I
In the opening pages of The Logic of Sense, Deleuze writes: “Alice and Through the Looking-Glass involve a very special kind of things: events, pure events.” Plus, he proposes the following example: “When I say ‘Alice becomes larger,’ I mean that she becomes larger than she was” but also “smaller than she is now,” because “it is at the same moment that one becomes larger than one was and smaller than one becomes.”
“This,” adds Deleuze, “is the simultaneity of a becoming whose characteristic is to elude the present,” and which thereby “pulls in both directions at once: Alice does not grow without shrinking, and vice versa.” “Good sense,” concludes Deleuze, “affirms that in all things there is a determinable sense or direction; but paradox is the affirmation of both senses at the same time.”
Deleuze then mentions Plato in the following terms: “Plato,” he says, “invites us” (in the Philebus and the Parmenides) “to distinguish [ex hypothesis] between two dimensions: (1) that of limited and measured things, of fixed qualities, permanent or temporary which always presuppose pauses and rests, the fixing of presents and the assignation of subjects (for example, a particular subject having a particular largeness or a particular smallness at a particular moment); and (2) [that of] a pure becoming without measure, a veritable becoming-mad, which never rests […] [but] eludes the present, causing future and past, more or less, too much and not enough to coincide in the simultaneity of a rebellious matter.”
Lastly, Deleuze is aware that Plato himself discards the notion of “pure becoming,” for he argues in the Parmenides that becomings cannot leap over the “now” in which they occur.
II
Let’s go back to the first passage, that is, to the example supplied by Deleuze. What does it mean that Alice becomes larger than she was but smaller than she becomes? It means that if, in the present moment (β) Alice measures X, and if in this present moment Alice is larger than she was in a previous one (α), in the immediately subsequent moment of her growth (γ) she will become larger than she is now but smaller than she will be in an even-further moment of her growth (δ).
Now, isn’t this reasoning reminiscent of Zeno’s paradox of Achilles and the Turtle and of Zeno’s paradox of the arrow that cannot reach its target? Isn’t it built upon the same premise, namely, the infinite divisibility of time in Deleuze’s case, of space in Zeno’s?
Interestingly, Zeno’s ghost is present throughout the problematisation of the notion of “pure becoming” in Plato’s Parmenides. Additionally, in the Phaedrus Plato evokes Zeno’s artful cum deceptive way of reasoning, which makes him trickily dissolve becoming into being. One wonders then: isn’t Deleuze simply reversing the direction of Zeno’s argument, that is to say, dissolving being into becoming to accomplish what Deleuze himself calls the “task of modern philosophy,” to wit, the “overturning of Platonism?”
III
It can be adduced, though, that Deleuze’s argument is as little convincing as Zeno’s. For while Alice’s becoming causes, as Deleuze says, past and future to “coincide in the simultaneity of a rebellious matter,” the fact remains that such “coincidence” takes place in a certain now, and so it does not exactly “elude the present.”
But there is more. Another, broader kind of now makes possible Alice’s becoming, which is viewed by Deleuze – I dare say – through the lens of what might be labelled an empty mega-present. For in order to dissolve the thickness of each provisional now into a dual flow of time towards the past and the future (on each now Alice becomes larger and smaller at the same time) it must all be seen not only from the standpoint of what has already happened at each stage, but also from the standpoint of Alice’s growing process as a whole, which implies retro-projecting onto its constitutive steps or segments their futurability. Put differently: it requires to take for granted Alice’s future growth before such growth is achieved, in a sort of free adaptation (and reversion) of Aristotle’s final causality (since Aristotle introduces the idea of τέλος to explain growth, not growth and de-growth at the same time).
IV
The problem with Platonism, says Deleuze, is the problem of “essences,” which prevent “becoming” (as well as “differences in themselves”) to enter the realm of the thinkable. For Plato’s dualism “is not the dualism of the intelligible and the sensible,” he says, but “a [more] subterranean dualism between that which receives the action of the idea and that which eludes this action,” or what amounts to the same, between the good and the bad copies of the idea, which Deleuze calls “simulacra.” These, he writes, are “like false pretenders, built upon a dissimilarity, implying an essential perversion or a deviation.” Like “pure becomings,” they fall short of, or else exceed, any order allegedly “imposed” by the ideas over the things themselves.
I cannot help the impression that a major misunderstanding, according to which Plato’s thought would be about subsuming the Real under the limits of the Ideal, crosses the history of philosophy from, say, Aristotle to Heidegger and beyond. Now, not only do late dialogues (as per the habitual chronology of the Platonic corpus) like the Sophist and the Parmenides nuance considerably the customary interpretation of Plato’s so-called “theory of forms.” As early as the Phaedo,Plato shows very precisely what he intends by introducing the notion of εἴδη and by qualifying them as unchanging.
Consider Phaedo 100e–102e. Socrates argues there that things are (or, rather, that we say they are) “big” and “small” because of the idea of “bigness” and the idea of “smallness,” respectively; and not, therefore, because of the size, say, of someone’s “head,” which might be bigger than someone else’s head but also smaller than someone else’s head in turn. This moreover entails, adds Phaedo, that one may be “big and small at the same time,” in the sense that one can be simultaneously bigger than someone else but smaller than someone else in turn. (Notice that, against what is commonly assumed, this amounts to admit the situatedness of all εἴδη qua predicates.) Nevertheless, an εἶδος as such (qua concept) can neither be turned into its opposite nor can it be exchanged for any other unrelated εἶδος, as otherwise thought would be impossible in the first place. And this is applicable to Deleuze’s example of Alice, because if Alice’s becoming “pulls in both directions at once” it nonetheless pulls in two directions (becoming “larger” and “smaller,” respectively) whose simultaneity does erase their conceptual distinctiveness in any possible way – furthermore, it is that distinctiveness that makes Deleuze’s Zenonian game possible to begin with. In this sense, it is not true that the simulacrum “eludes the action of the idea” – quite the opposite indeed; and there seems to be no difference in this regard either between “simulacra” and “copies,” to keep with Deleuze’s terminology. In fact, the difference I have just traced between εἴδη as concepts and εἴδη as predicates might supply, I think, a radically new theoretical frame for a post-metaphysical interpretation of the Platonic difference between “originals” and “copies.”