Summary: Rules for the Direction of the Mind (page 4)

From this point of view, Rule VI, which instructs us to identify, in a series of truths deduced from one another, the simplest, is the principal secret of the method, and there is none more useful in the whole of the present treatise ¹.

Why? Because it corresponds to a certain world-view — one that is vertiginous — according to which all things can be arranged in the form of series [...] in so far as they can be known from one another ².

As a result, from the point of view of knowledge, things are either absolute or relative.

They are absolute when they are knowable in themselves — that is, as Descartes puts it, when they contain in themselves, in a pure and simple state, the nature to which the question relates ³ — or when they are the simplest and easiest, with a view to their use in the resolution of questions ⁴.

The relative participates in one of the aspects of the absolute, by virtue of which it can be deduced from it through a series ⁵.

Descartes provides examples. The absolute includes: the cause, the simple, the universal, the one, the equal, the similar, the straight. The relative includes: the compound, the particular, the multiple, the unequal, the dissimilar, the oblique, and so forth.

Here, then, is the core of the method set out in the Regulae:

These relative terms move further away from absolutes the more they contain relations of this kind, subordinate to one another. The present rule warns us that we must distinguish all these relations and respect their mutual connection as their natural order, so that we may reach from the last term to the most absolute one, passing through all the others ⁶.

To sum up: The secret of the entire method lies here: In all things, carefully locate that which is most absolute ⁷.

Descartes observes that there are only few pure and simple natures, which we can intuit immediately and by themselves ⁸. It is these that we must carefully identify ⁹, for they stand at the beginning of every series.

Descartes then presents a series of minor rules, which serve only to clarify particular aspects of the fundamental rule already set out.

Rule VII insists that a complete science is one in which the entire chain of propositions, each deduced from the previous one, has been grasped in a single uninterrupted movement. This enumeration must be both sufficient and orderly ¹⁰.

In fact, as soon as a link, however insignificant, is forgotten, the chain is immediately broken, and the entire certainty of the conclusion collapses ¹¹.

Rule VIII warns us to halt our search if we fail to find a satisfactory intuition grounding the validity of each transition from one proposition to the next — that is, within a chain of deductions.

Rule IX returns to the principle of focusing on trivial and easy things rather than complex problems. The aim is to counter the natural psychological reflex of the scholar, who instinctively pursues complexity.

The mind must be trained on questions already solved by other scholars, so that it may develop sagacity (Rule X). Descartes confides that he practised this exercise himself from an early age.

In his explanation of this rule, we find this remarkable passage: the method [...] is most often nothing other than the scrupulous observation of an order ¹².

Here, Descartes once again criticises scholasticism, particularly the dialectic taught in these schools: arguments in which a thesis is defended through syllogistic reasoning. He argues that the syllogism is purely formal:

One can only conclude that what is deduced is true if one already knows the answer — or the material truth of it.

In other words, the syllogism is sterile.

In Rule XII, Descartes presents imagination, the senses, and memory as faculties that can help the understanding in the search for truth. However, they must be used with caution, as they can also be sources of error: The understanding alone, it is true, has the power to perceive the truth; yet it must be aided by the imagination, the senses, and memory ¹³.

He examines the general mechanism of sensation, drawing on the Aristotelian image of wax on which the shapes of objects are impressed.

Surprisingly, it is here — rather than in any introduction — that Descartes sets out the plan of his work.

He distinguishes between simple propositions and questions.

It is threefold:

The first twelve rules, which we have just seen, concern simple propositions — those that are self-evident.

The second part consists of the following twelve rules, which concern questions that are understood, even if the solution is unknown ¹⁴.

This part, which is less philosophical, contains questions that arise chiefly in arithmetic and geometry; they will therefore seem of little use to those unfamiliar with these sciences ¹⁵. We shall not pursue it here.

The third part addresses questions imperfectly understood ¹⁶. Descartes would never write this part.

Here ends our account of this work, published only posthumously. An unfinished early text, it would be reworked throughout Descartes' life. It may be seen as the earliest formulation of the Cartesian project as a whole.

¹ p.99
² Ibid.
³ p.100
⁴ Ibid.
⁵ Ibid.
⁶ p.101
⁷ Ibid.
⁸ p.102
⁹ Ibid.
¹⁰ p.106
¹¹ p.107
¹² p.124
¹³ p.131
¹⁴ p.152
¹⁵ p.153
¹⁶ p.152