Version: v1, Published online: 1998

Retrieved April 21, 2021, from https://www.rep.routledge.com/articles/biographical/descartes-rene-1596-1650/v-1

## 3. Method

Before beginning an account of the individual parts of Descartes’ tree of knowledge, it is necessary to discuss his method. Method was the focus of his earliest philosophical writing, the Rules, and appeared prominently in his first published writing, the Discourse on the Method. But what exactly that method was is somewhat obscure.

In the second part of the Discourse, the method is presented as having four rules: (1) ‘never to accept anything as true if I did not have evident knowledge of its truth: that is, carefully to avoid precipitate conclusions and preconceptions’; (2) ‘to divide each of the difficulties I examined into as many parts as possible’; (3) ‘to direct my thoughts in an orderly manner, by beginning with the simplest and most easily known objects in order to ascend little by little… to knowledge of the most complex’; and (4) ‘throughout to make enumerations so complete and reviews so comprehensive, that I could be sure of leaving nothing out’. Given the general nature and apparent obviousness of these rules, it is not surprising that many of Descartes’ contemporaries suspected him of hiding his *real* method from the public.

But Descartes’ account of the method in the Rules is somewhat fuller. In Rule 5 he says: ‘We shall be following this method exactly if we first reduce complicated and obscure propositions step by step to simpler ones, and then, starting with the intuition of the simplest ones of all, try to ascend through the same steps to a knowledge of all the rest’. This method is illustrated with an example in Rule 8. There Descartes considers the problem of the anaclastic line, the shape of a lens which will focus parallel lines to a single point. The first step in the solution of the problem, Descartes claims, is to see that ‘the determination of this line depends on the ratio of the angles of refraction to the angles of incidence’. This, in turn, depends on ‘the changes in these angles brought about by differences in the media’. But ‘these changes depend on the manner in which a ray passes through the entire transparent body, and knowledge of this process presupposes also a knowledge of the nature of the action of light’. Finally, Descartes claims that this last knowledge rests on our knowledge of ‘what a natural power in general is’. This last question can, presumably, be answered by intuition alone, that is, a purely rational apprehension of the truth of a proposition that has absolute certainty. Once we know what the nature of a natural power is, we can, Descartes thought, answer one by one all the other questions raised, and eventually answer the question originally posed, and determine the shape of the lens with the required properties. These successive answers are to be connected deductively (in a way outlined in the Rules) with the first intuition, so that successive answers follow intuitively from the first intuition.

The example of the anaclastic line suggests that Descartes’ method proceeds as follows. One starts with a particular question, q_{1}. The reductive moment in the method then proceeds by asking what we have to know in order to answer the question originally posed. This leads us from q_{1} to another question, q_{2}, whose answer is presupposed in order for us to be able to answer q_{1}; it is in this sense that q_{1} is said to be reduced to q_{2}. This reductive process continues until we reach a question whose answer we are capable of knowing through intuition, say q_{n}. At that point, we begin what might be called the constructive moment of the method, and successively answer the questions we have posed for ourselves, using the answer to q_{n} to answer
${q}_{n-1}$
, the answer to
${q}_{n-1}$
to answer
${q}_{n-2}$
, and so on until we arrive at q_{1}, the question originally posed, and answer that.

Understood in this way, the method has some very interesting properties. First, it results in knowledge that is completely certain. When we follow this method, the answer to the question originally posed is grounded in an intuition; the answers to the successive questions in the series are to be answered by deducing propositions from propositions that have been intuitively grasped as well. Second, the method imposes a certain structure on knowledge. As we follow the series of questions that constitute the reductive step of the method, we proceed from more specific questions to more general, from the shape of a particular lens to the law of refraction, and ultimately to the nature of a natural power. The answers that are provided in the constructive stage follow the opposite path, from the metaphysically more general and more basic to the more specific.

The Rules was written over a long period of time, and there are numerous strata of composition evident in the work as it survives. In a passage from Rule 8 that is probably in one of the last strata of composition, Descartes raises a problem for the method itself to confront, indeed the *first* problem that it should confront: ‘The most useful inquiry we can make at this stage is to ask: What is human knowledge and what is its scope?… This is a task which everyone with the slightest love of truth ought to undertake at least once in life, since the true instruments of knowledge and the entire method are involved in the investigation of the problem’. While it is not entirely clear what Descartes had in mind here, it is not implausible to interpret him as raising the problem of the justification of intuition itself, the epistemological foundation of the method. In framing the method in the Rules, Descartes takes for granted that he has a faculty, intuition, by which he is capable of grasping truth in some immediate way, and what he knows by intuition is worthy of trust. But why *should* we trust intuition? This, in essence, is one of the central questions in the Meditations, where Descartes argues that whatever we perceive clearly and distinctly is true.

Method was a central concern of Descartes’ earlier writings, in both the Rules and the Discourse. In later writings it seemed to play little explicit role in his thought, but the hierarchical structure of knowledge with which the method is closely connected – the idea that knowledge is grounded in a structure of successively more metaphysically basic truths, ultimately terminating in an intuition – remained basic to his thought. In his later work, that ultimate intuition is not the nature of a natural power, as it was in the anaclastic line example, but the intuition that establishes the existence of the knowing subject, the Cogito Argument.

Garber, Daniel. Method. Descartes, René (1596–1650), 1998, doi:10.4324/9780415249126-DA026-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/descartes-rene-1596-1650/v-1/sections/method.

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