Aristotle vs. Plato: Does “one” convert with being or participate in it?

In the first hypothesis of the Parmenides, Plato speaks of the one which is utterly unique and incomparable to others. This is “the one” that Aristotle would call “the one that is convertible with being” as opposed to the one that is the principle of number. For example:

a.) America is one nation under God

b.) America is one nation and France is another.

“A” means “unified” or “undivided” or even “unique”, whereas b. is the one of one, two, three; one and another; or the first member of a set.  “b” is a part of a larger whole, or, in Plato’s language, it participates in another.

At the conclusion of the first hypothesis of the Parmenides, however, Plato argues that everything that is one in the first sense is also one in the second sense, because one is different from being and therefore participates in it, and one consequence of this is that the one gives rise to number. Plato’s argument is this: if one is the same as being, then it is the same thing to say “one is” and “one is one”. But the two are not the same, therefore etc.

The Aristotelian/Scholastic response to this is well known: “one” in sense a. is the same thing as being, but it differs in ratio, in a way comparable to how the way up and the way down are the same staircase but they differ in the account one gives of it.  One Platonic response might be to point out that he is clearly taking “is” in an existential sense (where it is taken per se) but the second “is” taken only per accidens; and while the Aristotelian tradition can make sense of the accidental participating in the per se, it cannot make sense of the two being really the same and differing only in ratio.


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