Rules for the Direction of the Mind

Summary

The Regulae ad directionem ingenii is the young Descartes's attempt to write down the method he believed he had found in mathematics and to show that it could govern every inquiry. He planned thirty-six rules in three groups of twelve: rules for simple propositions, for problems that are perfectly understood, and for problems that are imperfectly understood. He finished only twenty-one, and the last three are bare statements without explanation. The manuscript lay among his papers when he died in Stockholm in 1650; a Dutch translation appeared in 1684 and the Latin was first printed in Amsterdam in 1701. Rule I sets the aim of study: to direct the mind so that it forms solid and true judgments about whatever comes before it. Descartes argues that the sciences are not separate habits, like the skills of different crafts, but one human wisdom that stays the same however many subjects it lights, as the sun's light is not altered by the variety of things it shines on. Rule II restricts study to objects of which certain knowledge is possible and sets aside merely probable opinion, which is why arithmetic and geometry are the model. Rule III names the only two sure acts of the mind: intuition, the undoubting grasp of a pure and attentive mind, and deduction, the necessary inference from things intuited. Rule IV insists that method is necessary and speaks of a universal mathematics concerned with order and measure in any subject. Rules V to VII describe the method itself: reduce complex and obscure propositions step by step to simpler ones, arrange things in series from the absolute to the relative, and survey every link by a complete enumeration. Rules VIII to XI discuss the limits of knowledge, the habit of dwelling on the simplest things, the training of sagacity on ordered crafts, and running through a chain of inferences until it can be seen almost at once. Rule XII discusses the faculties of understanding, imagination, sense and memory and the 'simple natures' from which all knowledge is composed. The second half applies these principles to problems of magnitude: strip a question to its essentials, represent magnitudes as lines and figures, draw them, use brief symbols to relieve the memory, and set up as many equations as unknowns. That programme reappears, worked out, in the Geometry of 1637. The Rules show Descartes's method before the radical doubt of the Meditations, and they let students ask whether rules of right thinking can be written down at all.

Plot or Argument

• Rules I-IV: The aim and unity of study

  The end of study is true judgment; all sciences make up one wisdom; only objects capable of certain knowledge should be studied; intuition and deduction are the only reliable acts of the understanding; and a method is needed, which Descartes connects with a universal mathematics of order and measure that he thinks the ancients glimpsed in Pappus and Diophantus.

• Rules V-VII: Order, series and enumeration

  The whole method consists in ordering the objects of attention: reduce involved propositions to simpler ones and then climb back by the same steps, distinguish what is absolute from what is relative in each series, and check every step by a sufficient and orderly enumeration, which Descartes also calls induction.

• Rules VIII-XI: Limits, perspicacity and sagacity

  Stop when a step cannot be intuited and ask instead what the mind can know at all. Train perspicacity by dwelling on the simplest truths until they are seen distinctly, and sagacity by working through ordered arts and crafts, such as weaving, before harder questions. Run over a chain of deductions in a continuous movement of thought so that it approaches a single intuition.

• Rule XII: The faculties and the simple natures

  Understanding alone perceives truth but must be helped by imagination, sense and memory. Descartes gives a physiological sketch of sensation, in which the senses receive figures as wax receives a seal and pass them to a common sense and a bodily imagination, and he divides the simple natures into purely intellectual, purely material and common ones.

• Rules XIII-XVIII: Perfectly understood problems

  A well-posed question is abstracted from superfluous ideas and reduced to its simplest form. Magnitudes are transferred to the real extension of bodies and represented by bare lines and rectangles, drawn out where they must be seen and noted by short symbols where they need only be remembered. The four arithmetical operations are reinterpreted on these figures; the exposition breaks off in Rule XVIII.

• Rules XIX-XXI: The unfinished end

  Only the statements survive: find as many magnitudes as there are unknown terms and express them in two ways to form equations, set aside equations that are not needed, and reduce the rest to as few as possible. The third group of twelve rules, on imperfectly understood problems, was never written.

Characters

• The scholastic disputants, foil

  Teachers who multiply probable opinions and syllogistic disputes; Descartes says probable cognition is to be rejected because two men who disagree cannot both know.

• Pappus and Diophantus, ancient witnesses

  Late Greek mathematicians in whom Descartes suspects traces of a true analytic method that the ancients kept hidden, offering demonstrations in its place.

• The student of the method, implied reader

  A learner told to begin with easy things, to practise on crafts and puzzles, and to trust intuition and orderly deduction rather than the authority of books.

Lessons

• One wisdom, many subjects

  Rule I denies that each science needs its own separate mind, as each craft needs its own trained hand. Wisdom is one, like sunlight on many objects, so the student should seek to strengthen the natural light of reason rather than collect specialisms. The claim echoes and also unsettles the classical idea of an ordered curriculum.

  • Why does Descartes reject the comparison between the sciences and the arts of the hand?
  • What might be lost if every subject is treated as an exercise of one method?
  • How does this rule compare with the medieval ordering of the liberal arts toward theology?

• Intuition and deduction as the only roads

  Rule III allows two acts of mind to yield knowledge: intuition, a conception so clear and attentive that no doubt remains, and deduction, which joins intuited steps by necessity. Reading the ancients is useful, Descartes says, but agreeing with their conjectures is not knowing. The rule sets the standard that the Meditations later test against radical doubt.

  • Give an example of something you know by intuition in Descartes's sense and something you know by deduction.
  • Why does a long deduction depend on memory, and why does that worry Descartes?
  • Is there any place in Descartes's scheme for testimony, including the testimony of Scripture?

• Break the hard problem into easy steps

  Rules V to VII say that the whole method is order: lead complex propositions back to the simplest, then climb back up, checking every link by enumeration. Rule X adds that sagacity is trained on simple ordered crafts and puzzles before difficult questions. Students can apply this directly to a hard proof or a long essay.

  • Take a problem from another class and reduce it to its simplest parts in Descartes's manner. Where did order help?
  • What does Descartes mean by enumeration, and how is it different from a list?
  • Why would weaving or a number puzzle be good practice for philosophy?

• Pictures and symbols as aids to a finite mind

  In Rules XIV to XVI Descartes admits that the understanding needs help: magnitudes are best pictured as lines and rectangles, and what need not be held in view should be written in brief signs so that memory is not overloaded. The method is designed for a limited human mind, not an angelic one, and it leads straight to the algebraic notation of the Geometry.

  • Why does Descartes want figures for some things and symbols for others?
  • Is notation only a convenience, or can a good symbol make discovery possible?
  • What does the work's unfinished state suggest about the limits of a method?

Context

Descartes wrote the Rules after his years of travel and military service and before he moved permanently to the Netherlands in 1628-1629. They reflect his collaboration with Isaac Beeckman in Breda from 1618, his dream of 10 November 1619, which he took as a call to found a unified science, and his work on mathematical problems in Paris in the mid-1620s. Their targets are the scholastic logic of the schools, with its probable opinions and disputations, and the Renaissance hope of a universal art of knowledge. Many scholars think the text was written in layers between about 1619 and 1628, which would explain shifts between the general rules and the mathematical second half.

Composition

Descartes stopped work on the Rules around 1628 and never published them. An inventory of his papers made at Stockholm after his death in 1650 lists the manuscript; it passed to Claude Clerselier in Paris, and copies circulated. A Dutch translation by Jan Hendrik Glazemaker was printed in 1684, and the Latin first appeared in Descartes's Opuscula posthuma (Amsterdam, 1701). A second manuscript copy, owned by Leibniz, survives at Hanover. English readers usually use the 1911 translation by Elizabeth Haldane and G. R. T. Ross or later versions.

Reception

Before publication the Rules influenced readers of the manuscript, notably Antoine Arnauld and Pierre Nicole in the Port-Royal Logic, and Leibniz, who copied it. After 1701 they were overshadowed by the Discourse and Meditations, but nineteenth- and twentieth-century scholars came to see them as the clearest statement of Descartes's mathematical conception of method. The work was chosen for the Great Books of the Western World (2nd ed., 1990), volume 28.

Comparisons

• Discourse on Method

  Part II of the Discourse compresses the Rules into four precepts: accept only the evident, divide difficulties, proceed in order, and enumerate completely. Reading the Rules first shows how much argument lies behind those four sentences and what Descartes chose not to publish.

• Novum Organum

  Bacon's New Organon (1620) also attacks the logic of the schools and proposes a new instrument for the mind, but it builds from careful collections of particulars toward axioms, whereas Descartes begins from intuition of the simplest truths and treats mathematics as the model. The two books are the period's rival accounts of method.

• The Geometry

  Rules XIV-XIX describe representing magnitudes by lines, using symbols to spare memory and setting up equations, but the exposition stops. The Geometry (1637) carries that programme through and adds the unit length that lets products of lines remain lines.

• Posterior Analytics and Physics

  Aristotle's account of demonstration from first principles grasped by nous is close in structure to Descartes's intuition and deduction, though Descartes dismisses the syllogism as useless for discovery. Comparing the two shows how much of the old theory of knowledge survives under the new language.

• A System of Logic, Book III: Of Induction

  Mill's Book III treats induction as the main road to knowledge of nature. Descartes uses 'induction' for a complete enumeration of steps in a deduction, not a generalisation from cases, a difference in the meaning of one word that students should notice before comparing the two.

Quotes

Medical Lens

The Rules are a treatise on method, not medicine, but Rule XII contains Descartes's earliest written sketch of the physiology of sensation and imagination: the external senses receive figures passively, they are conveyed to a common sense, and imagination or fantasy is described as a real part of the body connected with the nerves. This anticipates the mechanical psychology of the Treatise on Man and the Passions of the Soul. The repeated concern with the weakness of memory in long deductions (Rules VII, XI and XVI) is a cognitive rather than clinical theme.

• Rule XII

  Sketch of how sensation works: the senses are affected as wax by a seal, figures pass to the common sense and are impressed on the fantasy or imagination, which Descartes treats as a bodily organ able to move the nerves.

  Mind Body
• Rules VII, XI and XVI

  Descartes treats memory as the weak point of long chains of reasoning and prescribes rapid repeated surveys and written symbols to relieve it.

  Dementia Memory

Creative Prompts

• Classroom

  Write three of the fifteen missing rules for 'imperfectly understood problems' that Descartes planned but never wrote, each with a two-sentence explanation in his style, and test one on a real question from another class.

• Essay

  Descartes says probable opinions should be set aside because two people who disagree cannot both know. Is that a sound rule for study? Answer with examples from history, science and moral life.

• Dialogue

  Imagine Descartes and Francis Bacon meeting in 1625 to compare their new methods. Let each give one rule the other cannot accept, and end with the question they would most want the next generation to settle.

Further Reading

• The Philosophical Works of Descartes, vol. 1, trans. Elizabeth S. Haldane and G. R. T. Ross

  The 1911 English translation that includes the Rules; public domain and widely available.

• Discourse on Method, René Descartes

  The published, shortened account of the method.

• The Geometry of René Descartes, trans. David Eugene Smith and Marcia L. Latham

  The mathematical work that completes the programme of Rules XIII-XXI.

• Descartes: An Intellectual Biography, Stephen Gaukroger

  Discusses the layered composition of the Rules and their place in Descartes's early career.