Page:Mind (New Series) Volume 12.djvu/30

16 A. E. TATLOE: I there gave that the theory of "imitation" is not put forward as Plato's own solution of the difficulties he has raised about "participation". Here we may be content simply to remark that this interpretation is excluded by two very simple considerations; the new formula is shown to lead to the very result which was fatal to the old, the "third man" and the indefinite regress (132 d-133 a); also it is found to involve agnosticism pure and simple. For it amounts to declaring the absolute severance of Idea and thing. To recur to our mathematical example, the circle as studied by the geometer and the circle you can see are now placed in two distinct worlds, and we have just seen that we cannot bring them into relation by calling the one "like" the other without falling into the indefinite regress. Hence all the various properties of the curve of the geometer will belong solely to it and have nothing to do with the seen curve. For instance, suppose we deduce from the equation of the curve the equation of its tangent; the result will hold good only for the geometer's circle, and will have nothing at all to do with relations between the seen circle and the seen tangent. And therefore it will be no longer possible for us to hold, as Plato had done in the Phœdo, that the seen curve and tangent of a diagram "suggest" the relation between the conceptual curve and the conceptual tangent; with the destruction of all bridges between the seen and the conceptual now effected, it becomes impossible to understand how mathematical studies should ever have arisen. In short we have been brought to the same impasse to which Mill conducts us when he first declares that the lines, circles and points of the mathematician are copies of those which he has seen in the course of sense-perception, and then runs away from the consequences of his assertion by going on to say that no one has ever seen anything corresponding to the curves of mathematics and therefore the conclusions of the science are not really true. Hence we can see why Plato still maintains that unless we can find a way out of our difficulties consistent with maintaining the existence of Ideas, all science is impossible.

The result we have reached is in fact this. The science of quantity, and for Plato all real science is quantitative science,