Descartes and Method

A Search for a Method in Meditations

Clarence A. Bonnen, Daniel E. Flage

• Publisher: Routledge
• Year: 2002
• Print ISBN:
  9780415192507
• eBook ISBN:
  9781134738885
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Rene Descartes credited his success in philosophy, mathematics, and physics to the discovery of a universal method of inquiry, but he provided no systematic description of his method. Descartes and Method carefully examines Descartes' scattered remarks on his application and puts forward a systematic account of his method with particular attention to the role it plays in the Meditations.
Daniel E. Flage and Clarence A. Bonnen boldly and convincingly argue against the orthodox conception that Descartes had no method. Through a rigorous and thorough examination, Flage and Bonnen unearth and explain the role of the method of analysis in the Meditations.
Descartes and Method is a ground-breaking book that is sure to make a considerable impact on the philosophy community. Anyone wishing to gain a new understanding of Descartes's Meditations should read this book.

Part I

Descartes’s method

1 Analysis

The search for laws

At the end of the Second Objections to the Meditations, Mersenne invites Descartes to “set out the entire argument in geometrical fashion, starting from a number of definitions, postulates and axioms” (AT 7: 128, CSM 2: 92). While Descartes complies with Mersenne’s request (AT 7: 160–70, CSM 2: 113–20), he initially responds that the arguments of the Meditations are set forth in accordance with a geometrical method, namely, the method of analysis.

We begin with a sketch of what we believe Descartes meant by “analysis”. Next we examine the Cartesian texts to show the plausibility of our reconstruction of Cartesian analysis. In this chapter we focus on analysis as the search for general laws or principles. In the next we examine conceptual analysis: the search for clear and distinct ideas, or, more properly, the method by which ideas are clarified.¹ While we demonstrate the textual consistency of our reconstruction of Cartesian analysis, we shall deem it correct only to the extent that it clarifies the structure of the Meditations, since, as Descartes tells us, “it is analysis … alone which I employed in my Meditations” (AT 7: 156, CSM 2: 111).

Analysis

In the Second Replies, Descartes alludes to analysis as a method of demonstration. As a method of demonstration, analysis mirrors the method of discovery: “Analysis shows the true way by means of which the thing in question was discovered methodologically and as it were a priori” (AT 7: 155, CSM 2: 110). Given this mirroring, one should be able to delineate the steps operative in the method. Given its universality, the same method should be found in the physical sciences, mathematics, and metaphysics, although one might discover additional constraints appropriate to each of those fields. For example, the “method of doubt” is appropriate in metaphysical inquiries, since the primary notions in metaphysics are:

as evident as, or even more evident than the primary notions which the geometers study; but they conflict with many preconceived opinions derived from the senses which we have got into the habit of holding from our earliest years, and so only those who really concentrate and meditate and withdraw their minds from corporeal things, so far as is possible, will achieve perfect knowledge of them.

(AT 7: 157, CSM 2: 111)

While the “method of doubt” is a necessary supplement to the method of analysis in metaphysical inquiries, it is not identical to the Cartesian method.² What, then, is the nature of that method?

We suggest that the method of analysis is a search for eternal truths (common notions, axioms), propositions which are recognized as true as soon as they are considered (P 1: 49). Eternal truths vary in degrees of generality. Descartes’s paradigms of eternal truths are: “It is impossible for the same thing to be and not to be at the same time; What is done cannot be undone; He who thinks cannot but exist while he thinks” (P 1: 49: AT 8A: 24, CSM 1: 209, Descartes’s emphasis) and “Nothing comes from nothing” (P 1: 75: AT 8A: 38, CSM 1: 221). Eternal truths constitute the essences of things (AT 1: 152, CSM 3: 25). Consequently, the generality (simplicity) of eternal truths varies with the generality of the object(s) under consideration (see AT 1: 149, CSM 3: 24).

Insofar as analysis is the complement of synthesis and the latter is the deductive method found in works such as Euclid’s Elements and Spinoza’s Ethics (see AT 7: 156, 160–70; CSM 2: 110–11, 113–20), the method of analysis is the search for the most basic principles (axioms, eternal truths, common notions) in a certain domain. So geometrical analysis yields the most general principles in geometry; physical analysis yields the most general principles of physics; and metaphysical analysis yields the most general principle of metaphysics, namely, the existence of God (AT 1: 149, CSM 3: 24). Furthermore, as we show, the domains in which one seeks eternal truths stand in a hierarchical order: metaphysical truths are higher than mathematical truths which are higher than physical truths (see AT 9B: 14, CSM 1: 186). In general, the degree of fundamentality of a truth (or a domain of discourse) is inversely proportional to the corporeality of the domain. This is exemplified in the Geometry, where Descartes reduces the truths of geometry to those of arithmetic.

But while this might tell us what Descartes sought, it does not specify a procedure for discovering those truths. Is there such a procedure? And if there is, can one elucidate it in terms of a commonly understood model? In what follows we suggest that his procedure was to propose a hypothesis which, if true, would explain the phenomenon in question. Confirmation of the hypothesis is a two-fold process. First, its truth must be recognized by the natural light (light of reason). Second, either it must be subsumed under a more general hypothesis known by the natural light, or it must unify the domain from which it is taken. As we argue below, the sense of “truth” operative in these two cases is not the same. We argue that the natural light recognizes material truth (cf. Wilson 1978: 107–9; Wolfson 1934 vol. 2: 98–9); coherence is evidence of formal truth. Still, this fails to tell us how Descartes could claim to systematically construct hypotheses. To understand that, let us begin with his Geometry.

In the Geometry Descartes gives us a hint regarding the procedure for solving any problem. He writes:

Thus, if we wish to solve some problem, we should first of all consider it solved, and give names to all the lines – the unknown ones as well as the others – which seem necessary in order to construct it. Then, without considering any difference between the known and the unknown lines, we should go through the problem in the order which most naturally shows the mutual dependency between the lines, until we have found a means of expressing a single quantity in two ways. This will be called an equation, for the terms of the one of the two ways [of expressing the quantity] are equal to those of the other. And we must find as many such equations as we assume there to be unknown lines. Or else, if we cannot find many of them, and if nonetheless we have omitted nothing that is to be desired in the question, this indicates that it is not entirely determined; and in that case, we can take at random lines of known length, for all the unknown lines to which no equation corresponds.

(AT 6: 372, O 179)

Here the procedure is fairly straightforward. Assume you are given a triangle ABC (see Figure 1) and want to find the length of side BE of a similar triangle BDE (AT 6: 370; O 178). If the lines AC and DE are parallel, then:

Figure 1 Triangle

One cross multiplies:

BE × AB = BC × BD

and, assuming AB = 1 unit, one concludes that:

BE = BC × BD

This is a means of solving an equation for an unknown variable. Insofar as the lines of a geometric construct are treated in terms of numerical values, one reduces geometry to arithmetic, which was one of Descartes’s objectives in the Geometry (AT 6: 369–70, O 177).³ Insofar as the problem is arithmetic, the method is strictly deductive. But not all the problems which Descartes attempted to solve were arithmetic or reducible to arithmetic problems. Does this provide us with any general clues regarding the nature of the method?

We believe it does. Solving arithmetic equations for a given variable is analogous to finding the missing premise in an enthymematic argument. Given one premise and the conclusion, one can formally and unambiguously determine what premise, if any, will yield a valid categorical syllogism. If Descartes used a deductive nomological model of explanation, the search for an explanatory principle (natural law) may be construed as the search for the missing premise of a valid enthymematic argument.⁴ Of course, formal validity provides no more than a necessary condition for the acceptability of the missing principle. One must also recognize the truth of the principle by the natural light. So, did Descartes, like the logical positivists of our own time (see Hempel 1965), construe explanation in terms of a deductive nomological model?

Yes. Evidence for this can be drawn from his remarks on the methodology in the Optics and Meteorology. Descartes writes:

Should anyone be shocked at first by some of the statements I make at the beginning of the Optics and the Meteorology because I call them “suppositions” and do not seem to care about proving them, let him have the patience to read the whole book attentively, and I trust that he will be satisfied. For I take my reasonings to be so closely interconnected that just as the last are proved by the first, which are their causes, so the first are proved by the last, which are their effects. It must not be supposed that I am here committing the fallacy that the logicians call ‘arguing in a circle’. For as experience makes most of these effects quite certain, the causes from which I deduce them serve not so much to prove them as to explain them; indeed, quite to the contrary, it is the causes which are proved by the effects. And I have called them “suppositions” simply to make it known that I think I can deduce them from the primary truths I have expounded above; but I have deliberately avoided carrying out these deductions in order to prevent certain ingenious persons from taking the opportunity to construct, on what they believe to be my principles, some extravagant philosophy for which I shall be blamed.

(AT 6: 76–7, CSM 1: 150;
see also AT 9B: 5, CSM 1: 181, P 4: 206)

Notice the role of supposition or hypothesis formation.⁵ Descartes says that in the Optics and Meteorology he introduces various assumptions that are later proven insofar as they provide adequate causal explanations of the phenomena in question. His remark that there is a mutual proof of causes and effects – the assumption qua cause is proven insofar as it explains the phenomenon in question and the phenomenon is proven insofar as it follows deductively from the assumption qua cause – shows the role of coherence in his system. To the extent that the supposition explains and deductively implies the claim that a certain effect must occur, one is justified in accepting the (formal) truth of the cause qua supposition. Notice that the coherence Descartes has in mind is theoretical. Even if one recognizes a supposition as (materially) true by the natural light, it also must cohere with more general truths in a given system. As Descartes notes, “I have called them “suppositions” simply to make it known that I think I can deduce them from the primary truths I have expounded above.” Further, it is at least in part observable phenomena which are explained, since “experience makes most of these effects quite certain.”

Placing this discussion of suppositions in the context of the levels of wisdom enumerated in the Preface to the French edition of the Principles (AT 9B: 5, CSM 1: 181) suggests a deductive (explanatory) relationship between the levels of wisdom exemplified in Descartes’s method. He notes that the four standard levels of wisdom consist of, first, “notions which are so clear in themselves that they can be acquired without meditation,” second, “everything we are acquainted with through sensory experience,” third, “what we learn by conversing with people,” and fourth, “what is learned by reading books … written by people who are capable of instructing us well” (AT 9B: 5, CSM 1: 181). There is a fifth way which “consists in the search for the first causes and the true principles which enable us to deduce the reasons for everything we are capable of knowing” (AT 9B: 5, CSM 1: 181, our emphasis). Descartes’s call for deductive explanations ultimately suggests that one will develop a complete and coherent explanation of the world by following his method.

The double method of coherence to which Descartes alludes in the passage above was not original to him. At several points he suggests that his method was drawn from the Pappus and other ancient geometers (AT 10: 376, CSM 1: 18–19; AT 7: 4, CSM 2: 4). Pappus describes the method of analysis as follows:

Now analysis is the way from what is sought – as if it were admitted – through its concomitants [the usual translation reads: consequences] in order to something admitted in synthesis. For in analysis we suppose that which is sought to be already done, and we inquire from what it results, and again what is the antecedent of the latter, until we on our backward way light upon something already known and being first in order. And we call such a method analysis, as being a solution backwards. In synthesis, on the other hand, we suppose that which was reached last in analysis to be already done, and arranging in their natural order as consequences the former antecedents and linking them one with another, we arrive at the construction of the thing sought…. In the theoretical kind we suppose the thing sought as being and as true, and then we pass through its concomitants [consequences] in order, as though they were true and existent by hypothesis, to something admitted; then, if that which is admitted be true, the thing sought is true, too, and the proof will be the reverse of the analysis.

(Hintikka and Remes 1974: 8–9)

The methodological similarity between this passage and the description of his method that Descartes proposed in the Geometry is striking. Analysis consists of two phases. The first or upward phase is a search for principles. Here one assumes what one wants to prove and seeks principles that will...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• List of figures
• Acknowledgements
• Abbreviations
• Introduction
• Part I Descartes’s method
• Part II Descartes’s Meditations on First Philosophy
• Notes
• Bibliography
• Index