Plato's Parmenides VIII, The One III: Time

This is a long section, so I'm going to put it beyond a jump. It's important to note at the beginning that this dialogue was written before almost any of the philosophy of time. Aristotle wrote one of the most important pieces on time in the ancient world, Plotinus another, and St. Augustine wrote another one. None of that thinking was available to Plato or to Parmenides. We saw in the preface to this series that Zeno appears to have believed that time, like space, was atomic in nature; Aristotle rejected both, but his rejection has not yet appeared. 

There are a lot of philosophical problems about time. One of them is the status of things (like ourselves) that seem to be extended in time. I can remember existing yesterday. Does that me still exist somewhere? For Zeno, the answer might be yes: there might be a 'time atom' (or rather a whole series of them) in which yesterday me still exists, and permanently (and changelessly). Or it might be 'no,' just as easily: that only the present time atom exists, neither one before nor one after. Both views admit of his apparent theory that change is impossible: the first view for the reasons we've already seen, as about the arrow that must be frozen in time because at any atom of time it is frozen; the second because, if only the current time atom actually exists, there is nowhere to move from or to move towards. 

Lacking a built-out philosophy of time this bit is quite difficult to follow. It is at odds with the way that we tend to think about time. The basic problem is that the one cannot be many, but if it exists through time there will be a part of it that is younger than itself (i.e., the part that existed yesterday) and a part that is older (i.e., the part that will exist tomorrow). The One cannot, then, be in time. This is another reason it can neither 'come to be' nor perish.
To continue
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?
And that which is older, must always be older than something which
is younger?
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
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.

This strikes me as a strange argument given the way the immediately earlier section depended on "sameness" and "difference" as attributes attached to the thing; Xa and Yb, as mentioned in the previous discussion. Here Parmenides is saying something much more obvious to the contemporary reader: if it's different, it doesn't need anything to make it different. It already is different.  

That seems like a solution to the earlier set of problems about how the One cannot be different, or admit of difference, from anything else.

But, surely, the elder is a difference relative to the younger, and
to nothing else.
Then that which becomes older than itself must also, at the same time,
become younger than itself?
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?
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?
And do not "will be," "will become," "will have become," signify a
participation of future time?
And "is," or "becomes," signifies a participation of present time?
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.

Great, we can stop here! The One is not at all, and can't possibly be, clearly. Yet they don't stop; in fact, this section alone goes on for a long time. 

This may seem strange, but what is happening here remains of key importance in theology even today. Aquinas has to wrestle with these same questions, and has a theory of God and His relation to time that is ultimately rooted in this discussion from Plato. (Just the first heading gives it away: "That Creation is Neither Motion nor Change.")

In fact, this discussion will prove to be the root of substantial philosophical problems. It is quite difficult, but tremendously important to human thought over the millennia. 

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?
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.

Another serious problem for Socrates' view that Forms, which are unities, can be the source of knowledge.

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.
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
I shall be very happy to do so.

Aristotle occasionally makes this move: 'Let's try that again,' as for example at the end of Physics I. Here, Parmenides is going to run all the same traps again, but this time from the perspective that we accept that "the One is." If so, what follows? 

We say that we have to work out together all the consequences, whatever
they may be, which follow, if the one is?
Then we will begin at the beginning:-If one is, can one be, and not
partake of being?
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.

This is one of the trickiest parts that later philosophers have successfully navigated. The answer to how God could exist without 'partaking of being' is that while God is simple, His essence is existence. Existence and Goodness turn out to be the same thing -- 'the good is that which all things desire,' Aquinas quotes Aristotle as saying, and all things from you and me and squirrels and grass direct themselves towards continued existence. 

Yet God's goodness and existence are not goodness nor existence as we experience them. There is a categorical difference. Our ability to understand God is limited to being able to say what God is not, which is exactly coherent with Parmenides' remarks on the One, whose essence cannot be correctly "named, nor expressed, nor opined, nor known, nor does anything that is perceive it."

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

Therefore the One 'is not,' again; not, at least, as we or anything we encounter are.

Hold onto your hat for this next bit, which is about how the One generates infinite multiplicity. We've talked the first part through several times already -- how one necessarily creates three. Here's another version of that.

Let us take another direction.
What direction?
We say that the one partakes of being and therefore it is?
And in this way, the one, if it has being, has turned out to be many?
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?
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.
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?
And also of one?
Then now we have spoken of either of them?
Well, and when I speak of being and one, I speak of them both?
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?
And must not that which is correctly called both, be also two?
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?
And if each of them is one, then by the addition of any one to any
pair, the whole becomes three?

Here follows an example of ancient Greek mathematics, which makes a great deal of the concepts of odd and even numbers. The following is a proof that the three suffice for infinity, in the sense in which there are infinite numbers.

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?
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?
Here, then, we have even taken even times, and odd taken odd times,
and even taken odd times, and odd taken even times.
And if this is so, does any number remain which has no necessity to
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?
And if all number participates in being, every part of number will
also participate?
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.

So, whereas One is a perfect unity, Being by nature is infinitely multiple. Yet if Being is a Form in the Platonic or Socratic model, it needs to be a unity -- that's what Forms are like.

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?
But if it is at all and so long as it is, it must be one, and cannot
be none?
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?
But reflect: can one in its entirety, be in many places at the same
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.
And that which has parts will be as many as the parts are?

So if 'the One is,' then it isn't one; it's infinitely many. This is an apparent paradox that leads to a bunch more, as Parmenides helpfully rehearses. 

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 coextensive.
Certainly that is true.
The one itself, then, having been broken up into parts by being, is
many and infinite?
Then not only the one which has being is many, but the one itself
distributed by being, must also be many?
Further, inasmuch as the parts are parts of a whole, the one, as a
whole, will be limited; for are not the parts contained the whole?
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?
And because having limits, also having extremes?
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?
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?
Then the one will partake of figure, either rectilinear or round,
or a union of the two?
And if this is the case, it will be both in itself and in another
Every part is in the whole, and none is outside the whole.
And all the parts are contained by the whole?
And the one is all its parts, and neither more nor less than all?
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?
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.
The one then, being of this nature, is of necessity both at rest and
in motion?
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.
And that which is ever in the same, must be ever at rest?
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?
Then the one being always itself in itself and other, must always
be both at rest and in motion?
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?
Every thing 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.
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?
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?
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?
Then the one has been shown to be at once in itself and in another?
Thus, then, as appears, the one will be other than itself?
Well, then, if anything be other than anything, will it not be other
than that which is other?
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?
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.
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.
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.
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?
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?
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?
Since the one was shown to be other than the others, the others will
also be other than the one.
And the one is other than the others in the same degree that the others
are other than it, and neither more nor less?
And if neither more nor less, then in a like degree?

This next bit can be confusing. Parmenides obtains consent to the proposition that naming a thing names it rigidly (as Saul Kripke might say); and thus, when we mention it, we are using the name in the same way. That's not obviously correct in this example, though. If we say "The One and the other," 'the other' could be any other: it could be X or Y or Z, depending on which one was named. Say the One is the One and the 'other' was X. But now if I take the One and X together, and say, "These and the other," I might mean Y -- not X again. 

There is, however, a general point being raised that contrasts with the earlier proof that the One did not admit of relations. Because we can speak of it the same way as we can speak of any ordinary object, there must be a sense in which it is related to those things. It is affected by language the same way, apparently: we can designate it, name it, and contrast it with other things. Since Parmenides had already obtained consent that it was not possible to do that, this seems like a problem. 

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?
And you may say the name once or oftener?
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?
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?
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
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.
Again, the like is opposed to the unlike?
And the other to the same?
True again.
And the one was also shown to be the same with the others?
And to be, the same with the others is the opposite of being other
than the others?
And in that it was other it was shown to be like?
But in that it was the same it will be unlike by virtue of the opposite
affection to that which made it and this was the affection of otherness.
The same then will make it unlike; otherwise it will not be the opposite
of the other.
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.
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.
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?
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.

Now for another round on whether the One, or any unity like a Form, can exist physically.  

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?
And also in other things?
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.
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?
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.
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.

This is a definition of 'touching,' and what is important to note is that it requires multiple things. 

Two things, then, at the least ate 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?
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.
Whatever is the whole number of things, the contacts will be always
one less.
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?
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?
One, then, alone is one, and two do not exist?
Clearly not.
And if there are not two, there is no contact?
There is not.
Then neither does the one touch the others, nor the others the one,
if there is no contact?
Certainly not.
For all which reasons the one touches and does not touch itself and
the others?

Now Parmenides goes back through the greatness/smallness problem from the other direction, this time using it to prove that the One would seem to be equal and unequal to itself. 

Further-is the one equal and unequal to itself and others?
How do you mean?
If the one were greater or less than the others, or the others greater
or less than the one, they would not be greater or less than each
other in virtue of their being the one and the others; but, if in
addition to their being what they are they had equality, they would
be equal to one another, or if the one had smallness and the others
greatness, or the one had greatness and the others smallness-whichever
kind had greatness would be greater, and whichever had smallness would
be smaller?
Then there are two such ideas as greatness and smallness; for if they
were not they could not be opposed to each other and be present in
that which is.
How could they?
If, then, smallness is present in the one it will be present either
in the whole or in a part of the whole?
Suppose the first; it will be either co-equal and co-extensive with
the whole one, or will contain the one?
If it be co-extensive with the one it will be coequal with the one,
or if containing the one it will be greater than the one?
Of course.
But can smallness be equal to anything or greater than anything, and
have the functions of greatness and equality and not its own functions?
Then smallness cannot be in the whole of one, but, if at all, in a
part only?
And surely not in all of a part, for then the difficulty of the whole
will recur; it will be equal to or greater than any part in which
it is.
Then smallness will not be in anything, whether in a whole or in a
part; nor will there be anything small but actual smallness.
Neither will greatness be in the one, for if greatness be in anything
there will be something greater other and besides greatness itself,
namely, that in which greatness is; and this too when the small itself
is not there, which the one, if it is great, must exceed; this, however,
is impossible, seeing that smallness is wholly absent.
But absolute greatness is only greater than absolute smallness, and
smallness is only smaller than absolute greatness.
Very true.
Then other things not greater or less than the one, if they have neither
greatness nor smallness; nor have greatness or smallness any power
of exceeding or being exceeded in relation to the one, but only in
relation to one another; nor will the one be greater or less than
them or others, if it has neither greatness nor smallness.
Clearly not.
Then if the one is neither greater nor less than the others, it cannot
either exceed or be exceeded by them?
Certainly not.
And that which neither exceeds nor is exceeded, must be on an equality;
and being on an equality, must be equal.
Of course.
And this will be true also of the relation of the one to itself; having
neither greatness nor smallness in itself, it will neither exceed
nor be exceeded by itself, but will be on an equality with and equal
to itself.
Then the one will be equal to both itself and the others?
Clearly so.
And yet the one, being itself in itself, will also surround and be
without itself; and, as containing itself, will be greater than itself;
and, as contained in itself, will be less; and will thus be greater
and less than itself.
It will.
Now there cannot possibly be anything which is not included in the
one and the others?
Of course not.
But, surely, that which is must always be somewhere?
But that which is in anything will be less, and that in which it is
will be greater; in no other way can one thing be in another.
And since there is nothing other or besides the one and the others,
and they must be in something, must they not be in one another, the
one in the others and the others in the one, if they are to be anywhere?
That is clear.
But inasmuch as the one is in the others, the others will be greater
than the one, because they contain the one, which will be less than
the others, because it is contained in them; and inasmuch as the others
are in the one, the one on the same principle will be greater than
the others, and the others less than the one.
The one, then, will be equal to and greater and less than itself and
the others?
And if it be greater and less and equal, it will be of equal and more
and less measures or divisions than itself and the others, and if
of measures, also of parts?
Of course.
And if of equal and more and less measures or divisions, it will be
in number more or less than itself and the others, and likewise equal
in number to itself and to the others?
How is that?
It will be of more measures than those things which it exceeds, and
of as many parts as measures; and so with that to which it is equal,
and that than which it is less.
And being greater and less than itself, and equal to itself, it will
be of equal measures with itself and of more and fewer measures than
itself; and if of measures then also of parts?
It will.
And being of equal parts with itself, it will be numerically equal
to itself; and being of more parts, more, and being of less, less
than itself?
And the same will hold of its relation to other things; inasmuch as
it is greater than them, it will be more in number than them; and
inasmuch as it is smaller, it will be less in number; and inasmuch
as it is equal in size to other things, it will be equal to them in
Once more then, as would appear, the one will be in number both equal
to and more and less than both itself and all other things.
It will.

And, finally for today, we return to time and run those traps in the opposite direction. Supposing the One is, then it is now; and thus, it must become older than itself. All the paradoxes seem to follow again. 

Does the one also partake of time? And is it and does it become older
and younger than itself and others, and again, neither younger nor
older than itself and others, by virtue of participation in time?
How do you mean?
If one is, being must be predicated of it?
But to be (einai) is only participation of being in present time,
and to have been is the participation of being at a past time, and
to be about to be is the participation of being at a future time?
Very true.
Then the one, since it partakes of being, partakes of time?
And is not time always moving forward?
Then the one is always becoming older than itself, since it moves
forward in time?
And do you remember that the older becomes older than that which becomes
I remember.
Then since the one becomes older than itself, it becomes younger at
the same time?
Thus, then, the one becomes older as well as younger than itself?
And it is older (is it not?) when in becoming, it gets to the point
of time. between "was" and "will be," which is "now": for surely in
going from the past to the future, it cannot skip the present?
And when it arrives at the present it stops from becoming older, and
no longer becomes, but is older, for if it went on it would never
be reached by the present, for it is the nature of that which goes
on, to touch both the present and the future, letting go the present
and seizing the future, while in process of becoming between them.
But that which is becoming cannot skip the present; when it reaches
the present it ceases to become, and is then whatever it may happen
to be becoming.
And so the one, when in becoming older it reaches the present, ceases
to become, and is then older.
And it is older than that than which it was becoming older, and it
was becoming older than itself.
And that which is older is older than that which is younger?
Then the one is younger than itself, when in becoming older it reaches
the present?
But the present is always present with the one during all its being;
for whenever it is it is always now.
Then the one always both is and becomes older and younger than itself?
And is it or does it become a longer time than itself or an equal
time with itself?
An equal time.
But if it becomes or is for an equal time with itself, it is of the
same age with itself?
Of course.
And that which is of the same age, is neither older nor younger?
The one, then, becoming and being the same time with itself, neither
is nor becomes older or younger than itself?
I should say not.
And what are its relations to other things? Is it or does it become
older or younger than they?
I cannot tell you.
You can at least tell me that others than the one are more than the
one-other would have been one, but the others have multitude, and
are more than one?
They will have multitude.
And a multitude implies a number larger than one?
Of course.
And shall we say that the lesser or the greater is the first to come
or to have come into existence?
The lesser.
Then the least is the first? And that is the one?
Then the one of all things that have number is the first to come into
being; but all other things have also number, being plural and not
They have.
And since it came into being first it must be supposed to have come
into being prior to the others, and the others later; and the things
which came into being later, are younger than that which preceded
them? And so the other things will be younger than the one, and the
one older than other things?
What would you say of another question? Can the one have come into
being contrary to its own nature, or is that impossible?
And yet, surely, the one was shown to have parts; and if parts, then
a beginning, middle and end?
And a beginning, both of the one itself and of all other things, comes
into being first of all; and after the beginning, the others follow,
until you reach the end?
And all these others we shall affirm to be parts of the whole and
of the one, which, as soon as the end is reached, has become whole
and one?
Yes; that is what we shall say.
But the end comes last, and the one is of such a nature as to come
into being with the last; and, since the one cannot come into being
except in accordance with its own nature, its nature will require
that it should come into being after the others, simultaneously with
the end.
Then the one is younger than the others and the others older than
the one.
That also is clear in my judgment.
Well, and must not a beginning or any other part of the one or of
anything, if it be a part and not parts, being a part, be also of
necessity one?
And will not the one come into being together with each part-together
with the first part when that comes into being, and together with
the second part and with all the rest, and will not be wanting to
any part, which is added to any other part until it has reached the
last and become one whole; it will be wanting neither to the middle,
nor to the first, nor to the last, nor to any of them, while the process
of becoming is going on?
Then the one is of the same age with all the others, so that if the
one itself does not contradict its own nature, it will be neither
prior nor posterior to the others, but simultaneous; and according
to this argument the one will be neither older nor younger than the
others, nor the others than the one, but according to the previous
argument the one will be older and younger than the others and the
others than the one.
After this manner then the one is and has become. But as to its becoming
older and younger than the others, and the others than the one, and
neither older. nor younger, what shall we say? Shall we say as of
being so also of becoming, or otherwise?
I cannot answer.
But I can venture to say, that even if one thing were older or younger
than another, it could not become older or younger in a greater degree
than it was at first; for equals added to unequals, whether to periods
of time or to anything else, leave the difference between them the
same as at first.
Of course. Then that which is, cannot become older or younger than
that which is, since the difference of age is always the same; the
one is and has become older and the other younger; but they are no
longer becoming so.
And the one which is does not therefore become either older or younger
than the others which are
But consider whether they may not become older and younger in another
In what way?
Just as the one was proven to be older than the others and the others
than the one.
And what of that?
If the one is older than the others, has come into being a longer
time than the others.
But consider again; if we add equal time to a greater and a less time,
will the greater differ from the less time by an equal or by a smaller
portion than before?
By a smaller portion.
Then the difference between the age of the one and the age of the
others will not be afterwards so great as at first, but if an equal
time be added to both of them they will differ less and less in age?
And that which differs in age from some other less than formerly,
from being older will become younger in relation to that other than
which it was older?
Yes, younger.
And if the one becomes younger the others aforesaid will become older
than they were before, in relation to the one.
Then that which had become younger becomes older relatively to that
which previously had become and was older; it never really is older,
but is always becoming, for the one is always growing on the side
of youth and the other on the side of age. And in like manner the
older is always in process of becoming younger than the younger; for
as they are always going in opposite directions they become in ways
the opposite to one another, the younger older than the older and
the older younger than the younger. They cannot, however have become;
for if they had already become they would be and not merely become.
But that is impossible; for they are always becoming both older and
younger than one another: the one becomes younger than the others
because it was seen to be older and prior, and the others become older
than the one because they came into being later; and in the same way
the others are in the same relation to the one, because they were
seen to be older, and prior to the one.
That is clear.
Inasmuch then, one thing does not become older or younger than another,
in that they always differ from each other by an equal number, the
one cannot become older or younger than the others, nor the other
than the one; but inasmuch as that which came into being earlier and
that which came into being later must continually differ from each
other by a different portion-in this point of view the others must
become older and younger than the one, and the one than the others.
For all these reasons, then, the one is and becomes older and younger
than itself and the others, and neither is nor becomes older or younger
than itself or the others.
But since the one partakes of time, and partakes of becoming older
and younger, must it not also partake of the past, the present, and
the future?
Of course it must.
Then the one was and is and will be, and was becoming and is becoming
and will become?
And there is and was and will be something which is in relation to
it and belongs to it?
And since we have at this moment opinion and knowledge and perception
of the one, there is opinion and knowledge and perception of it?
Quite right.
Then there is name and expression for it, and it is named and expressed,
and everything of this kind which appertains to other: things appertains
to the one.
Certainly, that is true.
Yet once more and for the third time, let us consider: If the one
is both one and many, as we have described, and is, neither one nor
many, and participates in time, must it not, in as far as it is one,
at times partake of being, and in as far as it is not one, at times
not partake of being?
But can it partake of being when not partaking of being, or not partake
of being when partaking of being?
Then the one partakes and does not partake of being at different times,
for that is the only way in which it can partake and not partake of
the same.


james said...

Typo: "other would be in the game"

First thoughts:
The even/odd argument is extremely sloppy; simple induction is just as easy and more rigorous. Among other little bits, his even/odd construction leaves out almost all the prime numbers.

With things like "other" and "smallness" he is talking about relationships as though they were intrinsic properties. The number 1 does not "partake in smallness" except in relationship to other numbers.

Grim said...

I’m pretty sure that Aristotle makes that same error about primes, though I can’t recall exactly where. Euclid’s work on primes comes later; he wrote it in Alexandria, a city he came to around ten years after Alexander the Great founded it; which happened after he was educated by Aristotle.

Grim said...

It's a void in the way they think (or maybe just talk) about primes, by the way. They do know about them.

I can pull some stuff from the Metaphysics where Aristotle takes on this issue of 'great and small' as used in Plato and by others, and how it relates to numbers. Remind me.

james said...