René Descartes

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Edwin Arthur Burtt (essay date 1925)

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SOURCE: "Descartes," in The Metaphysical Foundations of Modern Physical Science: A Historical and Critical Essay, Kegan Paul, Trench, Trubner & Co., Ltd., 1925, pp. 96–116.

[In the following essay, Burtt examines Descartes' mathematical conception of nature and his motives for proposing a mind-body dualism.]

Descartes' importance in [the] mathematical movement [in science] was twofold; he worked out a comprehensive hypothesis in detail of the mathematical structure and operations of the material universe, with clearer consciousness of the important implications of the new method than had been shown by his predecessors; and he attempted both to justify and atone for the reading of man and his interests out of nature by his famous metaphysical dualism.

While still in his teens, Descartes became absorbed in mathematical study, gradually forsaking every other interest for it, and at the age of twenty-one was in command of all that was then known on the subject. During the next year or two we find him performing simple experiments in mechanics, hydrostatics, and optics, in the attempt to extend mathematical knowledge in these fields. He appears to have followed the more prominent achievements of Kepler and Galileo, though without being seriously affected by any of the details of their scientific philosophy. On the night of November 10th, 1619, he had a remarkable experience which confirmed the trend of his previous thinking and gave the inspiration and the guiding principle for his whole life-work.1 The experience can be compared only to the ecstatic illumination of the mystic; in it the Angel of Truth appeared to him and seemed to justify, through added supernatural insight, the conviction which had already been deepening in his mind, that mathematics was the sole key needed to unlock the secrets of nature. The vision was so vivid and compelling that Descartes in later years could refer to that precise date as the occasion of the great revelation that marked the decisive point in his career.

(A) Mathematics as the Key to Knowledge

The first intensive studies into which he plunged after this unique experience were in the field of geometry, where he was rewarded within a very few months by the signal invention of a new and most fruitful mathematical tool, analytical geometry. This great discovery not only confirmed his vision and spurred him on to further efforts in the same direction, but it was highly important for his physics generally. The existence and successful use of analytical geometry as a tool of mathematical exploitation presupposes an exact oneto-one correspondence between the realm of numbers, i.e., arithmetic and algebra, and the realm of geometry, i.e., space. That they had been related was, of course, a common possession of all mathematical science; that their relation was of this explicit and absolute correspondence was an intuition of Descartes. He perceived that the very nature of space or extension was such that its relations, however complicated, must always be expressible in algebraic formulae, and, conversely, that numerical truths (within certain powers) can be fully represented spatially. As one not unnatural result of this notable invention, the hope deepened in Descartes' mind that the whole realm of physics might be reducible to geometrical qualities alone. Whatever else the world of nature may be, it is obviously a geometrical world, its objects are extended and figured magnitudes in motion. If we can get rid of all other qualities, or reduce them to these, it is clear that mathematics must be the sole and adequate key to unlock the truths of nature. And it was not a violent leap from the wish to the thought.

During the following...

(This entire section contains 7069 words.)

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ten years, besides his numerous travels, Descartes was engaged in further mathematical studies, which were written down toward the end of this period, and he was also working out a series of specific rules for the application of his all-consuming idea. In these rules we find the conviction expressed that all the sciences form an organic unity,2 that all must be studied together and by a method that applies to all.3 This method must be that of mathematics, for all that we know in any science is the order and measurement revealed in its phenomena; now mathematics is just that universal science that deals with order and measurement generally.4 That is why arithmetic and geometry are the sciences in which sure and indubitable knowledge is possible. They "deal with an object so pure and uncomplicated that they need make no assumptions at all that experience renders uncertain, but wholly consist in the rational deduction of consequences."5 This does not mean that the objects of mathematics are imaginary entities without existence in the physical world.6 Whoever denies that objects of pure mathematics exist, must deny that anything geometrical exists, and can hardly maintain that our geometrical ideas have been abstracted from existing things. Of course, there are no substances which have length without breadth or breadth without thickness, because geometrical figures are not substances but boundaries of them. In order for our geometrical ideas to have been abstracted from the world of physical objects, granted that this is a tenable hypothesis, that world would have to be a geometrical world—one fundamental characteristic of it is extension in space. It may turn out that it possesses no characteristics not deducible from this.

Descartes is at pains carefully to illustrate his thesis that exact knowledge in any science is always mathematical knowledge. Every other kind of magnitude must be reduced to mathematical terms to be handled effectively; if it can be reduced to extended magnitude so much the better, because extension can be represented in the imagination as well as dealt with by the intellect. "Though one thing can be said to be more or less white than another, or a sound sharper or flatter, and so on, it is yet impossible to determine exactly whether the greater exceeds the less in the proportion two to one, or three to one, etc., unless we treat the quantity as being in a certain way analogous to the extension of a body possessing figure."7 Physics, as something different from mathematics, merely determines whether certain parts of mathematics are founded on anything real or not.8

What, now, is this mathematical method for Descartes in detail? Faced with a group of natural phenomena, how is the scientist to proceed? Descartes' answer early in the Rules is to distinguish two steps in the actual process, intuition and deduction. "By intuition I understand … the conception which an unclouded and attentive mind gives us so readily and distinctly that we are wholly freed from doubt about that which we understand."9 He illustrates this by citing certain fundamental propositions such as the fact that we exist and think, that a triangle is bounded by three lines only, etc. By deduction he means a chain of necessary inferences from facts intuitively known, the certitude of its conclusion being known by the intuitions and the memory of their necessary connexion in thought.10 As he proceeds further in the Rules, however, he realizes the inadequacy of this propositional method alone to yield a mathematical physics, and introduces the notion of simple natures, as discoveries of intuition in addition to these axiomatic propositions.11 By these simple natures he means such ultimate characteristics of physical objects as extension, figure, motion, which can be regarded as producing the phenomena by quantitative combinations of their units. He notes that figure, magnitude, and impenetrability seem to be necessarily involved in extension, hence the latter and motion appear to be the final and irreducible qualities of things. As he proceeds from this point he is on the verge of most far-reaching discoveries, but his failure to keep his thought from wandering, and his inability to work out the exceedingly pregnant suggestions that occur to him make them barren for both his own later accomplishments and those of science in general. Bodies are extended things in various kinds of motion. We want to treat them mathematically. We intuit these simple natures in terms of which mathematical deductions can be made. Can we formulate this process more exactly, with special reference to the fact that these simple natures must make extension and motion mathematically reducible? Descartes tries to do so, but at the crucial points his thought wanders, and as a consequence Cartesian physics had to be supplanted by that of the Galileo-Newton tradition. What are those features of extension, he asks, that can aid us in setting out mathematical differences in phenomena? Three he offers, dimension, unity, and figure. The development of this analysis is not clear12, but apparently a consistent solution of his idea would be that unity is that feature of things which enables simple arithmetic or geometry to gain a foothold in them, figure that which concerns the order of their parts, while dimension is any feature which it is necessary to add in order that no part of the facts shall have escaped mathematical reduction. "By dimension I understand not precisely the mode and aspect according to which a subject is considered to be measurable. Thus it is not merely the case that length, breadth, and depth are dimensions, but weight also is a dimension in terms of which the heaviness of objects is estimated. So, too, velocity is a dimension of motion, and there are an infinite number of similar instances." This conception of weight, velocity, etc., as further mathematical dimensions akin to length, breadth, and depth, except that they are dimensions of motion rather than of extension, harboured enormous possibilities which were entirely unrealized either in Descartes or in the work of later scientists. Had he succeeded in carrying the thought through, we might to-day think of mass and force as mathematical dimensions rather than physical concepts, and the current distinction between mathematics and the physical sciences might never have been made. It might be taken for granted that all exact science is mathematical—that science as a whole is simply a larger mathematics, new concepts being added from time to time in terms of which more qualities of the phenomena become mathematically reducible. In this sense he might have converted the world to his doctrine at the end of the second book of the Principles13, that all the phenomena of nature may be explained by the principles of mathematics and sure demonstrations given of them. There are passages in his later works in which he still seems to be thinking of weight as a dimension of motion. He criticizes Democritus for asserting gravity to be an essential characteristic of bodies, "the existence of which I deny in any body in so far as it is considered by itself, because this is a quality depending on the relationship in respect of situation and motion which bodies bear to one another."14 In general, however, he tended to forget this significant suggestion, and we find him denying weight as a part of the essence of matter because we regard fire as matter in spite of the fact that it appears to have no weight.15 It has apparently slipped his mind that he once conceived of such differences as themselves mathematical.

The fact is, Descartes was a soaring speculator as well as a mathematical philosopher, and a comprehensive conception of the astronomico-physical world was now deepening in his mind, in terms of which he found it easy to make a rather brusque disposal of these qualities which Galileo was trying to reduce to exact mathematical treatment, but which could not be so reduced in terms of extension alone. This scheme was in effect to saddle such qualities upon an unoffending ether, or first matter, as Descartes usually calls it, thereby making it possible to view the bodies carried about in this ether as possessing no features not deducible from extension. Descartes' famous vortex theory was the final product of this vigorous, all-embracing speculation. Just how did he reach it?

(B) Geometrical Conception of the Physical Universe

We have noted the biographical reasons for Descartes' hope that it would be possible to work out a physics which required no principles for its completion beyond those of pure mathematics; there were also certain logical prejudices operating, such as that nothing cannot possess extension, but wherever there is extension there must be some substance.16 Furthermore, as for motion, Descartes had been able to account for it in a manner which fairly satisfied him; God set the extended things in motion in the beginning, and maintained the same quantity of motion in the universe by his 'general concourse,'17 which, confirmed by more immediately conceived distinct ideas, meant that motion was just as natural to a body as rest, i.e., the first law of motion. Since the creation then, the world of extended bodies has been nothing but a vast machine. There is no spontaneity at any point; all continues to move in fixed accordance with the principles of extension and motion. This meant that the universe is to be conceived as an extended plenum, the motions of whose several parts are communicated to each other by immediate impact. There is no need of calling in the force or attraction of Galileo to account for specific kinds of motion, still less the 'active powers' of Kepler; all happens in accordance with the regularity, precision, inevitability, of a smoothly running machine.

How could the facts of astronomy and of terrestrial gravitation be accounted for in a way which would not do havoc with this beautifully simple hypothesis? Only by regarding the objects of our study as swimming helplessly in an infinite ether, or 'first matter,' to use Descartes' own term, which, being vaguely and not at all mathematically conceived, Descartes was able to picture as taking on forms of motion that rendered the phenomena explicable. This primary matter, forced into a certain quantity of motion divinely bestowed, falls into a series of whirlpools or vortices, in which the visible bodies such as planets and terrestrial objects are carried around or impelled toward certain central points by the laws of vortical motion. Hence the bodies thus carried can be conceived as purely mathematical; they possess no qualities but those deducible from extension and free mobility in the surrounding medium. Verbally, to be sure, Descartes made the same claim for the first matter itself, but it was the world of physical bodies that he was eager to explain, hence in terms of this hypothesis he imagined himself to have realized the great ambition of his life in the achievement of a thoroughly geometrical physics. What he did not appreciate was that this speculative success was bought at the expense of loading upon the primary medium those characteristics which express themselves in gravitation and other variations of velocity—the characteristics in a word which Galileo was endeavouring to express mathematically, and which Descartes himself in his more exact mathematical mood had conceived as dimensions. This procedure did not at all drive them out of the extended realm but merely hid under cover of vague and general terms the problem of their precise mathematical treatment. To solve that problem, Descartes' work had to be reversed, and the Galilean concepts of force, acceleration, momentum, and the like, reinvoked.

The unfortunate feature of the situation at this time was that thinkers were accepting the notion that motion was a mathematical concept, the object of purely geometrical study, whereas with the single exception of Galileo, they had not come to think of it seriously and consistently as exactly reducible to mathematical formulae. Galileo had caught this remarkable vision, that there is absolutely nothing in the motion of a physical body which cannot be expressed in mathematical terms, but he had discovered that this can be done only by attributing to bodies certain ultimate qualities beyond the merely geometrical ones, in terms of which this full mathematical handling of their motions can take place. Descartes realized well enough the facts that underlie this necessity—that bodies geometrically equivalent move differently when placed in the same position relative to the same neighbouring bodies—but thinking of motion as a mathematical conception in general and not having caught the full ideal of its exact reduction in a way comparable to his treatment of extension, he failed to work out to a clear issue his earlier suggestion of weight and velocity as dimensions, and turned instead to the highly speculative vortex theory, which concealed the causes of these variations in the vague, invisible medium, and thereby saved the purely geometrical character of the visible bodies.

The vortex theory was, none the less, a most significant achievement historically. It was the first comprehensive attempt to picture the whole external world in a way fundamentally different from the Platonic-Aristotelian-Christian view which, centrally a teleological and spiritual conception of the processes of nature, had controlled men's thinking for a millenium and a half. God had created the world of physical existence, for the purpose that in man, the highest natural end, the whole process might find its way back to God. Now God is relegated to the position of first cause of motion, the happenings of the universe then continuing in æternum as incidents in the regular revolutions of a great mathematical machine. Galileo's daring conception is carried out in fuller detail. The world is pictured concretely as material rather than spiritual, as mechanical rather than teleological. The stage is set for the likening of it, in Boyle, Locke, and Leibniz, to a big clock once wound up by the Creator, and since kept in orderly motion by nothing more than his 'general concourse.'

The theory had an important practical value for Descartes as well. In 1633 he had been on the point of publishing his earliest mechanical treatises, but had been frightened by the persecution of Galileo for his advocacy of the motion of the earth in the Dialogues on the Two Great Systems, just published. As the impact motion and vortex theory developed in his mind, however, he perceived that place and motion must be regarded as entirely relative conceptions, a doctrine which might also save him in the eyes of the Church. As regards place he had already reached this conviction, defining it in the Rules as "a certain relation of the thing said to be in the place toward the parts of the space external to it."18 This position was reaffirmed more strongly still in the Analytical Geometry and the Dioptrics, where he states categorically that there is no absolute place, but only relative; place only remains fixed so long as it is defined by our thought or expressed mathematically in terms of a system of arbitrarily chosen co-ordinates19. The full consequence of this for a true definition of motion is brought out in the Principles, in which, after noting the vulgar conception of motion as the "action by which any body passes from one place to another,"20 he proceeds to "the truth of the matter," which is that motion is "the transference of one part of matter or one body from the vicinity of those bodies that are in immediate contact with it, and which we regard as in repose, into the vicinity of others."21 Inasmuch as we can regard any part of matter as in repose that is convenient for the purpose, motion, like place, becomes wholly relative. The immediate practical value of the doctrine was that the earth, being at rest in the surrounding ether, could be said in accordance with this definition to be unmoved, though it, together with the whole vortical medium, must be likewise said to move round the sun. Was this clever Frenchman not justified in remarking that "I deny the movement of the earth more carefully than Copernicus, and more truthfully than Tycho?"22

Now during these years in which Descartes was developing the details of his vortex theory and the idea of the extended world as a universal machine, he was occupying himself with still more ultimate metaphysical problems. The conviction that his mathematical physics had its complete counterpart in the structure of nature was being continually confirmed pragmatically, but Descartes was not satisfied with such empirical probabilism. He was eager to get an absolute guarantee that his clear and distinct mathematical ideas must be eternally true of the physical world, and he perceived that a new method would be required to solve this ultimate difficulty. A sense of the genuineness and fundamental character of this problem appears definitely in his correspondence early in 1629, and in a letter23 to Mersenne, April 15, 1630, we learn that he has satisfactorily (to himself) solved it by conceiving the mathematical laws of nature as established by God, the eternal invariableness of whose will is deducible from his perfection. The details of this metaphysic are presented in the Discourse, the Meditations, and the Principles, where it is reached through the method of universal doubt, the famous 'cogito ergo sum,' and the causal and ontological proofs of the existence and perfection of God. As regards the subjection of his mental furniture to the method of universal doubt, he had decided ten years earlier, as he tells us in the Discourse, to make the attempt as soon as he should be adequately prepared for it; now, however, the main motive that impels him to carry it through is no mere general distrust of his own early beliefs, but a consuming need to get a solution for this specific problem. We shall not follow him through these intricacies, but concentrate our attention upon one famous aspect of his metaphysics, the dualism of two ultimate and mutually independent entities, the res extensa and the res cogitans.

(C) 'Res extensa' and 'res cogitans'

In Galileo the union of the mathematical view of nature and the principle of sensible experimentalism had left the status of the senses somewhat ambiguous. It is the sensible world that our philosophy attempts to explain and by the use of the senses our results are to be verified; at the same time when we complete our philosophy we find ourselves forced to view the real world as possessed of none but primary or mathematical characteristics, the secondary or unreal qualities being due to the deceitfulness of the senses. Furthermore, in certain cases (as the motion of the earth) the immediate testimony of the senses must be wholly renounced as false, the correct answer being reached by reasoned demonstrations. Just what is, then, the status of the senses, and how are we specifically to dispose of these secondary qualities which are shoved aside as due to the illusiveness of sense? Descartes attempts to answer these questions by renouncing empiricism as a method and by providing a haven for the secondary qualities in an equally real though less important entity, the thinking substance.

For Descartes it is, to be sure, the sensible world about which our philosophizing goes on24, but the method of correct procedure in philosophy must not rest upon the trustworthiness of sense experience at all. "In truth we perceive no object such as it is by sense alone (but only by our reason exercised upon sensible objects)."25 "In things regarding which there is no revelation, it is by no means consistent with the character of a philosopher … to trust more to the senses, in other words to the inconsiderate judgments of childhood, than to the dictates of mature reason."26 We are to seek the "certain principles of material things … not by the prejudices of the senses, but by the light of reason, and which thus possess so great evidence that we cannot doubt of their truth."27 Sensations are called 'confused thoughts,'28 and therefore sense, as also memory and imagination which depend on it, can only be used as aids to the understanding in certain specific and limited ways; sensible experiments can decide between alternative deductions from the clearly conceived first principles; memory and imagination can represent extended corporeality before the mind as a help to the latter's clear conception of it29. It is not even necessary, as a basis for a valid philosophy, that we always have the sensible experience to proceed from; reasoning cannot of course alone suffice to give a blind man true ideas of colours, but if a man has once perceived the primary colours without the intermediate tints, it is possible for him to construct the images of the latter30.

Our method of philosophical discovery, then, is distinctly rational and conceptual; the sensible world is a vague and confused something, a quo philosophy proceeds to the achievement of truth. Why, now, are we sure that the primary, geometrical qualities inhere in objects as they really are, while the secondary qualities do not? How is it that "all other things we conceive to be compounded out of figure, extension, motion, etc., which we cognize so clearly and distinctly that they cannot be analysed by the mind into others more distinctly known?"31 Descartes' own justification for this claim is that these qualities are more permanent than the others. In the case of the piece of wax, which he used for illustrative purposes in the second Meditation, no qualities remained constant but those of extension, flexibility, and mobility, which as he observes, is a fact perceived by the understanding, not by the sense or imagination. Now flexibility is not a property of all bodies, hence extension and mobility alone are left as the constant qualities of all bodies as such; they can by no means be done away with while the bodies still remain. But, we might ask, are not colour and resistance equally constant properties of bodies? Objects change in colour, to be sure, and there are varying degrees of resistance, but does one meet bodies totally without colour or resistance? The fact is and this is of central importance for our whole study, Descartes' real criterion is not permanence but the possibility of mathematical handling; in his case, as with Galileo, the whole course of his thought from his adolescent studies on had inured him to the notion that we know objects only in mathematical terms, and the sole type for him of clear and distinct ideas had come to be mathematical ideas, with the addition of certain logical propositions into which he had been led by the need of a firmer metaphysical basis for his achievements, such as the propositions that we exist, that we think, etc. Hence the secondary qualities, when considered as belonging to the objects, like the primary, inevitably appear to his mind obscure and confused32; they are not a clear field for mathematical operations. This point cannot be stressed too strongly, though we shall not pause over it now.

But now the addition of such logical propositions as the above to the mathematical definitions and axioms as illustrations of clear and distinct ideas, is quite important. It occurs as early as the Rules, and shows already the beginnings of his metaphysical dualism. No mathematical object is a more cogent item of knowledge than the 'cogito ergo sum'; we can turn our attention inward, and abstracting from the whole extended world, note with absolute assurance the existence of a totally different kind of entity, a thinking substance. Whatever may be the final truth about the realm of geometrical bodies, still we know that we doubt, we conceive, we affirm, we will, we imagine, we feel. Hence when Descartes directed his energies toward the construction of a complete metaphysic, this cleancut dualism was inescapable. On the one hand there is the world of bodies, whose essence is extension; each body is a part of space, a limited spatial magnitude, different from other bodies only by different modes of extension—a geometrical world—knowable only and knowable fully in terms of pure mathematics. The vortex theory provided an easy disposal of the troublesome questions of weight, velocity, and the like; the whole spatial world becomes a vast machine, including even the movements of animal bodies and those processes in human physiology which are independent of conscious attention. This world has no dependence on thought whatever, its whole machinery would continue to exist and operate if there were no human beings in existence at all33. On the other hand, there is the inner realm whose essence is thinking, whose modes are such subsidiary processes34 as perception, willing, feeling, imagining, etc., a realm which is not extended, and is in turn independent of the other, at least as regards our adequate knowledge of it. But Descartes is not much interested in the res cogitans, his descriptions of it are brief, and, as if to make the rejection of teleology in the new movement complete, he does not even appeal to final causes to account for what goes on in the realm of mind. Everything there is a mode of the thinking substance.

In which realm, then, shall we place the secondary qualities? The answer given is inevitable. We can conceive the primary qualities to exist in bodies as they really are; not so the secondary. "In truth they can be representative of nothing that exists out of our mind."35 They are, to be sure, caused by the various effects on our organs of the motions of the small insensible parts of the bodies36. We cannot conceive how such motions could give rise to secondary qualities in the bodies; we can only attribute to the bodies themselves a disposition of motions, such that, brought into relation with the senses, the secondary qualities are produced. That the results are totally different from the causes need not give us pause:

The motion merely of a sword cutting a part of our skin causes pain (but does not on that account make us aware of the motion or figure of the sword). And it is certain that this sensation of pain is not less different from the motion that causes it, or from that of the part of our body that the sword cuts, than are the sensations we have of colour, sound, odour, or taste.37

Hence all qualities whatever but the primary can be lumped together and assigned to the second member of the metaphysical wedding. We possess a clear and distinct knowledge of pain, colour, and other things of this sort, when we consider them simply as sensations or thoughts; but

… when they are judged to be certain things subsisting beyond our minds, we are wholly unable to form any conception of them. Indeed, when any one tells us that he sees colour in a body or feels pain in one of his limbs, this is exactly the same as if he said that he there saw or felt something of the nature of which he was entirely ignorant, or that he did not know what he saw or felt.38

We can easily conceive, how the motion of one body can be caused by that of another, and diversified by the size, figure, and situation of its parts, but we are wholly unable to conceive how these same things (size, figure, and motion), can produce something else of a nature entirely different from themselves, as, for example, those substantial forms and real qualities which many philosophers suppose to be in bodies …39

But since we know, from the nature of our soul, that the diverse motions of body are sufficient to produce in it all the sensations which it has, and since we learn from experience that several of its sensations are in reality caused by such motions, while we do not discover that anything besides these motions ever passes from the organs of the external senses to the brain, we have reason to conclude that we in no way likewise apprehend that in external objects which we call light, colour, smell, taste, sound, heat, or cold, and the other tactile qualities, or that which we call their substantial forms, unless as the various dispositions of these objects which have the power of moving our nerves in various ways….

Such, then, is Descartes' famous dualism—one world consisting of a huge, mathematical machine, extended in space; and another world consisting of unextended, thinking spirits. And whatever is not mathematical or depends at all on the activity of thinking substance, especially the so-called secondary qualities, belongs with the latter.

(D) Problem of Mind and Body

But the Cartesian answer raises an enormous problem, how to account for the interrelation of these diverse entities. If each of the two substances exists in absolute independence of the other, how do motions of extended things produce unextended sensations, and how is it that the clear conceptions or categories of unextended mind are valid of the res extensa? How is it that that which is unextended can know, and, knowing, achieve purposes in, an extended universe? Descartes' least objectionable answer to these difficulties is the same answer that Galileo made to a similar though not so clearly formulated problem—the appeal to God. God has made the world of matter such that the pure mathematical concepts intuited by mind are forever applicable to it. This was the answer that the later Cartesians attempted to work out in satisfactory and consistent form. The appeal to God was, however, already beginning to lose caste among the scientific-minded; the positivism of the new movement was above everything else a declaration of independence of theology, specifically of final causality, which seemed to be a mere blanket appeal to a king of answer to scientific questions as would make genuine science impossible. It was an answer to the ultimate why, not to the present how. Descartes himself had been a powerful figure in just this feature of the new movement. He had categorically declared it impossible for us to know God's purposes.40 Hence this answer had little weight among any but his metaphysically-minded followers, whose influence lay quite outside the main current of the times; and those passages in which he appeared to offer a more immediate and scientific answer to these overwhelming difficulties, especially when capitalized by such a vigorous thinker as Hobbes, were the ones which proved significant. In these passages Descartes appeared to teach that the obvious relationships between the two entities of the dualism implied after all the real localization of mind, but it was of the utmost importance for the whole subsequent development of science and philosophy that the place thus reluctantly admitted to the mind was pitifully meagre, never exceeding a varying portion of the body with which it is allied. Descartes never forswore the main philosophical approach which had led to his outspoken dualism. All the non-geometrical properties are to be shorn from res extensa and located in the mind. He asserts in words that the latter "has no relation to extension, nor dimensions,"41 we cannot "conceive of the space it occupies"; yet, and these were the influential passages, it is "really joined to the whole body and we cannot say that it exists in any one of its parts to the exclusion of the others"; we can affirm that it "exercises its functions" more particularly in the conarion, "from whence it radiates forth through all the remainder of the body by means of the animal spirits, nerves, and even the blood." With such statements to turn to in the great philosopher of the new age, is it any wonder that the common run of intelligent people who were falling into line with the scientific current, unmetaphysically minded at best, totally unable to appreciate sympathetically the notion of a non-spatial entity quite independent of the extended world, partly because such an entity was quite unrepresentable to the imagination, partly because of the obvious difficulties involved, and partly because of the powerful influence of Hobbes, came to think of the mind as something located and wholly confined within the body? What Descartes had meant was that through a part of the brain a quite unextended substance came into effective relation with the realm of extension. The net result of his attempts on this point for the positive scientific current of thought was that the mind existed in a ventricle of the brain. The universe of matter, conceived as thoroughly geometrical save as to the vagueness of the 'first matter,' extends infinitely throughout all space, needing nothing for its continued and independent existence; the universe of mind, including all experienced qualities that are not mathematically reducible, comes to be pictured as locked up behind the confused and deceitful media of the senses, away from this independent extended realm, in a petty and insignificant series of locations inside of human bodies. This is, of course, the position which had been generally accorded the 'soul' in ancient times, but not at all the 'mind,' except in the case of those philosophers of the sensationalist schools who made no essential distinction between the two.

Of course, the problem of knowledge was not solved by this interpretation of the Cartesian position, but rather tremendously accentuated. How is it possible for such a mind to know anything about such a world? We shall postpone for the present, however, considerations of this sort; all the men with whom we are immediately occupied either failed to see this enormous problem, or else evaded it with the easy theological answer.

Note, however, the tremendous contrast between this view of man and his place in the universe, and that of the medieval tradition. The scholastic scientist looked out upon the world of nature and it appeared to him a quite sociable and human world. It was finite in extent. It was made to serve his needs. It was clearly and fully intelligible, being immediately present to the rational powers of his mind; it was composed fundamentally of, and was intelligible through, those qualities which were most vivid and intense in his own immediate experience—colour, sound, beauty, joy, heat, cold, fragrance, and its plasticity to purpose and ideal. Now the world is an infinite and monotonous mathematical machine. Not only is his high place in a cosmic teleology lost, but all these things which were the very substance of the physical world to the scholastic—the things that made it alive and lovely and spiritual—are lumped together and crowded into the small fluctuating and temporary positions of extension which we call human nervous and circulatory systems. The metaphysically constructive features of the dualism tended to be lost quite out of sight. It was simply an incalculable change in the viewpoint of the world held by intelligent opinion in Europe.


1 An admirable account of this event in the light of the available sources, with critical comments on the views of other Cartesian authorities, is given in Milhaud, Descartes savant, Paris, 1922, p. 47, ff.

2The Philosophical Works of Descartes, Haldane and Ross translation, Cambridge, 1911. Vol. I, p. 1, ff., 9.

3 Vol. I, p. 306.

4 Vol. I, p. 13.

5 Vol. I, p. 4, ff.

6 Vol. II, p. 227.

7 Vol. I, 56.

8 Vol. I, 62.

9 Vol. I, 7.

10 Vol. I, 8, 45.

11 Vol. I, 42, ff.

12 Vol. I, 61, ff.

13Principles of Philosophy, Part II, Principle 64.

14Principles, Part IV, Principle 202.

15Principles, Part II, Principle 11.

16Principles, Part II Principles 8, 16.

17Principles, Part II, Principle 36.

18Philosophical Works, Vol. I, p. 51.

19 Cf. Dioptrics, Discourse 6 (Oeuvres Cousin ed., Vol. V, p. 54, ff.).

20 Part II, Principle 24.

21 Part II, Principle 25.

22Principles, Part III, Principles 19–31.

23Oeuvres (Cousin ed.) VI, 108, ff. Cf. an interesting treatment of this stage in Descartes biography in Liard, Descartes, Paris, 1911, p. 93, ff.

24Philosophical Works, Vol. I. p. 15.

25Principles, Part I, Principle 73.

26Principles, Part I. Principle 76. Cf. also Part II, Principles 37, 20.

27Principles, Part III, Principle I.

28Principles, Part IV, Principle 197.

29Philosophical Works, Vol. I, p. 35, 39, ff. Discourse, Part V.

30 Vol. I, p. 54.

31 Vol. I, p. 41.

32Philosophical Works, Vol. I, p. 164, ff.

33Oeuvres, Cousin ed., Paris, 1824, ff., Vol. X, p. 194.

34 In his Traité de l'homme Descartes had asserted that these subsidiary processes can be performed by the body without the soul, the sole function of the latter being to think. Cf. Oeuvres, XI, pp. 201, 342: Discourse (Open Court ed.), p.59, ff.; Kahn, Metaphysics of the Supernatural, p. 10, ff. His mature view, however, as expressed in the Meditations and Principles, is as above stated. Cf., for example, Meditation 11.

35Principles, Part I, Principles 70, 71.

36Oeuvres (Cousin), Vol. IV, p. 235, ff.

37Principles, Part IV, Principle 197.

38Principles, Part I, Principles 68, ff.

39 Part IV, Principles 198, 199.

40Principles, Part III, Principle 2.

41Passions of the Soul, Articles 30, 31 (Philosophical Works, Vol. I, 345, ff.). Italics ours. In his later writings Descartes was much more guarded in his language. Cf. Oeuvres (Cousin ed.), X, 96, ff.

Daniel Garber (essay date 1978)

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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 Meteorologywithout 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:


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


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.


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, 100a18–21 and 100b21–23, 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).

Charles Larmore (essay date 1980)

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SOURCE: "Descartes' Empirical Epistemology," in Descartes: Philosophy, Mathematics and Physics, edited by Stephen Gaukroger, The Harvester Press, Sussex, 1980, pp. 6–22.

[In the essay that follows, Larmore contends that Descartes' epistemology uses experimentation within a framework of a priori principles to advance human knowledge.]

There is something close to a general consensus that Descartes initiated a search for incorrigible foundations of knowledge that deeply shaped modern philosophy and that we have now learned to reject or even ignore. Characteristic of the Cartesian search for certainty, as opposed for example to some tendencies in Greek thought, was that these foundations must be located in individual subjectivity, in our immediate awareness of our own mental states. It implied that unless we could show how our beliefs about the world could be legitimately inferred from this basis, they would have no more rightful claim to being knowledge than would our wildest fantasies.

All the different kinds of errors that lie at the heart of the foundationalist enterprise do not need rehearsing once again. More directly of interest is the fact that a number of philosophers have taken the demise of this enterprise to mean the end of epistemology itself. What else can epistemology be but the search for the incorrigible foundations of knowledge? If that is so, then epistemology indeed amounts only to a subject with a glorious past. But this is not the proper conclusion to draw. The rejected forms of epistemology proved barren because they restricted themselves to the search for incorrigible truths, untainted by the revisability of the empirical truths they were meant to support. To discard epistemology as a dead subject no longer of interest to living philosophy, for this reason alone, merely continues the original error of believing that the theory of knowledge must be kept pure of all dependence upon the empirical sciences.

There are two areas of inquiry whose pursuit would dissociate epistemology from the ideal of a prima philosophia. First of all, we can focus the theory of knowledge upon examples of scientific knowledge in order to formulate criteria of scientific rationality. However, if we are to escape the ideal of a pure epistemology, we must draw out these criteria in a dialectical way from the history of science. Crudely put, we must abstract the criteria from some theories in order both to evaluate other theories in terms of them and to test the criteria against other examples of theories. Otherwise we may find ourselves, as indeed has often been the case in the philosophy of science, stuck with criteria of scientific rationality that no scientific theory has ever met. Obviously, the problems facing this kind of empirical epistemology are immensely difficult. Secondly, we can allow the theory of knowledge to confront what scientific theories imply about the status of our perceptual and experiential image of nature and about the relation between nature and ourselves as knowers. Here the concerns of an empirical epistemology would not be as in the first case methodological, but instead substantive. They would focus upon how we are to understand human knowledge given what we know about the world.

If with these possibilities of an empirical epistemology in mind we look once again at Descartes' theory of knowledge, the traditional picture of Descartes as the founder of a priori epistemology begins to appear importantly incomplete. As I shall show in this essay, his search for an incorrigible foundation of empirical knowledge forms but one strand in his theory of knowledge. There are other epistemological problems for whose solution he deliberately resorted to the results of empirical inquiry. First, it might be recalled, in regard to the project of setting out criteria of scientific rationality, that he recommended his idea of scientific method because he had found it successful. However, I shall be concerned with the more substantive area of his empirical epistemology, especially as it grows out of his attempt at the mathematization of nature. In the light of these generally ignored aspects of Cartesian philosophy, we will no longer be able to foist upon Descartes the onus of having encouraged the idea that an a priori approach is all to which epistemology may aspire. Indeed, for the whole of the seventeenth century the theory of knowledge brought together both a priori and empirical perspectives. In Descartes, the relation between these strands is governed by a conception of method, whereas in Locke, for example, the character of their relation is far less clear. The origin of the idea that epistemology, as a philosophical discipline, must proceed independently of the sciences belongs to a later time. It arises both with Kantian transcendentalism and with the more recent wish to analyse 'the meaning of the concept of knowledge'. One aim of this essay is to indicate why we need a more complex picture of the origins of modern epistemology in the seventeenth century. But, more directly, the aspects of Descartes' empirical epistemology which I shall treat will be among those that can still interest us today.

It is chiefly in his physiological treatises, such as the Treatise on Man and the Dioptrics, that we come upon his empirical epistemology. But in order to understand why at a certain point Descartes let his epistemology become empirical, we will first have to look at his conception of scientific method (Part I). In Part II I shall examine the initial physical problem—the mathematization of nature—with which his empirical epistemology begins, then tracing in Part III the broad implications he drew from that for an understanding of the place of knowledge within the natural order.

Part I Descartes' Conception of Scientific Method

Recently it has become increasingly clear just how erroneous was the traditional view that Descartes thought of physical inquiry as a strictly a priori concern. We can find no better proof of the untenability of that view than to listen to what Descartes himself had to say in the Discourse on Method about the respective roles of the a priori and experience:

I have first tried to discover generally the principles or first causes of everything that is or that can be in the world, without considering anything that might accomplish this end but God Himself…. But I must also confess that the power of nature is so ample and vast, and these principles are so simple and general, that I observed hardly any particular effect as to which I could not at once recognize that it might be deduced from the principles in many different ways; and my greatest difficulty is usually to discover in which of these ways the effect does depend on them. As to that, I do not know any other plan but again to try to find experiments of such a nature that their result is not the same if it has to be explained by one of the methods, as it would be if explained by the other.1

Thus, according to Descartes, an account of the physical make-up of the world falls into two distinct parts: one we can develop a priori, while the other makes essential use of experience. The 'principles or first causes', that cover the most general features of the world, are something that we can attain without appeal to experience or experiment. In this passage Descartes was referring to what he believed he had already accomplished in his earlier treatise Le Monde. There, from God's immutability alone, he had derived the three fundamental laws of nature:

1 Every bit of matter continues in the same state until constrained to change by encountering some other object.

2 When one body alters the state of another, it cannot give it any movement which it itself does not lose at the same time.

3 Every body tends to continue to move in a straight line.2

The same claim, that the validity of these laws has an a priori basis in an understanding of what it means for there to be a God, reappears in the Discourse and in the Principles as well.3 These laws of nature can be said to be true a priori, of course, only because Descartes thought that he could prove the existence of such a God in a purely a priori fashion, and not by means of some natural theology. Both the causal and the ontological proof take as a premise that I do have a concept of something than which nothing greater can be conceived. That I do have the ideas that I believe I do, whatever may be their material truth, is a result guaranteed by the indubitability of the cogito. Thus, contrary to what has been sometimes suggested, the cogito does play an essential role in the foundation of physical science. It lies at the basis, Descartes believed, of the a priori deduction of the three fundamental laws of nature.

It is important to notice how this a priori part of Cartesian physics lies on a continuum with a priori epistemology. For Descartes, a priori epistemology does not issue simply in a prescription for the kinds of propositions that should serve as foundations (that, of course, is the role that more recent phenomenalist epistemologies have taken on). Instead, the cogito and the proofs of God's existence imply, so he believed, the fundamental principles of physical science themselves. This continuity between a priori epistemology and physics should be borne in mind when we come to consider the continuity between physical theory and Descartes' empirical epistemology. It will become clear that it is his conception of scientific method that orders the a priori and empirical parts of the theory of knowledge and the theory of nature into a single enterprise. Now this a priori physics cannot, as we have seen Descartes admit, yield a complete picture of the physical world. Only the most general features of the world can be ascertained through deduction from the self-evident first principles. For example, from the three fundamental laws of nature he thought he could deduce the laws of impact among bodies. In Principles III, art 46 there occurs a passage where Descartes lists some of the more particular phenomena that we can uncover only through empirical inquiry: the size of the parts into which matter is divided, the speed with which they move, and what circles their movements describe. Clearly, this range of empirical phenomena consists in the numerical values that in any particular case can be given to the variables occuring in the a priori laws of motion and their deductive consequences. In the passage cited from the Discourse at the beginning of this section, he mentions another area of necessarily empirical inquiry. From the a priori laws alone we cannot determine what, in fact, is the mechanical constitution of many of the phenomena we observe. This is the domain of empirical inquiry that will be important in what follows. His empirical epistemology will depend upon understanding the operation of the human eye, for which he will appeal to empirical physiology as well as to a theory of the mechanical nature of light which he found himself forced to justify empirically.

Descartes thus believed that scientific inquiry must begin with an a priori demonstration of first principles and then, once the scope of a priori physics has been exhausted, it must turn to the construction of empirical hypotheses. Since earlier works like the Regulae often suggest a thoroughly aprioristic method, it is with his mature conception of scientific method that I shall henceforth be concerned.4

Those explanatory propositions belonging to the empirical part of physical inquiry Descartes himself termed 'hypotheses'. He said that if the consequences of an hypothesis agree with experience and, more particularly, if by way of a crucial experiment they agree with an experimental phenomenon that the deductive consequences of rival hypotheses fail to match, then we have every reason to believe that the hypothesis is true.5 (It is to be remembered that the Cartesian idea of deduction is broader than the logical concept of deduction—it covers any sequence of propositions where we perceive 'clearly and distinctly' that the conclusion follows from the premises.)

The hypothetico-deductive method, for Descartes, belongs only to the empirical part of physical theory; it does not touch the fundamental laws of nature and their deductive consequences. There is, of course, the famous passage at the close of the Principles (IV, art 204) where Descartes refers to the whole of his physical theory as an hypothesis whose truth can be guaranteed only by the match between its deductive consequences and experience. This and similar passages have sometimes encouraged the view either that toward the end of his life Descartes had begun to doubt his ability to demonstrate any a priori physical truths or that, in fact, he had never had that ambition.6 But this interpretation of the passage is seriously mistaken. At Principles IV, art 205, he says that the hypothetico-deductive method can give us only a 'moral certainty' in the truth of an hypothesis; by this he means that when an hypothesis coheres with the phenomena we have no reason to doubt its truth, though of course it could still possibly be false. But in the subsequent section (IV, art 206) he goes on to claim that about a number of propositions we have more than moral certainty, we have in fact 'metaphysical certainty', once we understand that God exists. These propositions are ones that we can deduce from God's existence and include, not only that we can indeed distinguish the true from the false, but also mathematical truths and physical truths that are equally self-evident. These physical truths are, he says, 'the principal and more general ones'—in other words, the three fundamental laws of nature. Thus, Descartes' position at the end of the Principles does not differ from what he said in the Discourse. His point in the final passages of the Principles where he describes the whole of his physical theory as an hypothesis is simply that, if we were not able to give an a priori demonstration of certain basic physical truths, they too would then have to assume the status of confirmable but ultimately corrigible hypotheses.7

Descartes' thesis that propositions lacking an a priori demonstration must be treated as hypotheses and tested by means of crucial experiments had an important methodological consequence. If we believe that principles explaining some physical phenomenon can be deduced from other self-evident principles but we do not see yet how the demonstration can be set up, we are not forced to let that part of physical theory lie fallow. Instead, we can admit those principles to the corpus of scientific knowledge if their experimental consequences are borne out. Later, of course, we could return to give them the a priori demonstration they deserve. This is, in fact, precisely what Descartes did in the Dioptrics and Meteorology. Instead of being demonstrated a priori, the mechanical nature of light has in these treatises the status of an hypothesis, from which he sought to deduce both the laws of refraction and, along with physiological data, the operation of the human eye.8 In the Discourse on Method, he maintained that in these treatises he has merely withheld the a priori demonstration of this hypothesis that he already possesses. But in a more candid letter to Mersenne of 17 May 1638 (shortly after the publication of the Discourse and the Dioptrics) he confessed that an a priori demonstration of the mechanical nature of light is still only a confident hope.9

I shall not comment here upon some of the insights about hypothetico-deductive method that Descartes had acquired at this time, such as the importance of consilient confirmations or the way the experimental confirmation of an hypothesis turns on its comparison with competing ones.10 Of chief concern for our purposes is that we recognize how a combination of a priori and empirical elements formed an abiding feature of Descartes' mature conception of scientific method. Naturally, there can be no question that he continually sought to render empirical hypotheses as certain as possible. The two principal ways that he considered for increasing their certainty lay either in giving them, at last, an a priori demonstration or in setting up crucial experiments to decide between competing hypotheses. However, he did not believe that every hypothesis could be brought into the first path of certainty. Although he seems never to have ceased hoping for an a priori proof of the mechanical nature of light, he never dreamed of finding this sort of demonstration for other hypotheses, such as how the human eye operates. For this kind of phenomenon we could only try, in accordance with the Fourth Rule of Method, for as complete an enumeration as possible of all the relevant hypotheses; then by appropriate experiments we could hopefully narrow the range of hypotheses to one."11 Clearly, this sort of quest for certainty is one that any rational inquiry must share.

The significant fact, then, about Descartes' mature conception of scientific method is not only that a priori demonstration and empirical testing form the means of justifying different parts of physical theory, but also the a priori area should be explored as far as possible before empirical investigation begins. Even if the ideal of a priori demonstration in physics now seems not just untenable, but perverse, we might still recognize an important truth dimly perceived in Descartes' conception of method. The building of empirical hypotheses should take place within a research programme (like the mechanism expressed in Descartes' a priori laws) that sets down some general constraints on permissible modes of explanation, indicates what are the important problems to tackle, and even has something to say about what will count as an acceptable solution—while itself having a far more indirect relation to empirical confirmation. However, instead of pursuing further this somewhat anachronistic line of thought, I shall now examine how, as his physical science shifts from the a priori to the empirical, Descartes' theory of knowledge takes up a new set of concerns.

Part II The Mathematization of Nature

As I mentioned at the beginning, there has in recent years been an increasing awareness of the extent to which Descartes meant physical inquiry to be empirical. This is so, even if these new treatments of Cartesian physics have often failed to capture, I believe, just what the role of empirical inquiry was for Descartes. But what has gone unnoticed altogether is that a central area of his empirical science has to do with investigating the character of human knowledge itself and its place in nature. Not only nature, but our knowledge of nature as well comes within the scope of inquiry turned empirical. This is what I shall be calling Descartes' empirical epistemology.

In order to understand how an empirical epistemology can emerge for Descartes, we might picture the Cartesian conception of inquiry as a grand circle. A priori epistemology provides the premises for a priori physical theory, but since such theory falls far short of giving a complete account of nature it must be supplemented by empirical hypotheses. But these hypotheses in turn can serve to deepen our understanding of the nature of human knowledge, from whose a priori insights the whole process set out. The path of inquiry, beginning with the a priori truths and then moving into the empirical, doubles back on itself in this way just because—in contrast to much of the philosophy that came after him—Descartes conceived of the theory of nature and the theory of knowledge as lying on a continuum, instead of being wholly different enterprises.

In fact, his empirical epistemology begins precisely at the point at which physical inquiry turns empirical. The character of physical inquiry shifts into a different key with the following questions. Are the qualities attributed to bodies by the a priori laws of nature—the mathematical qualities of extension, figure, and motion—the only qualities that physical bodies really have, contrary to what our perceptual experience would indicate? Or does physical theory concern itself only with certain properties of bodies, while abstracting from others? This problem concerns, of course, the mathematization of nature; since the mathematical qualities in question are geometrical ones (to the detriment of Cartesian physics), more exactly it is a geometricization of nature. Descartes' important insight, either overlooked or not pursued by his predecessors, from Cusanus to Galileo, who had espoused the programme of mathematizing nature, was that the development of this programme must proceed in tandem with a theory of perception that shows both that our ideas of nonmathematical properties, such as colour, resemble nothing in nature and that their occurrence is explicable in terms of a mathematical physics. Furthermore, the mathematization of nature was an empirical project. That is so, because he believed that the needed theory of perception must rest upon empirical hypotheses dealing with how the human eye works and what the nature of light is.

To be sure, the hypotheses that Descartes advanced about the structure of our perceptual system, in order to meet the mathematization of nature problem, form part of physiological theory. To what I am calling his empirical theory of knowledge belong, rather, the broad implications he drew from this to describe the relation between our scientific and perceptual images of nature as well as our relation as knowers to the natural order. Perhaps it may be objected that these are not 'philosophical' issues, supposedly because their pursuit must proceed against the backdrop of our knowledge of nature. Definitions of what counts as 'philosophical' are never very fruitful. Their usual intent is to exonerate the philosopher who makes them from having to learn anything about the areas of inquiry they exclude. Problems are a better guide than definitions. If our problem is to understand the relation between scientific knowledge and experience and the place of knowledge in nature, then a philosophical treatment of this problem is one that tries to approach it in the broadest possible way, making use of anything that may be appropriate. This was also Descartes' conception of philosophy, as the use of both a priori and empirical approaches to understand mind and nature in a book entitled The Principles of Philosophy would indicate. In this section, I shall discuss his mathematization of nature and the consequences he drew from it for an understanding of the relation between the scientific and perceptual images of nature. Descartes also exploited his physiological work to describe the place of knowledge within the natural order, and this I shall discuss in the subsequent section.

First, let us see just how the mathematization problem emerges as Cartesian physical inquiry becomes empirical. The three fundamental laws of nature and their deductive consequences are true a priori and characterize any possible physical world. That there does indeed exist such a world is something we infer, according to Descartes, from the fact that we experience many of our ideas as something passive, as a mental state caused by external objects, and that we have a divine guarantee that whatever we so clearly and distinctly perceive to be true must be true. Thus, once we see that there is a world of objects and movements, we may then conclude that it falls under the rubric of a 'physical world' governed by such a priori laws.12 Here the mathematization problem first presents itself. Do objects really have only the properties mentioned by these laws?

Significantly, Descartes did not try to establish the mathematization of nature apart from an appeal to empirical considerations, at least in his mature period. He frequently extolled the greater clarity and distinctness enjoyed by perceptions of extension, figure and motion, in contrast to the obscurity affecting perceptions of colour or of hot and cold. But in none of these passages did he make use of this greater clarity to establish the mathematization of nature; it is always some other point that he was concerned to make.13 In fact, there is a letter that Descartes wrote to Chanut, several years after the publication of the Principles, in which he said explicitly that in that work the proof that ideas such as those of colours are not resemblances comes only at the end of the fourth part, at Principles IV. arts 189–98, where he refers to the physiological account of perception, given in such previous works as the Dioptrics, to prove the mathematization thesis.14 Since these physiological hypotheses belong to the empirical part of physical theory, the mathematization of nature, for Descartes, is an empirical hypothesis.

Thus, it is also clear that for Descartes the mathematization of nature depends upon empirical scientific hypotheses about the physiology of perception, and not merely upon everyday observations. This is, in general, an important point just because some philosophers, for example Jonathan Bennett, have claimed that the thesis that colour-ideas do not resemble objective properties of bodies does not require any 'recherché scientific information'.15 According to Bennett, reflection upon obvious empirical facts shows that the perception of an object as having some colour does not hang together with the rest of our knowledge in any way so systematically as does our perception of it as having some shape. From this he believes that we may infer that colours do not inhere in the things themselves. But, however poorly entrenched our colour-predicates may be, this argument does not have the force that Bennett thinks it has. At most, it could serve only to render easier the acceptance of the thesis that colourideas are not resemblances once that thesis has been independently confirmed on scientific grounds. Thus, Descartes was on the right track when he rested his mathematization of nature upon physiological hypotheses.

Before looking at the use that Descartes made of these hypotheses in his empirical epistemology, we must first see just what was the explanation of colour-perception that he presented in the Meteorology. He traced the perception of different colours to the differing rotational velocities of the light-corpuscles which, interacting with our eye in a mechanically explicable way, cause us to have colour-ideas. We may indeed speak here of the rotational velocities of the light-corpuscles, since only in regard to being 'transmitted' instantaneously can light be but a tendency to movement. This explanation is an empirical one in that both the mechanical nature of light and the account of how the eye reacts to these light-corpuscles and transmits their 'movements' to the brain and then the mind are, according to him, hypotheses that must be confirmed by experience. Now the reason he offers for the causal connection between the rotational velocities of lightcorpuscles and ideas of colours is a rather slender one: such velocities form the only remaining degree of freedom for the corpuscles and colour is the only aspect in which our perceptions of light vary.16

But whatever the shakiness (not to mention the falsity) of his explanation of colour-perception, Descartes went on to draw from it, and the mathematization of nature it made possible, an important philosophical consequence. This first result in his empirical epistemology is one that even an adequate physiological explanation of colour would inspire. Descartes was not content with claiming merely that our perceptual belief in colours is false. What he did was to set up a generalized concept of representation, according to which there are a number of ways our representations may represent features of nature besides resembling them. The physiological explanation of colour-ideas shows, that, even if they do not resemble actual features of nature, there are nonetheless interconnections among them that represent real relations in nature: the closer to red in the spectrum a colour is, the faster, according to Descartes, the corresponding rotational velocity of the light-corpuscles. Moreover, he might naturally have gone on to speculate about what must be the actual constitution of an object in order for it to reflect light-corpuscles of a certain rotational velocity; then a colour-idea would represent something of the object, though without at all resembling it in that regard. But this was one of the rare cases where Descartes did not seize an opportunity to put forth an hypothesis.

Both in Le Monde and the Dioptrics this distinction between representation and resemblance is laid out explicitly. There, for example, he compared ideas of colour to scripts or languages that bear a systematic relation to what they represent without resembling it.17 Descartes needed the generalized concept of representation to make sense of the relation between the scientific and perceptual images of nature. Although his physiological theory shows that certain of our ideas are not resemblances, it also shows how they do, in fact, represent actual properties of nature. In other words, while rejecting our 'natural interpretation' of colour-ideas, what Descartes calls our 'natural belief that takes them as resemblances, the theory places a new interpretation on them that indicates how they do represent. In this way, only, could he do justice to the fact that our ideas of colour prove useful in guiding our activities in the world. Descartes' general concept of representation expresses a view that we, too, must adopt if we are to understand how modern scientific theory at once characteristically corrects our perceptual image of nature and yet must ultimately be tested against our perceptual experience. As in the case of Descartes' explanation of colour-perception, the scientific theory that refutes our 'natural interpretation' of what we perceive is one that purports to explain why we have the perceptions or ideas that we do; this explanation we can understand as a new interpretation that tells us how our ideas really do represent. Yet the new interpretation is not tested against sentences expressing the natural interpretation it refutes (an incoherency often used by instrumentalists to discredit the idea that the correcting theory could count as being true). It is tested against an account of what perceptual ideas we do have.

In the past an exclusive concern with Descartes' a priori epistemology has portrayed his theory of representation as if it strove chiefly to determine with what right we can come to know that a representation is true or not. Because the empirical dimension of his epistemology was then overlooked, his need to examine the different kinds of representation went unnoticed. Indeed, Descartes considered the generalized concept of representation one of his most important discoveries. To the absence of this concept he traced the failure of the older view that perception occurs through objects transmitting 'intentional species' to the mind; on that view perception could be a matter only of whether an idea resembles an object or not.18 The generalized concept of representation, explaining how the mathematization of nature is possible, is thus the first key concept of Descartes' empirical epistemology.

Part III The Natural Setting of Human Knowledge

The second set of issues belonging to Descartes' empirical epistemology are ones that have to do with the place of human knowledge within the natural world. This area of his empirical epistemology arose because his physiological theories led inevitably to localizing the mind at a determinate position within the causal order of nature, namely in the vicinity of the pineal gland.19 Indeed, this conflicted head-on with his a priori distinction between mind and body, where spatial location was supposedly a distinctive feature of bodies alone. However, it is not with this conflict between a priori and empirical developments and the inadequacies of Cartesian dualism that I intend to deal, but with his empirical epistemology. Before we look at these further aspects of it, we must first take a glance at the theory of ideas that he worked out on a priori grounds and that served as the background for how he further exploited his physiological work for epistemological ends.

It is well known that the Cartesian concept of an idea is quite broad in scope, meaning as it does any sort of representation, but chiefly the content of a thought or a perceptual content. Ideas arise from two sources, either from the innate capacities of the mind (these are the ideae innatae) or from experience (these are the ideae advenitae, or adventitious ideas). When we use any of our ideas to re-interpret or combine other of our ideas, we end up with constructed ideas (or ideae factae). As for the nature of ideas themselves, Descartes often, when hurried, treated them as immediate objects of thought or perception, in the sense that they are mental items separate from the acts of thinking or perceiving them. But his more considered view (justifiable, as we shall see, within his physiological theory) was what we might today call an adverbial theory. Then he understood ideas as features of the mental acts themselves of thinking or perceiving, and not as separate items toward which those mental acts are directed. For example, in this spirit he defined an idea as 'the form of any thought (cogitatio) … by the immediate awareness of which I am conscious of that said thought', just after he had defined a thought as the mental operation (operatio) of thinking, perceiving, or willing.20 On this view, we are immediately aware of our ideas only because we have immediate reflexive awareness of our thinking, and not because our ideas are separate items uncommonly close to our acts of thinking or perceiving.

Descartes used his physiological work to deepen his account of the character of human knowledge by placing human knowledge in its natural setting. He did this by examining the role of perceptual ideas in our empirical knowledge of nature. Remember then on a priori grounds Descartes believed that he could prove (in the Sixth Meditation) that the causal dependence of perceptual ideas on external objects is just as clear and distinct as our having such ideas at all. What he did in his physiological treatises, the Treatise on Man and the Dioptrics, was to show just how this causal chain proceeds. In general, he drew a mechanistic picture of how the impingement of the light from the object upon the eye causes certain movements to be transmitted along the optical nerve; these cause movements in the animal spirits of the brain, which in turn induce a particular movement of the pineal gland, which immediately gives rise to a particular idea in the mind.21 Now, to be sure, knowledge for Descartes consists not simply in having an idea but in the judgement that the idea is true or false. Thus, the causal chain of perception that results in a perceptual idea yields a necessary, but not a sufficient condition for empirical knowledge. The perceptual idea must figure in a judgement for there to be knowledge; and that perceptual idea may also be variously interpreted before a judgement is made. But we can think of Descartes' physiological work as placing empirical knowledge in its natural setting because the possibility and even the scope of such knowledge depends upon the physiology of perception. Furthermore, the mental acts of interpreting and judging, just as much as the ideas upon which they operate, occupy a determinate position in the causal order of nature. They, too, must take place in the vicinity of the pineal gland—contrary to what the distinction between mind and res extensa would seem to require.

I shall discuss two ways in which Descartes used his physiological work to fill in the natural setting of empirical knowledge. The first lay in his analysis of the causal link between the pineal movements and the resulting perceptual idea. Of course, he did believe that we cannot come to understand in what, in this case, the causal operation consists. But he did say something about the relation between pineal movements and perceptual ideas that is precisely as sophisticated as we should desire. In the Dioptrics he insisted that although the movement of the pineal gland causes the idea in the mind, it is not then the pineal movement that we perceive. The immediate object of perception consists in the content of the idea, while the pineal movements act upon the mind in such a way as to cause the mind to have such an idea.22 To believe that the pineal gland causes the mind to have a perception by causing the mind to perceive its movements would be to suppose, he wisely pointed out, that the mind itself has an eye to perceive those adjacent movements. Such passages indicate how successfully Descartes was able to integrate the representationalist and physiological components of his theory of perception.

Moreover, the very same kind of argument could have been used to justify his adverbial theory of ideas, the far more acceptable form of representationalism. No more than the mind has an eye to perceive brain-states does it have an eye to perceive ideas as separate mental items. Unfortunately, none of the passages that I have found where Descartes carefully laid out his adverbial theory indicates for what reason he preferred this account. It would not be unreasonable, however, to conjecture that behind this account lay his physiological claims about the relation in perception between brain-states and the mental states they cause.

In this way, Descartes' physiological speculations helped him to fill in his central epistemological thesis that our knowledge of the world takes place by means of our having ideas. Notice that his representationalist theory of empirical knowledge, as put forth on a priori grounds alone, was compatible with a range of different accounts. A priori introspection yields that adventitious ideas, that lie at the basis of our empirical knowledge, depend causally upon external objects. But this point is compatible with ideas being either the way things themselves look, or 'intentional species' of things transmitted without alteration to the mind.23 Both of these alternatives were ruled out in virtue of taking mental states as caused by brain-states. But Descartes went on to clarify just what this causal relation means for the character of perceptual ideas. It appears plausible that this clarification led Descartes to his adverbial conception of ideas.

There is a second and more important way in which his physiological work contributed to an empirical account of human knowledge. His physiological investigation of vision showed, not only why our colourideas are not resemblances, but also under what conditions even the perception of the mathematical qualities of bodies can go astray. In the Dioptrics he showed how the accuracy of distance-perception diminishes when the object is either too near or too far and that bright objects appear closer than they actually are because the intensity of the light causes the same contraction of the pupil that occurs when it is focussed upon nearby objects.24 Having ascertained the range of accuracy of the eye, he went on in the Dioptrics to show how the use of glass lenses, in telescopes or microscopes, could increase our access to the actual mathematical properties of bodies.

The important epistemological consequence that Descartes drew from this aspect of his physiological work lay in his coming to conceive our visual system as simply one kind of optical receptor among others. Our natural organs of perception he treated as lying on a continuum with what he called the 'artificial organs' that can supplement the deficiencies that nature has left us with.25 He listed four conditions that any optical receptor should meet, and envisaged that sometimes different organs, whether natural or artificial, might satisfy some of these conditions better than others. These four conditions were that the receptor produce images that do not distort features of the object, that these images be detailed, that the light forming the images be strong enough to move the fibres of the optical nerve, and that the images represent at the same time as many different objects as possible. In short, what he was working at was a generalized concept of an optical receptor, under which our visual system would fall as simply one among other, 'artificial' ones. This concept formed part of an overall generalizing of our perceptual systems. Descartes' generalized concept of representation, which I discussed in the previous section, was intended to make sense of the fact that much of our perceptual experience represents, without offering resemblances of things. Now, when it comes to those perceptual ideas that can be resemblances—the ideas of the mathematical properties of perceived bodies—we see him generalizing along this axis as well. Artificial organs can, under a great many conditions, yield us resembling images, where our natural organs fail.

This overall generalization is an exceptionally important aspect of Descartes' empirical epistemology. By stressing how in many ways our perceptual image of nature proves inaccurate and how, even where it does offer us resemblances of the way things are, it is far less serviceable than the instruments we can construct, it served to undermine the traditional conception (deriving from both Greek and Christian sources) that God or nature has given us the perceptual organs we have because they naturally display the nature of the world we desire to understand. In short, this aspect of his empirical epistemology served to de-teleologize our perceptual system. This is a much-neglected aspect of the break with teleology characteristic of modern physical science, and yet it proved just as significant as the rejection of teleological theories of motion. Its importance lay, not least of all, in recognizing that progress in our knowledge of nature will come, not from the mere observation of nature, but from experimentation. Thus, Descartes thought that the senses should be subservient to the intellect, not simply because in ordinary life we make perceptual errors, but because more fundamentally we must take our perceptual experience as only an indirect access to the actual structure of nature. In the seventeenth century, it was Locke and Robert Hooke who chiefly continued the Cartesian break with the teleology of perception; Hooke recommended that 'The footsteps of Nature are to be trac'd, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in indeavouring to avoid our discovery.'26 In fact, they went further in this development than Descartes himself. He was willing to de-teleologize our perceptual system probably only because he believed (it seems in contrast to Locke and Hooke) that he had a divine guarantee for the ability of our intellect to understand the world.

Since a characteristic feature of modern physical science has been not just its extension, but, in quite fundamental regards, its correction of our perceptual image of nature, physiological theories that de-teleologize perception have played a vital role in its development. In other words, put more generally, the modern theory of nature has required a theory of human knowledge as it exists within the natural setting physical theory describes. To that extent, modern epistemology had to have its empirical dimension, at least as long as it remained in contact with the growth of science. One of Descartes' unsung merits lies in his having perceived so distinctly and so fruitfully the need for an empirical epistemology.

The generalized concept of representation, the relation between perceptual ideas and the brain-states that cause them (as well perhaps as the adverbial theory of ideas), and the generalized concept of an optical receptor are the key features of Descartes' empirical epistemology. It is perhaps not surprising that his empirical epistemology has gone unnoticed for so long. Only recently has the myth been exploded that Cartesian physical science was thoroughly a priori. I have sought to show, what has not really been recognized, that for Descartes empirical inquiry was concerned not simply with a deeper understanding of nature, but also with a broader understanding of the nature of our knowledge of nature as well….


1Discourse on Method, VI, AT, [Oeuvres de Descartes, ed. C. Adam and P. Tannery, 13 vols., Paris: Vrin/CNRS, 1879–1913], VI, pp. 64–5 (HR, [The Philosophical Works of Descartes, trans. Elizabeth S. Haldane and G. R. T. Ross, 2 vols., Cambridge: Cambridge University Press, 1970], I, p. 121).

2Le Monde, VII, AT, XI, pp. 37–45.

3Discourse on Method, VI, AT, VI, p. 64 (HR, I, p. 121); Principles, II, art 36–42.

4 In Regulae, rule XII (AT, X, p. 427; HR, I, p. 47) Descartes does imply, as in the case of the nature of the magnet, that sometimes we must rest content with hypotheses that are only empirically confirmable; but this passage is surrounded by other comments (AT, X, pp. 419–28; HR, I, pp. 41–7) that imply that all scientific knowledge must be deduced from self-evident 'simple natures'. Since the Regulae is so obscure a work, I have chosen to discuss Descartes' conception of scientific method as it emerges with the Discourse. In Le Monde, four years before the Discourse, he boasted that from the three fundamental laws of nature he could deduce a priori a complete account of nature (AT, XI, p. 47).

5Discourse on Method, VI, AT, VI, p. 65 (HR, I, p. 121); Principles, III, art 43–4.

6 For a recent statement of the view that by the end of the Principles Descartes had surrendered the idea that any physical truths can be demonstrated a priori, see D. Garber, 'Science and Certainty in Descartes', in M. Hooker (ed.) Descartes: Critical and Interpretative Essays (Baltimore, 1978, p. 146). Garber takes Principles, IV, art 206 to indicate that Descartes was 'uncomfortable' with having just abandoned, in the previous section, the possibility of a priori physical truths; in contrast, I take it to express Descartes' simply having finished the thought he began in the previous section—without a knowledge of God all of science would be hypothetical, but we do know God and He lends metaphysical certainty to the basic principles of physical science. For the view that, throughout the whole of his writings, Descartes considered physical science as thoroughly empirical and hypothetical, see A. Gewirth, 'Experience and the Non-Mathematical in the Cartesian Method', Journal of the History of Ideas, II (1941), pp. 183 ff.; also E. Cassirer, Das Erkenntnisproblem, Vol. I (Wissenschaftliche Buchgesellschaft, 1974; originally 1922), p. 469 ff. R. M. Blake, 'The Role of Experience in Descartes' Theory of Method', in Theories of Scientific Method, Seattle, 1960, claims that both a priori demonstration and experimental confirmation serve to justify the three fundamental laws of nature. This is an interesting idea, but the passages Blake cites are not convincing. An account generally similar to the one that I have presented may be found in L. J. Beck, The Method of Descartes (Oxford, 1952), pp. 239 ff., as well as in L. Laudan, 'The Clock Metaphor and Probabilism', Annals of Science, XXII (1966), pp. 73 ff.

7 Furthermore, Descartes believed that if we did not know the existence of God we would have no right to believe that the experimental confirmation of hypotheses had anything to do with their being true. Thus, in Principles, III, art 43, he traces the link between confirmation and truth to a divine guarantee; but in the next section, where no mention is made of God, he begins to hedge on whether hypotheses may be no more than practically useful (as opposed to true).

8Dioptrics, I, AT, VI, p. 83.

9Discourse on Method, VI, AT, VI, p. 76 (HR, I, pp. 128–9); To Mersenne, 17 May 1638, AT, II, pp. 134 ff. (PL, pp. 55–6).

10 For consilience, see To Morin, 13 July 1638, AT, II, pp. 196 ff. (PL, pp. 58–9); for comparative confirmation see Discourse on Method, VI, AT, VI, p. 65 (HR, I, p. 121).

11 In the article cited above, D. Garber claims that at the time of the Discourse Descartes believed he could enumerate all possible hypotheses consistent both with the a priori principles and with the phenomena to be explained and then, by crucial experiments, he could show with deductive certainty which hypothesis was correct. But none of the passages cited by Garber rules out the interpretation that, according to Descartes, we should try for as complete an enumeration of possible hypotheses as we can; and this (if we leave aside the additional idea that they must be compatible with principles that are a priori) would hardly indicate that Descartes did not take the hypothetical method seriously (as, on his interpretation of the passages, Garber maintains). When in Discourse, V (AT, VI, pp. 40–1; HR, I, p. 106), Descartes writes that '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', he is referring to principles (as the rest of the sentence makes clear), and in particular to the three fundamental laws of nature (as the subsequent sentence makes clear). This passage is used by Garber to support his claim that Descartes believed at this time that he could make the truth of his hypotheses certain.

12 Although at this point the a priori laws of nature are known to apply to the physical world, there remains the problem how they may in fact be applied by us. Descartes' solution would lie in his theory of 'natural geometry' (see Nancy Maull's paper below).

13 See e.g. Third Meditation (AT, IX, p. 34; HR, I, p. 164). Probably as a result of the traditional view of Cartesian physics as thoroughly a priori his mathematization of nature is usually seen as a priori, not empirical. Cf. e.g., A. J. Kenny, Descartes (New York, 1968), p. 207.

14 To Chanut, 26 February 1649, AT, V. pp. 291–2:

It is necessary to remember, in reading this book [the Principles], that although I consider nothing in a body besides the sizes, figures, and movements of their parts, I claim nonetheless to explain there the nature of light, of heat and of all the other sensible qualities; so that I presupposed that these qualities are only in our senses, like tickling or pain, and not in the objects that we perceive, in which there is nothing but certain figures and movements, that cause the perceptions that we call light, heat, etc. This I did not explain and prove until the end of the fourth part….

[my translation].

15 J. Bennett, Locke, Berkeley, Hume (Oxford, 1971), p. 105.

16Meteorology, VIII, AT, VI, p. 334.

17Le Monde, AT, XI, pp. 3–4; Dioptric, IV, AT, VI, pp. 109–14.

18Dioptric, IV, AT, VI, p. 112.

19 See Treatise of Man, AT, XI, pp. 131, 143; Principles, IV, art 189; Passions of the Soul, AT, XI, p. 352 (HR, I, p. 345).

20Reply to Second Objections, AT, IX, p. 124 (HR, II, p. 52).

21 At times, Descartes wrote that the perceptual idea occurring at the end of this sequence must be 'innate'; what he meant was that, since the figures and the movements in the sense organs and the brain give rise to ideas that do not resemble them, the mind must have an innate faculty that governs what the content of the perceptual ideas corresponding to these figures and movements will be. See Notes Against a Program, AT, VIII, pp. 358–9 (HR, I, pp. 442–3). Clearly, Descartes is not denying here that the knowledge of the world we gain through perceptual ideas is empirical.

22Dioptric, VI, AT, VI, p. 130:

Now although this picture, in being so transmitted into our head, always retains some resemblance to the objects from which it proceeds, nevertheless … we must not hold that it is by means of this resemblance that the picture causes us to perceive the objects, as if there were yet other eyes in our brain with which we could apprehend it; but rather, that it is the movements of which the picture is composed which, acting immediately on our mind inasmuch as it is united to the body, are so established by nature as to make it have such perceptions.

[Translated by Olscamp, p. 101 in Discourse on Method, Optics, Geometry, and Meteorology (Indianapolis, 1965).]

Descartes did not have this insight from the beginning, since in an earlier work like the Treatise of Man he suggested that we perceive directly events in the brain; this is because he then thought of the ideas themselves as patterns in the animal spirits of the brain (AT, XI, pp. 176–7). N. K. Smith errs by attributing this earlier position to the whole of Descartes' thought, in his New Studies In the Philosophy of Descartes (London, 1952), p. 147.

23 By rejecting the view that our perceptual ideas are the 'looks' of the things themselves, Descartes' physiological account of perception broke with our everyday understanding of perceptual knowledge. Ordinarily (in the case of vision) we believe that we perceive objects directly. Thus, what we perceive of an object, we think, is how the object itself looks in that situation; even if I know that that elliptical shape is actually a circular one, I believe that from this angle the object looks that way. The reason why this view comes so naturally is that in seeing an object we see ourselves seeing it, we see our bodies in a certain position vis-á-vis the object. It is this reflexive element that leads us to believe that we can see the object itself as it is causing us to see it. On the everyday view, see J. L. Austin, Sense and Sensibilia (Oxford, 1962).

24Dioptric, VI, AT, VI, p. 144 ff.

25 For this whole discussion see Dioptric, VII, passim.

26 This passage is from the preface to Hooke's Micrographia (London, 1665). From Locke, see Essay Concerning Human Understanding, Book II, Ch XXIII, 12; there he says that God fitted our senses for our practical welfare, and not for our knowledge of nature (cf., however, Essay, Book IV, Ch IV, 4). For the same idea in Descartes, see Sixth Meditation, AT, IX, p. 66. Aristotle, as is well known, urged that the theory of nature should remain in harmony with 'ta phainomena'.

Desmond M. Clarke (essay date 1992)

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SOURCE: "Descartes' Philosophy of Science and the Scientific Revolution," in The Cambridge Companion to Descartes, edited by John Cottingham, Cambridge University Press, 1992, pp. 258–85.

[In the following essay, Clarke examines the epistemological and metaphysical underpinnings of Descartes' philosophy of science, contrasting it with scholasticism.]

Descartes' concept of science can be understood only by paying careful attention to the historical context in which it was constructed. The scientific revolution of the seventeenth century involved two related developments: a change in scientific practice (or, more accurately, a whole series of such changes) which is reflected in the founding of new scientific societies such as the Royal Society and the Académie royale des sciences, and a complementary change in how natural philosophers described the kind of knowledge that resulted from the new scientific practices. Descartes contributed to both developments. He shared this distinction with such eminent figures as Galileo Galilei, Francis Bacon, William Harvey, Robert Boyle, Christian Huygens, and Isaac Newton, all of whom were concerned both with improving our knowledge of nature and with clarifying the status of that knowledge.

It would be an obvious oversimplification to classify all the natural philosophers of the seventeenth century as, in some fundamental sense, proposing the same scientific theories. It is equally unsatisfactory to suggest that they all accepted the same theory of science or the same model of scientific knowledge. Yet, despite the pitfalls involved, it may be helpful—at least prior to examining Descartes' texts—to think of many of the most famous natural philosophers of the scientific revolution as sharing a number of new insights about the nature of scientific knowledge and, more importantly, as repudiating certain features of the model of science that was generally accepted in colleges and universities at that time. In fact, there was more agreement about what was being rejected than about what was being proposed in its place. Descartes occupies a pivotal role in the history of this development, in the transition from a widely accepted scholastic concept of science to its complete rejection by practising scientists and the endorsement of some kind of hypothetical, empirically based knowledge of nature. The historical context in which Descartes worked should lead us to expect, therefore, that he struggled with the epistemological and methodological issues involved in this transition. It should also lead us to expect that the transition was neither quick nor clear-cut. In other words, there is a strong likelihood that seventeenth-century natural philosophers continued to accept various features of precisely the model of science which they claimed explicitly to reject, while at the same time adopting elements of the newly developing concept of science that were incompatible with their traditional allegiance.

The traditional concept of science that was almost universally taught in colleges and universities included a number of key features; one was the certainty or necessity of genuine knowledge claims, and their universality. Aristotle says in the Posterior Analytics:

We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows, when we think that we know the cause on which the fact depends, as the cause of that fact and of no other, and, further, that the fact could not be other than it is…. Since the object of pure scientific knowledge cannot be other than it is, the truth obtaiped by demonstrative knowledge will be necessary.

The paradigm of this type of knowledge was pure mathematics. One begins with definitions or first principles which are known with absolute certainty, one proceeds "demonstratively" by deducing other propositions from those already known as certain, and the logical validity of our inferences guarantees the same degree of certainty for our conclusions as was available for the initial premisses. The mathematical model of demonstrated knowledge inspired one of the dominant features of the scholastic concept of science that was widely accepted in the early seventeenth century.

Another feature of this concept of science was the claim that our knowledge of physical nature depends ultimately on the reliability of our everyday observations and judgments.2 This involved two elements. One was the assumption that all our knowledge ultimately depends on sensory evidence and that it includes nothing that was not learned through sensory experience.3 Secondly, the cognitive faculties with which God has equipped us are completely reliable as long as they are used within the scope of their Creator's design. Thus we know the way the world is, and we can know it with certainty, by consulting the ways in which the world appears to us in sensation.

A further element of the scholastic tradition was the assumption that, if we wish to explain the natural phenomena which appear to us in sensations, we must use the distinction between "matter" and "form."4 This was a very widely used distinction which varied in meaning from one context to another. It was designed to reflect our common experience of the same type of thing being instantiated in a variety of different ways; for example, dogs may be small or large, their colors can vary, as may many other inessential features, without their ceasing to be dogs. The common, essential features of a dog could be described as the form of a dog, while the nonessential, variable features could be described (metaphysically) as the matter. What appears in sensation, therefore, is the appearance of an underlying reality (form) which, in turn, is the more fundamental dimension of any reality. This underlying reality, or form, is what explains whatever is necessary or essential in anything. Because the traditional concept of scientific knowledge was limited to knowledge of what is necessarily true, it follows that scholastic scientia was directed to acquiring knowledge of forms. Thus a scholastic explanation of a natural phenomenon is a discovery of the forms that underlie the appearances manifest to the human perceiver in reliable sensations.

This very brief summary is almost a caricature of what scholastics claimed about scientific understanding. However, many of Descartes' contemporaries argued that it was precisely this philosophy that obstructed the consideration of alternative ways of investigating nature. It was this simple-minded model of knowledge that was invoked by those who objected to the new sciences, and that was used as a foil by proponents of the new sciences to show in relief the distinctive features of their own philosophy of science.


Descartes began his account of the natural world in Le Monde (c.1632) by discussing the unreliability of our sensations as a basis for scientific knowledge.

In proposing to treat here of light, the first thing I want to make clear to you is that there can be a difference between our sensation of light … and what is in the objects that produces that sensation in us … For, even though everyone is commonly persuaded that the ideas that are the objects of our thought are wholly like the objects from which they proceed, nevertheless I can see no reasoning that assures us that this is the case…. You well know that words bear no resemblance to the things they signify, and yet they do not cease for that reason to cause us to conceive of those things … Now if words, which signify nothing except by human convention, suffice to cause us to conceive of things to which they bear no resemblance, why could not nature also have extablished a certain sign that would cause us to have the sensation of light, even though that sign in itself bore no similarity to that sensation?

(AT [Œuvres de Descartes, ed. C. Adam and P. Tannery, revised ed., 12 vols., Paris: Vrin/CNRS, 1964–76] XI 3–4)5

Descartes goes on to use the same example as Galileo, to argue that a tickling sensation caused by a feather does not resemble anything in the feather. "One passes a feather lightly over the lips of a child who is falling asleep, and he perceives that someone is tickling him. Do you think the idea of tickling that he conceives resembles anything in this feather?" (AT XI 6)6 In a similar way, there is no reason to believe "that what is in the objects from which the sensation of light comes to us is any more like that sensation than the actions of a feather … are like tickling" (AT XI 6).7 If we cannot argue validly from a description of our sensation of light to the claim that the light that causes this sensation resembles our experience, then we have a fundamental problem in attempting to base scientific knowledge on our sensations of the world around us. The distinction between our subjective experiences or sensations and their objective causes, between primary and secondary qualities, opens up an epistemic gap that can only be bridged by some other strategy apart from assumptions of resemblance. This strategy is hypothesis, or guesswork. Our guesses may turn out to be very secure, and there may eventually be many reasons for thinking that they are as certain as one can hope for in the circumstances; but that does not change the fact that we come to have these ideas, in the first place, by guesswork. What should a natural philosopher assume about the physical causes of our perceptions? There are a few reasons why Descartes opts for one assumption rather than another at this crucial juncture, some of which rely on his concept of explanation (which is discussed below). Apart from those reasons, he also presupposes a radical distinction between matter and mind for which he argues in the Meditations and the Principles. It follows from this that the objective causes of our sensations are material, in some sense. In order to fill in some of the relevant detail, Descartes must engage in elementary physical theory.

The speculations about matter on which Descartes' theory of matter and, subsequently, his concept of science depend include the assumption that the size, shape and motion of small particles of matter would be adequate to explain all their physical effects, including the physical effects on our sensory faculties which stimulate sensations. Some of the reasons for this degree of parsimony in theory construction are mentioned below. In postulating three types of matter in Le Monde, Descartes is not very convincing about why he assumes three (rather than more or fewer); however, once they have been introduced, he is quick to take refuge in the construction of a hypothetical world which allows his imagination complete freedom, without having to explain the rationale for each hypothesis as it is made.

Many other things remain for me to explain here, and I would myself be happy to add here several arguments to make my opinions more plausible. In order, however, to make the length of this discourse less boring for you, I want to wrap part of it in the cloak of a fable, in the course of which I hope that the truth will not fail to come out sufficiently …

(AT XI 31)8

By the time Descartes wrote the Principles twelve years later, he had become more self-conscious about the hypothetical character of his assumptions concerning the size, shape, etc. of particles of matter.

From what has already been said we have established that all the bodies in the universe are composed of one and the same matter, which is divisible into indefinitely many parts, … However, we cannot determine by reason alone how big these pieces of matter are, or how fast they move, or what kinds of circle they describe. Since there are countless different configurations which God might have instituted here, experience alone must teach us which configurations he actually selected in preference to the rest. We are thus free to make any assumption on these matters with the sole proviso that all the consequences of our assumption must agree with our experience.

(AT VIIIA 100–1: CSM [The PhilosophicalWritings of Descartes; ed. J. G. Cottingham, R. Stoothoff, and D. Murdoch; two vols.; Cambridge University Press, 1985] I 256–7)

Descartes does not claim that we are completely free to assume anything we wish about matter. He argues at great length about the fundamental properties of matter, i.e. their primary qualities, and discusses in detail the need to include or exclude certain primary qualities in a viable theory of nature. He also argues in some detail about the laws of motion or, as he calls them, the laws of nature, which determine the motions of material bodies and the ways in which they may transfer motion from one to another by contact action. However, the relevant point here is that, having decided which variables to attribute to matter, we cannot determine by similar arguments the values of these variables; we cannot decide a priori the number, size, or speed of the various small parts of matter which underpin the whole edifice of Cartesian physics. Nor could we hope to discover by observation which particles there are, what shapes they have or with what speed they move; they are much too small to be perceived directly, even with the use of a microscope. We can do no better than hypothesize answers to these questions, and then subsequently check the plausibility of our guesswork.

Thus the logic of Descartes' theory of sensation and the implications of his theory of matter both suggest that he would have to acknowledge a central place for hypotheses in any coherent account of physical phenomena. The extent to which he recognized this varied from his earlier reflections in the Regulae (c.1628), in which there was only a minimal recognition of the role of hypotheses in natural science, to his more mature considerations in the Discourse (1637), where the significance of hypotheses and experiments is explicitly acknowledged. The Discourse is of paramount importance in this context, because it was composed over a number of years while Descartes was preparing for publication the three major scientific essays for which it serves as a preface. In the "Discourse on the method of rightly conducting one's reason and seeking the truth in the sciences," Part VI, Descartes writes:

Should anyone be shocked at first by some of the statements I make at the beginning of the Optics and the Meteorology because I call them 'suppositions' and do not seem to care about proving them, let him have the patience to read the whole book attentively, and I trust that he will be satisfied. For I take my reasonings to be so closely interconnected that just as the last are proved by the first, which are their causes, so the first are proved by the last, which are their effects…. For as experience makes most of these effects quite certain, the causes from which I deduce them serve not so much to prove them as to explain them; indeed, quite to the contrary, it is the causes which are proved by the effects.

(AT VI 76: CSM I 150)

This passage raised a number of queries from readers, one of whom was Father Morin. Descartes replied to his concerns in 1638 and answered the objection that hypothetical essays should not be described as demonstrated: "there is a big difference between proving and explaining. To this I add that one can use the word 'demonstrate' to mean one or the other, at least if one understands it according to common usage and not according to the special meaning which philosophers give it" (13 July 1638: AT II 198: CSMK [The Philosophical Writings of Descartes; ed. Cottingham, Stoothoff, Murdoch, and Anthony Kenny; Cambridge University Press, 1991] 106). This shows Descartes explicitly breaking with the scholastic tradition, for which the term "demonstrate" had special connotations of deducing a conclusion rigorously from first principles. Instead he invites his readers to understand "demonstration" in a less strict sense in which it can include the reasoning process by which one argues from effects to hypothetical causes or, in the opposite direction, from assumed causes to observed effects.

The relative novelty of this type of demonstration is underlined in a letter to Mersenne in 1638, in which Descartes explains that the types of demonstration available in physics are very different from those which one expects in mathematics:

You ask if I think that what I wrote about refraction is a demonstration; and I think it is, at least insofar as it is possible to give one in this matter, without having first demonstrated the principles of physics by means of metaphysics … and to the extent that any other question of mechanics, optics or astronomy, or any other matter which is not purely geometrical or arithmetical, has ever been demonstrated. But to demand that I give geometrical demonstrations in a matter which depends on physics is to demand the impossible. And if one wishes to call demonstrations only the proofs of geometers, one must then say that Archimedes never demonstrated anything in mechanics, nor Vitello in optics, nor Ptolemy in astronomy, and so on; this, however, is not what is said. For one is satisfied, in these matters, if the authors—having assumed certain things which are not manifestly contrary to experience—write consistently and without making logical mistakes, even if their assumptions are not exactly true…. But as regards those who wish to say that they do not believe what I wrote, because I deduced it from a number of assumptions which I did not prove, they do not know what they are asking for, nor what they ought to ask for.9

One implication is clear. We cannot expect the same kind of demonstrations in physics as in pure mathematics, and we will have to settle for something else. However, it is not yet clear what this alternative is. Whatever its precise structure and the kind of results which it can deliver, it involves making assumptions about the causes of physical phenomena and then "demonstrating" the plausibility of these assumptions by examining their explanatory role in some comprehensive natural philosophy, a project to which Descartes repeatedly refers in his claim that he could (at least in principle) demonstrate those assumptions from some kind of metaphysical foundation.


Descartes shared with many of his contemporaries the insight that the forms and qualities of the scholastic tradition were, in some fundamental sense, nonexplanatory. If we notice some natural phenomenon such as the effect of a magnet on small pieces of iron, the scholastic tradition tended to explain this by saying that the magnetic stone attracts (or repels) certain bodies because it has a "magnetic form" or a "magnetic quality." There is an obvious sense in which this is true. If any natural object does something, then it must have the capacity to do so! As long as we do not understand what that capacity is or what it consists in, we might name the inscrutable property in question in terms of the effect it produces. Then sleeping pills have a dormitive power, magnets have magnetic powers, and human beings have thinking powers. So far, there is nothing wrong with this; it merely labels what needs to be explained.

However, if one follows the natural tendency of scholastic philosophy and reifies these newly named powers as if they were properties distinct from the natural objects which have them, then two problems emerge. One is a metaphysical one; namely, the multiplication of entities beyond demonstrated necessity. By applying Occam's principle, one would stop short of introducing hundreds of new forms or qualities which overpopulate one's metaphysical space.10 Descartes adverts to this question about the redundancy of forms in Chapter 2 of Le Monde, where he explains how a piece of wood burns and, as it burns, emits light and heat:

someone else may, if he wishes, imagine the form of 'fire', the quality of 'heat', and the action that 'burns' it to be completely different things in this wood. For my part, afraid of misleading myself if I suppose anything more than what I see must of necessity be there, I am content to conceive there the motion of its parts…. provided only that you grant me that there is some power that violently removes the subtler of its parts and separates them from the grosser, I find that that alone will be able to cause in the wood all the same changes that one experiences when it burns.

(AT XI 7–8)11

Secondly, the introduction of scholastic forms in this context gave the impression that one had made progress in explaining natural phenomena, and that little else remained to be done. However, the very forms which are assumed as explanatory entities are themselves in need of explanation: "If you find it strange that, in setting out these elements, I do not use the qualities called 'heat', 'cold', 'moistness', and 'dryness', as do the philosophers, I shall say to you that these qualities appear to me to be themselves in need of explanation" (AT XI 25–6).12

Thus, for Descartes, scholastic forms are both redundant and pseudo-explanatory. The alternative suggested was to find the material and efficient causes of natural phenomena. Descartes argued that these causes must be described mechanically; in fact, he notoriously argued in a reductionist way that most of the properties that natural phenomena exhibit can be explained ultimately in terms of the size, shape, and motions of the small parts of matter into which, he assumed, physical objects can be analyzed. Therefore to explain any natural phenomenon, in this sense, is equivalent to constructing a model of how small, imperceptible parts of matter can combine to form perceptible bodies, how the properties of bodies result from the properties of their constituent parts, and why we perceive them as we do as a result of the interaction of these bodies with our sensory organs.

It has already been indicated above that Cartesian scientific explanations must be hypothetical, and that one of the reasons for this admission was the unobservability of the particles of matter in terms of which the explanation of natural phenomena must be constructed. But how are we supposed to describe and measure the properties of unobservable particles of matter? Father Morin had this type of objection in mind when, having read the scientific essays of 1637, it seemed to him that Descartes might be attempting to explain what we can readily observe by reference to what we neither observe nor understand: " … problems in physics can rarely be resolved by analogies [comparaisons]; there is almost always some difference [between the model and reality], or some ambiguity, or some element of the obscure being explained by the more obscure" (12 August 1638: AT II 291). Part of Descartes' reply to this objection includes the claim that there is no way of proceeding in physics except by constructing large-scale models of what is happening at the microscopic level. Thus, for example, we might think of imperceptible particles of light by analogy with wooden spheres the size of billiard balls.

I claim that they [i.e. models and analogies] are the most appropriate way available to the human mind for explaining the truth about questions in physics; to such an extent that, if one assumes something about nature which cannot be explained by some analogy, I think that I have conclusively shown that it is false.

(12 September 1638: AT II 368: CSMK 122)

This point had already been made in correspondence with Plempius the previous year: "There is nothing more in keeping with reason than that we judge about those things which we do not perceive, because of their small size, by comparison and contrast with those which we see" (3 October 1637: AT I 421: CSMK 65). Descartes' reply to Father Morin also included the claim that the only relevant features of the model were the size and shape of the spheres, and the direction and speed of their motions, so that the disparity in size could be ignored in constructing an explanation.

in the analogies I use, I only compare some movements with others, or some shapes with others, etc.; that is to say, I compare those things which because of their small size are not accessible to our senses with those which are, and which do not differ from the former more than a large circle differs from a small one.

(12 September 1638: AT II 367–8: CSMK 122)

Apart from the interesting assumptions about which features of a model are relevant to constructing an explanation, Descartes' comments also raise a question about the extent to which hypotheses must be true in order to be explanatory. In other words, would it help in explaining a physical phenomenon if one constructed a mechanical model of its efficient cause which, in fact, is not true to the reality? Descartes thought so, or at least he argued that a plausible though incorrect model is better than none at all. Besides, it may be the case that we can never discover the values of the variables with which we describe microscopic particles of matter, so that we will have to settle for something less than the ideal understanding which is available to God.

The first concession about false hypotheses is made in a number of places where Descartes wonders about the evolution of the universe from its initial chaos to the highly structured world we see today. Theologians commonly believed in his day, based on a nonmetaphorical reading of Genesis, that the world as we see it had been created by God. Descartes comments:

even if in the beginning God had given the world only the form of a chaos, provided that he established the laws of nature and then lent his concurrence to enable nature to operate as it normally does, we may believe without impugning the miracle of creation that by this means alone all purely material things could in the course of time have come to be just as we now see them. And their nature is much easier to conceive if we see them develop gradually in this way than if we consider them only in their completed form.

(AT VI 45: CSM I 133–4)

This suggests that an explanation of the natural world is better if we imagine the world as gradually evolving from an initial chaos under the control of the laws of nature, than if we concede to the theologians' belief that God simply made it as it is. The same idea is expressed in the Principles:

There is no doubt that all the world was created with all of its perfection from the very beginning … Nevertheless, to understand the nature of plants or of man, it is much better to consider how they can gradually develop from seeds, than to consider how they were created by God at the beginning of the Universe. Thus if we can think of a few very simple and easily known principles from which we can show that the stars and the earth, and everything else we can observe on earth, could have developed as if from seeds—although we know they did not in fact develop in this way—we could explain their nature much better in this way than if we simply described them as they are now, or how we believe they were created.

(AT VIIIA 99–100: CSM I 256)

Thus, Descartes believed for theological reasons that his evolutionary account of the development of natural phenomena was false; he also claimed that, despite being false, it was explanatory.

The second reason for accepting hypotheses which are possibly false was Descartes' pessimism about the feasibility of identifying and accurately measuring relevant variables at the microlevel. There were a number of reasons for this which, in retrospect, would seem to have been well justified and would strike the modern reader as a realistic appraisal of the experimental techniques of the early seventeenth century. If one insisted on withholding hypotheses until all the complexity of the natural world is taken into account, one would make no progress whatsoever. Descartes argued along these lines in response to Mersenne's objections, in 1629, about the interference of the air in measuring the speed of falling bodies.

However, as regards the interference from the air which you wish me to take into consideration, I claim that it is impossible to cope with it and it does not fall within the scope of science; for if it is warm, or cold, or dry, or humid, or clear, or cloudy, or a thousand other circumstances, they can all change the air resistance.13

The same justification was offered, almost eighteen years later, for the apparent failure of the impact rules to coincide with our experience of colliding bodies. A number of correspondents objected that the rules proposed by Descartes in the Principles (Book II, arts. 46 ff) were contradicted by our experience. Descartes' response was:

Indeed, it often happens that experience can seem initially to be incompatible with the rules which I have just explained, but the reason for this is obvious. For the rules presuppose that the two bodies B and C are perfectly hard and are so separated from all other bodies that there is none other in their vicinity which could either help or hinder their movement. And we see no such situation in this world.

(AT IXB 93)

This was a standard reply to objections about a lack of fit between theory and reality. Cartesian explanations were constructed by analogy with the interactions of macroscopic physical bodies in motion. The underlying reality they purported to explain is microscopic, is inaccessible to human observation, and may involve so many interfering factors that our model is far short of adequately representing it.14

Thus a Cartesian explanation is a hypothesis that may be acknowledged to be either false or significantly inadequate to the reality it purports to explain. When we lack the evidence required to identify the actual cause of some phenomenon, "it suffices to imagine a cause which could produce the effect in question, even if it could have been produced by other causes and we do not know which is the true cause" (letter of 5 October 1646: AT IV 516). The suggestion that we settle for the best hypothesis available is reflected in the epistemic status claimed for various explanations in the Principles. For example, different astronomical hypotheses are examined, not to decide which one is true, but rather to find out which is more successful as an explanation: "Three different hypotheses, that is suggestions, have been discovered by astronomers, which are considered not as if they were true, but merely as suitable for explaining the phenomena" (AT VIIIA 85: CSM I 250). Descartes' preferred hypothesis is chosen "merely as a hypothesis and not as the truth of the matter" (AT VIIIA 86: CSM I 251).

Evidently it would be better if we could discover the true causes of natural phenomena; but if we cannot, it is still worth while to settle for a possible or plausible cause:

As far as particular effects are concerned, whenever we lack sufficient experiments to determine their true causes, we should be content to know some causes by which they could have been produced …

I believe that I have done enough if the causes which I have explained are such that all the effects which they could produce are found to be similar to those we see in the world, without inquiring whether they were in fact produced by those or by some other causes.

(AT IXB 185, 322)

The methodology suggested here, of constructing mechanical models as best we can, coincides with Cartesian scientific practice. Descartes and his followers in France in the seventeenth century were almost profligate in imagining hypothetical models to explain natural phenomena and, in some cases, to explain what could only be called alleged phenomena; they even constructed explanations of nonevents. It was this widespread and notorious dedication to unrestrained hypothesis construction that helps explain Newton's famous disclaimer: "I do not construct hypotheses."15

Yet, despite the fact that the logic of Descartes' philosophy implied that explanations of natural phenomena had to be hypothetical, there are equally clear intimations in his work of a very different methodology. Descartes often referred to the possibility of constructing a natural philosophy based on a metaphysical foundation that would realize the kind of certainty and unrevisability which is apparently at issue in the Meditations. This feature of his methodology needs some clarification before inquiring if it is compatible with the story told thus far.


In the Preface to the French edition of the Principles, Descartes introduces a metaphor that accurately expresses his views about the relationship of physics to metaphysics. "Thus the whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics and morals" (AT IXB 14: CSM I 187). There was nothing unusual in this suggestion. Descartes had maintained for about twenty-five years prior to this that physics, as he understood it, is based on or depends on metaphysics and that any natural philosopher worth his salt had better get his metaphysics in order first, before tackling the explanation of specific natural phenomena. For example, he wrote to Mersenne in 1630 about a short essay on metaphysics he himself had begun to write: "It is there that I have tried to begin my studies; and I can tell you that I would not have been able to discover the foundations of physics if I had not looked for them in this direction" (15 April 1630: AT I 144). This helps explain why he objected to Galileo's methodology. According to Descartes, the Italian natural philosopher had ignored questions about foundations and had applied himself instead directly to explaining particular physical phenomena: "without having considered the first causes of nature, he [Galileo] has merely looked for the explanations of a few particular effects, and he has thereby built without foundations" (to Mersenne, 11 October 1638: AT II 380: CSMK 124). The question arises, therefore, about the kinds of foundations Descartes envisaged for physics, and the connection between those foundations and the various sciences that depend on them. One way of focusing on this issue is to contrast Descartes' approach with what is standard practice in modern science. Physicists or physiologists of the twentieth century do not begin their research with a study of metaphysics, although they may well make metaphysical assumptions in the course of constructing their theories. Instead, they first develop scientific theories which are tested for viability, and the metaphysical implications of the theories are subsequently read off from the finished scientific product. In this approach there is no independent criterion for the acceptability of ontological commitments, apart from the success or otherwise of a given theory. Descartes held the opposite view. He assumed that we can, and ought, to construct our metaphysics first, and that we should subsequently consider physical theories which are consistent with our metaphysical foundation. Thus there must be available independent criteria for deciding which metaphysics to adopt.

On this issue Descartes is very close to scholastic philosophy. The epistemic foundation of Cartesian metaphysics is reflection on "common sense" or on our everyday experience of the natural world. Rule II of the method proposed in the Discourse, which reflects Rule IX of the Regulae, was "to begin with the simplest and most easily known objects in order to ascend little by little, … to knowledge of the most complex" (AT VI 19: CSM I 120).16 Where metaphysics is concerned, we begin with such everyday experiences as the experience of thinking, of feeling, of moving, etc. Among these experiences, Descartes favors the most simple, accessible and widely available experiences because he hopes thereby to find indubitable foundations. This strategy was outlined in Part VI of the Discourse:

I also noticed, regarding observations, that the further we advance in our knowledge, the more necessary they become. At the beginning, rather than seeking those which are more unusual and highly contrived, it is better to resort only to those which, presenting themselves spontaneously to our senses, cannot be unknown to us if we reflect even a little. The reason for this is that the more unusual observations are apt to mislead us when we do not yet know the causes of the more common ones, and the factors on which they depend are almost always so special and so minute that it is very difficult to discern them.

(AT VI 63: CSM I 143)

The privileged position of everyday experience coincides with a complementary distrust of sophisticated experiments; the latter are likely to mislead us because they may be poorly executed, their results may be incorrectly interpreted, or they may be compromised by various interfering factors of which we are unaware.17 Therefore, experimental evidence is too unreliable to provide metaphysical foundations for scientific theories; that can only be done by reflection on ordinary experience.

The central claims of Cartesian metaphysics are summarized in the Meditations and in Part I of the Principles. While they are discussed elsewhere in this volume, the relevant feature here is the extent to which Descartes relies on a scholastic set of concepts to interpret metaphysically the personal experiences for which he claims indubitability. For example, the distinction between a substance and its modes is central to the Cartesian argument in favor of a radical distinction between things that can think and those that cannot.18 The same distinction is put to work in defining the essence of matter and in denuding matter of many of the primary qualities other natural philosophers were willing to attribute to it, such as gravity or elasticity. In summary, Descartes' metaphysics is a subtle combination of scholastic categories, metaphysical axioms (e.g., ex nihilo nihil fit), and apparently incontrovertible common experience.19

Once this foundation is in place, the second stage of theory construction is the formulation of the so-called "laws of nature." Despite the fact that these are said to be "deduced" from a metaphysical foundation, the evidence adduced in favor of the laws, both in Le Monde and the Principles, is a mixture of metaphysical axioms and everyday observation. For example the first law, to the effect that a material object continues in its condition of rest or motion unless some cause intervenes to change its condition, is partly justified by reference to the general axiom that every event or change requires a cause, and partly by reference to our everyday experience: "our everyday experience of projectiles completely confirms this first rule of ours" (AT VIIIA 63: CSM I 241).20 The other two laws of nature are confirmed in the same manner, by appealing to metaphysical axioms and to our everyday experience of physical objects that move about in the world (AT VIIIA 64–5: CSM I 242).

Thus the metaphysical foundations Descartes claimed to establish for scientific knowledge included a number of related elements, which relied on the kind of the evidence just discussed: (a) a radical distinction between matter and spirit, and a preliminary identification of the primary qualities of matter. This included an equally confident dismissal of various properties which Descartes claimed matter does not have; (b) a rejection of the scholastic understanding of explanation and, in its place, the substitution of an uncompromising model of mechanical explanation; (c) a sketch of three fundamental laws of nature according to which material particles interact and exchange various quantities of motion.

Once these were in place, the question arose of how Descartes might make progress in constructing the type of mechanical models required by his method. What kind of inference was available to move from general principles to the explanation of specific natural phenomena?

Descartes' actual scientific practice coincided with his description of theory construction in Part VI of the Discourse. As he moved further away from general principles and closer to particular phenomena, he found he needed hypotheses and experimental tests:

First I tried to discover in general the principles or first causes of everything that exists or can exist in the world…. Next I examined the first and most ordinary effects deducible from these causes. In this way, it seems to me, I discovered the heavens, the stars, and an earth … and other such things which, being the most common of all and the simplest, are consequently the easiest to know. Then, when I sought to descend to more particular things, I encountered such a variety that I did not think the human mind could possibly distinguish the forms or species of bodies that are on the earth from an infinity of others that might be there if it had been God's will to put them there. Consequently I thought the only way … was to progress to the causes by way of the effects and to make use of many special observations…. I must also admit that the power of nature is so ample and so vast, and these principles so simple and so general, that I notice hardly any particular effect of which I do not know at once that it can be deduced from the principles in many different ways; and my greatest difficulty is usually to discover in which of these ways it depends on them. I know no other means to discover this than by seeking further observations whose outcomes vary according to which of these ways provides the correct explanation.

(AT VI 63–4: CSM I 143–4)

This text is clear in admitting that it is not possible to deduce, in an a priori manner, an explanation of particular natural phenomena from the very general laws of nature Descartes defended, because there is an almost infinite number of alternative paths—all consistent with the laws of nature—by which God might have caused particular natural phenomena. To discover which path he chose, i.e. to discover the mechanism by which natural phenomena are caused by the interaction of particles of matter, one has to have recourse to crucial experiments. And, as has been already acknowledged above, the results which can be gleaned by this method are still hypothetical.

However, Descartes is not consistent in acknowledging that hypothetical initiatives must remain hypothetical, and that they cannot be converted subsequently into something more like the purely formal deductions of mathematics. And, despite the need for experiments to help decide how a natural phenomenon occurs, he sometimes described the results of his scientific method in language which could almost have been taken directly from the section of Aristotle's Posterior Analytics quoted above: "As far as physics is concerned, I believed that I knew nothing at all if I could only say how things may be, without being able to prove that they could not be otherwise" (letter of 11 March 1640: AT III 39: CSMK 145). This raises a question about the kind of certainty Descartes claimed for the results of his scientific method when applied to natural phenomena.


Descartes' claims about the relative certainty of scientific explanations are appropriately ambivalent. The ambivalence reflects the comparatively unsophisticated concepts of certainty and uncertainty available to the early seventeenth century. The scholastic tradition was committed to a sharp dichotomy between two kinds of knowledge-claim; one was certain and demonstrated, and the other was dialectical and uncertain. As far as scholastics were concerned, therefore, one had to choose between claiming to have demonstrated, certain knowledge—which was the only kind worth having—or the type of uncertain opinion which hardly deserved further discussion, since it was completely uncorroborated. Descartes' efforts to describe the degree of certainty that resulted from his scientific practice are best understood as a doomed attempt to classify the probability produced by the new scientific method in the language of the scholastics. Thus he sometimes claims that his explanations are certain; he cannot concede that they are uncertain without automatically excluding them as genuine alternatives to the established explanations of the schools. At the same time he recognizes that they are not absolutely certain, that they do not enjoy the type of certainty that can be realized in mathematics, that they are only morally certain or as certain as one could hope to be in this type of enterprise.21 Another compromise, consistent with the claims about a metaphysical foundation, is the argument that the first principles are certain whereas the explanations of particular natural phenomena are more or less uncertain.

Descartes consistently claims that his first principles, or the more general claims about matter and the laws of nature, are very certain.

as regards the other things I assumed which cannot be perceived by any sense, they are all so simple and so familiar, and even so few in number, that if you compare them with the diversity and marvellous artifice which is apparent in the structure of visible organs, you will have far more reason to suspect that, rather than include some which are not genuine, I have omitted some which are in fact at work in us. And knowing that nature always operates in the most simple and easy way possible, you will perhaps agree that it is impossible to find more plausible explanations of how it operates than those which are proposed here.

(AT XI 201)

This point was reiterated on a number of occasions; the basic hypotheses of the Cartesian system were said to be simple and relatively few, and at the same time they explained a great variety of disparate natural phenomena. "Simple" had connotations of being easily understood, possibly by analogy with some natural phenomenon with which we are ordinarily familiar. It also implied that a hypothesis was consistent with the limited categories available in Cartesian natural philosophy, such as size, speed, and quantity of motion. In other words, it was possible to imagine or construct a mechanical model of a so-called "simple" hypothesis, whereas the kinds of explanations proposed by others were allegedly difficult to understand, not amenable to simple modeling, and probably expressed in the metaphysical language of the schools. Thus he wrote in Part III of the Principles: "I do not think that it is possible to think up any alternative principles for explaining the real world that are simpler, or easier to understand, or even more probable" (AT VIIIA 102: CSM I 257).

Descartes was aware of the objection that one could construct a hypothesis to explain any conceivable phenomenon and that, as a result, hypotheses could be accused of being ad hoc. His answer to this objection included a number of elements. One was that he used only a few hypotheses to explain many different phenomena: "it seems to me that my explanations should be all the more accepted, in proportion as I make them depend on fewer things" (AT VI 239). Given the few principles from which he begins, the variety of phenomena which are explained provides an extra degree of confirmation.

In order to come to know the true nature of this visible world, it is not enough to find causes which provide an explanation of what we see far off in the heavens; the selfsame causes must also allow everything which we see right here on earth to be deduced from them. There is, however, no need for us to consider all these terrestrial phenomena in order to determine the causes of more general things. But we shall know that we have determined such causes correctly afterwards, when we notice that they serve to explain not only the effects which we were originally looking at, but all these other phenomena, which we were not thinking of beforehand.

(AT VIIIA 98–9: CSM I 255)

Apart from the points just mentioned, Descartes also argued that the new natural philosophy should be compared, not with some abstract criterion of what counts as a good theory, but with other theories available in the 1630s to explain the same range of phenomena. In that context, Cartesian science was claimed to be the best available. This is clear from a letter to Father Morin of 13 July 1638:

Finally, you say that there is nothing easier than to fit some cause to any given effect. But although there are indeed many effects to which it is easy to fit different causes, one to one, it is not so easy to fit a single cause to many different effects, unless it is the true cause which produces them. There are often effects where, in order to prove which is their true cause, it is enough to suggest a cause from which they can all be clearly deduced. And I claim that all the causes which I have discussed are of this type … If one compares the assumptions of others with my own, that is, all their real qualities, their substantial forms, their elements and similar things which are almost infinite in number, with this one assumption that all bodies are composed of parts—something which can be observed with the naked eye in some cases and can be proved by an unlimited number of reasons in others … and finally, if one compares what I have deduced about vision, salt, winds, clouds, snow, thunder, the rainbow, and so on from my assumptions, with what they have deduced from theirs … I hope that would suffice to convince those with an open mind that the effects which I explain have no other causes apart from those from which I deduce them.

(AT II 199–200: CSMK 107)

The conclusion of the Principles repeats the same claim; if a few assumptions can explain a wide variety of disparate phenomena, then that argues well for their plausibility:

Now if people look at all the many properties relating to magnetism, fire and the fabric of the entire world, which I have deduced in this book from just a few principles, then, even if they think that my assumption of these principles was arbitrary and groundless, they will still perhaps acknowledge that it would hardly have been possible for so many items to fit into a coherent pattern if the original principles had been false.

(AT VIIIA 328: CSM I 290)

If we accept the point being made, that a few basic hypotheses are put to work in explaining all the natural phenomena mentioned, what degree of certainty should Descartes claim for his first principles? Not surprisingly, one finds two rather different claims in this context: one of them concedes that the confirmed principles are only more or less probable, whereas the other assumes that they are certain and demonstrated. The more modest claim is found in a letter to an unknown correspondent, written about 1646: "I would not dare claim that those [principles] are the true principles of nature. All I claim is that, by assuming them as principles, I have satisfied myself in all the many things which depend on them. And I see nothing which prevents me from making some progress in the knowledge of the truth" (AT IV 690). The more confident claim about moral and metaphysical certainty comes in the penultimate article of the Principles:

there are some matters, even in relation to the things in nature, which we regard as absolutely, and more than just morally, certain.… This certainty is based on a metaphysical foundation … Mathematical demonstrations have this kind of certainty, as does the knowledge that material things exist; and the same goes for all evident reasoning about material things. And perhaps even these results of mine will be allowed into the class of absolute certainties, if people consider how they have been deduced in an unbroken chain from the first and simplest principles of human knowledge…. it seems that all the other phenomena, or at least the general features of the universe and the earth which I have described, can hardly be intelligibly explained except in the way I have suggested.

(AT VIIIA 328–9: CSM I 290–1)

The French version of this text is even more explicit on the demonstrative character of the explanations found in Cartesian physics:

I think that one should also recognise that I proved, by a mathematical demonstration, all those things which I wrote, at least the more general things concerning the structure of the heavens and the earth, and in the way in which I wrote them. For I took care to propose as doubtful all those things which I thought were such.

(AT IXB 325)

The problem of classifying the type of certainty Descartes might reasonably have claimed for his principles and hypotheses is best understood historically, by taking account of the lack of a concept of probability in the early part of the seventeenth century and of the assumption of the scholastic tradition that anything less than demonstrated truths was as unreliable as mere opinion or guesswork. In this context, Descartes claimed that his natural philosophy was certain and demonstrated; at the same time, realizing that it could hardly be as certain as the formal proofs of mathematics, he conceded that only the more general assumptions of his system were certain, whereas the explanations of particular natural phenomena were more or less certain.

This point reopens the question about the kind of evidence Descartes thought was appropriate to supporting scientific claims, and the relative importance of metaphysical arguments vis-à-vis experiential evidence. There is no suggestion that Descartes ever reneged on the conviction, so clear in the Meditations, that one can realize a degree of certainty which is equivalent to indubitability by reasoning about concepts and axioms. This kind of metaphysical certainty is appropriate to the foundations of our knowledge, whether that knowledge is mathematical, physical, or otherwise.

However, if we wish to make judgments about the physical world, then we cannot assume naively that our sensations reflect the way the world is. Nor can we discover in any detail what kind of natural phenomena occur, nor what mechanisms explain their occurrence, by introspecting our ideas. There has to be some provision, therefore, for beginning with clear and distinct metaphysical concepts and axioms and somehow making the crucial transition to describing and explaining the natural world around us. This can be done only by consulting our experience of the natural world, and this implies that we use our senses in order to gain scientific knowledge.

At the same time, Descartes can be correctly described as a critic of the reliability of empirical evidence. His critique was carefully developed to identify a number of ways in which we might draw erroneous conclusions from our sensory experience. Two of these have already been identified: (a) We might ignore the distinction between primary and secondary qualities and, as a result, assume that our sensations resemble the causes of our sensations; and (b) we might argue too hastily from an experiment to some conclusion without taking account of the many ways in which an experiment can mislead. In general, we are in danger of spontaneously making naive, uncritical judgments about the physical world without questioning the reliability of our sensations or the logic of conclusions drawn from reliable observations. Such spontaneous judgments should be distinguished from other judgments, equally based on sensation, which we make after due deliberation and reflection. Unfortunately for the modern reader, Descartes expressed this distinction in terms of a contrast between experience and reason; what he meant was a contrast between two types of judgment, both equally based on experience. This is made explicit in the following text:

It is clear from this that when we say 'The reliability of the intellect is much greater than that of the senses,' this means merely that when we are grown up the judgments which we make as a result of various new observations are more reliable than those which we formed without any reflection in our early childhood; and this is undoubtedly true.

(Sixth Replies: AT VII 438: CSM II 295)

For this reason, a true philosopher "should never rely on the senses, that is, on the ill-considered judgments of his childhood, in preference to his mature powers of reason" (AT VIIIA 39: CSM I 232).

It is obvious, then, that one cannot avoid the necessity of relying on experientially based evidence. Descartes acknowledges the need for this kind of evidence in natural philosophy and uses it extensively in the scientific experiments which he describes. He says openly, in Part VI of the Discourse, "regarding observations, that the further we advance in our knowledge, the more necessary they become" (AT VI 63: CSM I 143). On this point, his scientific practice corresponded with his methodological rule, for he spent much more time doing experiments or reading about those done by others than he ever spent in mere thinking. However, for reasons already mentioned, he had little confidence in experiments he had not checked himself.22 Hence there were serious limits to the extent to which he could hope to complete a comprehensive explanation of nature; he was likely to be frustrated "by the brevity of life or the lack of observations" (AT VI 62: CSM I 143). For this reason, Descartes decided to devote his life to the pursuit of what he called a "practical philosophy which might replace the speculative philosophy taught in the schools" (AT VI 61: CSM I 142). "I will say only that I have resolved to devote the rest of my life to nothing other than trying to acquire some knowledge of nature from which we may derive rules in medicine which are more reliable than those we have had up till now" (AT VI 78: CSM I 151). This is equivalent to a commitment to doing experiments, the cost of which he often complained of. To attempt to gain this practical knowledge in any other way, apart from experimentally, would be to join those "philosophers who neglect experience and think that the truth will emerge from their own heads as Minerva did from that of Jupiter" (Regulae Rule V: AT X 380).

A full account of the contribution of Descartes to the history of philosophies of science would involve examining his work in the light of his successors in the seventeenth century. Without examining this supplementary evidence here—which would include the ways in which Descartes was understood by, for example, La Forge, Malebranche, Rohault, Poisson, Cordemoy and Régis—there is reason to believe that his successors shared a common interpretation of the main features of Descartes' philosophy of science.23 These common features are best understood in contrast with the scholastic philosophy for which they were proposed as a substitute. For Descartes, the contrast was between the practical and the speculative, the explanatory and the nonexplanatory, the critical and the naively uncritical, the mechanistic and the formal, the mathematical and quantitative versus the qualitative. Despite the favorable contrast with the natural philosophy of the schools, however, Descartes continued to accept the scholastic assumption that we should construct our metaphysics first, on the epistemic basis of reflection on ordinary experience, and that any subsequent explanations of natural phenomena must be consistent with the foundational metaphysics.

Once the foundations were in place, it was accepted that we could never know the way the world is by consulting our sensations and inferring from them that the causes of our sensations must resemble our subjective experiences. Besides, if we assume that physical phenomena are constituted by the interactions of very small particles of matter, then the sheer size of such particles of infinitely divisible matter would put their observation beyond our reach. For these two reasons, we can only come to know how the physical world is by hypothesis.

For Descartes, to explain a natural phenomenon is not to redescribe it in the language of forms and qualities, as was done in the schools. To explain, in this context, is to construct a mechanical model of how the phenomenon in question is caused. This model construction is necessarily hypothetical. So, beginning with the basic laws of nature and the metaphysical foundations established in the Meditations or in Book of the Principles, Descartes set out to construct the kind of models his concept of explanation demanded. Although he continued to claim absolute certainty for the foundations, it was clear that he could not be as confident about the more detailed explanations of natural phenomena. These explanations depended on observations, and on performing complex experiments the interpretation of which introduced new reasons for doubt. There was also another reason for caution which emerged at this stage, namely Descartes' skepticism about the possibility of ever identifying the multiplicity of variables involved in any complex natural phenomenon. What begins on "indubitable" foundations, therefore, quickly gets mired in the almost immeasurably complex detail of unobservable particles of matter interacting at unobservable speeds. The crucial experiments which we perform to help choose the most plausible explanation are open to various interpretations. Hence the birth of the well-known Cartesian tradition of simply imagining some mechanism by which small parts of matter in motion might have caused some natural phenomenon which we observe.

To those who objected: this does not result in the kind of demonstrated knowledge prized by the scholastic tradition, Descartes replied that those who demand such demonstrations do not know what they are looking for, nor what they ought to look for. It is not possible to realize the same kind of certainty in physics as in mathematics or metaphysics. We have to settle for less.

This suggests that Descartes' philosophy of science was very much a product of the time in which it was developed. The 1630s and 1640s were a time of transition from the science of forms and qualities to what we describe now as modern science. One finds features of both of these philosophies of science in Descartes. What was significantly new was the commitment to mechanical explanation rather than the "occult powers" of the scholastic tradition, and the recognition that this type of explanation must be hypothetical. But for Descartes, lacking a theory of probability, this seemed compatible with the continued claim that his natural philosophy was not only superior in explanatory power to that of the schools, but that it was just as certain; or at least, that its more fundamental principles were demonstrated.


1Posterior Analytics, 71b 8–12, 73a 21–2.

2 The extent to which scholastic philosophy influenced the curriculum of colleges and universities in France in the seventeenth century is comprehensively documented in Brockliss, French Higher Education in the Seventeenth and Eighteenth Centuries.

3 This was summarized in the axiom: "nihil est in intellectu quod prius non fuit in sensu." French Cartesians in the period immediately after Descartes understood his theory of innate ideas as, in part, a response to what they considered to be a generally accepted scholastic doctrine, that all ideas derive originally from sensation. See, for example, Poisson, Commentaire ou remarques sur la méthode de M. Descartes, unpaginated preface, which discusses the "famous principle on which depends some of the dogmas of scholasticism, that nothing enters the mind which does not pass first through the senses." The same doctrine is discussed at some length on pp. 124–38. Cf. Le Grand, An Entire Body of Philosophy, p. 4. Among scholastic defenders of the thesis, even after Descartes, see Huet, Censura Philosophiae Cartesianae, pp. 51–3.

4 Even dedicated Cartesians, such as Jacques Rohault, continued the tradition of explaining natural phenomena in terms of matter and form. See Rohault, A System of Natural Philosophy, translated by J. Clarke, pp. 21–2. The original French text was published in 1671.

5 Mahoney (trans.), The World, pp. 1–3.

6 Mahoney, The World, p. 5.

7 Mahoney, The World, p. 7.

8 Mahoney, The World, p. 49.

9 Letter to Mersenne, 27 May 1638 (AT II 141–2, 143–4:CSMK 103). The same use of the word "demonstration" is found in Descartes' letter to Plempius, 3 October 1637 (AT I 420:CSMK 64).

10 The principle of parsimony in metaphysics, that one should not postulate the existence of more distinct entities or types of entity than is necessary, is usually attributed to William of Occam (1280?-1349?). See for example his Quodlibeta V, Q.1

11 Mahoney, The World, p. 9.

12 Mahoney, The World, p. 39.

13 Although the letter was written in French, the italicized phrase was in Latin: sub scientiam non cadit. Descartes to Mersenne, 13 November 1629 (AT I 73). See also Descartes to Mersenne, 11 June 1640 (AT III 80); Descartes to Cavendish, 15 May 1646 (AT IV 416–17).

14 Cf. similar responses to Mersenne, 23 February 1643 (AT III 634) and 26 April 1643 (AT III 652).

15 In the original Latin text, "hypotheses non fingo." Isaac Newton, Mathematical Principles of Natural Philosophy and His System of the World, ed. Cajori, p. 547.

16 Cf. Rule Nine of the Regulae: AT X 400: CSM I 33.

17 Descartes frequently pointed to problems in interpreting experimental results, especially when they seemed to disconfirm his own theories. However, the objections he raised were, in principle, legitimate. See, for example, Descartes to Mersenne, 9 February 1639 (AT II 497–8), 29 January 1640 (AT III 7), 11 June 1640 (AT III 80), 4 January 1643 (AT III 609).

18 Cf. Principles Part I, arts. 51–7: AT VIIIA 24–7: CSM I 210–12.

19 In the Third Meditation, Descartes argues that "something cannot arise from nothing" (nec posse aliquid a nihilo fieri) (AT VII 40: CSM II 28). In the Second Replies to Objections, he says that the causal principle on which he relied in the Third Meditation was equivalent to "nothing comes from nothing" (a nihilo nihil fit) (AT VII 135: CSM II 97).

20 Cf. Mahoney, The World pp. 61–76: AT XI 38–47.

21 There was a tradition in scholastic philosophy and theology of distinguishing various degrees of certainty in terms of the kind of evidence required to achieve them and the relative importance of acting on our beliefs in different contexts. "Moral certainty" referred to the certainty required for important human actions, such as marrying one's partner or defending oneself against an aggressor. In this type of case, one does not usually have mathematical certainty about various relevant features of the context, but one is sufficiently certain to act and to be excused of responsibility if, despite taking normal precautions, one is mistaken. Cf. French version of Principles, Part IV, art. 205: "moral certainty is certainty which is sufficient to regulate our behaviour, or which measures up to the certainty we have on matters relating to the conduct of life which we never normally doubt, though we know that it is possible, absolutely speaking, that they may be false" (CSM I 289).

22 "I have little trust in experiments which I have not performed myself (letter to Huygens of 1643: AT III 617).

23 For an analysis of how these authors understood Descartes' philosophy of science, see Clarke Occult Powers and Hypotheses.

Jean-Marie Beyssade (essay date 1993)

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SOURCE: "On the Idea of God: Incomprehensibility of Incompatibilities?" translated by Charles Paul, in Essays on the Philosophy and Science of René Descartes, edited by Stephen Voss, Oxford University Press, 1993, pp. 85–94.

[In the essay that follows, Beyssade examines the paradoxical claims that form the basis of Descartes' metaphysics: that God is incomprehensible and that, to know anything, one must have a clear and distinct understanding of God.]

Here I would like to raise the question of the idea of God and its nature, because in the metaphysics of Descartes one thesis remains constant from his lost first draft, written in 1628–29, and because this thesis is paradoxical. The thesis is that the entire methodical structure of scientific knowledge depends on an assured knowledge of God. The paradox is that God is asserted to be incomprehensible.

The totality of Cartesian science is based on metaphysics, and two fundamental principles intersect within this metaphysics or first philosophy: one is called the cogito (I think, therefore I am; and I am a think ing substance); the other is called the divine veracity (God exists; and he cannot deceive me). To appreciate the function assigned to the idea of God one must understand "in what sense it can be said that, if one is ignorant of God, one cannot have any certain knowledge of any other thing."1 Any other thing: neither mathematics nor physics nor metaphysics. Mathematics, whose reasoning had provided the model of certainty and evidence before metaphysical reflection, does not suffice to give the atheist geometer a true and certain science; but Descartes believes that he "has found how one can demonstrate metaphysical truths in a manner that is more evident than the demonstrations of geometry,"2 how one can demonstrate the existence of God "in the same manner" as one demonstrates a property of the triangle, "or in a still more evident manner."3 Physics, which is the trunk of the Cartesian tree, derives its scientific validity from its metaphysical roots: "this is how I have attempted to begin my studies; and I will tell you that I could not have discovered the foundations of physics if I had not sought them in this way."4 Here order consists in passing from causes to effects, "without basing my reasons on any other principle than the infinite perfections of God;"5 for "we will undoubtedly pursue the best method that can be used to discover the truth [optimam philosophandi viam] if, from our knowledge of his nature [ex ipsius Dei cognitione], we proceed to the explanation of the things he has created, and if we attempt to deduce it from the notions that naturally reside in our souls in such a way that we have a perfect knowledge [science] of it, that is, in such a way that we know the effects from the causes [scientiam perfectissimam, quae est effectuum per causas]."6 Finally, in metaphysics—a discipline that is as fundamental for the physics which follows it as for the mathematics that preceded it—if the truth of the cogito is the first discovered therein, it appears as derived when retrospectively we connect it to the knowledge of God: "In some manner I had within me the notion of the infinite before [priorem quodammo do] I had the notion of the finite, that is, that of God before that of myself."7 The common root of that triple dependence is to be sought in the general rule of the method: "the very thing that I just now took as a rule [and it matters little whether this just now refers to my past as a mathematician or to the cogito, which is my first assertion as a metaphysician], namely, that those things which we can very clearly and very distinctly perceive are all true, is guaranteed only because God is or exists, and is a perfect being, and because everything within us derives from him."8 The evident, that is, the unique criterion of the universal method, namely, clarity and distinctness, therefore hangs on the divine veracity.

Now, by a paradox that is as old as Cartesian metaphysics itself, God is incomprehensible. This thesis appears as early as the letters to Mersenne of spring 1630 on the creation of the eternal truths—the first echo to reach us from the approach adopted in the previous year. "We cannot comprehend [comprendre] the greatness of God, even though we know it [connaissions]."9 "Since God is a cause whose power exceeds the limits of human understanding, and since the necessity of these truths (the eternal truths of mathematics) does not exceed our knowledge," one must surmise "that they are something less than this incomprehensible power, and subject to it" (6 May). "I say that I know it, not that I conceive it or comprehend it, because one can know that God is infinite and all-powerful even though our mind, being finite, can neither conceive nor comprehend it" (27 May). Here incomprehensibility is linked to the greatness of God, and in particular to his power. It is, throughout Cartesian metaphysics, the characteristic of the infinite. "The infinite, qua infinite, is never truly comprehended, but it is nevertheless understood [intelligi, entendu]."10 "In order to have a true idea of the infinite, it is in no way necessary that one comprehend it, inasmuch as incomprehensibility is itself contained in the formal reason of the infinite."11 We seem driven to ask whether the method, in requiring divine veracity, may not require a foundation which in its incomprehensibility would violate that very method. In basing the truth of everything that is evident on the divine infinity, the method seems to introduce an element that is irreducible to what is evident, an element perhaps intrinsically obscure and confused. We may go further. If the Cartesian God is not just provisionally misunderstood at the beginning of the process, but if he also reveals himself at the end of it to be definitively incomprehensible, is there not a danger that this avowed incomprehensibility in reality conceals internal contradictions, incompatibilities? "An infinite and incomprehensible being," Descartes had written on 6 May 1630.12 "An absolutely incomprehensible and contradictory being" is how the atheist critic will translate it, for example Baron d'Holbach in the eighteenth century.13

Incomprehensibility or inconsistencies—that is our question concerning the idea of God and the nature of God in the metaphysics of Descartes. The paradox can be extended in various directions. We shall develop only one of those directions. We raise the question how the idea of God is capable of satisfying the requirements of the method. The method is absolutely universal. It requires that every perception (or cognition or idea) without exception be clear and distinct if the corresponding proposition (or judgment or statement) is to be included in science. The idea of God must therefore be clear and distinct, and, if the judgment concerning God is the first one of the true science, this idea must be recognized as "the clearest and most distinct of all those present in my mind."14 Is there no inconsistency between these two assertions, namely, that the idea of God is incomprehensible and that it is the clearest and most distinct of all ideas?

God, qua infinite, is incomprehensible. The idea of God is the clearest and most distinct idea of all. These two theses are both incontestably Cartesian. Are they incompatible? Is there an inconsistency here? We do not think so.

First we need to dig deeper into the correlation between (divine) incomprehensibility and distinctness or differentiation. In fact, from 1630 on, Descartes quite rigorously associates the knowledge of God and the recognition of his inconceivable infinity. The knowledge of God is doubly positive: we know at the same time that he exists and, with respect to a certain number of attributes (e.g., omnipotence, immutability, creator of existences and of essences), what he is. The recognition of his incomprehensibility is negative at first: the impossibility that we should embrace or encompass or master his nature. If clarity corresponds to presence, then incomprehensibility instead marks an absence, and this is why it seems connected to obscurity and confusion. This contrast is not false, but it is simplistic and one-sided. The truth is that starting with the letters of 1630, the divine incomprehensibility does not only have the negative function of limiting our knowledge of God by the recognition of something beyond which escapes our grasp. In a positive way it introduces into our idea of God the original and true knowledge of an incommensurable distance. Thanks to it God is not beyond the idea we have of him, like a hidden God, in which case our idea of him would not display him as he is. To the contrary, his greatness is given directly as present, without any possible confusion with our own properties. Incomprehensibility is the positive manner in which the infinite reveals itself to a finite mind as it is, that is to say, as incomparable. By a reversal illustrated in the comparison made between God and a king, what at first seems to be a principle of confusion is shown to be a principle of distinctness.15 "We cannot comprehend the greatness of God, even though we know it": the phrase "even though," introducing a subordinate clause, contrasts what we know (which is positive, or clear) with what seems negative and obscure (namely, what we cannot comprehend). "But this very fact, that we judge it to be incomprehensible, makes us esteem it the more": the phrase "this very fact" marks the reversal, from a subordinate clause indicating opposition into an explanation indicating assimilation. The failure to reduce (by means of dominating through comprehension) is actually a success; it is the way a finite mind recognizes and esteems the more what in fact can never be esteemed too much, since it is absolute greatness. "Just as a king possesses greater majesty when he is less familiarly known by his subjects": thus distance is a mark of majesty, and to decrease familiarity is not to decrease knowledge, but to disclose to a subject the true knowledge of his unequal relation to his king. On the condition, to be sure, that the distant king is not a king who is hidden or unknown: "provided, however, that this does not make them think that they are without a king, and provided that they know him sufficiently well not to have any doubts about it." The phrase "provided that" leads us back again to the subordinated opposition of the "even though" between knowledge that is sufficient to dispel doubt (presence, or clarity) and noncomprehension (absence, such as distance and distinctness).

This equilibrium is maintained in the great systematic expositions, notably in the Third Meditation.16 "It is useless to object that I do not comprehend the infinite, or [vel] that there are an infinity of other [alia] attributes within God that I can neither comprehend nor even perhaps reach by thought in any way at all." Here incomprehensibility seems to function as a barrier between two categories of attributes, the ones that I perceive clearly and distinctly and the rest. The first ones ensure knowledge that is sufficient to dispel doubt: "everything real and true that my mind conceives clearly and distinctly and that contains in itself some perfection is entirely contained and enclosed in that idea." Here clarity of presence extends to conception (the Latin only gives percipio), and, it seems at first, to comprehension as well. The other category of attributes ensure distance and majesty. I can neither comprehend them nor perhaps, for certain of them, have any other species of idea of them: this is pure absence or obscurity, which surrounds my knowledge with a black line, like the curtain behind which the king withdraws. "For it is of the nature of infinity that my finite and limited nature cannot comprehend it." The axiom which makes of incomprehensibility the true relation between the infinite and the finite can be counted on to bring us back from opposition (alia) to an explanation indicating assimilation.

"And it is sufficient that I conceive this well [me hoc ipsum intelligere], and that [ac] I judge that all things that I conceive clearly and in which I know there to be some perfection, and perhaps also an infinity of others [atque etiam forte alia innumera] of which I am ignorant, are in God formally or eminently, in order for [ut] the idea I have of him to be the most true, the most clear, and the most distinct of all those existing in my mind." Two conditions must be met in order that the idea of God attains the maximum of clarity and distinctness. It is sufficient that I perceive thoroughly the link between (positive) infinity and incomprehensibility: hoc ipsum, "this very thing," was precisely the reversal of 1630. But this is not the only condition: it is also necessary that I endow God with predicates; and in an attenuated form the ac takes up again the phrase "provided that" of 1630. These predicates are of two kinds. One kind are unknown—innumerable alia which escape me entirely. The other kind, the first ones named, correspond to perfections recognized and identified by me; they constitute the positive element without which there could be no clarity.

A commentary for the benefit of Clerselier, of 23 April, 1649, fixes the doctrine once and for all. It refers quite specifically to our phrase "and it is sufficient that I understand this very thing well," which I have labeled the reversal. Descartes clarifies: "Yes, it is sufficient that I understand this very thing well, namely that God is not comprehended by me, in order that I understand [intelligam] God according to the truth of the thing [juxta rei veritatens] and such as he is [qualis est]."17 And so incomprehensibility is not an obstacle or a limit to our intellectual understanding of God; on the contrary, it reveals God in his truth, in his real and positive transcendence. This incomprehensibility does not reveal a regrettable and provisional failure of my limited mind, but instead a necessary incommensurability between the infinite and any finite mind, even one more perfect than my own, even the mind of an angel. The truth of my idea is ensured thanks to this lack of comprehension, this intellectual understanding of the incomprehensibility, and not in spite of it. Must we say, with Alquié, that our intellectual understanding of God consists "simply in the apprehension of his incomprehensible character"?18 To do so would be to forget the necessity of the other element, namely, the presence which is required by clarity. The letter to Clerselier restores to it all the amplitude of the subordinate clause; it revives the overly discreet ac to its true value, namely, "provided that." "Provided that in addition [modo prae terea] I judge that there are in him all the perfections that I know clearly [clare intelligo] and moreover [et insuper] many others which I cannot comprehend." Incomprehensibility is not devoid of perfections; it is superadded to them: the fact that these two terms are externally related, which is implied by the subordinate phrase (modo, "provided that"), is accentuated by praeterea, "in addition." And among the required perfections two species are recorded anew: those of which I have a clear intellection and those, much more numerous (multo plures), which I cannot comprehend. Does this mean that I comprehend the first kind? One might think so, and assimilate my perception of them to a conception, and even a comprehension. Only the second kind, the alia, would then be incomprehensible.

But this would be a mistake. This error must be corrected in order to present Descartes's doctrine in its perfect coherence. The end of the Third Meditation is instructive here. For in fact it discusses, not the divine perfections of which I am ignorant (no doubt there are an infinity of them), but those I know. God exists, therefore, "this same God, I say, the idea of which is within me, that is to say the one who possesses all those exalted perfections [illas perfectiones] which I can, as for myself, not comprehend, but in one manner or another [quocunque modo] reach [attingere] by thought."19 In the strict sense of the word my thought can never comprehend a single divine perfection. But there are a certain number of them which I can reach and, so to speak, touch by thought, in contrast to an infinity of others of which I am completely ignorant. The perfections to which I can attain are those of which I find marks within myself, such as my knowledge, my free will, my power. I comprehend those perfections within myself from the inside, intimately—even my freedom, which is often said to be infinite.20 They are like traces which allow me to form the idea of a divine (omniscient) understanding, a divine will, a divine omnipotence.21 I am able to form a con cept or a conception of each of them, and I should then conceive them in God as infinite or as indefinite, the two adjectives, usually contrasted, here being equivalent, not distinct from one another.22 But we must not allow this legitimate conception to become transformed erroneously into a comprehension, something that would correspond to a drift toward the univocal. It is precisely because all the intelligible perfections are united in God that each of them is, properly speaking, infinite, and none of them can be truly comprehended by me, but only reached by thought or conceived or, still better, understood (entendu).

Let us take up the train of thought as the Second Replies explicates it. It is necessary to begin with those "attributes of God of which we recognize some trace within ourselves": we comprehend them within ourselves, and, were no distance or distinctness to be added to their presence and clarity, we would be content to transfer them, in amplified form, into God, which would ensure the strict univocity of the attributes by turning God into a man writ large.23 "But in addition [praeterea] we understand [intelligimus, concevons] in God an absolute immensity, simplicity, and unity which embraces and contains all his other attributes, and of which we find no instance either in ourselves or elsewhere."24 This absolute unity, which is one of the most exalted of the divine perfections, is intelligible but neither comprehensible nor even conceivable. It ensures the absolute inseparability of the divine perfections, which is the same thing as the absolute simplicity of God, or what Spinoza was to call, by contrast with that which is merely infinite in its own kind, the absolutely infinite.25 This unity, which is not comprehensible by a finite mind, is itself comprehensive. Non tarn capere quam … capi: this divine unity is not comprehended, "grasped together," by finite minds; instead, it grasps them.26 And—what is a different matter—it grasps or comprehends, embraces, complectentem, all the divine attributes.27 Undoubtedly God comprehends himself; that is, he has an adequate concept of all his properties, both those we know and those of which we are ignorant.28 But it is different for us. First of all, there are attributes of which we have no idea: these are the alia, perhaps innumerable, which are as profoundly unknown as, for Spinoza, all the attributes except for extension and thought are unknown. For Descartes, only revelation is capable eventually of rendering them accessible to us. Then there are attributes of which there are traces within us (e.g., knowledge, will, and power). We may now return to them without risk of univocity.29 For their union with the other attributes, in other words, their connection with the absolute unity on which they depend, deprives them of any possibility of being comprehended. They are nonetheless conceivable, for their relation to our own perfections precludes our speaking of a simple equivocity. What we have here is analogy in the most traditional sense, since the clarity of presence (which alone leads to identity, to comprehension, to univocity) is qualified by distance as distinctness (which distance alone leads to otherness, to ignorance, to equivocity). The infinite is intelligible for the very reason that it is not comprehensible.

Let us conclude by investigating how the idea of God works in relation to the unique and universal method, whose general rule requires clarity and distinctness. We discover that these characteristics, whose conjunction defines the evident, undergo two successive transformations in the course of the operation carried out by metaphysics. Before that operation, clarity and distinctness had been separated, after the example of mathematics, which had served in the Rules for the Direction of the Mind and in Part II of the Discourse on Method both as their prototype and as their model. For an object presented to the view of the mind and made subject to its command, clarity signifies presence (the presence of a spectacle to a spectator, ob-versari, something which is there to see);30 and distinctness signifies difference (the difference between two objects next to each other, which are distinguished through juxta-posing them, as in the case of a polygon with 1,000 sides next to one with 999 sides).

The procedure of the cogito constitutes the first subversion: although the same general rule of evidence, namely, the rule of clarity and distinctness, is derived by reflection on this first truth, the prototype and model has changed, and with it the meaning of the criterion. For a mind which itself makes the discovery of itself, and gradually makes itself better known and more familiar to itself, clarity signifies presence to oneself (the consciousness of a subject which senses and experiences itself, in se con-versus);31 and distinctness signifies exclusion (by means of doubt I make myself distinct, in that I reject through denial everything I face, so that I may grasp myself on each occasion as the subject of that exclusion).32 Note well that nothing in the rule has changed—either its universality nor its univocity. The new example takes up within itself the previous ones, and deepens them; it leaves the mathematically evident with all of its brilliance, and simply lays claim to being still more evident, on the basis of the very criteria of the older prototype, which is not so much lowered in class as surpassed in class, and whose criteria have not so much changed as they have manifested what remained implicit in them, yet to be perceived.

The same operation is redoubled in the passage from the cogito to God. For the infinite, the intellectual grasp of which emerges as soon as I comprehend my finitude, clarity signifies the implicit presence of the being (an immediately given reality, a perfect unity prior to all limitation and fragmentation); and distinctness signifies transcendence (separation by distance, by incomprehensibility, which eliminates all confusion by establishing an insurmountable dissimilarity).

Of course, at each passage it is possible to reject the new model, to reduce rationality to the previous model, to consider the shift in foundation as foreign to the method. But what is characteristic of the Cartesian enterprise is that its methodic procedures remain univocal, and in this sense the idea of God must occupy the first place according to the very order of the true science.33 That is why this idea must be maximally evident according to the method itself.

It is therefore not sufficient to set in opposition God, who is incomprehensible, and the idea of God, which is clear and distinct. It is not sufficient to distinguish the properties of the idea from those of its object: the idea of red is not red, the idea of a sphere is not spherical, and the idea of obscurity may not be obscure, but clear and distinct.34 Certainly this difference between the idea and its object is important. In the case under consideration, God is infinite but the idea of God is not infinite: it is, on the contrary, finite and suited to the small capacity of our minds (finita et ad modulum ingenii nostri accommodata).35 Conversely, if the idea of God is the most clear and the most distinct of all, it would be absurd to speak of God as being clear and distinct: this characteristic pertains to an idea, not to its object. But incomprehensibility, which pertains to the nature of God, or to the nature of the infinite, is also a characteristic of his idea. Idea … infiniti, ut sit vera, nullo modo debet comprehendi: it is emphatically the idea of God, and not God himself, that is spoken of (pace the overzealous translation of Clerselier, not reviewed here by Descartes); and it is this idea which, if it is to be true, must not in any way be comprehended.36 A characteristic of the object, in this case God or the infinite, which is incomprehensible, is therefore introduced into the idea of the object: this idea, first of all (and then perhaps many other ideas, later on), cannot in any way be comprehended. But it is precisely in the case of this idea that this characteristic is eminently positive. It establishes the true relation—once it is noticed, the difference is incommensurable and impossible to miss—between the Being which it represents on the one hand and any knowable object and my knowing mind on the other hand. It is because God is incomprehensible that the idea of him is also incomprehensible; and it is not even though this idea is incomprehensible, but rather because it is incomprehensible that it is the most clear and the most distinct of all.37


1Principles of Philosophy I, a. 13, developing Meditation III: AT [Oeuvres de Descartes, ed. C. Adam and P. Tannery, 13 vols., Paris: Vrin/CNRS, 1879–1913] VII, 36, 11. 28–29; in CSM [The Philosophical Writings of Descartes; ed. J. G. Cottingham, R. Stoothoff, and D. Murdoch; two vols.; Cambridge University Press, 1985] II, 25: "for if I do not know this, it seems that I can never be quite certain about anything else."

2 To Mersenne, 15 April 1630: AT I, 144, 11. 14–17; Descartes: Oeuvres philosophiques, ed. Ferdinand Alquié, 3 vols. (Paris: Gamier, 1963–73) I, 259 and n. 1 (henceforth abbreviated FA).

3Discourse on Method IV: AT VI, 36, 11. 24 and 27–28, developed in Meditation V: AT VII, 65, 11. 28–29; AT IX, 52; FA II, 472 and n. 2; in HR [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] I, 104: "in the same manner … or even more evidently still."

4 To Mersenne, 15 April 1630: AT I, 144, 11. 8–11, developed in the letter to Mersenne of 28 January 1641: AT III, 297–298; FA II, 316–317.

5Discourse V: AT VI, 43, 11. 6–8; FA I, 615 and n. 2; in HR I, 108: "without resting my reasons on any other principle than the infinite perfections of God."

6Principles I, a. 24 (on the difference between the Latin and the French, see FA III, 106, n. 1).

7 Meditation III: AT VII, 45, 11. 27–29; AT IX, 36; in CSM II, 31: "my perception of the infinite, that is God, is in some way prior to my perception of the finite, that is myself."

8Discourse IV: AT VI, 38, 11. 16–21; FA I, 611 and n. 1; in HR I, 105: "that which I have just taken as a rule, that is to say, that all the things that we very clearly and very distinctly conceive of are true, is certain only because God is or exists."

9 To Mersenne, 15 April, 6 May, and 27 May 1630: respectively, AT I, 145, 11. 21–22; 150, 11. 18–22; 152, 11. 9–13; respectively, FA I, 260 and n. 4; 265 and n. 3; 267.

10 First Responses: AT VII, 112, 11. 21–23; AT IX, 89; FA II, 531; in CSM II, 81 (and n. 3): "the infinite, qua infinite, can in no way be grasped. But it can still be understood."

11 Fifth Responses: AT VII, 368, 11. 2–4; FA II, 811 and n. 2; in CSM II, 253: "for the idea of the infinite, if it is to be a true idea, cannot be grasped at all, since the impossibility of being grasped is contained in the formal definition of the infinite."

12 To Mersenne, 6 May 1630: AT I, 150, 11. 6–7; FA I, 265.

13Le bon sens du Curé J. Meslier, ch. 40, a work published anonymously in 1772 by d'Holbach, its author.

14 Meditation III: AT VII, 46, 11. 27–28; AT IX, 37; HR I, 166; CSM II, 32.

15 To Mersenne, 15 April 1630: AT I, 145, 11. 21–28; FA I, 260.

16 Meditation III: AT VII, 46, 11. 16–28; AT IX, 36–37; HR I, 166; CSM II, 32 and n. 1. On the relation between this passage and the end of the Third Meditation: AT VII, 52, 11. 2–6; AT IX, 41; HR I, 171; CSM II, 35, a passage which will be examined later, see J.-L. Marion, "Descartes et l'ontothéologie," Bulletin de la Societé Française de Philosophie (24 April 1982), 143; discussed by J.-M. Beyssade in Bulletin cartésien XIII, Archives de Philosophie 47, no. 3 (July-September 1984): 47; taken up again in Sur le prisme métaphysique de Descartes (Presses Universitaires de France: Epimethée, 1986), 119–120 and n. 54. It seems to us that the first passage conjoins comprehendere and attingere ("nec comprehendere nec attingere"), while the second one opposes them ("non comprehendere sed attingere"); but this is because the first passage does not deal with the idea of God in general; it deals only with the alia, the unknown perfections ("which I can neither comprehend nor even reach"), whereas the second one deals with the known perfections ("which I can certainly reach in thought but not comprehend").

17 To Clerselier, 23 April 1649: AT V, 356, 11. 22–27; FA III, 924 and n. 2.

18 F. Alquié, La découverte métaphysique de l'homme chez Descartes (Presses Universitaires de France, 1960 and 1966), ch. 10, 216 and n. 2, a formula developed by H. Gouhier in a remarkable commentary to which we owe a great deal, La pensée métaphysique de Descartes (Paris: Vrin, 1962), ch. 8, ii, 212 and n. 28.

19 Meditation III: AT VII, 52, 11. 2–6; AT IX, 41; HR I, 171; in CSM II, 35: "God, a God, I say, the very same being the idea of whom is within me, that is, the possessor of all the perfections which I cannot grasp, but can somehow reach in my thought."

20Principles I, a. 41: AT VIII, 20, 11. 25, 28–29; HR I, 235.

21 Second Responses: AT VII, 137; AT IX, 108; FA II, 560 and n. 1; CSM II, 98–99. We comment on this passage later.

22Indefinitae, sive infinitae, Second Responses: AT VII, 137, 11. 24–25; CSM II, 99, 1. 1: "indefinite (or infinite)." Cf. Conversation with Burman: AT V, 154; Descartes' Conversation with Burman, ed. John Cottingham (Oxford, 1976), 14–15.

23 To Regius, 24 May 1640: AT III, 64; FA II, 244 and n. 1.

24 Second Responses: AT VII, 137: 11. 15–18; AT IX, 108; FA II, 560 and n. 2; CSM II, 98–99; the relevant passage is AT VII, 137, 1. 8–138, 1. 1.

25 Meditation III: AT VII, 50, 11. 16–19; AT IX, 40; HR I, 169–170; CSM II, 34.

26 First Responses: AT VII, 114, 1. 7; AT IX, 90; in CSM II, 82: "not so much to take hold of them as to surrender to them."

27 Second Responses: AT VII, 137, 1. 17; AT IX, 108; in CSM II, 98: "which embraces all other attributes."

28 On adequate concepts, cf. Second, Third (no. 11), and Fifth Responses: respectively, AT VII, 140, 11. 3–4; 189, 11. 17–18; and 365, 11. 3–4. The debate of the Fourth Responses (AT VII, 220) is continued in the Conversation with Burman: AT V, 151–152; Descartes' Conversation, 10–11.

29Univoce, Second Responses: AT VII, 137, 1. 22; in CSM II, 98: "in the same sense." On the relation between Cartesianism and analogy, see Gouhier, La pensée métaphysique, ch. 8, ii and iii; and J.-L. Marion, Sur la théologie blanche de Descartes (Paris: Presses Universitaires de France, 1981).

30Obversari, Third Meditation: AT VII, 35, 11. 21–22; in HR I, 158: "were presented to my mind"; in CSM II, 24: "appeared before my mind."

31In se conversa, preface, Meditations: AT VII, 7–8; in HR I, 137: "reflecting on itself"; in CSM II, 7: "when directed towards itself."

32Principles I, 60: AT VIII, 29, 1. 2, excludere; in HR I, 244: "shut off from itself."

33 Marion, Sur le prisme métaphysique de Descartes, seems to us to be completely right in speaking, not of irrationality, but of "another rationality" (p. 243). But he believes that this metaphysical rationality must be "shielded from the method's domain of application" (p. 242, and again pp. 324–325, n. 29); we are not sure that this is necessary.

34 Second Responses: AT VII, 147, 11. 18–27; AT IX, 115; FA II, 573 and n. 1; CSM II, 105.

35 First Response: AT VII, 114, 11. 14–17; AT IX, 90; FA II, 533; in CSM II, 82: "knowledge of the finite kind just described, which corresponds to the small capacity of our minds."

36 Fifth Responses: AT VII, 368, 11. 2–3; Clerselier's translation in FA II, 811 and n. 2.

37 I am deeply indebted to Charles Paul and Stephen Voss for many linguistic and philosophical emendations. The remaining mistakes are mine.


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