The Paradox of Becoming: Growing Older and Younger at the Same Time, Plato, Parmenides, 152-155

by Corry Shores
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Deleuze takes interest in these passages by Plato. He wants to teach us pure events (événements purs). (Logique du Sens 7b, Logic of Sense 3b)

Consider that we light a match. The words "match" and "fire" denote real things. And these real things express the event of lighting a match. But there is a moment when the match is at the limit of being a match, and is virtually already fire. This is because, when it is at the limit of being a match, there is no extent of time between the match and the fire. Its tendency to become fire has such power at that instant, that the match might as well be fire. So to refer to the match as a "match" is a bit misleading. For, it is no less fire at that moment. The proposition, "the match is lighting," has a certain sense to it that cannot be reduced to the denoted things involved. For, if we say that "match" refers to the match, we are betraying the overpowering tendency that makes it no less fire at that instant. And if we say that "lighting" refers to the fire, we again are mis-describing the situation, because fire has not yet actualized. When we say "the match is being lit," our proposition has a meaning that in a sense hovers above the things denoted. It cannot be reduced to them. What hovers above is the pure event, which is the sense of the proposition.

Deleuze will use the example of Carroll’s Alice changing in size. He relates it to Plato's Parmenides. The point he will make is that when things are changing (during "the event of becoming") there is a unique temporality and reality involved. The match is both match and fire, and neither match nor fire. It is both in its state before the change, the match, and it is in its state after the change, the fire, all in the same instant. It is both before and after at the same, but also neither before nor after, all at once.

Now consider when Alice keeps growing. It would seem that at every moment, she is getting bigger. But if it is truly an event, then the changing has not ended. So she keeps moving into a state that precedes another state. She is never one precise size. She is always in a state of size-change. So right now she is in a state of size-change where she is at the same time becoming larger than she was, and smaller than she will be. It may seem that she is being pushed into the future. But because when she is still changing when she arrives in the future, she is becoming into a state that involves both her being in the past, for she is getting bigger than she was, and her being in the future, for she is getting smaller than she will become.

So the pure event is what the things (or terms) express, but which cannot be put into words.

The parts of the Parmenides Deleuze cites are 154-155. We will begin at 152 where the discussion of becoming older and younger begins. [For further background, see parts 149-152]

There was a theory that really there are not many things. There is only one, The One. The fact that The One is no more than one thing will present paradoxes when we begin to distinguish temporal phases of The One. So The One also existed in the past. In one sense, we must distinguish the past One from The One that exists in the present. But on the other hand, there is no more than one One. So there is The One as it is in the present; and there is The One as it was in the past and as it will be in the future. However, to compare the present One with The One in the past or future is to compare the present One with itself. For, there is only one One. The former and future Ones cannot be considered as in any way different from the present One. So to say that the present One comes after the past One is to say that the present One comes after itself.

From Plato’s dialogue:

Now we ask if The One participates in time.

Claim: The One

A) becomes older than itself and older than other things, while

B) it also in another sense becomes younger than itself and younger than other things. Also, in yet another sense, The One is

C) not older than itself and not older than other things, while also being

D) not younger than itself and not younger than other things. [151e]

The One Becomes Older than Itself

If there is The One, then it exists. It has being. Or as Plato puts it, The One shows itself 'to be.' But 'to be' is existence in present time, just as 'was' is existence in past time, and 'will be' is existence in future time.

So, The One exists in time. And time moves forward.

But if something is moving forward in time, then it is growing older.

To grow older is a comparative term. It is growing older than itself. [152a] In the image below, we consider The One in its present state as The One'', and The One in its former state is The One'.

The One Becomes Younger than Itself

But when one thing becomes older than a second thing, the second thing is becoming younger than the first thing.

Now let's consider The One as it was in the past. We compare it to what it is in the present. But what it is in the present is something that is in the process of moving into the future. So The One' of the past is becoming more and more younger than The One'' of the present, which is moving into being The One''' of the future.

But despite which perspective we take, we are still talking about one thing, The One. So The One becomes older than its (past) self, and younger than its (present) self.

Thus the one becomes older and younger than itself.[152b]

The One Is Older than Itself

So in the present moment, The One is moving from the past to the present. But it does not stop in this present moment. It continues into the future just as soon as it arrives in the present.

For while it moves forward it can never be arrested by the present, since that which moves forward touches both the present and the future, letting the present go and seizing upon the future, proceeding or becoming between the two, the present and the future. [152c]

But even though it never stops in the present, it still passes through the present. So it is becoming older than it was. Then when it reaches the present, it is older than it was.

So in the present moment, The One'' actually is older than it once was (The One'). Hence in the present, The One is older than itself.

The One Is Younger than Itself

But we saw that The One' in the past is continually becoming younger than The One in the present (The One''). So when The One reaches the present, it is younger than itself.

The One Always is Older and Younger than Itself

Consider this also. The One actually exists only in the present. It has being in the present alone. Which is to say, The One only is in the present, as it is moving through time.

the present is inseparable from the one throughout its whole existence; for it always is now whenever it is. [153a]

The One is always in the present now. And we saw above that when The One is in the present, it is older and younger than itself. Hence The One always is becoming older and younger than itself.

The One is Never Older or Younger than Itself

Now on the one hand, we might say that The One'' in the present has a greater age than The One' in the past. But on the other hand, we cannot say that there is more than one One. So in this second sense, The One is always the same age as itself. For to say otherwise would mean that there is more than one One. So in this other sense, The One is never older or younger than itself.

The One is Older than The Others

We also have the idea that there are many things. We will consider The One as a hypothetical idea, and we will also consider The Others as a hypothetical idea. We do so, in order to find contradictions between these ideas.

We know that there must be more than one other. For, if there was just one other, it would be one, and hence the same thing as The One. So when we speak of The Others we are referring to a multiplicity of things. Their number is greater than one.

Each of the many things is one thing. So a multiplicity presupposes there are single one things. Hence one comes into being before the many.

The one, therefore, has come into being first of all things that have number. [153b]

The Others came into being after The One. But things that are born later are younger. The sibling born after you is younger than you. So The One is older than The Others, and The Others are younger than The One.

The One is Younger than the Others

If something negates itself, then it becomes destroyed, and not born. So something cannot come into being while also contradicting its own nature. And if there is The One, it like all things must come into being, exist, and then pass away out of its existence. Hence, The One has these parts: a beginning, a middle, and an end. First the beginning comes into being, then all the middle parts, and lastly the end happens. But, all its temporal parts will not have existed until the very end when the last part appears. So it is not fully one until the very end. If The One were to come into being prior to the end, then it would not be one. In that case, it would be contrary to its own nature, which we said was impossible. So certainly The One only comes to be when the end part appears, after all the other parts have come about. Hence The One is also younger than The Others, and The Others are older than The One.

The One is Neither Older nor Younger than the Others

But let's consider matters in yet another sense. The beginning part is singular, otherwise it would be ‘the beginning parts’ in plural. So the beginning is already one. And the same holds for every other part. So The One was never anything but one.

Then the one would come into being simultaneously with the first part and with the second, and it is not wanting in any part which comes into being in addition to any part whatsoever which may precede it, until it reaches the end and becomes complete one; it will not be wanting in the middle, nor in the first, nor in the last, nor in any other part in the process of coming into being. [154a]

So the oneness of The Others is in this sense the same age as the oneness of The One. Both The Others and The One came into being simultaneously. But before we saw that in a different sense, The One is both older and younger than The Others, and likewise, The Others are both older and younger than The One.

Notice that in the above senses, we are saying that The One is older and younger. But what about this: does The One become older and younger than itself and the others?

The One does not Become Older or Younger than The Others

Imagine a younger brother or sibling. You get older. So does she. But the passage of time was the same for both of you. So presume your younger sibling was born one year after you. When you are 2, she is 1. When you become 3, she becomes 2. The age difference between you always stays the same. You will always be one year apart, despite the fact that you are both growing older all the time.

even if one thing be older than another, it cannot become older by any greater difference in age than that which existed at first, nor if younger can it become younger by any greater difference; for the addition of equals to unequals, whether in time or anything else whatsoever, makes the difference always equal to that which existed at first. [154c]

So you always are older than your younger sibling. But you are never becoming older than she is. For, the difference between you remains the same.

Then that which exists [154c] can never become older or younger than that which exists, if the difference in age is always the same; but it is and has become older, and the other is and has become younger, but it does not become so.

So it would seem that the One does not become older or younger than The Others; for, they are both aging at the same rate.

The Younger is Becoming Older than the Older, and The Older is Becoming Younger than the Younger

But now consider these things. If something is older than another thing, then the first one came into being before the second one. So it has been in being for a longer time.

But, if the older and the younger continue growing at an equal rate, their proportional difference will decrease. So imagine first that the older thing is twice as old.

One year from now, it will only be one third older.

Then one fourth, then one fifth.

After a long enough time, the proportional difference between them will approach nothing at all, even though there will always remain one year between them. So in this proportional sense, the younger one is becoming older in relation to the older one. And likewise, the older one is becoming younger in proportional relation to the younger one. We noted that The One comes before the others. But its proportional age difference will become less as time goes on. The Older (The One) becomes younger in proportional relation to The Others (The Younger). And likewise, The Younger (The Others) becomes older in proportional relation to The One (The Older). What comes into being later than something else is younger than it. In this case, The Others came later so they are younger. But what then in this case comes later (The Others, The Younger) becomes (proportionally) older than The Older one (The One), yet never is any older (because the same actual difference in age between The One and The Others remains the same). So The Others never are older (than The One), but they are always becoming (proportionally) older in relation to The One. Conversely, The Older (The One) is always becoming (proportionally) younger than The Younger (The Others).

that which differs less in age from something than before becomes younger than before in relation to those things than which it formerly was older?” “Yes, it becomes younger.” “But if the one becomes younger, must not those other things in turn become older than formerly in relation to the one?” “Certainly.” “Then that which came into being later, becomes older in relation to the older, which came into being earlier; yet it never is older, but is always becoming older; for the latter always tends towards being younger, [155a] and the former towards being older. And conversely the older becomes in the same way younger than the younger.

So in a sense, The Older (The One) and The Younger (The Others) are moving in opposite directions. The Older is becoming (proportionally) younger (in relation) to The Younger, all while The Younger (The Others) is becoming older (in relation) to The Older.

as they are moving in opposite directions, they are becoming the opposites of one another, the younger older than the older, and the older younger than the younger; but they cannot finish the process of becoming; for if they finished the process of becoming, they would no longer be becoming, they would be. But as the case is, they become older and younger than one another--the one becomes younger than the others, because, as we saw, it is older and came into being earlier, [155b] and the others are becoming older than the one, because they came into being later. [emphasis mine, Deleuze’s citation]

But we noted that from another perspective, they both remain equally older or younger than one another. So given that there are these two senses to "older" and "younger," we can say that The One and The Others both are and are becoming older and younger, while also are not and are not becoming older and younger, than one another.

For all these reasons, then, the one both is and becomes both older and younger than both itself and the others, and neither is nor becomes either older or younger than either itself or the others. [155d]

From the Fowler translation:

“And does the one partake of time and if it partakes of time, is it and does it become younger and older than itself and other things, and neither younger nor older than itself and the others?” “What do you mean?” “If one is, it is thereby shown to be.” “Yes.” “But is 'to be' anything else than participation in existence together with present time, [152a] just as 'was' denotes participation in existence together with past time, and 'will be' similar participation together with future time?” “True.” “Then the one partakes of time if it partakes of being.” “Certainly.” “And the time in which it partakes is always moving forward?” “Yes.” “Then it is always growing older than itself, if it moves forward with the time.” “Certainly.” “Now, do we not remember that there is something becoming younger when the older becomes older than it?” “Yes, we do.” “Then the one, since it becomes older than itself, [152b] would become older than a self which becomes younger?” “There is no doubt of it.” “Thus the one becomes older and younger than itself.” “Yes.” “And it is older (is it not) when in becoming older it is in the present time, between the past and the future; for in going from the past to the future it cannot avoid the present.” “No, it cannot.” “Then is it not the case that it ceases to become older [152c] when it arrives at the present, and no longer becomes, but actually is older? For while it moves forward it can never be arrested by the present, since that which moves forward touches both the present and the future, letting the present go and seizing upon the future, proceeding or becoming between the two, the present and the future.” “True.” “But if everything that is becoming is unable to avoid and pass by the present, then when it reaches the present it always ceases to become 152d] and straightway is that which it happens to be becoming.” “Clearly.” “The one, then, when in becoming older it reaches the present, ceases to become and straightway is older.” “Certainly.” “It therefore is older than that than which it was becoming older; and it was becoming older than itself.” “Yes.” “And that which is older is older than that which is younger, is it not?” “It is.” “Then the one is younger than itself, when in becoming older it reaches the present.” [152e] “Undoubtedly.” “But the present is inseparable from the one throughout its whole existence; for it always is now whenever it is.” “Of course.” “Always, then, the one is and is becoming younger than itself.” “So it appears.” “And is it or does it become for a longer time than itself, or for an equal time?” “For an equal time.” “But that which is or becomes for an equal time is of the same age.” “Of course.” “But that which is of the same age is neither older nor younger.” “No.” “Then the one, since it is and becomes for an equal time with itself, neither is nor becomes older or younger than itself.” “I agree.” “Well, then, is it or does it become older or younger than other things?” [153a] “I cannot tell.” “But you can at any rate tell that the others, if they are others, not an other--plural, not singular--are more than one; for if they were an other, they would be one; but since they are others, they are more than one and have multitude.” “Yes, they have.” “And being a multitude, they would partake of a number greater than one.” “Of course.” “Well, which shall we say come and have come into being first, the greater or the smaller numbers?” “The smaller.” “Then the smallest comes into being first and that is the one, is it not?” [153b] “Yes.” “The one, therefore, has come into being first of all things that have number; but all others also have number, if they are others and not an other.” “They have.” “And since it came into being first, it came into being, I suppose, before the others, and the others later; but things which have come into being later are younger than that which came into being before them and thus the other things would be younger than the one, and the one older than the other things.” “Yes, they would.”

“Here is another question: Can the one have come into being contrary to its own nature, or is that impossible?” “It is impossible.” [153c] “But surely the one was shown to have parts, a beginning, a middle, and an end.” “Yes.” “And the beginning of everything--of one and everything else alike--comes into being first, and after the beginning come all the other parts until the end arrives, do they not?” “Certainly.” “And we shall say also that all these others are parts of the whole and the one, and that it has become one and whole at the moment when the end arrives.” “Yes, we shall say that.” “The end, I imagine, comes into being last; and at that moment the one naturally comes into being; [153d] so that if the absolute one cannot come into being contrary to its own nature, since it has come into being simultaneously with the end, its nature must be such that it comes into being after all the others.” “That is clear.” “Then the one is younger than the others and the others are older than the one.” “I think that is clear, too.” “Well, must not a beginning or any other part whatsoever of one or of anything else whatsoever, if it be a part, not parts, be one, since it is a part?” “It must.” [153e] “Then the one would come into being simultaneously with the first part and with the second, and it is not wanting in any part which comes into being in addition to any part whatsoever which may precede it, until it reaches the end and becomes complete one; it will not be wanting in the middle, nor in the first, nor in the last, nor in any other part in the process of coming into being.” “True.” “Then one has the same age as all the others so that the absolute one, unless it is naturally contrary to nature, could not have come into being either before or after the others, but only simultaneously with them. [154a] And by this reasoning the one would be neither older nor younger than the others nor the others than the one, but of the same age; but by the previous reasoning the one would be both older and younger than the others, and likewise the others than the one.” “Certainly.” “In this state, then, it is and in this way it has come into being. But what about the one becoming older and younger than the others, and the others than the one, and becoming neither older nor younger? Is it the same with becoming as with being, or otherwise?” [154b] “I cannot say.” “But I can say as much as this, that even if one thing be older than another, it cannot become older by any greater difference in age than that which existed at first, nor if younger can it become younger by any greater difference; for the addition of equals to unequals, whether in time or anything else whatsoever, makes the difference always equal to that which existed at first.” “Yes, of course.” “Then that which exists [154c] can never become older or younger than that which exists, if the difference in age is always the same; but it is and has become older, and the other is and has become younger, but it does not become so.” “True.” “And the one, since it exists, never becomes either older or younger than the other things.” “No, it does not.” “But see whether they become older and younger in this way.” “In what way?” “Because the one was found to be older than the others, and the others than the one.” “What then?” “When the one is older than the others, [154d] it has come into being a longer time than the others.” “Yes.” “Then consider again. If we add an equal to a greater and to a less time, will the greater differ from the less by the same or by a smaller fraction?” “By a smaller fraction.” “Then the proportional difference in age which existed originally between the one and the others will not continue afterwards, but if an equal time be added to the one and the others, the difference in their ages will constantly diminish, will it not? [154e] “Yes.” “And that which differs less in age from something than before becomes younger than before in relation to those things than which it formerly was older?” “Yes, it becomes younger.” “But if the one becomes younger, must not those other things in turn become older than formerly in relation to the one?” “Certainly.” “Then that which came into being later, becomes older in relation to the older, which came into being earlier; yet it never is older, but is always becoming older; for the latter always tends towards being younger, [155a] and the former towards being older. And conversely the older becomes in the same way younger than the younger. For as they are moving in opposite directions, they are becoming the opposites of one another, the younger older than the older, and the older younger than the younger; but they cannot finish the process of becoming; for if they finished the process of becoming, they would no longer be becoming, they would be. But as the case is, they become older and younger than one another--the one becomes younger than the others, because, as we saw, it is older and came into being earlier, [155b] and the others are becoming older than the one, because they came into being later. By the same reasoning the others stand in the same relation to the one, since they were seen to be older than the one and to have come into being earlier.” “Yes, that is clear.” “Then from the point of view that no one thing becomes older or younger than another, inasmuch as they always differ by an equal number, the one cannot become older or younger than the others, nor the others than the one; but in so far as that which comes into being earlier must always differ by a different proportional part from that which comes into being later, [155c] and vice versa--from this point of view the one and the others must necessarily become both older and younger than one another, must they not?” “Certainly.” “For all these reasons, then, the one both is and becomes both older and younger than both itself and the others, and neither is nor becomes either older or younger than either itself or the others.” “Perfectly true.” “But since the one partakes of time and can become older and younger, [155d] must it not also partake of the past, the future, and the present?” “It must.” “Then the one was and is and will be and was becoming and is becoming and will become.” “Certainly.” “And there would be and was and is and will be something which is in relation to it and belongs to it?” “Certainly.” “And there would be knowledge and opinion and perception of it; there must be, if we are now carrying on all this discussion about it.” “You are right.” “And it has a name and definition, is named and defined, [155e] and all the similar attributes which pertain to other things pertain also to the one.”

Deleuze, Gilles. Logique de sens. Paris: Les Éditions de Minuit, 1969.

Deleuze, Gilles. Logic of Sense, Transl. Mark Lester. London: Columbia University Press, 1990; reprinted by Continuum, 2001.

Text from Perseus Project
Plato. Parmenides. in Plato in Twelve Volumes, Vol. 9. Transl. Harold N. Fowler. Cambridge, MA: HarvardUniversity Press; London: William Heinemann Ltd., 1925. OCLC: 20083931, 19433521, 377367, 21777623 ISBN: 0674990404, 0674991842, 0674991850, 0674991826 Available online at: http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.01.0174&query=head%3D%231