SOURCE: "Science and Certainty in Descartes," in Descartes: Critical and Interpretive Essays, edited by Michael Hooker, The Johns Hopkins University Press, 1978, pp. 114–51.

[In the following essay, Garber traces Descartes' approach to science and scientific practice from the Regulae to the Principia Philosopiae, contending that Descartes abandoned his early philosophy that science must be deductively certain, instead nearly coming to the conclusion that science relies on hypothetical arguments and experimentation.]

Descartes's principal project was to build a science of nature about which he could have absolute certainty. From his earliest writings he argues that unless we have absolute certainty about every element of science at every level, we have no genuine science at all. But while the very general sketches Descartes gave for his project were clear, the details of just how he was to build such a science and precisely what it was to look like when he finished were not. The traditional view is that what Descartes had in mind was a science structured somewhat like Euclid's Elements, starting with a priori first principles, and deriving "more geometrico" all there is to know about the world. On this view, it is fairly clear why Descartes might have thought that he was building a certain science. A science built more geometrico would seem to be as certain as geometry itself. But among most scholars the traditional view has given way to the realization that observation and experiment play an important role in Descartes's scientific method, both in theory and in practice.¹ There is no question in my own mind that this view of Descartes's science is correct. But this new realization of Descartes the experimenter raises a curious question. If the geometrical model of Cartesian science is not correct, then what of certainty? How could Descartes have thought that he could find certainty in an experimental science? Or for that matter, did Descartes, in the end, think that certainty is possible for science? It is my main goal in this paper to present an alternative to the traditional geometrical model of Cartesian science in which it will be evident why Descartes thought his science both experimental and certain.

But there is an historical dimension to this problem that is often ignored. Descartes's work in natural science falls roughly into two parts. In his earlier works, for the most part those which precede the Principia Philosophiae (1644), including the Regulae ad Directionem Ingenii (1628?), Le Monde(1633), the Discourse on the Method, Optics, and Meteorology (1637), and the Meditations (1641), Descartes is formulating his views on nature and presenting them little by little.² In this period, Descartes's work is filled with many promises: programmatic sketches of the science he claims to have formulated, and claims about arguments and deductions he thinks he has found. It is only in his later work, his Principia Philosophiae, that he attempts to present his science with any completeness. It is here that we find Descartes's earlier promises kept, and, all too often, broken. If we examine Descartes in this way, we find a noticeable difference between these two periods. In the earlier period Descartes is quite confident that he has found the way to certain knowledge, and it is in this period that the insistence on certainty is strongest. But in the later period, Descartes must come face to face with the extreme difficulty of actually presenting such a science, and his commitment to certainty undergoes interesting changes.

My discussion of certainty in Descartes's science falls into three sections. In the first, I shall discuss the notion of certainty in Descartes's earlier writings and present some of the basic reasons for rejecting the more traditional view of Cartesian science as a deductive system on the model of Euclidean geometry. In the second, main section of this paper, I shall try to replace the geometrical model with a model of the inferential structure of Cartesian science that better reflects Descartes's thinking, at least in the earlier period. I shall present it in such a way that it will be evident how Descartes could think that his science is both experimental and certain. In this section I shall also discuss the status of hypotheses at this point in Descartes's thought. Having seen the outlines of Descartes's early, grand program for the sciences, I shall in section three examine how Descartes's earlier conception fares in the Principles. There we shall see strong suggestions that Descartes is moving to give up his earlier conception of certainty in science.

Before I begin this ambitious project, one remark is in order. I shall not offer any general account of Cartesian method, nor shall I offer any systematic interpretation of the early and problematic Regulae, as is common practice in methodological discussions of Descartes's science.³ Rather, I shall concentrate on the many places in which Descartes talks specifically about the epistemic and inferential structure of his theory of the world. I shall bring in passages from the more general and abstract discussions of method when I feel that their interpretation is sufficiently obvious, and when they bear on the interpretation of some specific point Descartes is making about his conception of science. I make no general claim about the unity of Descartes's methodological thought over and above the specific continuities that I shall point out in the course of this paper.

One last caution before we begin. Though Descartes's goal was certainty, mine is not. In a paper as short as this, I cannot hope to present the case I would like to make in sufficient detail. My only hope is to clear away some of the obscurity surrounding some of the important questions about Descartes's science, and sketch, in broad strokes, one line for reinterpreting his scientific enterprise.

I Preliminary Remarks on Certainty

Early on in his youthful Regulae, Descartes declares:

We should be concerned only with those objects regarding which our minds seem capable of obtaining certain and indubitable knowledge [cognitionem].

All science [scientia] is certain, evident knowledge [cognitio], and he who doubts many things is not more learned than he who has never thought about these things…. And so, in accordance with this rule, we reject all knowledge [cognitiones] which is merely probable [probabiles] and judge that only those things should be believed which are perfectly known [perfecte cognitis] and about which we can have no doubts.

[Rule II: AT [Descartes; Oeuvres de Descartes; ed. Charles Adam and Paul Tannery; 12 vols.; Paris: Cerf, 1897–1910; reprinted, with new appendices, Paris: Vrin, 1964-] 10:362; HR 1:3]

Certainty was clearly of the greatest importance to Descartes. In this section I would like to explore briefly what he meant by certainty.

In the Regulae, Descartes gives us a straightforward account of what he means by certain knowledge, in terms of the cognitive operations that result in certainty, intuition and deduction, "From all these things we conclude … that there are no paths to the certain knowledge of truth open to man except evident intuition and necessary deduction" (Rule XII: AT 10:425; HR 1:45, emphasis added).⁴ Certain knowledge, then, is that which can be presented as the product of intuition or deduction.

Descartes explains what he means by intuition in the following passage:

By intuition I understand … the conception of the pure and attentive mind which is so simple and distinct that we can have no further doubt as to what we understand; or, what amounts to the same thing, an indubitable conception of the unclouded and attentive mind which arises from the light of reason alone.

[Rule III: AT 10:368; HR 1:7]

There is much over which one could pause in this account of intuition. For the moment, though, I would merely point out how open this definition is. In this passage of the Regulae, the only one in which he attempts a general characterization of intuition, Descartes sets no a priori limits to the domain of intuition. Precisely what knowledge it is that he thinks we can acquire through intuition can be settled only by examining the particular examples of intuition he presents, and cannot be derived from his definition alone. The examples he offers of intuited truths include our own existence, that we think, that a sphere has only one surface, and "other similar things" (AT 10:368; HR 1:7). More generally he associates the domain of intuition with what he calls "absolutes" and "simple natures."⁵

Descartes attempts to characterize deduction in the following passage:

Many things are known with certainty although they are not evident in themselves for the sole reason that they are deduced from true and known [cognitis] principles by a continuous and uninterrupted process of thought, in which each part of the process is clearly intuited…. We can therefore distinguish an intuition of the mind from a deduction which is certain by the fact that in the latter we perceive a movement or a certain [quaedam] succession of thought, while we do not in the former.

[Rule III: AT 10:369–70; HR 1:8, emphasis added.]⁶

Deduction, then, can be defined in terms of intuition. A deduction is a succession of propositions, ordered in such a way that each one follows from the preceding through an act of intuition.⁷ While it is possible to start such a deduction from any premise, Descartes usually limits the applicability of the term "deduction" to those arguments and conclusions which begin with a premise that is derived from intuition, or is the conclusion of another deduction.

As we remarked with respect to intuition, Descartes's conception of deduction is quite loose. A deduction as defined seems to be any argument, whatever its form might be, all of whose steps can be connected by acts of intuition. In the Regulae, Descartes is quite clear in disassociating the kind of argument he has in mind from the more formal syllogism:

But perhaps some will be astonished that … we omit all the rules by which the logicians think they regulate human reason…. (We) reject those forms of theirs [istas formas] as opposed to our teaching, and seek rather all the aids by which our mind may remain alert…. And so that it will be more evident that the syllogistic art is of practically no assistance in the search for truth, we should notice that logicians can form no syllogism which reaches a true conclusion unless the heart of the matter is given, that is, unless they previously recognized the very truth which is thus deduced.

[Rule X: AT 10:405–6; HR 1:32]

Obviously, Descartes conceived of deduction as a kind of argument much broader in scope than the syllogism. While nothing important will depend on my rather unorthodox reading, it looks as if he thought that deductive arguments (with intuitive premises, of course) could yield conclusions which are not merely contained in the premises, to criticize the "syllogistic art" the way he does. Precisely what arguments Descartes was willing to accept as deductive, though, cannot be determined by appeal to his definition. As was the case with intuition, to understand what he has in mind we must appeal to the examples of deductive reasoning Descartes gives, and note those arguments that he rejects as yielding uncertain conclusions.

Before I turn to later accounts of certainty in Descartes's writings, a short digression about the relation between certainty and method in the Regulae would be in order. The Regulae is intended to give us "directions" for finding certainties. Descartes gives a procedure that he thinks will put us in a position so that we can discover intuitive truths, and discover deductive connections. The certain knowledge that is the end product of the Regulae is certain, not because it was found using Descartes's method, but because it can be presented as the product of intuition and deduction. This plausible reading of the Regulae is supported by two features of that work. First of all, Descartes opens the work with a discussion of what certainty is (Rules I–III) and does not talk at all about the method for finding certainty until Rule IV. When he finally comes to discuss how we find certain truth, he uses a metaphor of finding the road that leads us to the "treasure" (Rule IV: AT 10:371; HR 1:9). This strongly suggests that the method is a way of finding something, like the treasure, whose worth and value lies in something other than the path we take to it. Also, Descartes admits that his method is not the only way of discovering certainty. He recognizes others, but argues that they are more difficult (Rule VI: AT 10:384–87; HR 1:17–19). Thus a given item of knowledge is certain not by virtue of the way we discover it (e.g., by using Cartesian method), but by the way in which we justify it (i.e., by presenting it as the product of intuition and deduction). Consequently, I see no problems in divorcing Descartes's notion of certainty in the Regulae from the details of the method offered there.

At the heart of the notion of certainty in the Regulae are the notions of intuition and deduction. Descartes's theory of certainty changes, however, in later works, where he adopts a new criterion for certainty, clearness and distinctness. Thus, in the Discourse on the Method, Descartes presents the rule that we quoted at the beginning of this section as follows:

The first rule was never to accept anything as true unless I recognize it to be evidently such: that is, carefully to avoid precipitation and prejudgment [preuention], and to include nothing in my conclusions unless it presented itself so clearly and distinctly to my mind that there was no occasion to doubt it.

[AT 6:18; HR 1:92.]

There are a number of anticipations of this somewhat different conception of certainty in the Regulae. Descartes often talks about intuition and deduction in terms that involve the notion of distinctness and, occasionally, clearness as well.⁸ But the clearness and distinctness account is substantially new in the Discourse.

With the introduction of this new vocabulary for discussing certainty come many problems for Descartes and the Cartesian scholar. For Descartes, with the new criterion of certainty comes a new enterprise, that of validating it. For the scholar comes the problem of explicating exactly what Descartes had in mind by clearness and distinctness, and exactly how he thought that his criterion of certainty could be validated (here is where the well-known Cartesian circle enters). In this paper I shall not discuss the criterion of clearness and distinctness or the difficulties raised by Descartes's attempt to validate that criterion. In fact, when discussing certainty I shall avoid the language of clearness and distinctness altogether, and return to the idiom of the Regulae, where certainty is characterized in terms of intuition and deduction. My avoidance of foundational problems with regard to certainty can be justified by noting that Descartes himself avoids such questions in his more narrowly scientific work, nor can I see any particularly good reason for raising the foundational problems in that context.⁹

My decision not to use the language of clearness and distinctness also derives from the texts. When talking about scientific questions and the structure of science, Descartes himself seems to avoid the terminology of clearness and distinctness, and falls more naturally into the terminology of intuition (sometimes) and deduction (quite often), as we shall see when we take up such passages in detail. There is thus a certain advantage to following Descartes in this, since it will be thereby easier for us to follow his discussions of certainty in science. The fact that the old way of talking about certainty persists throughout the later writings suggests strongly that Descartes thought that the earlier account could be translated into, or at least justified by, the later account. Just how such a justification, translation, or explication could be given is itself an interpretive problem of major proportions. I assume that everything I say (and Descartes said) about Cartesian science in terms of intuition and deduction can be given a reading salva veritate in terms of clearness and distinctness, though I shall not attempt to argue this. There are other problems raised by my choice of the earlier idiom. Most particularly, unlike clearness and distinctness, the characterization of certainty in terms of intuition and deduction gives us no real criteria that can be used for telling when something is certain and when it is not. Consequently we will have to appeal to what Descartes explicitly says is intuitive, deductive, or certain truth, as we noted earlier. But this is a small price to pay for what will turn out to be a major gain in simplicity and naturalness when we talk about Descartes's scientific reasoning.

So my criterion of certainty for Cartesian science will be the following: a body of scientific results will be certain for an individual if and only if that individual could present it as the product of intuition and deduction. The modal 'could' is important here. Descartes does not always have to present his science as derived from intuition and deduction for him to claim that it is certain. What makes it certain for him is that he could present it in that way.¹⁰

Having outlined Descartes's abstract notion of certainty and the relations it bears to intuition and deduction on the one hand, and clearness and distinctness on the other, I shall close this section with some remarks about the scope of certainty for Descartes.

I pointed out earlier that Descartes's notion of deduction is broader than the notion of deduction in syllogistic logic, and that it seems to allow for arguments that yield conclusions not "contained in" their premises. At this point it might be interesting to draw some consequences from this and bring in some related considerations. In the introduction I noted that the traditional conception of Cartesian science is that of a science more geometrico, conclusions derived logically from a priori first principles. What we noted and conjectured about deduction in Descartes already casts doubt on this picture, but there are other reasons for rejecting it. If that picture is correct, then Cartesian science is limited to a priori certain truth. But it is quite clear that Descartes was willing to admit certainties which can be classed only as a posteriori. For example, in the Meditations Descartes offers arguments which he claims meet his criteria for certainty. Yet at least one of these—the argument for the existence of material objects in Meditation VI—is quite definitely not an a priori argument. This argument depends upon a premise (itself apparently intuitive and certain) about the ideas we have of material objects that cannot be a priori on any conception of a priori truth I know of. Thus not everything certain is a priori, and the limitation of science to the certain does not commit Descartes to an a priori science. And furthermore, since the argument I have cited is itself part of Descartes's broadly scientific structure, it is clear that Cartesian science could not be a priori in any modern sense.

But if we are to reject the picture of Cartesian science in which truths of science are logically derived from a priori first principles, what are we to make of the passages in which Descartes compares his enterprise to that of the geometer? Consider the following such passage:

Those long chains of reasoning, so simple and easy, which enabled the geometricians to reach their most difficult demonstrations, had made me wonder whether all things knowable to men might not follow from one another in the same fashion [s' entresuiuent en mesme façon]. If so, we need only to refrain from accepting as true that which is not true, and carefully follow the order necessary to deduce each one from the others, and there cannot be any propositions so abstruse that we cannot prove them, or so recondite that we cannot discover them.

[Discourse, pt. II: AT 6:19; HR 1:92]

From what I said earlier it should be clear that Descartes is not looking to build a science like geometry in the sense in which geometry derives theorems from first principles using deductive reasoning taken in the narrowest sense. When he talks about "refraining from accepting as true that which is not true" (intuition?) and carefully following "the order necessary to deduce each one from the others," (deduction?) he seems quite consciously to be referring back to his theory of certainty in the Regulae. There too he talked about mathematics as a model for natural science, but his explicit conclusion there was that, "In seeking the correct path to truth we should be concerned with nothing about which we cannot have a certainty equal to that of the demonstrations of arithmetic and geometry" (Rule II: AT 10:366; HR 1:5, emphasis added).¹¹ So, if Descartes is to be construed as building a science more geometrico, it is not because he seeks to build a science that is a priori, like geometry, but rather because for Descartes "more geometrico" means only more certo.

The rejection of the naive geometrical model of Cartesian science, and the realization that not everything that is certain is, strictly speaking, a priori constitute an important part of the way toward a proper understanding of the nature of Descartes's science. But even if we understand the true significance of the geometrical model, we must still explain how and why Descartes thought that the science of nature he found was certain. This will be the task of the following section of this paper.

Having noted something that Descartes does not seem to exclude from the possibility of being certain, we should also note briefly something that he does want to exclude from the domain of the certain: probability. While it is traditional to see Descartes's demand for certainty as a response to scepticism, it is no less correct to regard the demand for certainty as a response to those who are willing to make do with probability.

When Descartes says that we must "reject all knowledge which is merely probable," as he does in the passage from the Regulae with which this section opened, he meant something somewhat different than we currently do by "probability." The notion of probability he had in mind was largely a notion from dialectic and rhetoric—the theories of debate and public speaking. "Probable" was one way in which the premises and arguments used in such debate were characterized.¹² In that context, "probable" meant something close to "generally accepted."¹³

The rejection of probability is part of Descartes's rejection of the whole rhetorical-dialectical tradition of education so prevalent in the Renaissance university.¹⁴ For the most part, though, Descartes gives little characterization of probability and particular probabilistic modes of argument, except negatively, as things which cannot be (or, maybe, are not) presented either intuitively or deductively. Only one kind of argument is singled out for Descartes's attention, the kind of argument that makes use of conjecture:

Let us also take heed never to confuse any conjectures [conjecturas] with our judgements about the true state of things. Attention to this matter is of no little importance, for there is no stronger reason why contemporary philosophy has found nothing so evident and so certain that it cannot be controverted, than because those eager for knowledge … venture to affirm even obscure and unknown things, about which we can make only plausible conjectures [probabilibus conjecturis] and then give their whole credence to these, confusing them indiscriminately with the true and evident. Thus they can finally reach no conclusion which does not seem to depend upon some proposition of this sort, and all of their conclusions are therefore doubtful.

[Regulae, Rule III: AT 10:367–68; HR l:6–7]¹⁵

It is not entirely clear what Descartes means by "conjecture" in this passage. The notion of a conjecture comes up only once again in the Regulae. There Descartes gives the following example:

Persons compose their judgments by conjecture if, for example, considering the fact that water, which is farther from the center of the globe than earth, is also more tenuous, and that air, higher than water, is still more tenuous, they conjecture that above the air there is nothing but a certain very pure ether, and that it is much more tenuous than the air itself, and so on.

[Rule XII: AT 10:424; HR 1:45]

This is something of an argument from analogy. But the earlier characterization of conjecture suggests that conjectures include more than such arguments from analogy. The formula that Descartes uses, talking of those who "venture to affirm even obscure and unknown things … and then give their whole credence to these" suggests (though not entirely clearly or unambiguously) that the modern hypothetico-deductive method or method of hypothesis in which we frame hypotheses that best explain experience and hold them until they are falsified would count as one such probabilistic argument by conjecture.¹⁶

II Cartesian Science in Theory: The Discourse

In the previous section I outlined Descartes's conception of certainty and made some comments about its scope. In the context of the latter discussion, I argued that the picture of science as logically deduced from a priori first principles is not correct. In this section I would like to outline the grand plan for all of science that Descartes presents in the period of the Discourse. In so doing, I hope to sketch something of an alternative to the traditional geometrical model of Cartesian science.

In this section I shall organize my discussion around what seems to be the clearest and most explicit statement of the inferential structure of Descartes's science in the earlier writings. I have divided this single passage up into four parts and labeled each. In the discussion that follows I shall refer to each by letter. The passage is the familiar and often quoted one from the Discourse:

A. My own procedure has been the following: I tried to discover the general principles or first causes of all that exists or could exist in the world, without taking any causes into consideration but God as creator, and without using anything save certain seeds of the truth which we find in our own minds.

B. After that I examined what were the first and commonest effects which could be deduced from these causes; and it seems to me that by this procedure I discovered skies, stars, and earth, and even, on the earth, water, air, fire, minerals, and several other things which are the commonest of all and the most simple, and in consequence the easiest to understand.

C. Then, when I wanted to descend to particulars, it seemed to me that there were so many different kinds that I believed it impossible for the human mind to distinguish the forms or species of objects found on earth from an infinity of others which might have been there if God had so willed. Nor, as a consequence, could we make use of things unless we discover causes by their effects, and make use of many experiments. After this, reviewing in my mind all the objects which had ever been presented to my senses, I believe I can say that I have never noticed anything which I could not explain easily enough by the principles I had found. But I must also admit that the powers of nature are so ample and vast, and that these principles are so simple and so general, that I hardly ever observed a particular effect without immediately recognizing several ways in which it could be deduced.

D. My greatest difficulty usually is to find which of these ways (of deducing the effect) is correct, and to do this I know no other way than to seek several experiments such that their outcomes would be different according to the choice of one or another ways of deducing the effect.

[pt. VI: AT 6:63–65; HR 1:121]

In what follows I shall try to extract the inferential structure of Descartes's science from this and related passages. More precisely, I shall be looking to explicate how Descartes conceived the structure of his science and whether he thought that it could be presented as the product of intuition and deduction. Consequently, we shall appeal to Descartes's scientific practice only insofar as it clarifies his intentions with respect to his theory of science. (I shall point out in the course of this discussion a number of places where Descartes's practice misleads us with respect to his theory.) Because I am interested in eliciting the outline of the whole of Descartes's grand program for science, I shall only give cursory glances at the details behind sections A and B, where the conception seems clearest and seems closest to the Euclidean model. Rather, I shall concentrate on sections C and D where the intentions become foggy, and where he seems, by the introduction of experiment, to diverge most clearly from the Euclidean model.

In A, Descartes discusses his discovery of "general principles or first causes." It is clear that Descartes has in mind at very least the metaphysical first principles outlined in part IV of the Discourse and presented in detail in the Meditations. These writings include the proof of his own existence, the proof that God exists, the validation of the criterion of clearness and distinctness, the proof that mind and body are distinct substances, and that the essence of material substance is extension, and the proof that there are material things. The "general principles or first causes" mentioned in A include more than these metaphysical matters, though. Given that B begins with Descartes's cosmology, it is reasonable to suppose that Descartes meant to include in the matters mentioned in A the laws of motion; in the Discourse account, these are sandwiched between the metaphysical first principles of part IV and the cosmology taken up at the beginning of part V (AT 6:43; HR 1:107–8).

In section A of his outline of the structure of science, there is relatively little problem with certainty. Though he is not entirely explicit, there is every indication that at this point certainty is maintained, and at least Descartes thought that all arguments referred to in A could be presented in terms of intuition and deduction. In fact, Descartes seemed to regard the metaphysical arguments, at least, as paradigms of proper and certain argumentation. Before going on, though, we might remind ourselves that even at this beginning stage, we have left the a priori, strictly speaking. While all of the arguments Descartes offers for the conclusions cited in this section proceed "without using anything save certain seeds [semences] of the truth which we find in our minds," certain of the arguments, like the argument for the existence of material objects, are a posteriori, as we noted earlier in section I.

So much for A. In B, Descartes discusses the first effects "which could be deduced" (deduire) from the "general principles or first causes" of A. These effects include the cosmology (sky, stars), the earth, and at least some of the contents of the earth (water, air, fire, minerals, and "several other things").¹⁷ Given that Descartes used the technical term "deduce" (of course, in its French translation) it seems evident that Descartes thought that the effects mentioned in B were, or could be, established with certainty. Though it is not clear just how such a deduction could be given, it seems as if the chain of intuition and deduction is not yet broken, at least in Descartes's own thinking.

One thing should be mentioned at this point. Though in B Descartes talks about "deducing" his cosmology, etc., from first principles, this is not exactly how the argument is presented in the passage of part V of the Discourse, where that argument is outlined as it was given in Le Monde. There he argues with respect to an imaginary world, not our own, "I therefore resolved to leave this world … and to speak only of what would happen in a new one, if God should now create somewhere in imaginary space enough matter to make one" (AT 6:42; HR 1:107). The "deduction" of cosmology that follows there is thus not for our world, but for this imaginary world, a world that Descartes builds on the basis of certain assumptions. Insofar as the phenomena so deduced resemble our world, Descartes takes his assumptions to be adequate and the explanations correct. Such an argument would not, it seems, particularly in the light of the passage of the Regulae about conjecture cited at the end of section I, tell us anything certain about our world. But, given the clear statement in B that cosmology is deduced from the first causes of A, we must suppose here, I think, that Descartes's practice does not reflect his theory of science. A number of explanations are possible. It is most likely that in this passage Descartes is describing the route he found he had to take in the early work, Le Monde, but in B he is describing a later version of his system, either actual or contemplated, presumably what he hoped would later become his Principles. In adopting this explanation, though, I do not mean to ignore the question of how Descartes argued in the part of his scientific practice corresponding to B. I intend only to put that discussion off to a more appropriate place.

In A we saw that the question of intuition, deduction, and the resulting certainty is relatively unproblematic. There can be little question but that certainty is preserved at this point. Section B is somewhat more problematic, since the outlined arguments in the Discourse that correspond to that section are given only hypothetically. But in this case it is not implausible to separate the practice of the earlier work (Le Monde in this case) from the program that Descartes outlines in B, as I have already suggested. Thus nothing we have seen so far would cause a radical revision of the traditional Euclidean model. While a careful examination of the arguments Descartes has in mind in sections A and B would show us that they are not strictly deductive in the modern sense, as I have argued, the Euclidean model is not a bad fit. But the Euclidean model breaks down completely when we progress to section C. There, where Descartes first explicitly introduces experiment, all hope of fitting his conception of science to the Euclidean model seems to end. For that matter, all hope of certainty in science seems to end as well. What, then, is to be made of C? What has happened to deduction and certainty?

Let us examine C carefully. The particulars he has in mind are not entirely obvious. Certainly he intended animals and human beings.¹⁸ Though the text is hardly explicit on this, I would presume that he would include things like magnets (a favorite example in Cartesian science) and other reasonably complex terrestrial phenomena. However, it does not seem tremendously important to specify precisely what belongs under C and what under B. By "descending to particulars" he seems to mean the process of giving an account of what these particulars are, i.e., an account of their natures, their internal structures. Again, though, Descartes is not entirely clear about the kind of account that he has in mind in this passage. If this is what Descartes is talking about here, then what he seems to be claiming is that we cannot give an account of the nature of the particulars in the world without appeal to experiment and reasoning from effect to cause. Furthermore, he also claims that even when we introduce experiments, there are a number of ways in which we can explain any particular on our first principles.

But what precisely does Descartes have in mind when he suggests that we must discover causes through their effects? Though Descartes is not explicit about this here, his scientific practice in two of the three essays (in particular, the Optics and the Meteorology) for which the Discourse serves as an introduction, in the parts of the earlier Le Monde that survive, and in the later Principles, and his methodological remarks, suggest that Descartes may have in mind some sort of reasoning that makes essential use of hypotheses, perhaps something like the modern hypothetico-deductive method. If we adopt this interpretation of Descartes, then we would reason from effects to causes by making a number of experiments, gathering the results, and framing a hypothesis that would explain those results in terms of our basic principles. If it is the hypothetico-deductive method that Descartes has in mind, then the hypothesis would be supported by virtue of explaining the experiments.¹⁹

The evidence in favor of the claim that Descartes was seriously committed to hypothetical arguments in science and that this is what he had in mind when he wrote C is substantial. Although I shall later argue against this reading, I shall try to present what seems to be the best evidence for this view. Since we are concerned with Descartes's attitudes and theories before the Principles, I shall not consider at this point many of the passages from the later work often cited and discussed in connection with whether or not Descartes adopted a hypothetical mode of argument. Those passages will be discussed in the following section when I discuss deduction and certainty in the Principles. And finally, I shall put off the question of certainty until after we present the case for Descartes's endorsement of hypothetical modes of argument.

The evidence that Descartes had some sort of hypothetical mode of argument in mind in this early period comes from both his scientific practice and from his more theoretical writings. I have already pointed out one passage from the Discourse where Descartes seems to describe the use of a hypothetical mode of argument in his scientific practice. That passage describes how he argued in Le Monde from an imaginary model of our world which in all respects is claimed to agree with ours at the level of phenomena (AT 6:42–44; HR 1:107–9). The hypothetical mode of argument is used in a different but related way in the Optics and the Meteorology. At the very beginning of the Optics Descartes notes:

Thus, not having here any other occasion to speak of light than to explain how its rays enter the eye…. I need not undertake to explain its true nature. And I believe that it will suffice that I make use of two or three comparisons which help to conceive it in the manner which seems the most convenient to explain [expliquer] all of its properties that experience acquaints us with, and to deduce [deduire] afterwards all the others which cannot be so easily observed; imitating in this the Astronomers, who although their assumptions [suppositions] are almost all false or uncertain, nevertheless, because these assumptions refer [rapportent] to different observations which they have made, never cease to draw many very true and well assured conclusions from them.

[AT 6:83; trans. Olscamp, 66–67]

And later, in the beginning of the Meteorology, Descartes notes:

It is true that since the knowledge [connaissance] of these matters depends on general principles of nature which have not yet, to my knowledge, been accurately explained, I shall have to use certain assumptions [suppositions] at the outset, as I did in the Optics. But I shall try to render them so simple and easy that perhaps you will have no difficulty in accepting them, even though I have not demonstrated [demonstrées] them.

[AT 6:233; trans. Olscamp, 364]

Though these passages seem to support the claim we are examining, a few comments are in order. First of all, the kinds of assumptions that Descartes has in mind here are quite general. In the Optics Descartes assumes that light is transmitted instantaneously, in straight paths, and so on, and in the Meteorology he assumes that things are made up of corpuscles, that there is no void, and so on.²⁰ These assumptions clearly correspond to the conclusions discussed in section B, and seem to have little to do with the particulars of C. Consequently, the appeal to these passages may establish little, if anything, about the sort of reasoning that Descartes had in mind in C. But leaving this aside, it is important to recognize that this method of proceeding, while hypothetical, is not strictly hypothetico-deductive. Descartes takes as his starting place certain assumptions, and claims to be able to explain a variety of phenomena on those assumptions. But he makes no claims that the ability to explain the phenomena and deduce new phenomena "which cannot be so easily observed" renders the assumptions in any way true, certain, or even confirmed. In fact, he compares his assumptions with those of astronomy, which he claims are all "false or uncertain." The conception of astronomy he is referring to is one according to which the problem of astronomy is to find hypotheses about the motion of heavenly bodies which will "save the phenomena," while making no claims about the true causes of any of the phenomena.²¹ This kind of instrumentalistic conception of theories is often appropriate in astronomy, where for many practical purposes (the construction of calendars, navigation, etc.) it is more important to know when and where in the sky particular bodies will be observed, than why they are there. But such a procedure would seem much less valuable in physics, where we have a greater interest in understanding the phenomena than in saving them. In fact, by the 1630s the traditional instrumentalistic attitude toward astronomical theories had long been given up in favor of a more realistic attitude among the best astronomers, including Copernicus, Tycho Brahe, Kepler, and Galileo.²² It seems curious that Descartes would recommend that physicists adopt the approach of the astronomers, long after astronomers had given up that approach in favor of the more realistic project of finding the true explanations of things, a project which they borrowed from physics.

Elsewhere, though, Descartes does argue in a more straightforwardly hypothetico-deductive fashion:

And in all of this, the explanation [raison] accords so perfectly with experience [l'experience] that I do not believe it possible, after one has studied both carefully, to doubt that the matter is as I have just explained it [l'expliquer].

[Meteorology, discourse VIII: AT 6:334; trans. Olscamp, 338]

Here Descartes is talking about his explanation of the rainbow, a matter much closer to the concerns of section C than is discussed in the earlier passages. Also here, unlike those earlier passages, it does seem as if the explanans gains significant credibility by virtue of its explanatory power. This claim is defended quite explicitly in another passage, one that looks like an unambiguous and theoretical endorsement of the hypothetico-deductive mode of argument, both when we are dealing with particulars, such as rainbows and their nature, and when we are dealing with the sort of general assumptions discussed earlier and compared with astronomical assumptions:

If some of the matters I deal with at the beginning of Optics and Meteorology should at first sight appear offensive, because I call them assumptions [suppositions] and do not try to prove [prouver] them, let the reader have the patience to read all of it with attention, and I hope that he will be satisfied with the result. For it seems to me that the explanations [raisons] follow one another in such a way, that just as the last are demonstrated [demonstrées] by the first, which are their causes, so these first are demonstrated [demonstrées] by the last which are their effects. And one must not suppose that I have here committed the fallacy which logicians call circular reasoning; for as experience makes most of the effects very certain [car l'experience rendant la plus part de ces effets tres certains], the causes from which I deduce [deduits] them serve not so much to prove [prouuer] as to explain them [expliquer]; but, on the contrary, the causes are proved by their effects [ce sont elles qui sont prouuées par eux].

[Discourse VI: AT 6:76; HR 1: 128–29].²³

This passage, which bears a striking resemblance to modern discussions of hypothetico-deductive method, is echoed in some of the correspondence following the publication of the Discourse and the accompanying essays.²⁴ This passage and the corresponding theoretical comments in the correspondence strike me as the best evidence there is for the claim that Descartes was genuinely committed to the use of hypothetical arguments in science, and that the hypothetico-deductive method is what he has in mind in section C.

Let us review the story up to now. There is considerable evidence that Descartes had in mind some kind of hypothetical mode of argument in the period of the Discourse. There are complications, however. For one, it looks as if there are two distinctly different kinds of hypothetical argument in the texts, an astronomical argument, and a hypothetico-deductive argument (it is not clear to me that Descartes distinguished between these two kinds of argument, though). There is a further complication, one that arises when we attempt to argue that this hypothetical argument is what Descartes has in mind in C. Many of the texts supporting Descartes's endorsement of hypothetical modes of argument involve general sorts of assumptions of the sort that arise in B and not in C. These complications hardly seem decisive. However, if this is what Descartes meant by reasoning from effects to causes in C, what of certainty? What of the grand picture of a science grounded in intuition and deduction, as indubitable as geometry?

At this point in the argument there seem to be only two directions in which we can go. We can argue either that Descartes thought (quite mistakenly) that the hypothetical mode of argument yielded certain knowledge, or that by this point, Descartes had abandoned his goal of a science that is certain, having realized that experimental reasoning from effect to cause and certainty are not compatible. One should be somewhat suspicious of both these alternatives. The former seems doubtful, given the remarks concerning assumptions I cited earlier in section I of this paper, and even more doubtful considering Descartes's apparent recognition in C of the multiplicity of causes all of which can explain the same effect. The latter account seems suspicious considering that in part II of the Discourse Descartes once again declares his intent to construct a science as certain as mathematics (AT 6:19; HR 1:92–93) and that he reasserts this at the very beginning of his outline of physics in part V: "I have always remained true to the resolution I made … not to admit anything as true which did not seem to me clearer and more certain than the demonstrations of the geometricians" (AT 6:40–41; HR 1:106). What then are we to do?

I would like to suggest that a serious mistake has been made in supposing that the hypothetical mode of argument is what Descartes really has in mind in C, and in believing that the hypothetical mode of argument plays a role in Descartes's considered views on reasoning in science, at this stage in his thinking. While we shall find a somewhat different situation when we examine the Principles, I shall maintain that in the works we are considering, those written before the Principles, Descartes has neither adopted any hypothetical mode of argument, nor has he given up his plan for a certain science, and that, furthermore, this certain science is one in which experiment plays an indispensable role. My argument will be in two parts. I shall first argue that Descartes considered the hypothetical mode of argument only a convenient way of presenting his scientific results without having to present his entire system, and he at least claimed to have in mind a truly deductive argument in cases where he appealed to hypothetical arguments. And secondly, I shall argue for an interpretation of C in which the reasoning Descartes has in mind is both experimental and certain. This will allow us to say that at least before the Principles, Descartes had retained the program of building a certain science founded on intuition and deduction.

The hypothetical reasoning that Descartes uses in the Optics and the Meteorology seems to have been one feature of those works that most disturbed his readers. One of the most revealing insights into Descartes's true intentions in presenting his work in that way comes in a letter to Vatier, where he explains why he chose to argue in a hypothetical mode:

I cannot prove a priori [i.e., from cause to effect] the assumptions I proposed at the beginning of the Meteorology without expounding my whole physics; but the phenomena which I have deduced necessarily from them, and which cannot be deduced in the same way from other principles, seem to me to prove them sufficiently a posteriori [i.e., from effect to cause]. I foresaw that this manner of writing would shock my readers at first, and I think I could easily have prevented this by refraining from calling these propositions 'assumptions' and by enunciating them only after I had given some reasons to prove them. However, I will tell you candidly that I chose this manner of expounding my thoughts for two reasons. First, believing that I could deduce them in order from the first principles of my Metaphysics, I wanted to pay attention to other kinds of proofs; secondly I wanted to try whether the simple exposition of truth would be sufficient to carry conviction without any disputation or refutations of contrary opinions.

[AT 1:563; K 48, emphasis added.]²⁵

Descartes makes two important claims in this passage: that the use of a hypothetical mode of argument is a matter of convenience that allows him to present his findings in a convincing way without revealing the full foundations of his physics; and that for the conclusions presented in those works, he can give complete and certain deductions from first principles.

It is somewhat surprising that Descartes has to go into the question in such detail in the letter quoted and in the two others cited. Both of the points he raises in the letters were mentioned explicitly in the Discourse. On the first point, Descartes explicitly notes that in the essays that follow the Discourse, he does not intend to divulge fully the principles or the arguments on which his physics rests (pt. VI: AT 6:68–76; HR 1:123–28). In writing the essays he hoped only to:

choose some topics which would not be too controversial, which would not force me to divulge more of my principles than I wished to, and which would demonstrate clearly enough what I could or could not do in the sciences.

[AT 6:75; HR 1:128]

Furthermore, even in the Discourse, the hypothetical mode of argument is defended not as a method of establishing conclusions, either with certainty or without, but as a convenient way of presenting material that is in no way intended to replace a proper deduction from first principles. Immediately following the lengthy and eloquent defense of the hypothetico-deductive mode of argument in the Discourse quoted above, Descartes declares:

And I have called them [i.e., the assumptions at the beginning of the Optics and Meteorology] assumptions only to let it be known that although I think I can deduce them from first truths …, I expressly desired not to make the deduction.

[AT 6:76; HR 1:129, emphasis added.]²⁶

Though these remarks are directed largely at the very general assumptions that Descartes makes at the beginning of the Optics and Meteorology, some at least can be interpreted as indicating that the hypothetical mode of arguing with respect to assumptions about the nature and inner working of particular things was adopted for similar pragmatic reasons. Elsewhere, Descartes deals more specifically with those kinds of hypothetical arguments. In another letter written shortly after the Discourse and essays appeared, Descartes defends argument in the hypothetical mode with regard to the inner make-up of water, given without full demonstrative argument in the Meteorology as follows, "But if I had tried to derive all these conclusions like a dialectician, I would have worn out the printers' hands and the readers' eyes with an enormous volume" (AT 1:423–24; K 40).

Though Descartes talks here and elsewhere as if he has all of the deductions worked out, it is probably more accurate to say that he only thought that he could work them out given sufficient time, and in the case of particulars, given a sufficiently large body of experimental data. But even this position, somewhat weaker than the rather stronger claims that Descartes often makes, is quite sufficient for the argument I am making that the hypothetical arguments offered in Descartes's scientific works of this period do not represent a genuine commitment to that method of arguing in science. So, the hypothetical mode of presenting his science, at least in the essays, is intended only to save Descartes the trouble of presenting (or, perhaps, working out) his full system in complete detail, and does not represent a serious commitment to the use of hypothetical arguments in science. Similarly, his apparent defense of hypothetico-deductive method from a theoretical point of view is a defense of it as a method of presentation. In no way does Descartes intend the hypothetical mode of argument to replace strict Cartesian deduction as a way to insure the certainty of our scientific conclusions.²⁷

But if the appeal to hypotheses is a matter of expository convenience, what, then, are we to make of section C? What kind of reasoning did Descartes have in mind there? What role does experiment play in that reasoning? What role does certainty play in that reasoning? In what follows I shall make a conjecture about the kind of argument Descartes may have had in mind in C when he talks about arguing from effects to causes.

Let us look back to C. It is interesting to note that while Descartes claims that when dealing with particulars, he found that he had to argue from effects to causes, and that when doing so, he could always envision a multiplicity of different causes for a given effect, he does not explicitly assert that it is impossible to argue from effects to causes either deductively or with certainty. In fact, after noting that there are often a number of ways of causally explaining a given effect, Descartes tells us just how it is that one can eliminate false causal explanations. The device he has in mind and mentions in D is that of crucial experiment. When we have an effect which can be explained by (deduced from) first principles in more than one way, Descartes tells us that we should "seek several experiments such that their outcomes will be different according to the choice" of causal hypothesis. Section D is not the only place in his writings where Descartes brings up crucial experiments in such an explicit way. In the Description du Corps Humain (1648), which is admittedly from a period later than the one we are dealing with, in the context of an argument against Harvey's theory of the heart, Descartes observes:

And all of this proves nothing but that experiments themselves can on occasion deceive us, when we don't examine well enough all of the causes they can have…. But in order to be able to note which of two causes is the true cause, it is necessary to consider other experiments which cannot agree with one another.

[AT 11:242]²⁸

It is thus clear that Descartes was well aware of the utility of crucial experiments in scientific reasoning.

So, if there is a Cartesian deduction of the nature of particulars outlined in C, it appears that it makes use of crucial experiments. But crucial experiment, by itself, cannot lead to certainty. Even after we eliminate all but one cause using crucial experiments, we still don't know that it is the correct one, since there may be other possible causes that we just have not thought of yet. But, if we can enumerate all possible causes, then it seems as if we can use crucial experiments to eliminate all but one of those causes, and we will know for certain that the one that remains is the true cause. This, in essence, is what I suggest Descartes has in mind in sections C and D.

Before elaborating on this and defending it, let me return to those two sections. What I am claiming is not only that in these sections Descartes is not adopting a hypothetical mode of argument with respect to particulars, but that in those passages, Descartes is outlining what a certainty-preserving deduction with respect to particulars would look like. But if this is what is going on in those sections, why does it look so much as if Descartes is giving up deduction and certainty? Two things are in need of explanation. First of all, why, if Descartes claims to have found a way of deducing explanations about particulars, does he declare at the very beginning of C that "it seemed to me that there were so many different kinds [of particulars] that I believed it impossible for the human mind to distinguish the forms or species of objects found on earth from an infinity of others which might have been there if God had so willed"? It seems clear that though he believed that at one time, he later came to believe the contrary, and reports this later in C and D. In a semiautobiographical account like the Discourse we must be careful to distinguish intermediary positions from those that Descartes later adopts. But there is a more serious problem here. If my claim is right, then sections C and D should be enthusiastic reports of a bold new way of reasoning to the nature of particulars with absolute certainty. Why, if certainty is preserved, is the passage so pessimistic? To explain this, we must put the passage into its proper context. Earlier I mentioned that it is more accurate to say that Descartes finds, in principle, no reason for thinking that certainty cannot be attained at every level than it is to say that he has actually found all of the necessary arguments. This is especially true with respect to particulars. Such arguments are especially difficult because they require great numbers of experiments. This seems to be the main point of C and D. Immediately following D in the Discourse, not even beginning a new paragraph, Des cartes laments the fact that so many experiments are required and that he has so few:

As for the rest [i.e., those whose true explanation he has not yet been able to find (?)], I have reached the point, it seems to me, where I see clearly enough the direction in which we should go in this research; but I also see that the character and the number of experiments required is such that neither my time nor my resources, were they a thousand times greater than they are, would suffice to do them all. In proportion, therefore, to the opportunity I shall have in the future to do more or fewer of them, I will advance more or less in the understanding of nature. This I expected to convey in my treatise, and I hoped to show clearly how useful my project might be that I would oblige all those who desire human benefit, all those who are truly virtuous and not merely so in affectation or reputation, both to communicate to me the experiments that they have already made and to assist me in the prosecution of what remained to be done.

[pt. VI: AT 6:65; HR 1:121–22]

So, the despair is not one of having to give up deduction and the certainty that comes with deductive argument when we "descend to particulars." The despair is clearly over the difficulty of providing such arguments.

Let me now set out the argument I have suggested more explicitly. My suggestion is that, for explaining the nature of particulars, Descartes imagined that we would begin with some general principles: metaphysics, the laws of motion, basic facts about the contents of the universe. This, presumably, is the conclusion of sections A and B. We also begin with immediate acquaintance with the phenomena to be explained, the particulars and their properties. This comes from observation and experiment. We then enumerate all of the possible causes that both explain the phenomena, and which are consistent with our general principles. Finally, we perform crucial experiments until we have eliminated all possible explanations except one. This is the true explanation.

There is another way of describing this mode of argument which is equivalent, even though it does not appeal to crucial experiments. On this way of proceeding, we would begin with the same first principles, but with a much wider variety of experimental data, perhaps, the data that we would have gotten if we had performed all of the crucial experiments. Examining the first principles, and the observational data, we would conclude (by intuition or deduction) that there is one and only one explanation of the phenomena consistent with both the phenomena and the first principles.

An example may make this clearer. Suppose that we are trying to find the nature of the magnet. We would begin with our first principles, and with common observations about how magnets behave. We would then, following the first version of this mode of argument, enumerate all possible explanations of the known phenomena that are consistent with our first principles, and eliminate all but one through crucial experiments. Following the second version, we would do the experiments first, and then intuit or deduce the single explanation that satisfies both the phenomena and our assumed first principles.

This form of argument is what I shall call an argument by complete enumeration of explanations, or more simply, argument by enumeration. It should be evident that the two versions of the argument (for convenience I shall call the first version A, and the second version B) are essentially equivalent, differing only in the temporal sequence of steps. In particular, in version B we do not frame any hypotheses until all of the experimental evidence is in, whereas in version A, we frame hypotheses before we have performed all of the experiments. It should be evident that the argument from enumeration is not a kind of hypothetico-deductive argument. While the two are very similar, in the argument by enumeration we have a complete enumeration of all possible explanations of phenomena. This is a step lacking in characteristic accounts of hypotheticodeductive argument. Because of this complete enumeration, the argument by enumeration can insure that a particular explanation is true, whereas in a hypothetico-deductive argument the most that can be established is that, since the explanation in question agrees with all observed phenomena, it is plausible to think that it may be true. Thus the argument by enumeration can make a prima facie claim to true and certain knowledge that cannot be made for the hypothetico-deductive argument. With this added power, though, come certain difficulties. It may not always be possible to produce a complete enumeration of possible explanations, nor may it always be possible to eliminate all but one by crucial experiments.²⁹ But we shall not consider these difficulties.

If the argument by enumeration is what Descartes has in mind, this casts a very interesting perspective on the notion of experiment in Cartesian science. Experiment is required, not as in Bacon or in more modern theories of experimental method to start possible lines of induction, but to close off possible lines of deduction. In the argument by enumeration, experiment eliminates incorrect deductive chains from first principles. It establishes what the facts of the world are that need to be explained, and does so with such finality that, at least in idealization, there is only one possible deductive path for us to follow. It seems curious to us to talk about experiment eliminating incorrect deductions. It would seem as if any deduction from first principles must be true. But in saying that experiment eliminates incorrect deductions, I don't mean to say that these other deductive paths are false, exactly. Rather, these other deductions simply lead to possible effects of our first principles not realized in the specific group of particulars with which we are dealing, which we are trying to explain. The problem experiment solves is the problem of distinguishing the "objects found on earth from the infinity of others which might have been there." Experiment does not eliminate incorrect deductions by showing them false, but by showing them inappropriate to the particular phenomena at hand. Consequently, there is an important sense in which an argument by enumeration is not strictly an argument from effect to cause. The argument is still from previously known causes to their effects, except that experiments tell us which are the "appropriate" effects.

This, then, is the argument that I think Descartes had in mind in sections C and D and in the numerous places where he claimed to be able to give deductive accounts of the nature of particulars. In what follows I shall argue that the argument by enumeration is a deductive argument for Descartes, and that it is the kind of argument that he had in mind in sections C and D.

The best argument for showing that the argument by enumeration is a deductive argument on Descartes's terms is that Descartes uses arguments of exactly the same form in circumstances where it is clear that he intended to give deductive and certain arguments. Most notable of these are the arguments for the existence of God and for the existence of material objects, the latter mentioned earlier as an example of an a posteriori deductive argument. These arguments can be represented schematically as follows:

GOD

1. First principles (assumed)

2. To be explained: I have an idea of God.

3. Possible explanations:

1. I caused that idea.
2. Nothing caused that idea.
3. God caused that idea.

4. Elimination: Further argument convinces me that only God could have caused that idea.

5. Conclusion: God exists.³⁰

MATERIAL OBJECTS

1. First principles (assumed)

2. To be explained: I have ideas of sensible objects.

3. Possible explanations:

1. I caused those ideas.
2. God caused those ideas.
3. Bodies caused those ideas.

4. Elimination: Further argument convinces me that only bodies could have caused those ideas.

5. Conclusion: Material objects exist.³¹

Both of these arguments very clearly have the form of an argument by enumeration. If arguments like the arguments for the existence of God and material bodies lead us to true and certain knowledge of their conclusions, so should all arguments by enumeration.

There is one worry about this reasoning, though, a difference between the arguments I just outlined and arguments by enumeration that may be serious enough to warrant our withholding the certainty from the argument by enumeration that Descartes attributes to the other two arguments. In the two arguments from the Meditations that I just outlined, alternative hypotheses are eliminated by reasoning, whereas in the argument by enumeration, it is experience, in the form of crucial experiments, that eliminates alternative hypotheses. Given Descartes's well-known distrust of the senses, might this render the argument uncertain and probable, despite the strong parallels in form between that argument and those other clearly deductive arguments? While I cannot here give a complete defense of the use of experience in a deductive argument of the form of an argument by enumeration, a few remarks are in order. As has been pointed out before, Descartes's distrust of experience has been vastly overemphasized and misinterpreted.³² Although Descartes does distrust experi ence improperly used, he is equally emphatic about the necessity of using experience properly in scientific reasoning.³³ An example of experience properly used is given in the wax example of Meditation II. There, as part of a digression on the utility of experience in gaining knowledge, Descartes discusses the "nature" of a piece of wax. He concludes that the wax is by nature an extended thing, using reasoning strongly suggesting an argument by enumeration. He considers a number of different candidates, color, shape, size, taste, odor, etc., and eliminates all but one by appealing to experience. Though Descartes concludes that "perception [perceptio] is not a vision, a touch, nor an imagination … but is solely an inspection by the mind [inspectio mentis ]" (AT 7:31; HR 1:155), this seems too strong a conclusion. In the wax example, it seems as if experience does play a crucial role, that of eliminating incorrect hypotheses. It would be more accurate to say that for Descartes, experience is useless unless properly used by the understanding. And it looks from the wax example as if one of the proper uses of experience is in the context of an argument by enumeration. Thus, the particular use of experience in the argument by enumeration does not render its conclusions uncertain, and it is not a significant difference between the argument by enumeration and the arguments for the existence of God and material bodies that the one appeals to experience where the other appeals to reasoning.

So, the argument by enumeration is a deductive argument. But is it what Descartes had in mind in sections C and D? The evidence that it is is of two kinds. First of all, there is a very strong suggestion of a use of the argument by enumeration in one of the letters where Descartes is defending the claim that he made in the Meteorology, that water is made up of oblong, eel-like corpuscles. In the first discourse of the Meteorology (AT 6:237–38; trans. Olscamp, 267–68) this claim is presented as one of Descartes's assumptions, and given a hypothetico-deductive defense. But in the correspondence he outlines what he calls there a "proof (demonstratio) (AT 1:422–24; K 39–40). The "proof involves showing that the account of the make-up of water that Descartes favors is the only one consistent with all the phenomena. This argument closely resembles version B of the argument by enumeration, and thus supports my claim that this is what Descartes had in mind in sections C and D, where he is talking in general terms about such explanations of particulars, even though "water" is placed (misplaced, I think) among the elements in section B.

But there is another reason for thinking that the argument by enumeration is what Descartes had in mind, a reason that is derived more from Descartes's theoretical comments than from his scientific practice.

As I stressed earlier, Descartes does introduce the notion of a crucial experiment in D. Given the context, of course, the only thing that prevents us from saying with complete confidence that Descartes has in mind an argument by enumeration is the fact that Descartes does not explicitly say that we must make a complete enumeration of all possible causal hypotheses. But in the Discourse, while discussing the rules of method in science, Descartes adopts the following rule, "The last rule was always to make enumerations [denombremens] so complete and reviews so general that I would be certain that nothing was omitted" (pt. II: AT 6:19; HR 1:92). It seems reasonable to suppose that it is the violation of this rule that Descartes had in mind when, later, in the Description du Corps Humain he introduces the brief discussion of crucial experiment by noting that "experiments themselves can on occasion deceive us, when we don't examine well enough all of the causes they can have." It thus seems reasonable to suppose in C and D, where crucial experiment comes up as well, that Descartes has followed this rule and made an enumeration of possible explanations "so complete … that I would be certain that nothing was omitted," though Descartes did not mention this enumeration explicitly in that passage. So, while the interpretation that Descartes has the argument by enumeration in mind in C and D would involve reading something into that passage, all we have to assume is that Descartes means to follow the very rule that he earlier states, and later appeals to in a corresponding context.³⁴

There is considerable further evidence in the Regulae that Descartes had an argument like the argument by enumeration in mind.³⁵ Moreover, I think that my conjectured argument by enumeration is supported by the simple fact that there seems to be no other way to explain how Descartes thought he could unite experiment, deduction, and certainty. But what is most important is that Descartes thought that an experimental argument could be given to establish facts about the nature of particulars with certainty; and that he thought that he could exhibit his entire science, or, at very least, the science presented in the Optics and Meteorology, as a deductive system. As we have found, this deductive system has a structure considerably different from that of Euclid's Elements. At the top are the first principles of metaphysics and the laws of nature, not established a priori in our sense, but established with certainty nevertheless (A). Next come the general principles of Cartesian cosmology, presented hypothetically in Le Monde, the Optics, and the Meteorology, but with deduction (and thus certainty) promised in B. And lastly comes the explanation of particulars. Here the argument gets complex, and we must appeal more and more to experimental arguments. But there is no indication that even at this stage Descartes was prepared to give up the claim to certainty, and much indication that he was not. This is what I propose to replace the traditional geometrical model of Cartesian science. If carried out, it would be a science both experimental and certain.

III Cartesian Science in Practice: The Principia

I shall now turn to the Principia Philosophiae, the synoptic and systematic work of Descartes's last period, and examine the extent to which Descartes is able to carry out the program of the earlier period and provide a science based on intuition and deduction. In the earlier period, we found that in certain crucial respects Descartes's theory of science and his scientific practice bear only an indirect relation to one another. Though Descartes believes that his science can be presented as the product of intuition and deduction, he makes no serious attempt to do so in the scientific writings. Thus, as I argued, the hypothetical modes of argument used there do not represent an abandonment of the deductive picture of science. In the Principles there can be no such gap between theory and practice, insofar as the Principles is supposed to fulfill the program that Descartes earlier sketched. Descartes's principal excuse for using hypotheses in the earlier essays was that this mode of argument did not "force me to divulge more of my principles than I wish to" (Discourse, pt. VI: AT 6:75, HR 1:128). The fact that in the Principles Descartes starts from first principles leaves little doubt that it is there that he intended to fill in all the foundations and complete arguments lacking in the essays, mentioned in the Discourse, and promised in the correspondence.³⁸ But we shall find that, contrary to his earlier promises, Descartes finds that he is unable to present his science deductively, and that, as earlier, he has to appeal to hypotheses. But here he can no longer explain this appeal to hypotheses by claiming that it is not his intention to present the full system and all of the arguments. It is thus in the Principles that the necessities of scientific practice force some changes in the Cartesian program for science. I shall argue that in the Principles, Descartes makes some important moves away from the earlier program of a certain science founded in intuition and deduction.

Let us begin by examining Descartes's scientific practice in the Principles. There is little reason for us to pause over the first two of the four parts into which the Principles is divided. It is there that Descartes presents the first principles of metaphysics and the laws of nature described in section A of the programmatic outline in the Discourse. There is no question that Descartes was convinced both that the reasoning could be set out with intuitive and deductive certainty, and that he did set it out with certainty there. The arguments of Principles I correspond closely to those of the Meditations and part IV of the Discourse, and have been studied at great length. The arguments of Principles II, while less well known, are a direct continuation of the mode of argument of Principles I. At no point in these first two parts of the Principles is there any indication that Descartes is diverging from the master plan of the Discourse.

In Principles III Descartes begins the presentation of his cosmology and general theory of the universe. In this part, which corresponds to at least some of the material included in section B of the Discourse program, Descartes offers a general theory of matter (the three elements), a theory of the origin of the universe, and a theory of the nature and behavior of heavenly bodies. In the Optics and Meteorology he had discussed some of this material hypothetically, as we earlier saw. Descartes framed a certain number of plausible assumptions, and showed how all of the phenomena could be explained by (i.e., deduced from) these assumptions. But the material could be presented deductively, Descartes claimed, assuming nothing but first principles. The Principles, and more particularly, this part of the Principles, is where he was to have given this deduc tion. It is interesting to see just how well Descartes succeeds.

Descartes begins Principles III with the claim that we must first examine the phenomena, the effects, as a prelude to a proper deduction of effects from causes:

The principles we have discovered so far [in Principles I and II] are so vast and so fertile, that their consequences are far more numerous than the observable contents of the visible universe…. For an investigation of causes, I here present a brief account (historiam) of the principal phenomena (phaenomen n) of nature. Not that we should use these as grounds (rationibus) for proving anything; for our aim is to deduce an account of the effects from the causes, not to deduce an account of the causes from the effects. It is just a matter of turning our mind to consider some effects rather than others out of an innumerable multitude; all producible, on our view, by a single set of causes.

[III 4: AT 8(1): 81–82: AG 223; emphasis added]

In this passage, highly reminiscent of section C from the Discourse, Descartes looks as if he is preparing for an argument by enumeration by setting out the body of data necessary for such an argument. Note at this point, Descartes explicitly says that he intends to give a deduction of effects from first principles.³⁷

In the sections that follow, Descartes presents a body of data about the heavenly bodies, the heavens, and so on. The data are not exactly what we would call observational, but they are, by and large, presented in the spirit of facts in need of explanation, and appear to be in preparation for a deductive argument, perhaps an argument by enumeration. (Descartes also presents an astronomical hypothesis, which he compares with those of Copernicus and Tycho. But this seems something of a digression, an anticipation of material to be discussed in greater detail later.)

Having given some data, Descartes seemingly returns to the main thread of his deductive argument in III. 43:

And certainly, if the only principles we use are such as we see to be most evident, if we infer nothing from them except through mathematical deduction, and if these inferences agree accurately with all natural phenomena; then we should, I think, be wronging God if we were to suspect this discovery of the causes of things to be delusive.

[AT 8(1):99; AG 223–24]

So, Descartes implies that a demonstratively certain argument to the causes of things is possible. (Note how this passage suggests the argument by enumeration.) But, though such an argument is implied, it is not the kind of argument that Descartes intends to give. Rather, in the section following, he declares his intention to argue hypothetically:

However, to avoid the apparent arrogance of asserting that the actual truth has been discovered in such an important subject of speculation, I prefer to waive this point; I will put forward everything I am going to write just as a hypothesis [hypothesin]. Even if this be thought to be false, I shall think my achievement is sufficiently worth while if all inferences from it agree with experience [experiments]; for in that case we shall get as much practical benefit from it as we should from the knowledge of the truth.

[AT 8(1):99; AG 224]

And at this point in the argument, Descartes follows the well-worn path he took in the Optics and Meteorology. He frames a number of hypotheses, some of which he claims to be outright false, and derives "explanations" of the phenomena from these (e.g. III. 45; AT 8(l):99–100; AG 224–25). Given that he has opted to argue hypothetically, the only restriction he places on these hypotheses is that their consequences agree with experience, "We are free to make any assumption we like … so long as all the consequences agree with experience" (III. 46: AT 8(1): 101; AG 225).

It should be clear that by this point in the Principles, Descartes has broken the promise of section B. He has not given us a deduction of his cosmological principles from first principles. Rather, he has used the hypothetical mode of argument he used earlier. Why? He cannot argue, as he did in the Discourse, that he did not want to present his first principles and give an exposition of his whole system. The first principles are given in parts I and II, and the purpose of the Principles is just to give an exposition of the whole system. Perhaps one should take him at his word, and explain the hypothetical mode of inquiry by saying that Descartes was too modest to assert that he had found the truth about "such an important subject of speculation." But Descartes is hardly modest on other occasions, even earlier in the Principles where he doesn't hesitate to declare that he has found the truth about other matters. It is hardly less arrogant to imply that one has found the truth, as he does in III. 43. The natural explanation for the hypothetical mode of argument in this context is that, though he was earlier quite confident that he had a deductive argument for his cosmology, when he came to present it in the Principles, he discovered that it did not work. When it came to actually giving a deduction, he found that he had no deduction to give, even given his broad notion of deduction, and he was forced to return to his hypothetical mode of argument.

Before continuing with the argument, though, an alternative explanation for Descartes's use of hypotheses must be considered. There is a strong suggestion in these texts that Descartes may think he can deduce the hypotheses in question from first principles, but is reluctant to make that claim explicitly or display the deductions for religious reasons. The hypotheses that Descartes frames in Principles III. 46 relate to the original state of the universe. Might Descartes have suppressed his deduction and, in fact, even labeled the hypotheses false, in order to avoid a clash with the doctrine of creation in Genesis? This is suggested by considerations raised in Principles III. 45 and later in Principles IV. 1. But I find it implausible to suppose here that Descartes is purposely hiding a deduction. It is clear that he did not think that he could give a direct, nonexperiential deduction of the sort originally promised in section B, since he does admit with respect to the particles that made up the original state of the universe that "we cannot determine by reason how big these pieces of matter are, how quickly they move, or what circles they describe. God might have arranged these things in countless different ways" (AT 8(l):100–101; AG 225). This leaves open the possibility of a suppressed argument by enumeration, and Descartes suggests just this when he immediately comments that "which way he [God] in fact chose rather than the rest is a thing we must learn from experience." But in order to argue deductively from experience he would have to show that the hypothesis he adopts is the only one consistent with experience. The most he claims about these hypotheses is that he cannot imagine any principles that are "more simple or easier to understand, or indeed more credible [probabiliora]" (III. 47: AT 8(1): 102; AG 225). Nowhere does he even suggest that the hypotheses in question are the only possible ones. In fact, in Principles III. 48 he suggests that a number of different hypotheses, including the assumption of initial chaos, would work just as well. So a suppressed argument by enumeration is also ruled out. The idea that Descartes has a deductive argument in mind will be made still more implausible when we later note the changes in the place of certainty in Descartes's theory of science, changes that he would hardly have made if he really had deduction in question. I would claim that Descartes is not presenting something he can deduce as a hypothesis for religious reasons, but rather, he seems to be appealing to religious considerations to hide the fact that he cannot make the deduction.³⁸

Though, as it turns out, Descartes finds in practice that he has to appeal to hypotheses, there is evidence in the Principles that this is a move that Descartes strenuously resisted. In Principles III. 43, there is still the strong implication that a deduction is possible, even if, as it turned out, Descartes was not able to give one. And in Principles III. 4, as we have already seen, Descartes interrupts his deductions to consider some observed phenomena, with the promise that he will return to deduction. There is another notable instance of the earlier deductivism embedded in the account of the magnet given in Principles IV. There Descartes claims to have shown how the nature of the magnet follows (sequentur) from the principles of nature (ex principiis Naturae) (IV. 145; AT 8(1):284). Of course, if the principles of nature include the material of Principles II, then the hypothetical mode of reasoning introduced in Principles III. 44, makes such a claim obviously false. Another interesting passage is at the very end of Principles IV where Descartes is describing the way in which he claims to have found the nature of particulars:

Starting from the simplest and most familiar principles which are implanted in our understanding by nature, I have considered in general the chief possible differences in size, shape, and position between bodies whose mere minuteness makes them insensible, and the sensible effects of their various interactions. When I have observed similar effects among sensible things, I judged [existimasse] that they arose from similar interactions among such bodies, especially since this appeared to be the only possible way of explaining them.

[IV. 203: AT 8(l):325–26; HR 1:299]

What is notable about this passage, besides the apparent reference to version B of the argument by enumeration, is the fact that, while Descartes was claiming to be describing his practice, there is no mention of any general hypotheses of the sort required in Principles III. My conjecture is that these last three passages, Principles III. 4, IV. 145, and IV. 203 were all written at an earlier stage in the composition of the Principles, when Descartes still thought that it would be possible to iron out the wrinkle in the argument of Principles III and before he realized that he would have to appeal to hypotheses. Their presence in the completed Principles suggests that it was not until the final stages in the composition of the Principles that Descartes finally realized that he had to argue hypothetically. This in turn supports my claim that Descartes attempted to give a wholly deductive argument in the Principles, but found in the end that he could not.

The deductive chain is broken in practice, and the argument offered is hypothetical. Starting in Principles III. 44, the only standard for correctness Descartes actually uses in practice is that theory should agree with experience. What is particularly interesting is that Descartes did not even have to get as far as section C of our outline from the Discourse before deduction failed. Deduction fails in the material that corresponds to B, where Descartes earlier seemed quite confident of being able to produce deductive arguments without having to appeal to experiment. Insofar as he argues hypothetically about his entire cosmology and his general theory of the world, his explanations of the nature of particulars must fail to have deductive certainty as well. Even if he could give deductive arguments with regard to the nature of particulars from his cosmology, they would not be true deductions, because they begin not with certainties, but with hypotheses.

So far we have been talking about Descartes's scientific practice. We have noted that there he makes do with hypothetical arguments. But what of the earlier goal of certainty? For this we must turn back to his program for science. In the earlier works, Descartes could tolerate a great deal of divergence between his theory of science and his scientific practice. But insofar as it was Descartes's seeming intention to realize his program in the Principles, such divergence should be an embarrassment. Thus we find that, although Descartes resisted the use of hypothetical reasoning as long as he could, once he finally adopted it his attitude seemed to change. Evidently, if the world will not bend to fit his conception of science, Descartes must bend his conception of science to fit the world. In the Principles, hypotheses and hypothetical reasoning seem no longer quite as objectionable as they earlier were in the Regulae and in the Discourse. Having come to them out of necessity (if my claim is correct) Descartes comes close to embracing them in his theory of science as acceptable modes of reasoning. The first hint of this is in Principles III. 44, where Descartes remarks:

Even if this the hypothesis be thought to be false, I shall think my achievement is sufficiently worth while if all inferences from it agree with observation; for in that case we shall get as much practical benefit from it as we should from the knowledge of the actual truth.

[AT 8(1):99; AG 224]

Descartes here seems to indicate that it is sufficient for a science to agree with the data of experiment. Truth (not to mention certain truth) seems not to matter.

This position is the one Descartes seems to adopt at the very end of the Principles. Descartes admits that, at best, what he has provided is an account of things that agrees with experiment and observation, but which may not give us truth. But, he claims, this is his only goal:

I believe that I have done all that is required of me if the causes I have assigned are such that they correspond to all the phenomena manifested by nature. And it will be sufficient for the usages of life to know such causes, for medicine and mechanics and in general all these arts to which the knowledge of physics subserves, have for their end only those effects which are sensible and which are accordingly to be reckoned among the phenomena of nature.

[IV. 204: AT 8(1):327; HR 1:300. Emphasis added.]

In the course of claiming that all he seeks is an explanation that agrees with the phenomena, Descartes admits that such an account is less than absolutely certain. To put it another way, Descartes admits that this way of proceeding, which he was forced to adopt, yields not true knowledge, or true certainty, but only moral certainty:

That nevertheless there is a moral certainty that everything is such as I have shown it to be.

In fairness to the truth, however, it must be borne in mind that some things are considered as morally certain—certain for all practical purposes—although they are uncertain if we take into account God's absolute power…. They who observe how many things regarding the magnet, fire, and the fabric of the whole world are deduced from so few principles even if they thought my assumption of those principles haphazard and groundless, would admit that so many things could hardly cohere if they were false.

[IV. 205: AT 8(1):327–28; HR 1:301. Emphasis added.]

So, Descartes claims, the results established in the Principles, at least as regards the sensible world, are established with moral certainty. But it should be quite evident that moral certainty is just a species of probability. And this, he argues, is quite sufficient and "all that is required" of him.³⁹

The progression in Descartes's thought from the Regulae, through the Discourse and contemporary writings, ending up in the Principles, is quite remarkable. In the Regulae, Descartes is quite opposed to all use of probabilities in science, including the use of hypotheses or assumptions. All true scientific reasoning must be able to be formulated in terms of intuition and deduction. The attitude changes somewhat in the Discourse and other writings of the same period. There Descartes does make use of hypothetical and consequently nondeductive arguments. However, he consistently insists that such hypothetical arguments do not mean that he has abandoned the search for a deductive science. Rather, he claims to use such arguments as a matter of convenience, so as not to have to give the full argument in all of its deductive glory. He claims, at this point, to be able to give full deductive arguments for everything that he presents hypothetically. But in the Principles, it turns out not to be possible to give the full deductions, though he tries. Although he resists, he finds that he must make use of hypotheses, and in the end, seems finally to give up hope of a certain science grounded in intuition and deduction. In the end the practical difficulties of building a science from intuition and deduction force an important change in his very conception of science: scientific knowledge has become probable knowledge, it seems.

Although I say that in the end, Descartes gave up his earlier program and was willing to make do with moral certainty and probability, this is probably too strong a statement. Though in the passages I quoted from the end of the Principles Descartes does give this impression, it is also clear that he is not at all comfortable with this position. Before ending the Principles, in the penultimate section he says:

That we possess even more than a moral certainty.

Moreover there are certain things even among natural objects that we judge to be absolutely and mathematical demonstrations, the knowledge that material objects exist, and all evident reasonings about them. And with these my own assertions may perhaps find a place when it is considered how they have been deduced in an unbroken chain from the simplest primary principles of human knowledge. And the more so if it is sufficiently realized that we can have no sensation of external objects unless they excite some local motion in our nerves, and that the fixed stars, being a vast distance from us, can excite no such motion unless there is also some motion taking place in them and in the whole of the intermediate heavens; for once these facts are admitted, then, at least as regards the general account I have given of the world and the Earth, an alternative to the rest of my explanation appears inconceivable.

[IV. 206: AT 8(1):328–29; HR 1:301–2]

So, having admitted that probability is all we can have, Descartes makes one last attempt at saving his old program for certainty in science.

Descartes's extreme reluctance to give up his deductive program is also manifest in the introduction he wrote for Abbé Picot's French translation of the Principles in 1647, fully three years after the original Latin edition. There Descartes talks quite emphatically about how the proper method in science is to "seek out the first causes and the true principles from which reasons may be deduced for all that we are capable of knowing"⁴⁰ This apparent forgetfulness of the difficulties encountered in Principles III shows just how tentative Descartes's rejection of deductivism at the end of the Principles was, and how uncomfortable he was with that conclusion.

Although Descartes is forced to admit, however unwillingly and tentatively, that natural science cannot be deductive and certain, it is only later in the history of philosophy that deductivism is decisively rejected and natural science is unambiguously associated with the probable. This stop occurs in a philosopher usually counted among Descartes's contraries, but who is in some ways the direct successor to his enterprise, John Locke.⁴¹ For Locke, knowledge is not the only product of the rational faculties. Unlike Descartes, he takes the notion of probability to be an important one for epistemology.⁴² Knowledge for Locke is very close to Descartes's conception of certainty, in that the primary ways of attaining knowledge are intuition and deduction.⁴³ But Locke is aware of the narrow extent to which we have genuine scientific knowledge of material things in the world.⁴⁴ This conclusion has caused many to consider Locke a skeptic. But Locke's conclusion is not that we must despair with respect to scientific knowledge, but that where there is no certainty or true knowledge, we must make do with probability. In natural science this means that we must make do with experiment, and whatever can be inferred from experiment by a basically hypothetico-deductive reasoning.⁴⁵ It was, then, Locke who took the final step in the retreat from the certainty and deductivism of the Regulae. But it was a step that Descartes prepared in his Principles.

Notes

¹ The traditional view is too widespread to require citation. On the latter view, see e.g., A. Gewirth, "Experience and the Non-Mathematical in the Cartesian Method," Journal of the History of Ideas 2 (1941):183–210; R. M. Blake, "The Role of Experience in Descartes' Theory of Method," in E. H. Madden, ed., Theories of Scientific Method (Seattle, 1960); L. J. Beck, The Method of Descartes (Oxford, 1952); G. Buchdahl, Metaphysics and the Philosophy of Science (Cambridge, Mass., 1969); A. C. Crombie, "Some Aspects of Descartes' Attitude to Hypothesis and Experiment," Collection des Travaux de l'Academie International d'Histoire des Sciences 11 (1960):192–201; and the introduction in Discourse on Method, Optics, Geometry, and Meteorology trans. P. J. Olscamp (Indianapolis, 1965).

² Throughout I have given a reference to an English translation of the passage, when possible to HR [René Descartes; The Philosophical Works of Descartes; trans. Elizabeth S. Haldane and G. R. T. Ross; Cambridge: Cambridge University Press, 1911–12; reprinted, with corrections, 1931; reprinted New York: Dover, 1955]. The translations used in the text, though, usually come from other sources, since there are many inaccuracies in HR, particularly in the Regulae. I have consulted: AG [Descartes, Philosophical Writings, trans. and ed. Elizabeth Anscombe and Peter Thomas Geach, London: Nelson, 1954]; CB [Descartes, Descartes' Conversation with Burman, trans. and ed. John Cottingham, Oxford: Clarendon Press, 1976]; K [Descartes, Philosophical Letters, trans. and ed. Anthony Kenny, Oxford: Clarendon Press, 1970]; Rules for the Direction of the Mind (Indianapolis: 1961), and Discourse on Method and Meditations (Indianapolis: 1960) both translated by L. J. Lafleur; Discourse, trans. Olscamp. When no translation is available in HR, I will refer to the otherwise most available translation.

³ See Gewirth, "Experience in the Cartesian Method"; Blake, "Role of Experience"; Buchdahl, Metaphysics; and Beck, Method of Descartes.

⁴ Emphasis added. See also AT 10:366, 368 (the text here is disputed), 370, 400; HR 1:5, 7, 8, 28.

⁵ Cf. Regulae, Rule VI: AT 10:381–83; HR 1:15–16.

⁶ Emphasis added. See also AT 10:440; HR 1:55.

⁷ Alternatively, a deduction may be a proposition arrived at through such a succession of intuitively made inferential leaps. Descartes recognizes the ambiguity in his use. See Regulae, Rule XI: AT 10:407–8; HR 1:33.

⁸ See Regulae: AT 10:368, 401, 416, 418, 425, 427; HR 1:7, 28, 39, 41, 45, 46.

⁹ For a rare exception, see the letter to Regius, 24 May 1640: AT 3:64–65; K 73–74.

¹⁰ Presenting the criterion of certainty in this way leaves out the problems of validation and atheistic science discussed in the letter cited in note 9.

¹¹ Emphasis added. Cf. AT 5:177; CB 48–49.

¹² See, e.g., Aristotle, Topics, 100^a18–21 and 100^b21–23, and the various Latin translations in Aristoteles Latinus, ed. L. Minio-Paluello, 5:1–3 (Leiden, 1969) for the use of the world probabilis.

¹³ See I. Hacking, The Emergence of Probability (Cambridge: 1975), ch. 3. Hacking's account is not entirely accurate in that it emphasizes the use of this archaic notion of probability and ignores quite definite instances of distinctly modern probability concepts in antiquity and the Middle Ages.

¹⁴ Cf. Regulae: AT 10:367; HR 1:6; and Discourse: AT 6:6, 8, 16, 69, 71; HR 1:84, 85–86, 91, 124, 125. For studies of the rhetorical-dialectical tradition of education in the 16th century see W. S. Howell, Logic and Rhetoric in England, 1500–1700 (Princeton, 1956); N. W. Gilbert, Renaissance Concepts of Method (New York, 1960); and W. J. Ong, Ramus, Method, and the Decay of Dialectic (Cambridge, Mass., 1958).

¹⁵ See also AT 10:424 and HR 1:44–45. There is some dispute about this last text.

¹⁶ There are at least two places in the Regulae where Descartes uses hypotheses. Cf. Regulae, Rule XII: AT 10:412, 417; HR 1:36, 40. Nothing Descartes says here throws light on the epistemic status of hypotheses.

¹⁷ Precisely what Descartes included here and what he meant to include among the "particulars" of C is not entirely clear. But this will not be an issue.

¹⁸ Cf. Discourse, part V: AT 6:45; HR 1:109.

¹⁹ Cf., e.g., introduction in Discourse, trans. Olscamp; Buchdahl, Metaphysics; and J. Morris, "Descartes and Probable Knowledge," Journal of the History of Philosophy 8 (1970):303–12.

²⁰ Cf. Optics, discourse I: AT 6:83–88; trans. Olscamp, 67–70; and Meteorology, discourse I: AT 6:233–35; trans. Olscamp, 264–65.

²¹ Cf. P. Duhem, To Save the Phenomena (Chicago, 1969). Duhem has a definite philosophical ax to grind, but he has presented a very accurate and useful catalogue of historical citations on the question.

²² See ibid., pp. 61–65, 96–97, 100–104, 108–9.

²³Discourse, part VI: AT 6:76; HR 1:128–29. What precisely Descartes means by "prove" and "explain" in this text are interesting questions, but ones that I shall not enter into.

²⁴ See AT 2:141–44, 197–99; K 55–56, 57–58.

²⁵ Emphasis added. See also AT 2:196–200; K 57–59; and AT 3:39; K 70–71.

²⁶ Emphasis added. Cf. AT 2:200; K 59; and AT 3:39; K 71.

²⁷ The only passage I know of that is at all difficult to reconcile with this reading is from a letter to Mersenne, 17 May 1638: AT 2:141–44; K 55–56. Read in the context of the other passages cited, though, this letter does not raise any serious problems for my view.

²⁸ This is a curious thing for Descartes to say, though, given that he thinks that Harvey's theory is inconsistent with the basic principles of his physics.

²⁹ The difficulty of enumerating possible explanations may not be insuperable, since, given the first principles Descartes is working with, there may be a rather limited set of possible explanations for any given phenomenon. This was pointed out to me by David Kolb.

³⁰ Cf. Discourse, part IV: AT 6:33–35; HR 1:102–3; and Meditation III: AT 7:40–45; HR 1:161–65. My schematic version is closer to the text of the Discourse.

³¹ Cf. Meditation VI: AT 2:79–80; HR 1:191.

³² Cf. Gewirth, "Experience in the Cartesian Method," part III.

³³ Contrast Regulae, Rule II: AT 10:365; HR 1:4–5, with Rule V: AT 10:380; HR 1:14–15.

³⁴ "Enumeration" in the Regulae seems to have a narrower meaning than later on. There, enumeration is characteristically the process of going through the steps of a deduction in order—cf. Rules VII and XI. However, elsewhere in the Regulae it seems to take on a broader meaning; see AT 10:390, 395, 404–5 and HR 1:21, 24, 31. Cf. also Gewirth, "Experience in the Cartesian Method," pp. 200–201, and Beck, Method of Descartes, pp. 126–33. In the Discourse it clearly has a broader meaning still.

³⁵ Cf. Regulae: AT 10:410, 427, 430–31, 434–35, 439; HR 1:35, 46–47, 49–50, 52, 54–55. The argument suggested in these passages is close to version B of the argument by enumeration. In Gewirth, "Experience in the Cartesian Method," pp. 198–99, a similar interpretation of these passages is suggested.

³⁶ See, e.g., AT 2:200; K 59.

³⁷ The claim that he seeks arguments from cause to effect suggests that it is not an argument by enumeration, a kind of argument from effect to cause like that of section C, that Descartes has in mind here, but a more straightforward sort of deduction as described in B. On the other hand, as I noted in section II, above, the argument by enumeration can be considered as a kind of argument from cause to effect.

³⁸ For Descartes's later remarks on this, see, e.g., AT 4:698; and AT 5:168–69; CB 36–37. In the latter passage, dating from 1648, Descartes tells Burman that he thinks that he could give an explanation (a deductive explanation?) consistent with Genesis and his first principles. However, he admits both that Genesis is difficult to interpret, and that he has not found a satisfactory account yet.

³⁹ This is not, by the way, the first time that the notion of moral certainty comes up in Descartes' writings. It is mentioned a few times in the Discourse, and in the correspondence—e.g., Discourse: AT 6:37, 56, 57; HR 1:104, 116. But it is not until the Principles that Descartes even suggests that moral certainty is sufficient in science.

⁴⁰ AT 9(2):5; HR 1:206. Cf. AT 9(2):2, 9–11, 12–13; HR 1:204, 208–9, 210. Note that his account of the role and necessity of experiment in scientific deduction accords perfectly with my account in section II, above. Cf. AT 9(2):20; HR 1:214.

⁴¹ I do not want to suggest that Locke is the only such figure; he is the most influential of those to follow Descartes, and the one responsible for breaking the influence of Cartesian deductivism. Other 17th-century figures did reject deductivism as well; see, e.g., Pierre Gassendi, Dissertations en forme de Pareadoxes con tre les Aristotéliciens (Exercitationes Paradoxicae Adversus Aristoteleos) trans. and ed. Bernard Ro-chot (Paris, 1959), liber secundus, exercitatio V.

⁴²Essay IV, ch. 1, 14, 15. All references to Locke are from An Essay Concerning Human Understanding, ed. P. H. Nidditch (Oxford, 1975). The references are given in such a way as to be locatable in any currently used edition.

⁴³ See Essay IV, ch. 2. Locke adds sensation to Descartes's account. But his conception of sensation makes it look like a species of Cartesian intuition. Essay IV, ch. 11.

⁴⁴ See Essay IV, ch. 3 (sect. 9–17, 25–26), 4 (sect. 11–12), 6 (sect. 10–15).

⁴⁵ Above, notes 42–44, Essay IV, ch. 16 (sect. 12).