Summary: Rules for the Direction of the Mind (page 3)

Descartes defines deduction as: Everything that is necessarily concluded from certain other things known with certainty ¹.

Through deduction, some ideas can be considered certain, even if they are not self-evident in themselves ². It is enough that they are deduced with certainty from other ideas that are themselves self-evident.

Intuition, therefore, validates each stage of a deduction—from first principles to conclusion—and these are the two most certain paths to science ³.

According to Rule IV, one cannot search for the truth without a method ⁴.

Seeking truth without a method is like searching for treasure by digging at random: it is clear that no result could be expected from such a haphazard approach.

If, by some miracle, success were achieved, it would be due to luck rather than science.

Hence, it is better never to think of seeking the truth about anything than to attempt it without method ⁵.

Disordered reflections disturb the natural light ⁶ of the mind. This expression, characteristic of Cartesian thought, appears in several of his works.

We can speak of natural light precisely because every mind naturally possesses two faculties—intuition and deduction—by which it can, through its own power, recognise certain truths.

What is a method? Etymologically, a method is a route by which a goal can be reached. For Descartes, however, it is defined as: A set of certain and easy rules, by the exact observance of which one will be sure never to mistake an error for a truth, and to arrive at the true knowledge of everything of which one is capable ⁷.

The method must explain how intellectual intuition should be employed to avoid error […] and how deductive paths should be followed to attain knowledge of all things ⁸.

Descartes writes: To set out the method by which certain knowledge is to be attained in every discipline—and thus to constitute them as sciences—this is now the main task I have assigned myself in the present treatise ⁹.

This method, though not yet conceptualised, has already produced spontaneous fruits ¹⁰: arithmetic and geometry. Indeed, these disciplines unknowingly followed the principles of this method and achieved remarkable results.

Descartes’ contribution, therefore, was to conceptualise something that already existed but had been used unconsciously.

The advantage is that we will be able to apply this method to subjects beyond numbers and geometric figures. Thus, this method is not confined to mathematics. Properly understood, it enables truths to emerge from any field of inquiry ¹¹.

So, if Descartes uses mathematical examples here, it is only for the sake of illustration. We must always remember that, in reality, he is presenting another discipline altogether ¹².

Here is how he puts it:

“This science must contain the first rudiments of human reason, and extend so far as to bring forth truths from any subject. It is preferable to all other knowledge transmitted to us by human means, for it is the source of all others” ¹³.

The object of mathematics is those things in which order or measure is examined ¹⁴. Thus, we can define universal mathematics (mathesis universalis) as the general science that explains everything it is possible to investigate concerning order and measure ¹⁵, regardless of the object considered (figures, stars, sounds, and so on).

The fundamental principle of the method is to begin with simple things and gradually progress to more complex objects, as Rule V teaches us.

This is, in fact, the only precept in which lies the essence of the entire human resource ¹⁶—a kind of Ariadne's thread for finding one’s way through the labyrinth of knowledge.

Descartes criticises scholars who, instead, immediately tackle the most complex and difficult questions.

¹ p.86
² Ibid.
³ p.87
⁴ p.88
⁵ Ibid.
⁶ Ibid.
⁷ p.89
⁸ Ibid.
⁹ p.91
¹⁰ Ibid.
¹¹ p.92
¹² Ibid.
¹³ Ibid.
¹⁴ p.96
¹⁵ Ibid.
¹⁶ p.98