Abstract

The old question whether or no the doctrine of ‘intermediate mathematical objects’ ascribed to Plato by Aristotle is to be found in the Divided Line of Republic vi, has been recently raised again in a careful and lucid discussion by Mr. W. F. R. Hardie. I may clear the ground by saying at once that I agree with that part of Mr. Hardie's chapter which deals with those criticisms of the traditional view that have been put forward by Prof. Ferguson and the late Prof. Stocks; nevertheless I do not believe that the objects of the third segment are intermediate between Forms and Sensibles: I propose to argue that they, like the objects of the highest segment, are Forms