ON THE FIEST PAET OF PLATO'S PARMENIDES. 7
tive and original work, Les Philosophes-geometres de la Grece, that the metaphysical problem suggested by the existence of the mathematical concept is the very basis of Plato's whole theory.[1] I venture to think that this would have been recognised long ago but for the assumption that Aristotle cannot have omitted anything in his account of the influences under which Plato's thought took shape. Yet what more likely than that Aristotle, whose own mathematical attainments are shown by numerous passages in his writings to have been, to say the least, common-place, should have failed to do full justice to the particular element in his master's thought which he was personally least fitted to understand?
If the foregoing argument be accepted, as I think it must be, it will follow that Plato conceived the relation between an Idea and the corresponding sensible particular to be in principle the same as that between what we should now call the general equation to a curve and such a special instance of the curve in question as can be got by giving a numerical value to the coefficients of the equation and proceeding to trace the line thus determined. And we may at once draw a consequence which will account for many of the peculiar difficulties which Aristotle and every later critic have found in the Ideal theory. Plato, like Spinoza after him,[2] unconsciously evaded the worst difficulties of his doctrine by taking as the typical case of the relation of universal and particular a case in which the particular is no more a concrete physical thing than the universal itself. Hence, among other things, the insoluble puzzle of the relation of his Ideas to causality. In the realm of mathematical truth, in which the whole theory originated, causality has no place; but the moment you transfer your attention to the problems of the physical world the question at once arises, Do the Ideas, or do they not, determine the corresponding particulars into existence? If you say Yes, there is the difficulty acutely formulated by Aristotle, How is it then that e.g. a particular horse cannot come into existence without the copulation of a pair of pre-existing horses, and again how can artificial
products, of which there is not, according to the view which
- ↑ See especially op. cit., bk. 2, ch. v., to my own mind far the most original and important of recent contributions to the study of Plato. I shall draw exceedingly freely in what follows upon the learned author's results.
- ↑ See Ethics, ii., 7, schol., where Spinoza without the least misgiving takes as his illustration of the identity of a mode of, extension and the idea of that mode the case of the "circle existing in nature" and the idea of the circle in the mind of God.
