Do forms exist?

Why do we need to seek other things besides the sensible things and the intermediate things, such as Forms?

Some say we must seek them because the mathematical objects [numbers] are different [from abstract qualitative objects].

But the mathematical objects [numbers] do not differ at all in some cases when there are many like individuals [of the same type or quality].

In this case, the principles behind mathematical objects [numbers] will not be numerically definite.

This is similar to the principles of the letters which here are not numerically definite for all, but definite only in form. This is unless one takes this particular syllable or sound.

And then they will also be numerically definite.

Similarly, this applies to the intermediate things since the like individuals are infinite there too.

Beyond the sensible and the mathematical objects, there are only the Forms.

If so, then:

• there will one substance in kind, but not numerically one.
• the principles of existing things will not be some number numerically, but in kind.*

But impossible consequences follow if:

• the Forms exist
• the principles are one numerically but not in kind

One such consequence is the difficulty as to whether the elements exist potentially or in some other way.

If they exist in some other way, something else will be prior to the principles (prior [35] to…).

[1003a1] This is because 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 [physically] exist [metaphysically]
• what is not yet existing [physically] to exist [metaphysically]

This is because what does not exist [in physicality] comes into existence [in metaphysicality].

Thus, being [metaphysical existence] and nothing [nonphysical existence] comes into being [existence] of those things whose being [physical existence] is impossible.

If so are the principles universal or particular?

If they are universal, then the principles will not be substances since none of the common words signify a ’this something’ but a ‘such-like’.

But substance is a ’this something’.*

If that which is predicated in common is a ’this something’ and one, then Socrates will be many animals, both himself and Man and Animal, if each signifies a ’this something’ and one).

If the principles are particulars, they will not be knowable.

This is because knowledge is universal for all things).

This means that there will be other principles prior to the principles—those that are predicated universally—if there is to be knowledge of them.