Plato's Parmenides VII, The One II

We continue from yesterday.

Neither will [the One] be the same with itself or other; nor again, other
than itself or other.

How is that?

If other than itself it would be other than one, and would not be
one.

True.

And if the same with other, it would be that other, and not itself;
so that upon this supposition too, it would not have the nature of
one, but would be other than one?

It would. 

Then it will not be the same with other, or other than itself?

It will not.

That part was straightforward: the One is not the same as anything else, because it's itself and not the other thing (whatever that thing might be). The next part is trickier. 

Neither will it be other than other, while it remains one; for not

one, but only other, can be other than other, and nothing else.

True.

Then not by virtue of being one will it be other?

Certainly not.

But if not by virtue of being one, not by virtue of itself; and if
not by virtue of itself, not itself, and itself not being other at
all, will not be other than anything?

Right.

Neither will one be the same with itself.

How not?

Surely the nature of the one is not the nature of the same.

Why not?

It is not when anything becomes the same with anything that it becomes
one.

What of that?

Anything which becomes the same with the many, necessarily becomes
many and not one.
True.

But, if there were no difference between the one and the same, when
a thing became the same, it would always become one; and when it became
one, the same?

Certainly.

And, therefore, if one be the same with itself, it is not one with
itself, and will therefore be one and also not one.

Surely that is impossible.

This argument that pure unity cannot admit of 'sameness' is going to end up being a problem for Plato and even for Socrates, because the unity he is seeking is supposed to explain something else. The idea was that largeness was supposed to have a Form, and that Form was the thing that somehow produces the sameness by virtue of which all large things are large; or all good things are good. If the kind of unity Parmenides is describing cannot even admit of 'sameness' to the degree that it can be said to be 'the same as itself' the whole concept is going to be unworkable. This is sort of the third man problem in reverse: instead of producing an infinite number of additional forms, it can't even produce one additional thing. If that's true, it can't do what Socrates proposed it should do. 

The One cannot be the same in part, also, because the concept of sameness requires a concept of difference; and that is two things (in addition to itself). Once again, the idea of a unity produces a trinity. (See the comments to yesterday's post for further discussion). If the One is a kind of mind, this realization is itself productive: of that which is different, and sameness, and then a space between them for similarity and difference. The Neoplatonists will explain creation -- including the creation of the Platonic Forms -- in terms of the way that the thinking of the One ends up producing everything else. 

Parmenides is not going to make that move; he's going to block it by trying to show that the One not only cannot be the same as another, it cannot even be like another. 

And therefore the one can neither be other than other, nor the same

with itself.

Impossible.

And thus the one can neither be the same, nor other, either in relation
to itself or other?

No.

Neither will the one be like anything or unlike itself or other.

Why not?

Because likeness is sameness of affections.

Yes.

And sameness has been shown to be of a nature distinct from oneness?

That has been shown.

But if the one had any other affection than that of being one, it
would be affected in such a way as to be more than one; which is impossible.

Why is it impossible? Because motion and therefore change in the unity have already been shown to be impossible.

True.

Then the one can never be so affected as to be the same either with
another or with itself?

Clearly not.

Then it cannot be like another, or like itself?

No.

Nor can it be affected so as to be other, for then it would be affected
in such a way as to be more than one.

It would.

That which is affected otherwise than itself or another, will be unlike
itself or another, for sameness of affections is likeness.

True.

But the one, as appears, never being affected otherwise, is never
unlike itself or other?

Never.

Then the one will never be either like or unlike itself or other?

Plainly not.

The Archangel Michael's name is translated in a way that captures the Judeo-Christian-Islamic sense of this difficulty. "In art St. Michael is often represented as an angelic warrior, fully armed with helmet, sword, and shield, as he overcomes Satan, sometimes represented as a dragon and sometimes as a man-like figure. The shield at times bears the inscription: Quis ut Deus, the translation of the archangel's name, but capable also of being seen as his rhetorical and scornful question to Satan." The difference between God (or the One) and everything else is so categorical that it does not admit of likeness. 

It seems stranger to say that it does not, then, admit of unlikeness: it seems as if everything is unlike God, both categorically and in degree. Partly that is because we think differently than the Greeks here. Aristotle will divide the world into substances and the attributes they have. A relation, then, is a kind of attribute of a substance. If X and Y are related, X has attribute a which is 'is like Y,' and Y has attribute b which is 'is like X.' Xa and Yb thus produce the relationship, which is not 'real' in itself (i.e., it is not a substance); it is a product of their similar but distinct attributes.

Thus, you can see how from the Greek perspective it makes sense that the One, being a pure unity, cannot admit of a relation such as 'is unlike Z.' Being a pure unity, it cannot carry any attributes -- not sameness, not difference, not like nor unlike, neither red nor blue.

Our metaphysical approach to relations is different, such that it seems illogical to say that A is not like B, and also not unlike B. Whether or not our approach is better is a topic for another day. For now, keep it in mind as Parmenides runs through several more apparent paradoxes. 

Again, being of this nature, it can neither be equal nor unequal either

to itself or to other.

How is that?

Why, because the one if equal must be of the same measures as that
to which it is equal.

True.

And if greater or less than things which are commensurable with it,
the one will have more measures than that which is less, and fewer
than that which is greater?

Yes.

And so of things which are not commensurate with it, the one will
have greater measures than that which is less and smaller than that
which is greater.

Certainly.

But how can that which does not partake of sameness, have either the
same measures or have anything else the same?

Impossible.

And not having the same measures, the one cannot be equal either with
itself or with another?

It appears so.

But again, whether it have fewer or more measures, it will have as
many parts as it has measures; and thus again the one will be no longer
one but will have as many parts as measures.

Right.

And if it were of one measure, it would be equal to that measure;
yet it has been shown to be incapable of equality.

It has.

Then it will neither partake of one measure, nor of many, nor of few,
nor of the same at all, nor be equal to itself or another; nor be
greater or less than itself, or other?

Certainly.

Well, and do we suppose that one can be older, or younger than anything,
or of the same age with it?

Why not?

Why, because that which is of the same age with itself or other, must
partake of equality or likeness of time; and we said that the one
did not partake either of equality or of likeness?

We did say so.

And we also said, that it did not partake of inequality or unlikeness.

Very true.

How then can one, being of this nature, be either older or younger
than anything, or have the same age with it?

In no way.

The next argument changes grounds from the previous series, so we'll proceed with it in the next post.