our account of the way in which they are the substances of perceptible things is empty talk; for 'sharing', as we said before, means nothing. Nor have the Forms any connexion with that which we see to be the cause in the case of the arts, and for whose sake mind and nature produce all that they do produce,—with this cause which we assert to be one of the first principles; but mathematics has come to be the whole of philosophy for modern thinkers, though they say that it should be studied for the sake of other things. Further, one might suppose that the substance which according to them underlies as matter is too mathematical, and is a predicate and differentia of the substance, i. e. of the matter, rather than the matter itself; i. e. the great and the small are like the rare and the dense which the physical philosophers speak of, calling these the primary differentiae of the substratum; for these are a kind of excess and defect. And regarding movement, if the great and the small are to be movement, evidently the Forms will be moved; but if they are not, whence did movement come? If we cannot answer this the whole study of nature has been annihilated.
And what is thought to be easy—to show that all things are one—is not done; for by the separating of the universal from particulars all things do not come to be one but there comes to be a One-in-itself, if we grant all the assumptions. And not even this follows, if we do not grant that the universal is a class; and this in some cases it cannot be.
Nor can it be explained either how the lines and planes and solids that come after the numbers exist or can exist, or what meaning they have; for these can neither be Forms (for they are not numbers), nor the intermediates (for those are the objects of mathematics), nor the perishable things. This is evidently a distinct fourth class.
In general, if we search for the elements of existing things without distinguishing the many senses in which things are said to exist, we cannot succeed, especially if the search for
- Sc. the final cause.
- Cf. b. 996a29-b1.
- Cf. Plato, Rep. vii. 531 d, 533 b-d.
- For this Platonic method cf. b. 1003a10, z. 1031b21, m. 1086b 10.
- Cf. z. 1028b24, m. 1080b23.