Meanwhile a new and powerful agency was about to interpose with decisive effect in the doubtful struggle. This was the study of mathematics. Revived by the Arabians and never wholly neglected during the Middle Ages, it had profited by the general movement of the Renaissance, and was finally applied to the cosmical problem by Galileo. In this connexion, two points of profound philosophical interest must be noted. The first is that, even in its fall, the Aristotelian influence survived, to some extent, both for good and for evil. To Aristotle belongs the merit of having been the first to base astronomy on physics. He maintains the earth’s immobility on experimental no less than on speculative grounds. A stone thrown straight up in the air returns to its starting-point instead of falling to the west of it; and the absence of stellar parallax seems to show that there is no change in our position relatively to the heavenly bodies. After satisfying himself, on empirical considerations, that the popular astronomy is true, he proceeds to show that it must be true, by considerations on the nature of matter and motion, which, although mistaken, are conceived in a genuinely scientific spirit. Now Galileo saw that, to establish the Copernican system, he must first grapple with the Peripatetic physics, and replace it by a new dynamical theory. This, which he could hardly have effected by the ordinary mathematical methods, he did by borrowing the analytical method of Atomism and applying it to the measurement of motion. The law of falling bodies was ascertained by resolving their descent into a series of moments, and determining its rate of velocity at successive intervals; and curvilinear motions were similarly resolved into the combination of an impulsive with an accelerating force, a method diametrically opposed to that of Bacon, who would not even accept the rough analysis of the apparent celestial motions proposed by Greek astronomers.
It seems strange that Galileo, having gone so far, did not go a step further, and perceive that the planetary orbits, being curvilinear, must result from the combination of a centripetal with a tangential force. But the truth is that he never seems to have grasped his own law of inertia in its full generality. He understood that the planets could not have been set in motion without a rectilinear impulse; but his idea was that this impulse continued only so long as was necessary in order to give them their present velocity, instead of acting on them for ever as a tangential force. The explanation of this strange inconsequence must be sought in a survival of Aristotelian conceptions, in the persistent belief that rectilinear motion was necessarily limited and temporary, while circular motion was natural, perfect, and eternal.[548] Now such conceptions as Nature, perfection, and eternity always rebel against an analysis of the phenomena wherein they are supposed to reside. The same prejudice will explain why Galileo should have so persistently ignored Kepler’s Laws, for we can hardly imagine that they were not brought under his notice.
The philosophical affinities of the new science were not exhausted by the atomistic analysis of Democritus and the regulative method of Aristotle. Platonism could hardly fail to benefit by the great impulse given to mathematical studies in the latter half of the sixteenth century. The passionate love of its founder for geometry must have recommended him as much to the most advanced minds of the period as his religious mysticism had recommended him to the theologians of the earlier Renaissance. And the increasing ascendency of the heliocentric astronomy, with its splendid defiance of sense and opinion, was indirectly a triumph for the philosophy which, more than any other, had asserted the claims of pure reason against both. We see this distinctly in Galileo. In express adhesion to Platonism, he throws his teaching into a conversational form, endeavouring to extract the truth from his opponents rather than convey it into their minds from without; and the theory of reminiscence as the source of demonstrative knowledge seems to meet with his approval.[549] He is always ready with proofs drawn from observation and experiment; but nothing can be more in Plato’s spirit, nothing more unlike Aristotle and Bacon, than his encomium on the sublime genius of Aristarchus and Copernicus for having maintained a rational hypothesis against what seemed to be the evidence of their senses.[550] And he elsewhere observes how much less would have been the glory of Copernicus had he known the experimental verification of his theory.[551]
The Platonic influence told even more efficaciously on Galileo’s still greater contemporary, Kepler. With him as with the author of the Republic, mysticism took the direction of seeking everywhere for evidence of mathematical proportions. With what brilliant success the search was attended, it is needless to relate. What interests us here is the fact, vouched for by Arago, that the German astronomer was guided by an idea of Plato’s, that the world must have been created on geometrical principles.[552] Had Bacon known anything about the work on which his adventurous contemporary was engaged, we may be sure that it would have afforded him another illustration for his Idôla, the only difficulty being whether it should be referred to the illusions of the Tribe, the Den, or the Theatre.
Meanwhile Atomism continued to exercise a powerful influence on the method even more than on the doctrines of science. The analytical mode of treatment, applied by Galileo to dynamics, was applied, with equal success, by other mathematicians, to the study of discrete and continuous quantity. It is to the division of numbers and figures into infinitesimal parts—a direct contravention of Aristotle’s teaching—that we owe logarithms, algebraic geometry, and the differential calculus. Thus was established a connexion between spiritualism and materialism, the philosophy of Plato and the philosophy of Democritus. Out of these elements, together with what still survived of Aristotelianism, was constructed the system of Descartes.
IV.
To understand Descartes aright, we must provisionally disregard the account given in his work on Method of the process by which he arrived at a new theory of the world; for, in truth, there was nothing new about it except the proportion in which fragments taken from older systems were selected and recombined. As we have already noticed, there is no such thing as spinning philosophies out of one’s own head; and, in the case of Descartes, even the belief that he was so doing came to him from Plato; for, along with Aristotle’s dogmatic errors, his sound teaching with regard to the derivation of knowledge had fallen into oblivion. The initial doubt of the Discourse on Method and the Meditations is also Platonic; only it is manifested under an individual and subjective, instead of a universal and objective form. But to find the real starting-point of Descartes’ enquiries we must look for it in his mathematical studies. A geometrician naturally conceives the visible world under the aspect of figured extension; and if he thinks the figures away, nothing will remain but extension as the ultimate material out of which all determinate bodies are shaped. Such was the result reached by Plato in his Timaeus. He identified matter with space, viewing this as the receptacle for his eternal and self-existent Ideas, or rather the plastic medium on which their images are impressed. The simplest spatial elements are triangles; accordingly it is with these that he constructs his solid bodies. The theory of triangular elements was probably suggested by Atomism; it is, in fact, a compromise between the purely mathematical and the materialistic methods. Like all Plato’s fancies, this theory of matter was attacked with such convincing arguments by Aristotle that, so long as his physics remained in the ascendent, it did not find a single supporter; although, as we saw in the last chapter, Plotinus very nearly worked his way back to it from the Peripatetic definition. Even now, at the moment of Aristotle’s fall, it might have failed to attract attention, had not the conditions under which it first arose been almost exactly repeated. Geometrical demonstration had again become the type of all reasoning; there was again a sceptical spirit abroad, forcing men to fall back on the most elementary and universal conceptions; an atomistic materialism again threatened to claim at least the whole field of physical enquiry for its own. That Descartes followed the Timaeus in identifying matter with extension cannot be doubted; especially when we see that he adopts Plato’s analysis of body into elementary triangles; but the theory agreed so well with his intellectual predispositions that he may easily have imagined it to be a necessary deduction from his own à priori ideas. Moreover, after the first two steps, he parts company with Plato, and gives himself up, so far as his rejection of a vacuum will permit, to the mechanical physics of Democritus. Much praise has recently been bestowed on his attempt to interpret all physical phenomena in terms of matter and motion, and to deduce them from the unaided operation of natural causes; but this is no more than had been done by the early Greek thinkers, from whom, we may observe, his hypothesis of an initial vortex was also derived. His cosmogony is better than theirs, only in so far as it is adapted to scientific discoveries in astronomy and physiology not made by Descartes himself; for where his conjectures go beyond these they are entirely at fault.
Descartes’ theory of the universe included, however, something more than extension (or matter) and motion. This was Thought. If we ask whence came the notion of Thought, our philosopher will answer that it was obtained by looking into himself. It was, in reality, obtained by looking into Aristotle, or into some text-book reproducing his metaphysics. But the Platonic element in his system enabled Descartes to isolate Thought much more completely than it had been isolated by Aristotle. To understand this, we must turn once more to the Timaeus. Plato made up his universe from space and Ideas. But the Ideas were too vague or too unintelligible for scientific purposes. Even mediaeval Realists were content to replace them by Aristotle’s much clearer doctrine of Forms. On the other hand, Aristotle’s First Matter was anything but a satisfactory conception. It was a mere abstraction; the unknowable residuum left behind when bodies were stripped, in imagination, of all their sensible and cogitable qualities. In other words, there was no Matter actually existing without Form; whereas Form was never so truly itself, never so absolutely existent, as when completely separated from Matter: it then became simple self-consciousness, as in God, or in the reasonable part of the human soul. The revolution wrought by substituting space for Aristotle’s First Matter will now become apparent. Corporeal substance could at once be conceived as existing without the co-operation of Form; and at the same stroke, Form, liberated from its material bonds, sprang back into the subjective sphere, to live henceforward only as pure self-conscious thought.
This absolute separation of Form and Matter, under their new names of Thought and Extension, once grasped, various principles of Cartesianism will follow from it by logical necessity. First comes the exclusion of final causes from philosophy, or rather from Nature. There was not, as with Epicurus, any anti-theological feeling concerned in their rejection. With Aristotle, against whom Descartes is always protesting, the final cause was not a mark of designing intelligence imposed on Matter from without; it was only a particular aspect of Form, the realisation of what Matter was always striving after by virtue of its inherent potentiality. When Form was conceived only as pure thought, there could be no question of such a process; the most highly organised bodies being only modes of figured extension. The revival of Atomism had, no doubt, a great deal to do with the preference for a mechanical interpretation of life. Aristotle had himself shown with masterly clearness the difference between his view of Nature and that taken by Democritus; thus indicating beforehand the direction in which an alternative to his own teaching might be sought; and Bacon had, in fact, already referred with approval to the example set by Democritus in dealing with teleological enquiries.
Nevertheless Bacon’s own attitude towards final causes differs essentially from Descartes’. The French mathematician, had he spoken his whole mind, would probably have denied their existence altogether. The English reformer fully admits their reality, as, with his Aristotelian theory of Forms, he could hardly avoid doing; and we find that he actually associates the study of final with that of formal causes, assigning both to metaphysics as its peculiar province. This being so, his comparative neglect of the former is most easily explained by the famous comparison of teleological enquiries to vestal virgins, dedicated to the service of God and bearing no offspring; for Mr. Ellis has made it perfectly clear that the barrenness alluded to is not scientific but industrial. Our knowledge is extended when we trace the workings of a divine purpose in Nature; but this is not a kind of knowledge which bears fruit in useful mechanical inventions.[553] Bacon probably felt that men would not be very forward to improve on Nature if they believed in the perfection of her works and in their beneficent adaptation to our wants. The teleological spirit was as strong with him as with Aristotle, but it took a different direction. Instead of studying the adaptation of means to ends where it already existed, he wished men to create it for themselves. But the utilitarian tendency, which predominated with Bacon, was quite exceptional with Descartes. Speaking generally, he desired knowledge for its own sake, not as an instrument for the gratification of other wants; and this intellectual disinterestedness was, perhaps, another aspect of the severance effected between thought and matter.