They seemed to have an inexhaustible application, partly because their true limits were not yet understood.

These Plato himself is beginning to investigate; though not aware that number and figure are mere abstractions of sense, he recognizes that the forms used by geometry are borrowed from the sensible world.

He seeks to find the ultimate ground of mathematical ideas in the idea of good, though he does not satisfactorily explain the connexion between them; and in his conception of the relation of ideas to numbers, he falls very far short of the definiteness attributed to him by Aristotle (Met.).

But if he fails to recognize the true limits of mathematics, he also reaches a point beyond them; in his view, ideas of number become secondary to a higher conception of knowledge.

The dialectician is as much above the mathematician as the mathematician is above the ordinary man.