Thomas Aquinas, Commentary on Aristotle's Physics

25. Having disproven the opinion of Parmenides and Melissus that being is one, the Philosopher here shows that certain later philosophers fell into difficulty on this very same problem.

Parmenides and Melissus erred because they did not know how to distinguish the uses of the term 'one'. Thus, what is one in a certain respect, they said was one simply. But the later philosophers, also not knowing how to distinguish the uses of the term 'one', thought it absurd that one and the same thing should be in some way one and many. Yet, being convinced by the arguments, they were forced to believe it. And so Aristotle says that the later philosophers were 'disturbed' (that is, fell into a difficulty similar to that of the ancients, i.e., Parmenides and Melissus) lest they be forced to say that one and the same thing is one and many. Now this seemed absurd to both groups of philosophers. So the earlier philosophers, holding that all is one, rejected all multiplicity. The later philosophers, on the other hand, tried to remove multiplicity from anything they held to be one.

26. Thus some, such as Lycophron, removed the verb is from propositions. They said that we must not say 'man is white' but rather 'white man'. For they thought that man and white were in some way one, otherwise white would not be predicated of man. And it seemed to them that the word 'is', since it is a verbal copula, must serve as a copula between two. And so, wishing to remove all multiplicity from that which is one, they said the verb 'is' must not be used.

But because such speech seemed to be imperfect, and because an imperfect understanding was produced in the soul of him who heard if names were spoken without the addition of any verb, some, wishing to correct this, changed the mode of speech. They did not say 'white man' because of the imperfection of this mode of speech. Nor did they say 'man is white' lest they give the impression that there is multiplicity. Rather they said 'man whitened', because by this expression 'whitened' [albari] a thing is not understood (as it seemed to them), but rather a certain change in the subject. And in like manner they said that we must not say 'man is walking' but 'man walks', lest by the addition of the verbal copula 'is' they make that which they thought to be one (i.e., white man) to be many, as if one and being were used in only one way and not in many.

27. But this is false. For that which is one in one respect can be many in some other respect, as what is one in subject can be many in definition [ratio]. Thus the white and the musical are the same in subject but many in definition [ratio]. Hence it can be concluded that the one may be many.

This may happen also in another way. That which is actually one as a whole may be many according to a division of parts. Whence the whole is one in its totality, but it has multiplicity of parts.

And although those who wished to remove the verb 'is' or alter it, as was said above, found some solution to the objection that things could be one in subject and many in definition [ratio], they failed altogether to answer the objection that a thing may be one as a whole but many in its parts. They still believed it to be something of an absurdity that the one should be many.

But it is not absurd if the one and the many are not taken as opposites. For the one in act and the many in act are opposed, but the one in act and the many in potency are not opposed. And because of this he adds that 'one' is said in many ways, i.e., one in potency and one in act. And so nothing prohibits the same thing from being one in act and many in potency, as is clear with regard to the whole and the parts.

28. Finally he draws the conclusion which he had uppermost in mind, namely, that it is clear from the foregoing arguments that it is impossible for all beings to be one.