TWO: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 pro388portion 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 con389ceptions; 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 �� 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.The most effectual means of securing a uniform effect from a tempering bath is by violent agitation, either of the bath or the piece; this also adds to the rapidity of cooling.

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TWO:The nature of dialectic is still further elucidated in the Phaedrus, where it is also contrasted with the method, or rather the no-method, of popular rhetoric. Here, again, discussions about love are chosen as an illustration. A discourse on the subject by no less a writer than Lysias is quoted and shown to be deficient in the most elementary requisites of logical exposition. The different arguments are strung together without any principle of arrangement, and ambiguous terms are used without being defined. In insisting on the necessity of definition, Plato followed Socrates; but he defines according to a totally different method. Socrates had arrived at his general notions partly by a comparison of particular instances with a view to eliciting the points where they agreed, partly by amending the conceptions already in circulation. We have seen that the earliest Dialogues attributed to Plato are one long exposure of the difficulties attending such a procedure; and his subsequent investigations all went to prove that nothing solid could be built on such shifting foundations as sense and opinion. Meanwhile increasing familiarity with the great ontological systems had taught him to begin with the most general notions, and to work down from them to the most particular. The consequence was that dialectic came to mean nothing but classification or logical division. Definition was absorbed into this process, and reasoning by syllogism was not yet differentiated from it. To tell what a thing was, meant to fix its place in the universal order of existence, and its individual existence was sufficiently accounted for by the same determination. If we imagine first a series of concentric circles, then a series of contrasts symmetrically disposed on either side of a central dividing line, and finally a series of transitions descending from the most absolute unity to the most irregular diversity��we shall, by combining the three schemes, arrive at some understanding of the Platonic dialectic. To assign anything its place in these various sequences was at once to define it and to demonstrate the necessity of222 its existence. The arrangement is also equivalent to a theory of final causes; for everything has a function to perform, marked out by its position, and bringing it into relation with the universal order. Such a system would inevitably lead to the denial of evil, were not evil itself interpreted as the necessary correlative of good, or as a necessary link in the descending manifestations of reality. Moreover, by virtue of his identifying principle, Plato saw in the lowest forms a shadow or reflection of the highest. Hence the many surprises, concessions, and returns to abandoned positions which we find in his later writings. The three moments of Greek thought, circumscription, antithesis, and mediation, work in such close union, or with such bewildering rapidity of alternation, through all his dialectic, that we are never sure whither he is leading us, and not always sure that he knows it himself.

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