Do forms exist?

But, altogether, one might raise the difficulty as to why one needs to seek other things besides the sensible things and the intermediate things, such as those we posit as Forms.

For if [we must seek them] because the mathematical [15] objects differ from those here in some other respect, but in respect of there being many like individuals they do not differ at all, then their principles will not be numerically definite (just as the principles of the letters here are not numerically definite for all, but definite in form, unless one takes this particular syllable [20] or this particular sound: and of these they will also be numerically definite—and similarly also in the case of the intermediate things: for the like individuals are infinite there too). Therefore, if there are no other things besides the sensible and the mathematical objects, such as some say the Forms are, there will not be one substance numerically but in kind, nor will the principles of [25] existing things be some number numerically, but in kind.

If, then, this is necessary, it is also necessary for this reason to posit that the Forms exist. For even if those who speak do not articulate well, at least this is what they want, and it is necessary for them to say these things: that each of the Forms is a certain substance and nothing by accident. [30]

But if we are to posit that the Forms exist and that the principles are one numerically but not in kind, we have stated the impossible consequences that must follow.

Close to these is the difficulty as to whether the elements exist potentially or in some other way. For if in some other way, something else will be prior to the principles (prior [35] to…)

[1003a1] for the power of that cause [the mover] is one, but what is potential is not necessarily all like that. But if the elements exist potentially, it is possible that none of the things that exist should be: for it is possible for what is not yet to be; for what is not comes into being, and nothing [5] comes into being of those things whose being is impossible.

It is necessary, then, to raise these difficulties about the principles, and whether they are universal or as we say particular. For if they are universal, they will not be substances (for none of the common terms signifies a ’this something’ but a ‘such-like’, but substance [10] is a ’this something’: and if we are to posit that which is predicated in common is a ’this something’ and one, Socrates will be many animals, both himself and Man and Animal, if each signifies a ’this something’ and one).

If, then, the principles are universal, these consequences follow: but if they are not universal, but as particulars, they will not be knowable (for knowledge is [15] universal for all things), so that there will be other principles prior to the principles—those that are predicated universally—if there is to be knowledge of them.