Summary: Rules for the Direction of the Mind (page 2)

Why are arithmetic and geometry much more certain than all the other disciplines ¹?

This is where Descartes reveals himself as a rationalist, in contrast to the empiricism that would later emerge with Locke.

For Descartes, this superiority arises from the fact that they alone deal with an object so pure and simple that they then admit absolutely nothing that experience has rendered uncertain, and that they consist entirely of drawing consequences by way of rational deduction ².

While empiricism holds that experience is a source of truth — the very origin of our knowledge — for rationalism it is a source of error (as illustrated by the example of the stick that appears broken when plunged into water), and it is Reason alone that allows us to reach truth.

The primacy Descartes grants to these two sciences is nevertheless limited: we should not conclude from this that we should study only arithmetic and geometry, but that we should only concern ourselves with objects about which we can obtain a certainty equal to the demonstrations of arithmetic and geometry ³.

This model does not therefore "invalidate" the other disciplines, but constitutes a genuine paradigm — one to be followed if a discipline is to become a true science.

In Rule III, Descartes defines intuition and deduction as the two faculties capable of yielding certain truth — to the exclusion of authority:

We must seek [only] that of which we can have a clear and evident intuition, or that which we can deduce with certainty; for it is not otherwise that we acquire science ⁴.

Reading the works of the ancients can certainly be useful, but we must bear in mind that they may contain errors and should not be taken as established truth. Here, Descartes criticises the scholastic teaching he had received as a student, which presented Aristotle's ideas as unquestionable doctrine. Indeed, it was common in these schools, during scholastic disputations, to invoke the argument from authority: "Aristoteles dixit" — it is true because Aristotle said so.

This type of teaching belongs more to history than to science.

The root of all our errors lies in confusing the certain with the probable: We are warned that we must never mix a single conjecture with our judgements bearing on the truth of things ⁵. It is from such confusion that controversies and disputes spring.

If we cannot find certain truths in books or in teaching, how should we proceed? By thinking for ourselves. For we possess two faculties — or rather, two acts of our understanding, by which we can come to the knowledge of things without any fear of error ⁶: intuition and deduction.

Intuition, of course, should not be understood in the sense commonly associated with the term, as in the expression "women's intuition" — meaning an almost magical presentiment of a future event.

Descartes defines it as a representation so easy and distinct that no doubt remains as to what is understood in it, which arises from the sole light of reason ⁷.

There is nothing irrational, then, in Cartesian intuition. Descartes offers several examples:

Everyone can see by intuition that he exists, that he thinks, that a triangle is bounded by only three lines, a sphere by a single surface, [etc.] ⁸

Unlike intuition in the modern sense — often viewed as a gift possessed only by the few — Cartesian intuition is accessible to everyone.

It is, however, often scorned, precisely because the truths it reveals are elementary. Yet this scorn is misplaced, for intuition lies at the heart of the second "act of understanding" that enables us to discover complex truths — deduction.

The various steps of a deduction must in fact be validated one by one by the mind performing it. It is by intuition that the mind grasps the truth of each of these steps, as well as the validity of each transition from one to the next.

¹ p.82
² Ibid.
³ Ibid.
⁴ Ibid.
⁵ p.84
⁶ Ibid.
⁷ p.85
⁸ Ibid.