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 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.

Notes

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.