Plato's Parmenides IX, The One IV

Again, I'll put this past the jump.  Just to remind you, this is a very extended discussion in which Parmenides proposes to talk through both sides of every part of the question. So the traps get run one way: "What if the One is not?" And then the other: "What if the One is?" Problems abound on every side. At this point the problems are going to start looking familiar, because we found them running the traps the one way; you'll see the same problems arising if we make the contrary assumption about the One.

With any luck we'll get through this in one more post after this one. 

Continuing from last time; if this seems confusing, review the last bit because the same 'time makes you multiple' forces are in play.

And is there not also a time at which [the one] assumes being and relinquishes being-for how can it have and not have the same thing unless it receives and also gives it up at; some time?

Impossible.
And the assuming of being is what you would call becoming?

I should.
And the relinquishing of being you would call destruction?

I should.
The one then, as would appear, becomes and is destroyed by taking and giving up being.

Certainly.
And being one and many and in process of becoming and being destroyed, when it becomes one it ceases to be many, and when many, it ceases to be one?

Certainly.
And as it becomes one and many, must it not inevitably experience separation and aggregation?

Inevitably.
And whenever it becomes like and unlike it must be assimilated and dissimilated?

Yes.
And when it becomes greater or less or equal it must grow or diminish or be equalized?

True.
And when being in motion it rests, and when being at rest it changes to motion, it can surely be in no time at all?

How can it?
But that a thing which is previously at rest should be afterwards in motion, or previously in motion and afterwards at rest, without experiencing change, is impossible.

Impossible.
And surely there cannot be a time in which a thing can be at once neither in motion nor at rest?

There cannot.

Notice that "but that a thing which is previously at rest should be afterwards in motion, or previously in motion and afterwards at rest, without experiencing change, is impossible," is exactly equivalent to Newton's First Law of Motion. This discussion is antiquated, because we no longer think that anything is really 'at rest' in the sense the ancients meant. Newton also treats objects as 'at rest' or 'in motion,' but we have to understand his idea in terms of velocity/direction being unchanging if net force on an object is zero.

Odd that we don't call it Parmenides' law of motion, really, since he was there well more than a thousand years earlier. 

But neither can it change without changing.

Obviously.

True.
When then does it change; for it cannot change either when at rest, or when in motion, or when in time?

Because it has already been established that it cannot change in previous sections of the argument.

It cannot.
And does this strange thing in which it is at the time of changing really exist?

What thing?
The moment. For the moment seems to imply a something out of which change takes place into either of two states; for the change is not from the state of rest as such, nor, from the state of motion as such; but there is this curious nature, which we call the moment lying between rest and motion, not being in any time; and into this and out of this what is in motion changes into rest, and what is at rest into motion.

So it appears.
And the one then, since it is at rest and also in motion, will change to either, for only in this way can it be in both. And in changing it changes in a moment, and when it is changing it will be in no time, and will not then be either in motion or at rest.

It will not.

I regard this section as similarly antiquated; I'm not sure it's even valid as an objection in a case in which there is never a change from 'at rest to in motion.' One can, of course, regard any change in motion as being equivalent to the change from rest to motion; but I think the Greeks meant that there was a more categorical change at work. It's up to you, dear reader, to decide how to think about this.

And it will be in the same case in relation to the other changes, when it passes from being into cessation of being, or from not-being into becoming-then it passes between certain states of motion and rest, and, neither is nor is not, nor becomes nor is destroyed.

Very true.

The unity can't be multiple; and changing requires part of it be one thing (in the past) and another part be another (in the future). We've seen that the unity being in time is a problem in general. The unity -- Forms, for example -- can't change, and don't exist in the temporal world. They are eternal. It was proven running the traps one way, and it works out the same way running the traps backwards.

And on the same principle, in the passage from one to many and from many to one, the one is neither one nor many, neither separated nor aggregated; and in the passage from like to unlike, and from unlike to like, it is neither like nor unlike, neither in a state of assimilation nor of dissimilation; and in the passage from small to great and equal and back again, it will be neither small nor great, nor equal, nor in a state of increase, or diminution, or equalization.

True.
All these, then, are the affections of the one, if the one has being.

Of course.

But if one is, what will happen to the others -is not that also to be considered?

Yes.
Let us show then, if one is, what will be the affections of the others than the one.

Let us do so.
Inasmuch as there are things other than the one, the others are not the one; for if they were they could not be other than the one. Very true.

Very true.

Again, familiar problems from the earlier passage through the traps.

Nor are the others altogether without the one, but in a certain way they participate in the one.

In what way?
Because the others are other than the one inasmuch as they have parts; for if they had no parts they would be simply one.

Right.
And parts, as we affirm, have relation to a whole?
So we say.
And a whole must necessarily be one made up of many; and the parts will be parts of the one, for each of the parts is not a part of many, but of a whole.

How do you mean?
If anything were a part of many, being itself one of them, it will surely be a part of itself, which is impossible, and it will be a part of each one of the other parts, if of all; for if not a part of some one, it will be a part of all the others but this one, and thus will not be a part of each one; and if not a part of each, one it will not be a part of anyone of the many; and not being a part of any one, it cannot be a part or anything else of all those things of none of which it is anything.

This depends on an assumption about the natures of parts and wholes. Parts here are discrete, so that your arm is part of you, but not part of your other arm. Your arm is also not 'part of you arm,' it's the whole arm. (Thus, it is 'impossible' for a part to be 'a part of itself.') 

Parts have to make up a whole, and not 'a many' for the same reason that your arm is a part of a whole (you) and not of a collective (your neighborhood). Well, so he says; but it might make sense to say that a collective many has a part in common. "My sword for Scotland!" is comparable to "My right arm for Scotland!", and it would not be completely senseless to say that 'my right arm' was then an important 'part' of Scotland. Not, however, in the same sense that my right arm is a part of me.

What sense is really meant by Parmenides? I ran this section by my mereologist friend, and he says, "I take him to mean that parthood is a derivative of some kind of constitution relationship. Like, my arm is a part of me in virtue of the matter it's made of partially constituting me qua organism-that-has-arms. It's not just that the atoms that make up my arm are among the atoms that make up me. That's too loose a relationship to be sufficient for parthood. The former is a more abstract relationship like set membership, whereas the part-whole relationship presupposes a specific functional relationship."

Clearly not.
Then the part is not a part of the many, nor of all, but is of a certain single form, which we call a whole, being one perfect unity framed out of all-of this the part will be a part.

Certainly.
If, then, the others have parts, they will participate in the whole and in the one.

True.
Then the others than the one must be one perfect whole, having parts.

Certainly.
And the same argument holds of each part, for the part must participate in the one; for if each of the parts is a part, this means, I suppose, that it is one separate from the rest and self-related; otherwise it is not each.

True.
But when we speak of the part participating in the one, it must clearly be other than one; for if not, it would merely have participated, but would have been one; whereas only the itself can be one.

Very true.
Both the whole and the part must participate in the one; for the whole will be one whole, of which the parts will be parts; and each part will be one part of the whole which is the whole of the part.

True.

This is an important part. The Form of One is indispensable to all of these ideas. Even "many" requires the notion of "one." You can't have many except by having many individuals, each of which are one. A whole is one thing that is made up of many parts; and each part is 'one part.' So the world we conceive of being made up of many extended, divisible objects depends conceptually on the notion of a unity. 

Yet a true unity, as we have been exploring, can't exist in this world. It can't exist in time, and it can't exist in space. We can't understand the world without something that can't exist in the world.

And will not the things which participate in the one, be other than it?

Of course.
And the things which are other than the one will be many; for if the things which are other than the one were neither one nor more than one, they would be nothing.

True.

Well, no, you might say: it could be 0.25. That's not one, and not more than one, but it's not nothing either. But hang on.

But, seeing that the things which participate in the one as a part, and in the one as a whole, are more than one, must not those very things which participate in the one be infinite in number?

How so?
Let us look at the matter thus:-Is it not a fact that in partaking of the one they are not one, and do not partake of the one at the very time. when they are partaking of it?

Clearly.
They do so then as multitudes in which the one is not present?

Very true.
And if we were to abstract from them in idea the very smallest fraction, must not that least fraction, if it does not partake of the one, be a multitude and not one?

It must.

Return to 0.25, which is equivalent to a quarter. Well, it's "one" quarter -- but only if we take everything from 0.0 to 0.25. If we take just 0.25, it's a point on a number line. It's literally nothing but a designation; the line is not made up of points, which exist in a lower dimension and thus have no extension.  

So it turns out that he was right after all: if it doesn't partake in one (whether as the whole of "0.0-1.0" or in the sense of "one quarter"), and it's also not more than one, it's nothing. It has meaning, but no extension.

And if we continue to look at the other side of their nature, regarded simply, and in itself, will not they, as far as we see them, be unlimited in number?

Certainly.
And yet, when each several part becomes a part, then the parts have a limit in relation to the whole and to each other, and the whole in relation to the parts.

Just so.
The result to the others than the one is that of themselves and the one appears to create a new element in them which gives to them limitation in relation to one another; whereas in their own nature they have no limit.

That is clear.
Then the others than the one, both as whole and parts, are infinite, and also partake of limit.

Certainly.
Then they are both like and unlike one another and themselves.

How is that?
Inasmuch as they are unlimited in their own nature, they are all affected in the same way.

True.
And inasmuch as they all partake of limit, they are all affected in the same way.

Of course.
But inasmuch as their state is both limited and unlimited, they are affected in opposite ways.

Yes.
And opposites are the most unlike of things.
Certainly.
Considered, then, in regard to either one of their affections, they will be like themselves and one another; considered in reference to both of them together, most opposed and most unlike.

That appears to be true.
Then the others are both like and unlike themselves and one another?

True.

Aristotle will make contraries central to his idea of how motion is possible. There is a sense in which contraries are both alike and not-alike. They are not-alike in the sense that "red" and "not-red" are logical opposites. But they are alike in that they are both degrees of redness. "Red" and "Dandelion" are not contraries, but they're also not the terminal points on a continuum together. 

And they are the same and also different from one another, and in motion and at rest, and experience every sort of opposite affection, as may be proved without difficulty of them, since they have been shown to have experienced the affections aforesaid?

True.

Suppose, now, that we leave the further discussion of these matters as evident, and consider again upon the hypothesis that the one is, whether opposite of all this is or is not equally true of the others.

By all means.
Then let us begin again, and ask, If one is, what must be the affections of the others?

Let us ask that question.
Must not the one be distinct from the others, and the others from the one?

Why so?
Why, because there is nothing else beside them which is distinct from both of them; for the expression "one and the others" includes all things.

Yes, all things.
Then we cannot suppose that there is anything different from them in which both the one and the others might exist?

There is nothing.
Then the one and the others are never in the same?
True.
Then they are separated from each other?
Yes.
And we surely cannot say that what is truly one has parts?

Impossible.
Then the one will not be in the others as a whole, nor as part, if it be separated from the others, and has no parts?

Impossible.
Then there is no way in which the others can partake of the one, if they do not partake either in whole or in part?

It would seem not.
Then there is no way in which the others are one, or have in themselves any unity?

There is not.

You already have seen why that's not workable. But we're going to do it again, running this way. There is new insight to be had.

Nor are the others many; for if they were many, each part of them would be a part of the whole; but now the others, not partaking in any way of the one, are neither one nor many, nor whole, nor part.

True.
Then the others neither are nor contain two or three, if entirely deprived of the one?

True.
Then the others are neither like nor unlike the one, nor is likeness and unlikeness in them; for if they were like and unlike, or had in them likeness and unlikeness, they would have two natures in them opposite to one another.

That is clear.
But for that which partakes of nothing to partake of two things was held by us to be impossible?

Impossible.
Then the others are neither like nor unlike nor both, for if they were like or unlike they would partake of one of those two natures, which would be one thing, and if they were both they would partake of opposites which would be two things, and this has been shown to be impossible.

True.
Therefore they are neither the same, nor other, nor in motion, nor at rest, nor in a state of becoming, nor of being destroyed, nor greater, nor less, nor equal, nor have they experienced anything else of the sort; for, if they are capable of experiencing any such affection, they will participate in one and two and three, and odd and even, and in these, as has been proved, they do not participate, seeing that they are altogether and in every way devoid of the one.

Very true.

Therefore if one is, the one is all things, and also nothing, both in relation to itself and to other things.

Certainly.

The consequence here is that the world we observe is impossible without the one. Things can't move, or change, or become, or cease to be; they can't be two or three. The unity is again found to be fundamentally necessary to our ability to conceive the world, but whether we run the traps this way or the other way, such a unity can't exist in the world we're using it to conceive.  

 Now let's run it another way!

Well, and ought we not to consider next what will be the consequence if the one is not?

Yes; we ought.
What is the meaning of the hypothesis-If the one is not; is there any difference between this and the hypothesis-If the not one is not?

There is a difference, certainly.
Is there a difference only, or rather are not the two expressions-if the one is not, and if the not one is not, entirely opposed?

They are entirely opposed.

In formal logic we might write the two propositions "¬∃x(Ox)" versus "¬∃x(¬Ox)", except they're both being offered as the antecedent term of a material conditional. They are not in fact 'entirely opposed.' The strict contrary of the first one is either "∃x(Ox)" or "¬(¬∃x(Ox))", while the strict contrary to the second is either "¬(¬∃x(¬Ox))" or "∃x(¬Ox)". 

Or to put it in natural language, "The One does not exist" is not in fact a contrary to "The Not-One does not exist." You'd either want to say, "The One does exist," or "It is not the case that the One does not exist"; or, for the other, "The Not-One does exist," or "It is not the case that the Not-One does not exist." 

To take the set theory approach, whether or not there are any xs in O tells you nothing about whether or not there are xs in some other set. O and ¬O are contraries, but these expressions are not. 

And suppose a person to say:-If greatness is not, if smallness is not, or anything of that sort, does he not mean, whenever he uses such an expression, that "what is not" is other than other things?

To be sure.
And so when he says "If one is not" he clearly means, that what "is not" is other than all others; we know what he means-do we not?

Yes, we do.
When he says "one," he says something which is known; and secondly something which is other than all other things; it makes no difference whether he predicate of one being or not being, for that which is said "not to be" is known to be something all the same, and is distinguished from other things.

Certainly.

That's a little slippery, but Parmenides is pointing out that the fact that we can predicate things of the One implies that we know it; whether we say that it 'is' or 'is not,' we know what we're talking about, and we think we are saying something true about it. Thus, in some sense, it must exist.

Well, yes: "Unicorns have one horn" is a true statement. Do unicorns exist because I can predicate true statements about them? Yes, by the same proof! But at the same time, also, no: they exist as ideas, but you won't run into a unicorn tomorrow while walking through the forest.

The minimum upshot here is that the Form of One exists as an idea, like a unicorn. Only it's much more important than a unicorn, because our ability to conceive of the world hangs entirely upon our notion of what it is for something to be 'one.' It's absolutely fundamental at least to our ability to think; whether it has metaphysical as well as psychological reality is still an open question.

Then I will begin again, and ask: If one is not, what are the consequences? In the first place, as would appear, there is a knowledge of it, or the very meaning of the words, "if one is not," would not be known.

True.
Secondly, the others differ from it, or it could not be described as different from the others?

Certainly.
Difference, then, belongs to it as well as knowledge; for in speaking of the one as different from the others, we do not speak of a difference in the others, but in the one.

Clearly so.

That's an interesting consequence: the pure unity allows us to distinguish difference, because it is only by knowing what is the One that we can test whether another thing is. It's another way in which the concept is vital to everything we think we know about the world, even though we've seen again and again that it can't belong to the world.

Moreover, the one that is not is something and partakes of relation to "that," and "this," and "these," and the like, and is an attribute of "this"; for the one, or the others than the one, could not have been spoken of, nor could any attribute or relative of the one that is not have been or been spoken of, nor could it have been said to be anything, if it did not partake of "some," or of the other relations just now mentioned.

True.
Being, then, cannot be ascribed to the one, since it is not; but the one that is not may or rather must participate in many things, if it and nothing else is not; if, however, neither the one nor the one that is not is supposed not to be, and we are speaking of something of a different nature, we can predicate nothing of it. But supposing that the one that is not and nothing else is not, then it must participate in the predicate "that," and in many others.

Certainly.
And it will have unlikeness in relation to the others, for the others being different from the one will be of a different kind.

Certainly.
And are not things of a different kind also other in kind?

Of course.
And are not things other in kind unlike?
They are unlike.
And if they are unlike the one, that which they are unlike will clearly be unlike them?

Clearly so.
Then the one will have unlikeness in respect of which the others are unlike it?

That would seem to be true.

Does it? That seems like a problem to me. If the One is a pure unity, then it admits of no multiplicity; but to say that it is unlike everything other than it in respect of how they are unlike it means it must carry many different ways of 'being unlike.' The One just is; it is unlike other things by being itself, not in respect of the ways in which they aren't like it.

And if unlikeness to other things is attributed to it, it must have likeness to itself.

How so?
If the one have unlikeness to one, something else must be meant; nor will the hypothesis relate to one; but it will relate to something other than one?

Quite so.
But that cannot be.
No.
Then the one must have likeness to itself?
It must.

We have seen already a proof that it cannot carry 'likeness' either.

Again, it is not equal to the others; for if it were equal, then it would at once be and be like them in virtue of the equality; but if one has no being, then it can neither be nor be like?

It cannot.
But since it is not equal to the others, neither can the others be equal to it?

Certainly not.
And things that are not equal are unequal?
True.
And they are unequal to an unequal?
Of course.
Then the one partakes of inequality, and in respect of this the others are unequal to it?

Very true.
And inequality implies greatness and smallness?
Yes.
Then the one, if of such a nature, has greatness and smallness?

That appears to be true.
And greatness and smallness always stand apart?
True.
Then there is always something between them?
There is.

That last is an important point to philosophers. What exactly Plato meant by "the great and the small" is still today hotly debated. Aristotle treats it sometimes as a unitary principle (i.e., 'the great and the small' is something like the number line, with things getting smaller on one end and bigger on the other) and sometimes as a dyad, two different things that work to define reality between them. Here Plato (or Parmenides) is treating it clearly as the latter. 

OK, one more go after this. Hope you're enjoying it.