Book 13
12
And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this promise.
1
As regards the objects of mathematics, then, the foregoing account may be taken as sufficient to show that they exist, and in what sense they exist, and in what sense they are prior and in what they are not. But as regards the Ideas we must first consider the actual theory in relation to the Idea, without connecting it in any way with the nature of numbers, but approaching it in the form in which it was originally propounded by the first exponentsIt seems quite obvious that Aristotle intends this vague phrase to refer to Plato. Cf. Aristot. Met. 1.6.1-3, with which the following sections 2-5 should be compared. On the whole subject see Introduction. of the Ideas.
2
The theory of Forms occurred to those who enunciated it because they were convinced as to the true nature of reality by the doctrine of Heraclitus, that all sensible things are always in a state of flux; so that if there is to be any knowledge or thought about anything, there must be certain other entities, besides sensible ones, which persist. For there can be no knowledge of that which is in flux.
3
Now Socrates devoted his attention to the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a superficial grasp of the subjectCf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24. and defined, after a fashion, the hot and the cold; while the PythagoreansCf. Aristot. Met. 1.5.2, 16. at an earlier date had arrived at definitions of some few things—whose formulae they connected with numbers—e.g., what opportunity is, or justice or marriage); and he naturally inquired into the essence of things;
