of the sentence, if it is kept, seems to be that in AB we have one complete axnoKivrfrov : A may accidentally through B impart motion to r : but r is irrelevant to the avroKivtjTOP that we are considering.

motion residing primarily in things that are potentially divisible.

From what has been said, then, it is evident that that 5 which primarily imparts motion is unmoved : for, whether the series is closed at once by that which is in motion but moved by something else deriving its motion directly from the first unmoved, or whether the motion is derived from what is in motion but moves itself and stops its own motion, on both suppositions we have the result that in all cases of things being in motion that which primarily imparts motion is unmoved.

io Since there must always be motion without intermission, 6 there must necessarily be something, one thing or it may be a plurality, that first imparts motion, and this first movent must be unmoved. Now the question whether each of the things that are unmoved but impart motion 1 is eternal is irrelevant to our present argument: but the following considerations will make it clear that there must necessarily be some such thing, which, while it has the capacity of moving something else, is itself unmoved and exempt from 15 all change, 2 which can affect it neither in an unqualified nor in an accidental sense. 3 Let us suppose, if any one likes, that in the case of certain things 4 it is possible for them at different times to be and not to be, without any process of becoming and perishing (in fact it would seem to be necessary, if a thing that has not parts at one time is and at another time is not, 5 that any such thing should without undergoing any process of change at one time be and at

1 e. g. individual yjivxai

2 Omitting in 1. 14 r?)s before €kt6s with Simplicius and three MSS. one of which has r< for rijr and another *al before n darjs : any one of these variations will give the sense required. Simplicius gives no hint of a reading rijs «Ver6s u€rafio\r}s i which would have to be taken as a loose genitive after aid»T)Tov—‘ unmoved in respect of all external change' : this, though possible, is not quite the sense required: we want to have exemption from ptra&oXr) clearly marked as an additional attribute, more extensive than exemption from ir.

* i. e. neither directly norindirectly : e. g. a man walking fierapdWu chrX&v, a man sailing in a ship prra&dXKtt Kara avfiftcftrjKde.

* sc. V'vxou : Aristotle is answering an objection to the effect that here we may find an aiuVr;ror dpxf} Kivyirues that is not dlftios.

* Reading in 1. 19 a comma before avtv and not before 6r L another time not be). And let us further suppose it ao possible that some principles that are unmoved but capable of imparting motion at one time are and at another time are not. Even so, this cannot be true of all such principles, since there must clearly be something that causes things that move themselves 1 at one time to be and at another not to be. For, since nothing that has not parts can be in motion, that which moves itself must as a whole have 3 5 magnitude, though nothing that we have said makes this necessarily true of every movent. So the fact that some things become and others perish, and that this is so continuously, cannot be caused by any one of those things that, though they are unmoved, do not always exist : nor again can it be caused by any of those which move certain particular things, while others 2 move other things. The eternity and continuity of the process cannot be caused either by any one of them singly or by the sum of them, because this causal relation must be eternal and necessary, 30 whereas the sum of these movents is infinite and they do not all exist together. It is clear, then, that though there may be countless instances of the perishing of some principles that are unmoved but impart motion, and though »59* many things that move themselves 3 perish and are succeeded by others that come into being, and though one thing that is unmoved moves one thing while another moves another, nevertheless there is something that comprehends them all, and that as something apart from each one of them, and this it is that is the cause of the fact that some things are and others are not and of the continuous process of change : and this causes the motion of the 5 other movents, while they are the causes of the motion of other things. Motion, then, being eternal, the first movent, if there is but one, will be eternal also : if there are more than one, there will be a plurality of such eternal movents.

We ought, however, to suppose that there is one rather than many, and a finite rather than an infinite number.

When the consequences of either assumption are the same, 1 we should always assume that things are finite rather than io infinite in number, since in things constituted by nature that which is finite and that which is better ought, if possible, to be present rather than the reverse : and here it is sufficient to assume only one movent, the first of unmoved things, which being eternal will be the principle of motion to everything else.

The following argument also makes it evident that the first movent must be something that is one and eternal.

5 We have shown 2 that there must always be motion. That being so, motion must also be continuous, because what is always is continuous, whereas what is merely in succession is not continuous. But further, if motion is continuous, it is one : and it is one only if the movent and the moved that constitute it are each of them one, since in the event of a thing’s being moved now by one thing and now by another the whole motion will not be continuous but successive.

jo Moreover a conviction that there is a first unmoved something may be reached not only from the foregoing arguments, but also by considering again the principles operative in movents. Now it is evident that among existing things there are some that are sometimes in motion and sometimes at rest. This fact has served above 3 to make it clear that it is not true either that all things are in motion or that all things are at rest or that some things are always at rest

5 and the remainder always in motion : on this matter proof is supplied by things that fluctuate between the two and have the capacity of being sometimes in motion and sometimes at rest. The existence of things of this kind is clear to all : 4 but we wish to explain also the nature of each of the other two kinds and show that there are some things that are always unmoved and some things that are always

1 i.e. when either will equally explain the facts.

2 Chapter i.

8 Chapter 3.

4 The apodosis to the eW clause does not begin till by kt\.).

259 b 3 (ravta in motion. In the course of our argument directed to this end we established the fact that everything that is in motion 30 is moved by something, 1 and that the movent is either unmoved or in motion, and that, if it is in motion, it is moved either by itself or by something else and so on throughout the series : 2 and so we proceeded to the position 3 that the first principle that directly 4 causes things that are in motion to be moved is that which moves itself, and the first principle of the whole series 5 is the unmoved. Further it is evident from actual observation that there are 259 things that have the characteristic of moving themselves, e. g. the animal kingdom and the whole class of living things. 6 This being so, then, the view was suggested 7 that perhaps it may be possible for motion to come to be in a thing without having been in existence at all before, because we see this actually occurring in animals : they are 5 unmoved at one time and then again they are in motion, as it seems. We must grasp the fact, therefore, that animals move themselves 8 only with one kind of motion, 9 and that this is not strictly originated by them. The cause of it is not derived from the animal itself: it is connected with other natural motions in animals, which they do not experience through their own instrumentality, e. g. increase, decrease, and respiration: these are experienced by every 10 animal while it is at rest and not in motion in respect of the motion set up by its own agency; 10 here the motion is caused by the atmosphere and by many things that enter into the animal : thus in some cases the cause is nourishment : when it is being digested animals sleep, and when it is being distributed through the system they awake and

1 Chapter 4.

2 «ei. i.e. if a particular klvovv derives its motion from another kivovv the .same question arises with regard to the second kivov v, and so on.

5 Chapter 5.

4 Ktvovfitva>v n 4 v in 1 . 33 can hardly stand. It may have displaced irpoarfX') s which Simp, seems to read, or Kivyatcts.

6 SC. Kivovfjievct and & avro ^avro jam together.

* Reading in 1 . 7 avra, with Simp.

0 sc. locomotion. 10 sc, locomotion.

move themselves, the first principle of this motion being thus originally derived from outside. Therefore animals are not always in continuous motion by their own agency: 15 it is something else that moves them, itself being in motion and changing as it comes into relation with each several thing that moves itself. (Moreover in all these self-moving things the first movent and cause of their self-motion 1 is itself moved by itself, 2 though in an accidental sense : that is to say, the body changes its place, so that that which is in the body changes its place also and is a self-movent 20 through its exercise of leverage. 3 ) Hence we may confidently conclude that if a thing belongs to the class of unmoved movents that are also themselves moved accidentally, it is impossible that it should cause continuous motion. So the necessity that there should be motion continuously requires that there should be a first movent that is unmoved even accidentally, 4 * if, as we have said, 6 35 there is to be in the world of things an unceasing and undying motion, and the world is to remain 6 permanently self-contained and within the same limits: for if the first principle is permanent, the universe must also be permanent, since it is continuous with the first principle. (We must distinguish, however, between accidental motion of a thing by itself and such motion by something else, the former being confined to perishable things, whereas the latter belongs also to certain first principles of heavenly 30 bodies, of all those, that is to say, that experience more than one locomotion. 7 )

1 SC. If

2 i. e. it is not a true aKlvrfrov after all.

8 Reading in 1 . 19 (with three MSS.) *ai rrj fwxkiicL : the ordinary reading #cal to iv rfi poxXu? seems meaningless. The sense appears to be that the soul may be said to move itself by means of the body, the body acting as a sort of lever.

4 Reading in 1 . 24 *a< Kara (rvn&f&r)K6s : the fifj before Kara is omitted by one MS. and erased in another : also it clearly was not read by Simplicius. It might quite easily have been inserted by some one who, not understanding the construction, thought that the words following Kai must denote another attribute in addition to aKwrjrov.

6 Chapter 1.

6 Reading in L 26 ficv€lv f with Themistius.

7 sc the planets.

And further, if there is always something of this nature, a movent that is itself unmoved and eternal, then that a6o a which is first moved by it must be eternal. Indeed this is clear also from the consideration that there would otherwise be no becoming and perishing and no change of any kind in other things, which require something that is in motion to move them : for the motion imparted by the unmoved will always be imparted in the same way and be one and the same, since the unmoved does not itself change in relation to that which is moved by it. But that 1 which 5 is moved by something 2 that, though it is in motion, is moved directly by the unmoved stands in varying relations to the things that it moves, so that the motion that it causes will not be always the same : by reason of the fact that it occupies contrary positions or assumes contrary forms at different times it will produce contrary motions in each several thing that it moves and will io cause it to be at one time at rest and at another time in motion.

The foregoing argument, then, has served to clear up the point about which we raised a difficulty at the outset 3 — why is it that instead of all things being either in motion or at rest, or some things being always in motion and the remainder always at rest, there are things that are sometimes in motion and sometimes not ? The cause of this is now plain : it is because, while some things are moved by an eternal unmoved movent and are therefore always in motion, 4 other things are moved by a movent that is in 1 5 motion and changing, so that they too must change. But the unmoved movent, as has been said, since it remains permanently simple and unvarying and in the same state, will cause motion that is one and simple.

1 e. g. any one of the heavenly bodies.

2 sc. 6 ovpauos , which imparts motion to terrestrial things through the medium of the various heavenly bodies. I see no reason to depart from the reading adopted by Bekker with most MSS. : to my mind this reading will account for the reading of K and of Simplicius (adopted by Prantl) r6 di Kivovpfvov vno rov aKivryrov ff Kivovpevov more easily than vice versa .

8 Chapter 3.

4 Reading in 1 . 15 dih del wiw « t with EK Them. Phil. Simp.

20 This matter will be made clearer, however, if we start afresh from another point. We must consider whether it is or is not possible that there should be a continuous motion, and, if it is possible, which this motion is, and which is the primary motion : for it is plain that if there must always be motion, and a particular motion is primary 2 5 and continuous, then it is this motion that is imparted by the first movent, and so it is necessarily one and the same and continuous and primary.

Now of the three kinds of motion that there are — motion in respect of magnitude, motion in respect of affection, and motion in respect of place — it is this last, which we call locomotion, that must be primary. This may be shown as follows. It is impossible that there should be increase 30 without the previous occurrence of alteration : for that which is increased, although in a sense it is increased by what is like itself, is in a sense increased by what is unlike itself : thus it is said that contrary is nourishment to contrary: 1 but growth is effected only by things becoming like to like. There must be alteration, then, in that there a6o b is this change from contrary to contrary. But the fact that a thing is altered requires that there should be something that alters it, something e. g. that makes the potentially hot into the actually hot : so it is plain that the movent does not maintain a uniform relation to it but is at one time nearer to and at another farther from that which is 5 altered: and we cannot have this without locomotion. If, therefore, there must always be motion, there must also always be locomotion as the primary motion, and, if there is a primary as distinguished from a secondaiy form of locomotion, it must be the primary form. Again, all affections have their origin in condensation and rarefaction : thus 10 heavy and light, soft and hard, hot and cqld, are considered to be forms of density and rarity. But condensation and rarefaction are nothing more than combination and separation, processes in accordance with which substances are said to become and perish : and in being combined and separated things must change in respect of place.

1 Cf. De An, ii. 4. 4l6 a 2i sqq.

And further, when a thing is increased or decreased its magnitude changes in respect of place.

Again, there is another point of view from which it will 15 be clearly seen that locomotion is primary. As in the case of other things so too in the case of motion the word ‘ primary ’ may be used in several senses. A thing is said to be prior to other things when, if it does not exist, the others will not exist, whereas it can exist without the others : and there is also priority in time and priority in perfection of existence. Let us begin, then, with the firstsense. Now there must be motion continuously, and there 20 may be continuously either continuous motion or successive motion, the former, however, in a higher degree than the latter: moreover it is better that it should be continuous rather than successive motion, and we always assume the presence in nature of the better, if it be possible: since, then, continuous motion is possible (this will be proved later : 1 for the present let us take it for granted), and no other motion can be continuous except locomotion, loco- 35 motion must be primary. For there is no necessity for the subject of locomotion to be the subject either of increase or of alteration, nor need it become or perish: on the other hand there cannot be any one of these processes without the existence of the continuous motion imparted by the first movent.

Secondly, locomotion must be primary in time: for this is the only motion possible for eternal things. It is true 30 indeed that, in the case of any individual thing that has a becoming, locomotion must be the last of its motions: for after its becoming it first experiences alteration and increase, and locomotion is a motion that belongs to such things only when they are perfected. But there must previously s*6i a be something else that is in process of locomotion to be the cause even of the becoming of things that become, without itself being in process of becoming, as e.g. the begotten is preceded by what begot it : otherwise becoming might be thought to be the primary motion on the ground that the thing must first become. But though this is so in the case 5 1 Chapter 8.

a6i a of any individual thing that becomes, nevertheless before anything becomes, something else must be in motion, not itself becoming but being, and before this there must again be something else. And since becoming cannot be primary — for, if it were, everything that is in motion would be perishable — it is plain that no one of the motions next in order io can be prior to locomotion. By the motions next in order I mean increase and then alteration, decrease, and perishing. All these are posterior to becoming : consequently, if not even becoming is prior to locomotion, then no one of the other processes of change is so either.

Thirdly, that which is in process of becoming appears universally as something imperfect and proceeding to a first principle : and so what is posterior in the order of becoming is prior in the order of nature. Now all things that go through the process of becoming acquire locomotion last. 15 It is this that accounts for the fact that some living things, e. g. plants and many kinds of animals, owing to lack of the requisite organ, are entirely without motion, whereas others acquire it in the course of their being perfected. Therefore, if the degree in which things possess locomotion corresponds to the degree in which they have realized their natural development, then this motion must be prior to all 20 others in respect of perfection of existence : and not only for this reason but also because a thing that is in motion loses its essential character less in the process of locomotion than in any other kind of motion : it is the only motion that does not involve a change of being in the sense in which there is a change in quality when a thing is altered and a change in quantity when a thing is increased or decreased. Above all it is plain that this motion, motion in respect of place, is what is in the strictest sense produced 25 by that which moves itself ; but it is the self-movent that we declare to be the first principle of things that are moved and impart motion and the primary source to which things that are in motion are to be referred.

It is clear, then, from the foregoing arguments that locomotion is the primary motion. We have now to show which kind of locomotion is primary. The same process

26l a of reasoning will also make clear at the same time the truth of the assumption we have made both now and at a previous stage 1 that it is possible that there should be 3° a motion that is continuous and eternal. Now it is clear from the following considerations that no other than locomotion can be continuous. Every other motion and change is from an opposite to an opposite : thus for the processes of becoming and perishing the limits are the existent and the non-existent, for alteration the various pairs of contrary affections, and for increase and decrease either greatness 35 and smallness or perfection and imperfection of magnitude : and changes to the respective contraries are contrary changes. Now a thing that is undergoing any particular a6i b kind of motion, but though previously existent has not always undergone it, must previously have been at rest so far as that motion is concerned. It is clear, then, that for the changing thing the contraries will be states of rest. 2 * And we have a similar result in the case of changes that are not motions : a for becoming and perishing, whether regarded simply as such without qualification or as affecting something in particular, are opposites : therefore pro- 5 vided it is impossible for a thing to undergo opposite changes at the same time, the change will not be continuous, but a period of time will intervene between the opposite processes. The question whether these contradictory changes are contraries or not makes no difference, provided only it is impossible for them both to be present to the same thing at the same time : the point is of no importance to the argument. 4 * Nor does it matter if the thing need 10 not rest in the contradictory state, or if there is no state of rest as a contrary to the process of change : 6 it may be true

1 253® 29. Omit the second to in l. 29, with EK Simp.

a Hence the Kivr)<ns in question cannot be arvptxfi *'•

* It seems necessary to translate p* rafio\d>p here in this way: Aristotle has been dealing with /Acru^oXm all along, but so far only with such of them as are also kip fatis: he now extends his results to include (itrafioXat that are not Kiurjaas in the strict sense, namely and

<j) 0 o(jd t which also proceed from dpnKtiptPop to dpriK(iptPOP t though in this case the dvrtK€tp§pa are not cvavria.

that the non-existent is not at rest, and that perishing is a process to the non-existent. All that matters is the intervention of a time : it is this that prevents the change from being continuous: so, too, in our previous instances 1 the important thing was not the relation of contrariety but the impossibility of the two processes being present to a thing at the same time. And there is no need to be disturbed by the fact that on this showing there may be more than one contrary to the same thing, that a particular motion will be contrary both to rest and to motion in the contrary direction. We have only to grasp the fact that a particular motion is in a sense the opposite both of a state of rest and of the contrary motion, in the same way as that which is of equal or standard measure is the opposite both of that which surpasses it and of that which it surpasses, and that it is impossible for the opposite motions or changes to be present to a thing at the same time. Furthermore, in the case of becoming and perishing it would seem to be an utterly absurd thing if as soon as anything has become it must necessarily perish and cannot continue to exist for any time : and, if this is true of becoming and perishing, we have fair grounds for inferring the same to be true of the other kinds of change, since it would be in the natural order of things that they should be uniform in this respect.

Let us now proceed to maintain that it is possible that 8 there should be an infinite motion that is single and continuous, and that this motion is rotatory motion. The motion of everything that is in process of locomotion is either rotatory or rectilinear or a compound of the two: consequently, if one of the former two is not continuous, that which is composed of them both cannot be continuous either. Now it is plain that if the locomotion of a thing is rectilinear and finite it is not continuous locomotion : for the thing must turn back, and that which turns back in a straight line undergoes two contrary locomotions, since, so far as motion in respect of place is concerned, upward

1 sc. the instances of Kivfi<r*ts given above.

26l b motion is the contrary of downward motion, forward motion of backward motion, and motion to the left of motion to 35 the right, these being the pairs of contraries in the sphere of place. But we have already 1 defined single and con- 262* tinuous motion to be motion of a single thing in a single period of time and operating within a sphere admitting of no further specific differentiation (for we have three things to consider, first that which is in motion, e. g. a man or a god, secondly the 4 when’ of the motion, that is to say, the time, and thirdly the sphere within which it operates, which may be either place or affection or essential form or magnitude) : and contraries are specifically not one and the 5 same but distinct : and within the sphere of place we have the above-mentioned distinctions. Moreover we have an indication that motion from A to B is the contrary of motion from B to A 2 in the fact that, if they occur at the same time, they arrest and stop each other. And the same is true in the case of a circle: the motion from A towards B is the contrary of the motion from A towards T 3 : for even if they are continuous and there is no turning back )° they arrest each other , 4 because contraries annihilate or obstruct one another. On the other hand lateral motion is not the contrary of upward motion . 6 But what shows most clearly that rectilinear motion cannot be continuous is the fact that turning back necessarily implies coming to a stand, not only when it is a straight line that is traversed, but also in the case of locomotion in a circle (which is 15 not the same thing as rotatory locomotion : for, when a thing merely traverses a circle, it may either proceed on its course without a break or turn back again when it has reached the same point from which it started). We may assure ourselves of the necessity of this coming to a stand

8 sc. here we havetthe opposite conclusion from the fact that these two motions do not interfere with each other.

a6a ft not only on the strength of observation, but also on theoretical grounds. We may start as follows : we have three points, starting-point, middle-point, and finishing- 20 point, of which the middle-point in virtue of the relations in which it stands severally to the other two is both a starting-point and a finishing-point, and though numerically one is theoretically two. We have further the distinction between the potential and the actual. So in the straight line in question any one of the points lying between the two extremes is potentially a middle-point : but it is not actually so unless that which is in motion divides the line by coming to a stand at that point and beginning its 25 motion again : thus the middle-point becomes both a starting-point and a goal, the starting-point of the latter part and the finishing-point of the first part of the motion. This is the case e. g. when A in the course of its locomotion comes to a stand at B and starts again towards T : but when its motion is continuous A cannot either have come to be or have ceased to be at the point B: it can 30 only have been there at the moment of passing, its passage not being contained within any period of time except the whole 1 of which the particular moment is a dividingpoint. To maintain that it has come to be and ceased to be there will involve the consequence that A in the course of its locomotion will always be coming to a stand : for it 26a b is impossible that A should simultaneously have come to be at B and ceased to be there, so that the two things must have happened at different points of time, and therefore there will be the intervening period of time : consequently A will be in a state of rest at B, and similarly at all other points, since the same reasoning holds good in every case. 5 When to A, that which is in process of locomotion, B, the middle-point, serves both as a finishing-point and as a starting-point for its motion, A must come to a stand at B, because it makes it two just as one might do in thought. However, the point A is the real starting-point at which the moving body has ceased to be, and it is at f that it

a6a b has really come to be when its course is finished and it comes to a stand. So this is how we must meet the difficulty that then arises, which is as follows. Suppose the line 10 E is equal to the line Z, that A proceeds in continuous locomotion from the extreme point of E to T, and that, at the moment when A is at the point B, A is proceeding in uniform locomotion and with the same velocity as A from the extremity of Z to H : 1 then, says the argument, A will have reached H before A has reached P : for that which makes an earlier start and departure must make an earlier arrival: the reason, then, for the late arrival of A is that 15 it has not simultaneously come to be and ceased to be at B : otherwise it will not arrive later : for this to happen it will be necessary that it should come to a stand there. Therefore we must not hold that there was a moment when A came to be at B and that at the same moment A was in motion from the extremity of Z : for the fact of As having come to be at B will involve the fact of its also 20 ceasing to be there, and the two events will not be simultaneous, whereas the truth is that A is at B at a sectional point of time and does not occupy time there. In this case, therefore, where the motion of a thing is continuous * it is impossible to use this form of expression. 2 3 On the other hand in the case of a thing that turns back in its course we must do so. For suppose H in the course of its locomotion proceeds to A and then turns back and proceeds downwards again : 4 then the extreme point A has served

2 The MSS. in 1 . 22 vary between nj? (sc. kivtjvws ) and tov crvpcxovs (Bekker) with which it is difficult to see what word to supply. I suspect the true reading to be to 0 (sc. icti/ovfJLtVOV.

8 sc. to speak of it as yey ovos at any intermediate point.

as finishing-point and as starting-point for it, one point thus 25 serving as two: therefore H must have come to a stand there : it cannot have come to be at A and departed from A simultaneously, for in that case it would simultaneously be there and not be there at the same moment. And here we cannot apply the argument used to solve the difficulty stated above : we cannot argue that H is at A at a sectional point of time and has not come to be or ceased to be there. 30 For here the goal that is reached is necessarily one that is actually, not potentially, existent. Now the point in the middle is potential : but this one is actual, and regarded from below it is a finishing-point, while regarded from above it is a starting-point, so that it stands in these 263* same two respective relations to the two motions . 1 Therefore that which turns back in traversing a rectilinear course must in so doing come to a stand. Consequently there cannot be a continuous rectilinear motion that is eternal . 2 3

The same method should also be adopted in replying to 5 those who ask, in the terms of Zeno’s argument, a whether we admit that before any distance can be traversed half the distance must be traversed, that these half-distances are infinite in number, and that it is impossible to traverse distances infinite in number — or some on the lines of this same argument put the questions in another form, and would have us grant that in the time during which a motion is in progress it should be possible to reckon a half-motion before the whole for every half-distance that we get, so that we have the result that when the whole distance is traversed 10 we have reckoned an infinite number, which is admittedly impossible. Now when we first discussed the question of motion we put forward a solution 4 of this difficulty turning

1 i. e. it is TtXevrr] in relation to the first (upward) part of the motion (up to A) and dpxh in relation to the second (downward) part (down from A).

2 Reading in 1 . 3 «Vr* rrjs tvSdas diSiov. Bekker’s reading tnl cUSiov rrfs tide las is apparently a mere slip.

3 Ka\ d(iovvru£ in 1. 5 seems to be a gloss introduced undet the influence of d£iovvrts, 1. 7.

on the fact that the period of time occupied in traversing the distance contains within itself an infinite number of units: there is no absurdity, we said, in supposing the traversing of infinite distances in infinite time, and the element of infinity is present in the time no less than in the distance. But, although this solution is adequate as 15, a reply to the questioner (the question asked being whether it is possible in a finite time to traverse or reckon an infinite number of units), nevertheless as an account of the fact and explanation of its true nature it is inadequate. For suppose the distance to be left out of account and the question asked to be no longer whether it is possible in a finite time to traverse an infinite number of distances, and suppose that 20 the inquiry is made to refer to the time taken by itself (for the time contains an infinite number of divisions) : then this solution will no longer be adequate, and we must apply the truth that we enunciated in our recent discussion, stating it in the following way. In the act of dividing the continuous distance into two halves one point is treated as two, since we make it a starting-point and a finishing-point : and this same result is also produced by the act of reckon- 25 ing halves as well as by the act of dividing into halves.

But if divisions are made in this way, neither the distance nor the motion will be continuous : for motion if it is to be continuous must relate to what is continuous: and though what is continuous contains an infinite number of halves, they are not actual but potential halves. If the halves are made actual, we shall get not a continuous but an intermittent motion. In the case of reckoning the halves, 30 it is clear that this result follows : for then one point must be reckoned as two : it will be the finishing-point of 263 b the one half and the starting-point of the other, if we reckon not the one continuous whole but the two halves. Therefore to the question whether it is possible to pass through an infinite number of units either of time or of distance we must reply that in a sense it is and in a sense it is not. If the units are actual, it is not possible : if they are 5 potential, it is possible. For in the course of a continuous motion the traveller has traversed an infinite number of units in an accidental sense but not in an unqualified sense : for though it is an accidental characteristic of the distance to be an infinite number of half-distances, this is not its real and essential character. It is also plain that unless io we hold that the point of time that divides earlier from later always belongs only to the later so far as the thing is concerned, we shall be involved in the consequence that the same thing is at the same moment existent and not existent, and that a thing is not existent at the moment when it has become. It is true that the point is common to both times, the earlier as well as the later, and that, while numerically one and the same, it is theoretically not so, being the finishing-point of the one and the starting-point of the other : but so far as the thing is concerned it belongs 15 to the later stage of what happens to it. Let us suppose a time ABr 1 and a thing A, A being white in the time A and not-white in the time B. Then A is at the moment T white and not-white : for if we were right in saying that it is white during the whole time A, it is true to call it white at any moment of A, and not-white in B, and T is in both A ao and B. We must not allow, therefore, that it is white in the whole of A, but must say that it is so in all of it except the last moment T. T belongs already to the later period, 2 and if in the whole of A not-white was in process of becoming and white of perishing, at T the process is complete. And so T is the first moment at which it is true to call the thing white or not-white respectively. 3 Otherwise a thing may be non-existent at the moment when it has become and existent at the moment when it has perished : or else 35 it must be possible for a thing at the same time to be white and not white and in fact to be existent and non-existent. Further, if anything that exists after having been previously non-existent must become existent and does not exist when it is becoming, time cannot be divisible into time-atoms.

1 Reading in 1 . 15 ArB. Bekker has ABr, apparently a slip. The first and third letters denote periods of time, the second the moment that divides them.

* Reading in 1 . 21 toO vorcpov, with (apparently) Phil. Simp.

* Only the latter case has been mentioned above.

For suppose that A was becoming white in the time A and that at another time B, a time-atom consecutive with the last atom of A, A has already become white and so is white at that moment: then, inasmuch as in the time A it was 30 becoming white and so was not white and at the moment B it is white, there must have been a becoming beween A and B and therefore also a time in which the becoming took place. On the other hand, those who deny atoms of 264* time (as we do) are not affected by this argument : according to them A has become and so is white at the last point of the actual time in which it was becoming white : and this point has no other point consecutive with or in succession to it, whereas time-atoms are conceived as successive. Moreover it is clear that if A was becoming white in the whole time A, the time occupied by it in having become white in 5 addition to having been in process of becoming white is no more than all that it occupied in the mere process of becoming white. 1

These and such-like, then, are the arguments for our conclusion that derive cogency from the fact that they have a special bearing on the point at issue. If wc look at the question from the point of view of general theory, the same result would also appear to be indicated by the following arguments. Everything whose motion is continuous must, on arriving at any point in the course of its 10 locomotion, have been previously also in process of locomotion to that point, if it is not forced out of its path by anything : e. g. on arriving at B a thing must also have been in process of locomotion to B, and that not merely when it was near to B, but from the moment of its starting on its course, since there can be no reason for its being so at any particular stage rather than at an earlier one. So, too, in the case of the other kinds of motion. Now we are to suppose that a thing proceeds in locomotion from A to T and that at the moment of its arrival at T the continuity 15 of its motion is unbroken and will remain so until it has

1 sc. and therefore ro w ytyovt cannot be X(x> v °tj since it makes no addition to the total : it is merely a cnifirfov xp&ov.

045. lfi R arrived back at A. Then when it is undergoing locomotion from A to P it is at the same time undergoing also its locomotion to A from P ; consequently it is simultaneously undergoing two contrary motions, since the two motions that follow the same straight line are contrary to each other. With this consequence there also follows another: we have a thing that is in process of change from a position in which it has not yet been : so, inasmuch as this is impossible, the thing must come to a stand at T. 20 Therefore the motion is not a single motion, since motion that is interrupted by stationariness is not single.

Further, the following argument will serve better to make this point clear universally in respect of every kind of motion. If the motion undergone by that which is in motion is always one of those already enumerated, and the state of rest that it undergoes is one of those that are the opposites of the motions (for we found 1 that there could be no other besides these), and moreover that which is undergoing but does not always undergo a particular 25 motion (by this I mean one of the various specifically distinct motions, not some particular part of the whole motion) must have been previously undergoing the state of rest that is the opposite of the motion, the state of rest being privation of motion; 2 then, inasmuch as the two motions that follow the same straight line are contrary motions, and it is impossible for a thing to undergo simultaneously two contrary motions, that which is undergo going locomotion from A to F cannot also simultaneously be undergoing locomotion from T 3 to A : and since the latter locomotion is not simultaneous with the former but is still to be undergone, before it is undergone there must occur a state of rest at T : for this, as we found, 4 is the state of rest that is the opposite of the motion from T . The foregoing argument, then, makes it plain that the motion in question 6 is not continuous.

* Reading in 1. 28 a colon before «?, with Bonitz.

8 Reading in 1. 30 r. Bekker’s A is apparently a mere slip.

BOOK VIII. 8 a 64 b

Our next argument has a more special bearing than the a 64 b foregoing on the point at issue. We will suppose that there has occurred in something simultaneously a perishing of not-white and a becoming of white. Then if the alteration to white and from white is a continuous process and the white does not remain any time, there must have 5 occurred simultaneously a perishing of not-white, a becoming of white, and a becoming of not-white: for the time of the three will be the same.

Again, from the continuity of the time in which the motion takes place we cannot infer continuity in the motion, but only successiveness : in fact, how could contraries, e. g. whiteness and blackness, meet in the same extreme point ? 1

On the other hand, in motion on a circular line we shall find singleness and continuity : for here we are met by no impossible consequence: that which is in motion from A io will in virtue of the same direction of energy be simultaneously in motion to A (since it is in motion to the point at which it will finally arrive), and yet will not be undergoing two contrary or opposite motions : for a motion to a point and a motion from that point are not always contraries or opposites : they are contraries only if they are on the same straight line (for then they are contrary to one another in 15 respect of place, as e. g. the two motions along the diameter of the circle, since the ends of this are at the greatest possible distance from one another), and they are opposites only if they are along the same line. 2 Therefore in the case we are now considering there is nothing to prevent the motion being continuous and free from all intermission : for rotatory motion is motion of a thing from its place to its place, 3 whereas rectilinear motion is motion 30 from its place to another place.

1 sc. as would be necessary if there is to be oW*«a between the two contrary processes.

2 i. e. they must traverse the same course in opposite directions, though their apxv an d reXfvrr) need not be ir\u<rrov aw€\ovcrai as in the case of tvavriai Kivr)cru$, which, however, are of course included in the term dvriKtiptvcu.

Moreover the progress of rotatory motion is never localized within certain fixed limits, whereas that of rectilinear motion repeatedly is so . 1 Now a motion that is always shifting its ground from moment to moment can be continuous : but a motion that is repeatedly localized within certain fixed limits cannot be so, since then the same thing would have to undergo simultaneously two opposite motions. So, too, there cannot be continuous motion in 35 a semicircle or in any othet arc of a circle, since here also the same ground must be traversed repeatedly and two contrary processes of change must occur. The reason is that in these motions the starting-point and the termination do not coincide, whereas in motion over a circle they do coincide, and so this is the only perfect motion . 2

This differentiation also provides another means of showing that the other kinds of motion cannot be continuous 30 either: for in all of them we find that there is the same ground to be traversed repeatedly : thus in alteration there are the intermediate stages of the process, and in quantitative change there are the intervening degrees of magnitude : and in becoming and perishing the same thing is true. It makes no difference whether we take the intermediate stages of the process to be few or many, or whether we 265* add or subtract one : for in either case we find that there is still the same ground to be traversed repeatedly. Moreover it is plain from what has been said that those physicists who assert that all sensible things are always in motion are wrong : for their motion must be one or other of the ‘ 5 motions just mentioned : in fact they mostly conceive it as alteration (things are always in flux and decay, they say), and they go so far as to speak even of becoming and perishing as a process of alteration. On the other hand, our argument has enabled us to assert the fact, applying universally to all motions, that no motion admits of continuity except rotatory motion : consequently neither altera-

1 i. e. the ap\h and riK^nrj of the line are fixed extreme points, and the motion is repeatedly taking place between them, whereas on the circle there are no such points.

2 Because finite lines may be extended, whereas a circle is once for all complete.

tion nor increase 1 admits of continuity. We need now say 10 no more in support of the position that there is no process of change that admits of infinity or continuity except rotatory locomotion.

9 It can now be shown plainly that rotation is the primary locomotion. Every locomotion, as we said before, 2 is either rotatory or rectilinear or a compound of the two: and the 15 two former must be prior to the last, since they are the elements of which the latter consists. Moreover rotatory locomotion is prior to rectilinear locomotion, because it is more simple and complete, which may be shown as follows. The straight line traversed in rectilinear motion cannot be infinite: for there is no such thing as an infinite straight line ; and even if there were, it would not be traversed by anything in motion : for the impossible does not happen and it is impossible to traverse an infinite distance. On 20 the other hand rectilinear motion on a finite straight line is if it turns back a composite motion, in fact two motions, while if it does not turn back it is incomplete and perishable : and in the order of nature, of definition, and of time alike the complete is prior to the incomplete and the imperishable to the perishable. Again, a motion that admits of being eternal is prior to one that does not. Now rotatory motion 25 can be eternal : but no other motion, whether locomotion or motion of any other kind, can be so, since in all of them rest must occur, and with the occurrence of rest the motion has perished. Moreover the result at which we have arrived, that rotatory motion is single and continuous, and rectilinear motion is not, is a reasonable one. In rectilinear motion we have a definite starting-point, finishing-point, and middle-point, which all have their place in it in such 30 a way that there is a point from which that which is in motion can be said to start and a point at which it can be said to finish its course (for when anything is at the limits of its course, whether at the starting-point or at the finishing-pointy it must be in a state of rest 3 ). On the

1 atifrjaris and <f>0t<ris regarded as one process.

8 And therefore the motion must have limits.

other hand in circular motion there are no such definite points : for why should any one point on the line be a limit rather than any other ? Any one point as much as any other is alike starting-point, middle-point, and finishingpoint, so that we can say of certain things 1 both that they are always and that they never are at a starting-point and 26s b at a finishing-point (so that a revolving sphere, while it is in motion, is also in a sense at rest, for it continues to occupy the same place). The reason of this is that in this case all these characteristics belong to the centre : that is to say, the centre is alike starting-point, middle-point, and finishing-point of the space traversed ; consequently 5 since this point is not a point on the circular line, there is no point at which that which is in process of locomotion can be in a state of rest as having traversed its course, because in its locomotion it is proceeding always about a central point and not to an extreme point : therefore it remains still, and the whole is in a sense always at rest as well as continuously io motion. Our next point gives a convertible result : on the one hand, because rotation is the measure 2 of motions it must be the primary motion io (for all things are measured by what is primary) : on the other hand, because rotation is the primary motion it is the measure of all other motions. Again, rotatory motion is also the only motion that admits of being regular. In rectilinear locomotion the motion of things in leaving the starting-point is not uniform with their motion in approaching the finishing-point, since the velocity of a thing always increases proportionately as it removes 3 itself farther from its position of rest : on the other hand rotatory motion is the only motion whose course is naturally such that it has 15 no starting-point or finishing-point in itself but is determined from elsewhere.

As to locomotion being the primary motion, this is

1 sc. things that rotate about an axis.

3 I translate afyvrrjTcu as a true middle in order to bring out the fact that this remark refers only to things that are in motion Kara (pvaiv ; the motion of things that are moved iraph 4 >v<nv f e. g. of a stone thrown upwards, becomes slower : cf. v. 6. 230^23 sqq.

26s b a truth that is attested by all who have ever made mention of motion in their theories : they all assign their first principles of motion to things that impart motion of this kind.

Thus 4 separation * and ‘ combination ’ are motions in respect of place, and the motion imparted by ‘Love’ and ao ‘ Strife * 1 takes these forms, the latter £ separating * and the former ‘ combining'. Anaxagoras, too, says that ‘Mind’, his first movent, ‘ separates *. Similarly those 2 who assert no cause of this kind but say that ‘ void ’ accounts for motion — they also hold that the motion of natural sub- 35 stance is motion in respect of place : for their motion that is accounted for by ‘void* is locomotion, and its sphere of operation may be said to be place. Moreover they are of opinion that the primary substances are not subject to any of the other motions, though the things that are compounds of these substances are so subject: the processes of increase and decrease and alteration, they say, are effects of the ‘combination* and ‘separation* of ‘atoms*. It is 30 the same, too, with those who make out that the becoming or perishing of a thing is accounted for by ‘density* or 4 rarity * : 3 for it is by ‘ combination * and ‘ separation * that the place of these things in their systems is determined. Moreover to these we may add those who make Soul the cause of motion : 4 for they say that things that undergo motion have as their first principle ‘that which moves itself* : and when animals and all living things move themselves, the motion is motion in respect of place. Finally it 266* is to be noted that we say that a thing 4 is in motion * in the strict sense of the term only when its motion is motion in respect of place : if a thing is in process of increase or decrease or is undergoing some alteration while remaining at rest in the same place, we say that it is in motion in some particular respect : we do not say that it 4 is in motion * without qualification. 5

Our present position, then, is this : We have argued that

1 The motive forces in the system of Empedocles.

2 Leucippus and Democritus.

3 The early Ionian school : Thales, Anaximenes, and Heraclitus, the last two of whom are known to have employed these terms.

4 Plato and the Platonists.

there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion : we have explained further which is the primary motion and which is the only motion that can be eternal : and we have pronounced the first movent to be unmoved.

10 We have now to assert that the first movent must be without parts and without magnitude, beginning with the io establishment of the premisses on which this conclusion depends.

One of these premisses is that nothing finite can cause motion during an infinite time. We have three things, the movent, the moved, and thirdly that in which the motion takes place, namely the time : and these are either all infinite or all finite or partly — that is to say two of them 15 or one of them — finite and partly infinite. Let A be the movent, B the moved, and T the infinite time. Now let us suppose that A 1 moves E, a part of B. Then the time occupied by this motion cannot be equal to T : for the greater the amount moved, the longer the time occupied. 2 It follows that the time Z :i is not infinite. Now we see that by continuing to add to A I shall use up A and ao by continuing to add to E I shall use up B : but I shall not use up the time by continually subtracting a corresponding amount from it, because it is infinite. Consequently the duration of the part of F which is occupied by all A in moving the whole of B, will be finite. Therefore a finite thing cannot impart to anything an infinite motion.

It is clear, then, that it is impossible for the finite to cause motion during an infinite time.

35 It has now to be shown that in no case is it possible for an infinite force to reside in a finite magnitude. This can be shown as follows : we take it for granted that the greater force is always that which in less time than another does an equal amount of work when engaged in any activity —

1 sc. a part of A.

2 Clearly A must be a larger fraction of A than E is of B.

3 The time occupied by A in moving E to the same extent as B is moved by A. Read in 1. 19 6 to Z.

a66 a in heating, for example, or sweetening or throwing ; in fact, in causing any kind of motion. Then that on which the forces act must be affected to some extent by our supposed finite magnitude possessing an infinite force as well as by anything else, in fact to a greater extent than by anything else, since the infinite force is greater than any other. But 30 then there cannot be any time in which its action could take place. Suppose that A is the time occupied by the infinite power in the performance of an act of heating or pushing, and that AB 1 is the time occupied by a finite power in the performance of the same act : then by adding to the latter another finite power and continually increasing a66 b the magnitude of the power so added I shall at some time or other reach a point at which the finite power has completed the motive act in the time A : for by continual addition to a finite magnitude I must arrive at a magnitude that exceeds any assigned limit, and in the same way by continual subtraction I must arrive at one that falls short of any assigned limit. So we get the result that the finite force will occupy the same amount of time in performing the motive act as the infinite force. But this is impossible. 5 Therefore nothing finite can possess an infinite force. So it is also impossible for a finite force to reside in an infinite magnitude. It is true that a greater force can reside in a lesser magnitude : but the superiority of any such greater force can be still greater if the magnitude in which it resides is greater. Now’ let AB be an infinite magnitude. Then B T 2 possesses a certain force that occupies a certain time, let us say the time EZ, a in moving A. Now if I take 10 a magnitude twice as great as Br, the time occupied by this magnitude in moving A will be half of EZ (assuming this to be the proportion 4 ) : so we may call this time ZH.

That being so, by continually taking a greater magnitude in this way I shall never arrive at the full AB, whereas

2 sc. a part of AB.

8 E being presumably the time occupied by AB in moving A.

* He assumes that the force increases proportionately to the magnitude, so that the time decreases proportionately. This simplifies the argument, though of course it is not essential to it.

I shall always be getting a lesser fraction of the time originally given. Therefore the force must be infinite, 15 since it exceeds any finite force. Moreover the time occupied by the action of any finite force must also be finite: for if a given force moves something in a certain time, a greater force will do so in a lesser time, but still a definite time, in inverse proportion. 1 But a force must always be infinite — just as a number or a magnitude is — if ao it exceeds all definite limits. This point may also be proved in another way — by taking a finite magnitude in which there resides a force the same in kind as that which resides in the infinite magnitude, so that this force will be a measure of the finite force residing in the infinite magnitude. 2

35 It is plain, then, from the foregoing arguments that it is impossible for an infinite force to reside in a finite magnitude or for a finite force to reside in an infinite magnitude. But before proceeding to our conclusion it will be well to discuss a difficulty that arises in connexion with locomotion. If everything that is in motion with the exception of things that move themselves is moved by something else, how is it that some things, e. g. things thrown, continue to be in motion when their movent is no longer in contact with 30 them ? If we say that the movent in such cases moves something else at the same time, that the thrower e.g. also moves the air, and that this in being moved is also a movent, then it would be no more possible for this second thing than for the original thing to be in motion when the original movent is not in contact with it or moving it : all the things moved would have to be in motion simultaneously and also to have ceased simultaneously to be in motion 267* when the original movent ceases to move them, even if,

1 i. e. greater force : lesser force = time occupied by lesser force; time occupied by greater force.

* The argument is left incomplete : the point is that then either the finite magnitude is the measure of the infinite magnitude (which is impossible) or it is a measure of so much of the infinite magnitude as can be said to possess the force, the rest not possessing any force, in which case it is not justifiable to say that it is the infinite magnitude that possesses the finite force.

like the magnet, it makes that which it has moved capable of being a movent. 1 Therefore, while we must accept this explanation to the extent of saying that the original movent gives the power of being a movent either to air 2 or to water or to something else of the kind, naturally adapted for imparting and undergoing motion, we must say further 5 that this thing does not cease simultaneously to impart motion and to undergo motion : it ceases to be in motion at the moment when its movent ceases to move it ; but it still remains a movent, and so it causes something else 3 consecutive with it to be in motion, and of this again the same may be said. The motion begins to cease when the motive force produced in one member of the consecutive series is at each stage 4 less than that possessed by the preceding member, and it finally ceases when one member no longer causes the next member to be a movent but only causes it to be in motion. The motion of these last two — 10 of the one as movent and of the other as moved — must cease simultaneously, and with this the whole motion ceases. Now the things in which this motion is produced are things that admit of being sometimes in motion and sometimes at rest, and the motion is not continuous but only appears so : for it is motion of things that are either successive or in contact, there being not one movent but a number of movents consecutive with one another: and 15 so motion of this kind takes place in air and water. Some say 6 that it is 4 mutual replacement’: but we must recognize that the difficulty raised cannot be solved otherwise than in the way we have described. 0 So far as they

1 Reading in 1. I (with H Simp.) noift, <w<nrf p rj \l0ot, olov iavtlv f which seems clearly indicated by the next sentence : Kivti gives no satisfactory sense and seems to contradict rrawrjrai immediately preceding. The point is that the magnet can attract one piece of iron through the medium of another.

3 Reading in 1. 7 n «XXo, with K.

4 Reading in 1. 8 orav d«i Adrrwi/, with EK Simp,, and in 1. 9 tyyivrjrm, with FH Them. Simp.

8 Cf. PI, Tim. 59 a, 79 B, C, E, 80C.

0 i. e. avTiirtpiarraaif may be a fact, but it does not in itself constitute an explanation. (Simplicius defines avrintpivTams thus : dvr m<pl<rr avis tvripf orav e£<x> 6 ovptvov nvbt a par os vrrb v&puiros dvraWayr) ytvqrai rwv are affected by ‘mutual replacement \ all the members of the series are moved and impart motion simultaneously, so that their motions also cease simultaneously: but our present problem concerns the appearance of continuous 20 motion in a single thing, and therefore, since it cannot be moved throughout its motion by the same movent, the question is, what moves it ?

Resuming our main argument, we proceed from the positions that there must be continuous motion in the world of things, that this is a single motion, that a single motion must be a motion of a magnitude (for that which is without magnitude cannot be in motion), and that the magnitude must be a single magnitude moved by a single movent (for otherwise there will not be continuous motion but a consecutive series of separate motions), and 1 that if the movent is a single thing, it is either itself in motion or 35 itself unmoved : if, then, it is in motion, it will have to be subject to the same conditions as that which it moves, that is to say it will itself be in process of change and in being 267* so will also have to be moved by something : so we have a series that must come to an end, and a point will be reached at which motion is imparted by something that is unmoved. Thus we have a movent that has no need to change along with that which it moves but will be able to cause motion always (for the causing of motion under these conditions 2 involves no effort): and this motion alone is regular, or at least it is so in a higher degree than any other, since the movent is never subject to any 5 change. So, too, in order that the motion may continue to be of the same character, the moved must not be subject to change in respect of its relation to the movent. 3 t^tjw, Kot to pep e^ooOtjaav ip rw rov c£<t>3i)dcvros arfj tottw, r6 de (£a>0r}6iv TO TTpQ(rt)(h KCLl €K€LPO TO €)(6fUV0V } QTdP TrXfLOPa »/, €Q>S hp TO t(T\aTOV cV T(p t6tt(o yivrjrai rov rrpctTov *£<a$rj(ravTO$.

1 Reading d* in L 24, and a colon after op in 1 . 25 (so Bonitz).

8 Reading in 1. 5 (with three MSS. and almost certainly Simplicius) (Ktivo. It is hard to see how any satisfactory sense can be got out of tictiPoVf since to tupovpepop obviously pera&dXXu tt pos (r= imd) rov KiPovpTos ; the point is that ptTafioXr) must always be the same p*ranamely KvKXo<f>opta, Cf. 1 . 17.

Moreover 1 the movent must occupy either the centre or the circumference, since these are the first principles from which a sphere is derived. But the things nearest the movent are those whose motion is quickest, and in this case it is the motion of the circumference 2 that is the quickest : therefore the movent occupies the circumference.

There is a further difficulty in supposing it to be possible for anything that is in motion to cause motion continuously and not merely in the way in which it is caused by some- io thing repeatedly pushing (in which case the continuity amounts to no more than successiveness). Such a movent must either itself continue 3 to push or pull or perform both these actions, or else the action must be taken up by something else and be passed on from one movent to another (the process that we described before as occurring in the case of things thrown, since the air or the water, being divisible, is a movent only in virtue of the fact that different parts of the air are moved one after another 4 ) : and in either case the motion cannot be a single motion, 15 but only a consecutive series of motions. The only continuous motion, then, is that which is caused by the unmoved movent : and this motion is continuous because the movent remains always invariable, so that its relation to that which it moves remains also invariable and continuous.

Now that these points are settled, it is clear that the first unmoved movent cannot have any magnitude. For if it has magnitude, this must be either a finite or an infinite magnitude. Now we have already 5 proved in our course *o on Physics 6 that there cannot be an infinite magnitude: and we have now proved that it is impossible for a finite

2 Reading in 1 . 9 kvk\ov with HK Simp. If o\ov be kept, the general sense will have to be the same, but it is in that case very much obscured : in particular the reference of iii the next clause becomes very awkward.

» (ii c e See note on 25 i a 9.

PHYSICA, BOOK VIII. io a67 b magnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first movent causes a motion that is eternal and does cause it during an infinite *5 time. It is clear, therefore, that the first movent is indivisible and is without parts and without magnitude.