the formulae and those in the substratum; and whether the principles of perishable and of imperishable things are the same or different; and whether they are all imperishable or those of perishable things are perishable. Further there is the question which is hardest of all and most perplexing, whether unity and being, as the Pythagoreans and Plato said, are not attributes of something else but are the substance of existing things, or this is not the case, but the substratum is something else,—as Empedocles says, love; as someone else says, fire; while one says water and one, air. Again we ask whether the principles are universal or like individual things, and whether they exist potentially or actually; further, whether they are potential or actual in any other sense than in reference to movement; for these questions also would present much difficulty. Further, whether are numbers and lines and figures and points a kind of substance or not, and if they are substances whether are they separate from sensible things or present in them? With regard to all these matters not only is it hard to get possession of the truth, but it is not easy even to think out the difficulties well.
First then with regard to what we mentioned first, whether does it belong to one or to more sciences to investigate all the kinds of causes? How could it belong to one science to know the principles if these are not contrary?
Further, there are many things to which not all the principles pertain. For how can a principle of change or the nature of the good be present in unchangeable things, since everything that in itself and by its own nature is good is an end, and a cause in the sense that for its sake the other things both come to be and are, and since an end or purpose is the end of some action, and all actions imply change; so that in unchangeable things this principle could not exist nor could there be a good-in-itself. This is why in mathematics nothing
- Cf. 999b24-1000a4.
- Cf. 1000a5-1001a3.
- Cf. 1001a4-b25.
- Cf. 1003a5-17.
- Cf. 1002b32-1003a5.
- Cf. 1001b26-1002b11.