6 A. E. TAYLOR : Ideas which are cited fall into two main classes ; there are (1) first and foremost, Ideas of mathematical properties and relations, equality, magnitude, multitude, paucity, and (2) of moral and aesthetic qualities, the just, the beautiful. The mention of an Idea of Life may perhaps be taken to show that the series of organic types was also already recognised as belonging to the system of Ideas. And it is instructive to observe that it is from a mathematical relation, that of equality, that the whole discussion starts. Similarly in the Parmenides, when Parmenides questions Socrates as to the contents of his assumed Ideal world, it is our moral and mathematical ideals, which form a body of standards or norms to which experience only imperfectly approxi- mates, that are chosen as the most certain and obvious instances of Ideal existences. Then follow organic types, the Idea of man, etc., and in the third place, and more doubtfully, other things possessed of common qualities and called by a common name. If I had space here to write out the results of an experiment I once performed of noting down very carefully the examples of Ideas given in the more important dialogues, the list would, I believe, of itself prove that, except where the theory has to be made intelligible to persons who are assumed to stand outside the strict philo- sophic curriculum of Plato's school, all the cases which occur are those either of (1) mathematical, moral, and aesthetic " norms," or (2) of organic types and the organs and elements which enter into their composition. And both these classes can be ultimately reduced to one common type, that of mathematical relation. For it is, on the one hand, in order and proportion that Plato sees the fundamental character both of moral goodness and of aesthetic beauty, and on the other, every organic type is for him determined by a special quantitative relation between constituent elements, which in their turn are themselves constituted by mathematical laws out of the primary triangles. 1 Thus in the end we seem justified in concluding, with M. Milhaud in his most instruc- some dialogues, to have corresponding Ideas. It is because the purpose for which the implement is fashioned demands a certain mathematical proportion between its various parts, and it is this proportion which is the fldos of " bed " or " shuttle ". For roof of this I must refer to the body of the present paper. I see no adequate ground for attributing to Plato himself the Academic view often referred to by Aristotle that there are no Ideas of o-Keuao-ra. If the on-do-a <v<rei, to which according to Aristotle Plato confined the Ideas, may include the triangle (which does not exist till you draw it), why not the bed or the shuttle ? 1 See Philebus, 51 d ff. (beauty), 64 c ff. (goodness), 31 c ff. (animal organism).
