Parmenides

By all means, said Zeno.

And who will answer me? he said. Shall I propose the youngest? He will not make difficulties and will be the most likely to say what he thinks; and his answers will give me time to breathe.

I am the one whom you mean, Parmenides, said Aristoteles; for I am the youngest and at your service. Ask, and I will answer.

Parmenides proceeded: 1.a. If one is, he said, the one cannot be many?

Impossible.

Then the one cannot have parts, and cannot be a whole?

Why not?

Because every part is part of a whole; is it not?

Yes.

And what is a whole? would not that of which no part is wanting be a whole?

Certainly.

Then, in either case, the one would be made up of parts; both as being a whole, and also as having parts?

To be sure.

And in either case, the one would be many, and not one?

True.

But, surely, it ought to be one and not many?

It ought.

Then, if the one is to remain one, it will not be a whole, and will not have parts?

No.

But if it has no parts, it will have neither beginning, middle, nor end; for these would of course be parts of it.

Right.

But then, again, a beginning and an end are the limits of everything?

Certainly.

Then the one, having neither beginning nor end, is unlimited?

Yes, unlimited.

And therefore formless; for it cannot partake either of round or straight.

But why?

Why, because the round is that of which all the extreme points are equidistant from the centre?

Yes.

And the straight is that of which the centre intercepts the view of the extremes?

True.

Then the one would have parts and would be many, if it partook either of a straight or of a circular form?

Assuredly.

But having no parts, it will be neither straight nor round?

Right.

And, being of such a nature, it cannot be in any place, for it cannot be either in another or in itself.

How so?

Because if it were in another, it would be encircled by that in which it was, and would touch it at many places and with many parts; but that which is one and indivisible, and does not partake of a circular nature, cannot be touched all round in many places.

Certainly not.

But if, on the other hand, one were in itself, it would also be contained by nothing else but itself; that is to say, if it were really in itself; for nothing can be in anything which does not contain it.

Impossible.

But then, that which contains must be other than that which is contained? for the same whole cannot do and suffer both at once; and if so, one will be no longer one, but two?

True.

Then one cannot be anywhere, either in itself or in another?

No.

Further consider, whether that which is of such a nature can have either rest or motion.

Why not?

Why, because the one, if it were moved, would be either moved in place or changed in nature; for these are the only kinds of motion.

Yes.

And the one, when it changes and ceases to be itself, cannot be any longer one.

It cannot.

It cannot therefore experience the sort of motion which is change of nature?

Clearly not.

Then can the motion of the one be in place?

Perhaps.

But if the one moved in place, must it not either move round and round in the same place, or from one place to another?

It must.

And that which moves in a circle must rest upon a centre; and that which goes round upon a centre must have parts which are different from the centre; but that which has no centre and no parts cannot possibly be carried round upon a centre?

Impossible.

But perhaps the motion of the one consists in change of place?

Perhaps so, if it moves at all.

And have we not already shown that it cannot be in anything?

Yes.

Then its coming into being in anything is still more impossible; is it not?

I do not see why.

Why, because anything which comes into being in anything, can neither as yet be in that other thing while still coming into being, nor be altogether out of it, if already coming into being in it.

Certainly not.

And therefore whatever comes into being in another must have parts, and then one part may be in, and another part out of that other; but that which has no parts can never be at one and the same time neither wholly within nor wholly without anything.

True.

And is there not a still greater impossibility in that which has no parts, and is not a whole, coming into being anywhere, since it cannot come into being either as a part or as a whole?

Clearly.

Then it does not change place by revolving in the same spot, nor by going somewhere and coming into being in something; nor again, by change in itself?

Very true.

Then in respect of any kind of motion the one is immoveable?

Immoveable.

But neither can the one be in anything, as we affirm?

Yes, we said so.

Then it is never in the same?

Why not?

Because if it were in the same it would be in something.

Certainly.

And we said that it could not be in itself, and could not be in other?

True.

Then one is never in the same place?

It would seem not.

But that which is never in the same place is never quiet or at rest?

Never.

One then, as would seem, is neither at rest nor in motion?

It certainly appears so.

Neither will it 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.

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.

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.

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.

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.

Then one cannot be older or younger, or of the same age, either with itself or with another?

Clearly not.

Then the one, being of this nature, cannot be in time at all; for must not that which is in time, be always growing older than itself?

Certainly.

And that which is older, must always be older than something which is younger?

True.

Then, that which becomes older than itself, also becomes at the same time younger than itself, if it is to have something to become older than.

What do you mean?

I mean this: – A thing does not need to become different from another thing which is already different; it IS different, and if its different has become, it has become different; if its different will be, it will be different; but of that which is becoming different, there cannot have been, or be about to be, or yet be, a different – the only different possible is one which is becoming.

That is inevitable.

But, surely, the elder is a difference relative to the younger, and to nothing else.

True.

Then that which becomes older than itself must also, at the same time, become younger than itself?

Yes.

But again, it is true that it cannot become for a longer or for a shorter time than itself, but it must become, and be, and have become, and be about to be, for the same time with itself?

That again is inevitable.

Then things which are in time, and partake of time, must in every case, I suppose, be of the same age with themselves; and must also become at once older and younger than themselves?

Yes.

But the one did not partake of those affections?

Not at all.

Then it does not partake of time, and is not in any time?

So the argument shows.

Well, but do not the expressions 'was,' and 'has become,' and 'was becoming,' signify a participation of past time?

Certainly.

And do not 'will be,' 'will become,' 'will have become,' signify a participation of future time?

Yes.

And 'is,' or 'becomes,' signifies a participation of present time?

Certainly.

And if the one is absolutely without participation in time, it never had become, or was becoming, or was at any time, or is now become or is becoming, or is, or will become, or will have become, or will be, hereafter.

Most true.

But are there any modes of partaking of being other than these?

There are none.

Then the one cannot possibly partake of being?

That is the inference.

Then the one is not at all?

Clearly not.

Then the one does not exist in such way as to be one; for if it were and partook of being, it would already be; but if the argument is to be trusted, the one neither is nor is one?

True.

But that which is not admits of no attribute or relation?

Of course not.

Then there is no name, nor expression, nor perception, nor opinion, nor knowledge of it?

Clearly not.

Then it is neither named, nor expressed, nor opined, nor known, nor does anything that is perceive it.

So we must infer.

But can all this be true about the one?

I think not.

1. b. Suppose, now, that we return once more to the original hypothesis; let us see whether, on a further review, any new aspect of the question appears.

I shall be very happy to do so.

We say that we have to work out together all the consequences, whatever they may be, which follow, if the one is?

Yes.

Then we will begin at the beginning: – If one is, can one be, and not partake of being?

Impossible.

Then the one will have being, but its being will not be the same with the one; for if the same, it would not be the being of the one; nor would the one have participated in being, for the proposition that one is would have been identical with the proposition that one is one; but our hypothesis is not if one is one, what will follow, but if one is: – am I not right?

Quite right.

We mean to say, that being has not the same significance as one?

Of course.

And when we put them together shortly, and say 'One is,' that is equivalent to saying, 'partakes of being'?

Quite true.

Once more then let us ask, if one is what will follow. Does not this hypothesis necessarily imply that one is of such a nature as to have parts?

How so?

In this way: – If being is predicated of the one, if the one is, and one of being, if being is one; and if being and one are not the same; and since the one, which we have assumed, is, must not the whole, if it is one, itself be, and have for its parts, one and being?

Certainly.

And is each of these parts – one and being – to be simply called a part, or must the word 'part' be relative to the word 'whole'?

The latter.

Then that which is one is both a whole and has a part?

Certainly.

Again, of the parts of the one, if it is – I mean being and one – does either fail to imply the other? is the one wanting to being, or being to the one?

Impossible.

Thus, each of the parts also has in turn both one and being, and is at the least made up of two parts; and the same principle goes on for ever, and every part whatever has always these two parts; for being always involves one, and one being; so that one is always disappearing, and becoming two.

Certainly.

And so the one, if it is, must be infinite in multiplicity?

Clearly.

Let us take another direction.

What direction?

We say that the one partakes of being and therefore it is?

Yes.

And in this way, the one, if it has being, has turned out to be many?

True.

But now, let us abstract the one which, as we say, partakes of being, and try to imagine it apart from that of which, as we say, it partakes – will this abstract one be one only or many?

One, I think.

Let us see: – Must not the being of one be other than one? for the one is not being, but, considered as one, only partook of being?

Certainly.

If being and the one be two different things, it is not because the one is one that it is other than being; nor because being is being that it is other than the one; but they differ from one another in virtue of otherness and difference.

Certainly.

So that the other is not the same – either with the one or with being?

Certainly not.

And therefore whether we take being and the other, or being and the one, or the one and the other, in every such case we take two things, which may be rightly called both.

How so.

In this way – you may speak of being?

Yes.

And also of one?

Yes.

Then now we have spoken of either of them?

Yes.

Well, and when I speak of being and one, I speak of them both?

Certainly.

And if I speak of being and the other, or of the one and the other, – in any such case do I not speak of both?

Yes.

And must not that which is correctly called both, be also two?

Undoubtedly.

And of two things how can either by any possibility not be one?

It cannot.

Then, if the individuals of the pair are together two, they must be severally one?

Clearly.

And if each of them is one, then by the addition of any one to any pair, the whole becomes three?

Yes.

And three are odd, and two are even?

Of course.

And if there are two there must also be twice, and if there are three there must be thrice; that is, if twice one makes two, and thrice one three?

Certainly.

There are two, and twice, and therefore there must be twice two; and there are three, and there is thrice, and therefore there must be thrice three?

Of course.

If there are three and twice, there is twice three; and if there are two and thrice, there is thrice two?

Undoubtedly.

Here, then, we have even taken even times, and odd taken odd times, and even taken odd times, and odd taken even times.

True.

And if this is so, does any number remain which has no necessity to be?

None whatever.

Then if one is, number must also be?

It must.

But if there is number, there must also be many, and infinite multiplicity of being; for number is infinite in multiplicity, and partakes also of being: am I not right?

Certainly.

And if all number participates in being, every part of number will also participate?

Yes.

Then being is distributed over the whole multitude of things, and nothing that is, however small or however great, is devoid of it? And, indeed, the very supposition of this is absurd, for how can that which is, be devoid of being?

In no way.

And it is divided into the greatest and into the smallest, and into being of all sizes, and is broken up more than all things; the divisions of it have no limit.

True.

Then it has the greatest number of parts?

Yes, the greatest number.

Is there any of these which is a part of being, and yet no part?

Impossible.

But if it is at all and so long as it is, it must be one, and cannot be none?

Certainly.

Then the one attaches to every single part of being, and does not fail in any part, whether great or small, or whatever may be the size of it?

True.

But reflect: – Can one, in its entirety, be in many places at the same time?

No; I see the impossibility of that.

And if not in its entirety, then it is divided; for it cannot be present with all the parts of being, unless divided.

True.

And that which has parts will be as many as the parts are?

Certainly.

Then we were wrong in saying just now, that being was distributed into the greatest number of parts. For it is not distributed into parts more than the one, into parts equal to the one; the one is never wanting to being, or being to the one, but being two they are co-equal and co-extensive.

Certainly that is true.

The one itself, then, having been broken up into parts by being, is many and infinite?

True.

Then not only the one which has being is many, but the one itself distributed by being, must also be many?

Certainly.

Further, inasmuch as the parts are parts of a whole, the one, as a whole, will be limited; for are not the parts contained by the whole?

Certainly.

And that which contains, is a limit?

Of course.

Then the one if it has being is one and many, whole and parts, having limits and yet unlimited in number?

Clearly.

And because having limits, also having extremes?

Certainly.

And if a whole, having beginning and middle and end. For can anything be a whole without these three? And if any one of them is wanting to anything, will that any longer be a whole?

No.

Then the one, as appears, will have beginning, middle, and end.

It will.

But, again, the middle will be equidistant from the extremes; or it would not be in the middle?

Yes.

Then the one will partake of figure, either rectilinear or round, or a union of the two?

True.

And if this is the case, it will be both in itself and in another too.

How?

Every part is in the whole, and none is outside the whole.

True.

And all the parts are contained by the whole?

Yes.

And the one is all its parts, and neither more nor less than all?

No.

And the one is the whole?

Of course.

But if all the parts are in the whole, and the one is all of them and the whole, and they are all contained by the whole, the one will be contained by the one; and thus the one will be in itself.

That is true.

But then, again, the whole is not in the parts – neither in all the parts, nor in some one of them. For if it is in all, it must be in one; for if there were any one in which it was not, it could not be in all the parts; for the part in which it is wanting is one of all, and if the whole is not in this, how can it be in them all?

It cannot.

Nor can the whole be in some of the parts; for if the whole were in some of the parts, the greater would be in the less, which is impossible.

Yes, impossible.

But if the whole is neither in one, nor in more than one, nor in all of the parts, it must be in something else, or cease to be anywhere at all?

Certainly.

If it were nowhere, it would be nothing; but being a whole, and not being in itself, it must be in another.

Very true.

The one then, regarded as a whole, is in another, but regarded as being all its parts, is in itself; and therefore the one must be itself in itself and also in another.

Certainly.

The one then, being of this nature, is of necessity both at rest and in motion?

How?

The one is at rest since it is in itself, for being in one, and not passing out of this, it is in the same, which is itself.

True.

And that which is ever in the same, must be ever at rest?

Certainly.

Well, and must not that, on the contrary, which is ever in other, never be in the same; and if never in the same, never at rest, and if not at rest, in motion?

True.

Then the one being always itself in itself and other, must always be both at rest and in motion?

Clearly.

And must be the same with itself, and other than itself; and also the same with the others, and other than the others; this follows from its previous affections.

How so?

Everything in relation to every other thing, is either the same or other; or if neither the same nor other, then in the relation of a part to a whole, or of a whole to a part.

Clearly.

And is the one a part of itself?

Certainly not.

Since it is not a part in relation to itself it cannot be related to itself as whole to part?

It cannot.

But is the one other than one?

No.

And therefore not other than itself?

Certainly not.

If then it be neither other, nor a whole, nor a part in relation to itself, must it not be the same with itself?

Certainly.

But then, again, a thing which is in another place from 'itself,' if this 'itself' remains in the same place with itself, must be other than 'itself,' for it will be in another place?

True.

Then the one has been shown to be at once in itself and in another?

Yes.

Thus, then, as appears, the one will be other than itself?

True.

Well, then, if anything be other than anything, will it not be other than that which is other?

Certainly.

And will not all things that are not one, be other than the one, and the one other than the not-one?

Of course.

Then the one will be other than the others?

True.

But, consider: – Are not the absolute same, and the absolute other, opposites to one another?

Of course.

Then will the same ever be in the other, or the other in the same?

They will not.

If then the other is never in the same, there is nothing in which the other is during any space of time; for during that space of time, however small, the other would be in the same. Is not that true?

Yes.

And since the other is never in the same, it can never be in anything that is.

True.

Then the other will never be either in the not-one, or in the one?

Certainly not.

Then not by reason of otherness is the one other than the not-one, or the not-one other than the one.

No.

Nor by reason of themselves will they be other than one another, if not partaking of the other.

How can they be?

But if they are not other, either by reason of themselves or of the other, will they not altogether escape being other than one another?

They will.

Again, the not-one cannot partake of the one; otherwise it would not have been not-one, but would have been in some way one.

True.

Nor can the not-one be number; for having number, it would not have been not-one at all.

It would not.

Again, is the not-one part of the one; or rather, would it not in that case partake of the one?

It would.

If then, in every point of view, the one and the not-one are distinct, then neither is the one part or whole of the not-one, nor is the not-one part or whole of the one?

No.

But we said that things which are neither parts nor wholes of one another, nor other than one another, will be the same with one another: – so we said?

Yes.

Then shall we say that the one, being in this relation to the not-one, is the same with it?

Let us say so.

Then it is the same with itself and the others, and also other than itself and the others.

That appears to be the inference.

And it will also be like and unlike itself and the others?

Perhaps.

Since the one was shown to be other than the others, the others will also be other than the one.

Yes.

And the one is other than the others in the same degree that the others are other than it, and neither more nor less?

True.

And if neither more nor less, then in a like degree?

Yes.

In virtue of the affection by which the one is other than others and others in like manner other than it, the one will be affected like the others and the others like the one.

How do you mean?

I may take as an illustration the case of names: You give a name to a thing?

Yes.

And you may say the name once or oftener?

Yes.

And when you say it once, you mention that of which it is the name? and when more than once, is it something else which you mention? or must it always be the same thing of which you speak, whether you utter the name once or more than once?

Of course it is the same.

And is not 'other' a name given to a thing?

Certainly.

Whenever, then, you use the word 'other,' whether once or oftener, you name that of which it is the name, and to no other do you give the name?

True.

Then when we say that the others are other than the one, and the one other than the others, in repeating the word 'other' we speak of that nature to which the name is applied, and of no other?

Quite true.

Then the one which is other than others, and the other which is other than the one, in that the word 'other' is applied to both, will be in the same condition; and that which is in the same condition is like?

Yes.

Then in virtue of the affection by which the one is other than the others, every thing will be like every thing, for every thing is other than every thing.

True.

Again, the like is opposed to the unlike?

Yes.

And the other to the same?

True again.

And the one was also shown to be the same with the others?

Yes.

And to be the same with the others is the opposite of being other than the others?

Certainly.

And in that it was other it was shown to be like?

Yes.

But in that it was the same it will be unlike by virtue of the opposite affection to that which made it like; and this was the affection of otherness.

Yes.

The same then will make it unlike; otherwise it will not be the opposite of the other.

True.

Then the one will be both like and unlike the others; like in so far as it is other, and unlike in so far as it is the same.

Yes, that argument may be used.

And there is another argument.

What?

In so far as it is affected in the same way it is not affected otherwise, and not being affected otherwise is not unlike, and not being unlike, is like; but in so far as it is affected by other it is otherwise, and being otherwise affected is unlike.

True.

Then because the one is the same with the others and other than the others, on either of these two grounds, or on both of them, it will be both like and unlike the others?

Certainly.

And in the same way as being other than itself and the same with itself, on either of these two grounds and on both of them, it will be like and unlike itself?

Of course.

Again, how far can the one touch or not touch itself and others? – consider.

I am considering.

The one was shown to be in itself which was a whole?

True.

And also in other things?

Yes.

In so far as it is in other things it would touch other things, but in so far as it is in itself it would be debarred from touching them, and would touch itself only.

Clearly.

Then the inference is that it would touch both?

It would.

But what do you say to a new point of view? Must not that which is to touch another be next to that which it is to touch, and occupy the place nearest to that in which what it touches is situated?

True.

Then the one, if it is to touch itself, ought to be situated next to itself, and occupy the place next to that in which itself is?

It ought.

And that would require that the one should be two, and be in two places at once, and this, while it is one, will never happen.

No.

Then the one cannot touch itself any more than it can be two?

It cannot.

Neither can it touch others.

Why not?

The reason is, that whatever is to touch another must be in separation from, and next to, that which it is to touch, and no third thing can be between them.

True.

Two things, then, at the least are necessary to make contact possible?

They are.

And if to the two a third be added in due order, the number of terms will be three, and the contacts two?

Yes.

And every additional term makes one additional contact, whence it follows that the contacts are one less in number than the terms; the first two terms exceeded the number of contacts by one, and the whole number of terms exceeds the whole number of contacts by one in like manner; and for every one which is afterwards added to the number of terms, one contact is added to the contacts.

True.

Whatever is the whole number of things, the contacts will be always one less.

True.

But if there be only one, and not two, there will be no contact?

How can there be?

And do we not say that the others being other than the one are not one and have no part in the one?

True.

Then they have no number, if they have no one in them?

Of course not.

Then the others are neither one nor two, nor are they called by the name of any number?