different, which shows that it is not a substance. And evidently the same is true of points and lines and planes; for the same argument applies, as they are all alike either limits or divisions.
In general one might raise the question why, besides perceptible things and the intermediates, we have to look for another class of things, such as the Forms which we posit. If it is for this reason, because the objects of mathematics, while they differ from the things in this world in some other respect, differ not at all in that there are many of the same kind, so that their first principles cannot be limited in number (just as the elements of all the language in this sensible world are not limited in number, but in kind, unless one takes the elements of this individual syllable or of this individual articulate sound—whose elements will be limited even in number—, so is it also in the case of the intermediates; for there also the members of the same kind are infinite in number), so that if there are not—besides perceptible and mathematical objects—others such as some maintain the Forms to be, there will be no substance which is one in number as well as in kind, nor will the first principles of things be determinate in number, but only in kind,—if then this must be so, the Forms also must therefore be held to exist. Even if those who support this view do not express it distinctly, still this is what they mean, and they must be maintaining the Forms just because each of the Forms is a substance and none is by accident. But if we are to suppose that the Forms exist and the principles are one in number, not in kind, the impossible results that we have mentioned necessarily follow.
Closely connected with this is the question whether the elements exist potentially or in some other way. If in some other way, there will be something else prior to the first
- With 1001b26-1002b11 cf. 996a12-17. For the answer cf. m, n, esp. 1090b5-13.
- For these cf. a. 6. 987b14.
- Sc. Platonists.