Dialogue on LOGIC OF SENSE (2): Wild Logic and Non-Standard Negation

Transcript of the second conversation between Terence Blake and Kent Palmer, on Deleuze’s LOGIC OF SENSE, Series 2. Full text here.

Excerpt

Kent Palmer 1:20:08

So maybe we could briefly just talk about this fourth question, which is, what is Deleuze’s relation to logic and the different types of alternative logics? And is he doing meta-logic? Could you explain that?

Terence Blake 1:20:23

Well, I think he is doing meta-logic from the very beginning. He’s taking a step back from logic as we know it in the 20th century, due to the work of Analytic philosophy. I mean, they took over, they went back to Boolean algebra and stuff. But the logic that we know today, that Symbolic Logic was formed in the 20th century, on the bases that Frege set up, but it was Russell and Whitehead that really started getting the canonical ideas and symbols straight.

And Deleuze is taking a step back from that sort of logic and saying well, maybe there is another sort of logic that’s possible. In Symbolic Logic, extensional logic, as we know it, there’s no room for paradox. Paradox is a problem that you have to explain away or get rid of, or create axiomatic structures so that it can’t occur any more, which you see with the paradoxes in set theory, that first Russell tried to eliminate with the theory of logical types. And when that didn’t really work you got the Zermelo-Fraenkel axioms for set theory, which don’t allow the sort of paradoxical sets to be formed within them.

And Deleuze said maybe we can take another tack, because in all the art and literature that I see around me, I see that the paradoxes are being used with pleasure and to great effect. The paradoxes are cognitive devices, for probing ordinary assumptions, and for making us, or helping us, re-conceptualize things. So maybe there would be a point in creating a different sort of logic, which would find a place for these sorts of paradoxes.

So that’s the methodological step, he’s reflecting on logic and what use it is, and what possibilities there are. And then he does a sort of descent into logic, but at another point, no longer in the logic that we know, but in a logic that he puts together from bits and pieces – Carroll, Frege, Wittgenstein and the Stoics. And sets that up as a philosophical logic, not as a mathematical logic, as a counter Logic, or alternative logic, which leaves open the question of whether a mathematical or symbolical formalization of his logic would be possible. And there has been lots of progress in logic over the whole 20th century and up to now, and lots of progress in logic that Deleuze didn’t know about, and since Logic of Sense, so it may be possible, that in fact he has created a concept that can correlate with new logical inventions, new formal inventions.

But despite the title of the book, I don’t think he has really created a full blown concept of alternative logic. It’s more intuitive concepts, and bits and pieces of different logics. And I don’t think you can say: that’s great, because you can’t create a system, Deleuze is totally anti-system, and the fact that it’s fragmentary, shows that his logic is not betraying itself. I don’t think that’s true. I think Deleuze is very systematic. And if he had been able to find a logical systematization of the ideas that he was coming up with, I think he would have been quite favourable towards it. So once again, you know more about logic and meta-logic than me. How do you think Logic of Sense stands up?

Kent Palmer 1:25:02

I think you’re right, we’ll see as we go along, but I think that he doesn’t really formulate a logic here, a deviant logic of the kind we’re talking about, that can include paradox. But he makes overtures toward it, he works on the problem here. So someone who does try to formalize the structure of Wild being is Castoriadis and his idea of the Magma, and he produces a kind of non-intuitive set of axioms that would formalize the nature of Wild being. And so I think that’s one example we can see of what that kind of logic of indistinction and indeterminism might look like.

But I think that where Deleuze has formalized this is in Anti-Oedipus with these passive syntheses of the unconscious, which are connection, disjunction and conjunction, by which he means juxtaposition. Basically logic, the basic structure of logic, has to do with AND, OR, and NOT as operations. And so, usually conjunction and disjunction are the “and” and the “or”, but Deleuze in Anti-Oedipus uses one of the terms differently. Instead of calling the ‘and’ conjunction, he calls the “and’ connection. And so the way he changes it is he says, and, and, and, and, rather than just one “and”, and the way that he changes the or of disjunction, is or, or, or, or, a series of “or”s. And so one way that he changes the logic is to have the “and”, and the “or” multiplied, repeated, then downplays the “not”.

But then he introduces this term of conjunction, and that term of conjunction is also used for a little plus sign in the complex numbers, because the complex number is made up of a real number and an imaginary number with a little plus sign between them. The addition never actually happens, it’s a juxtaposition of those two elements. And so he incorporates that. And he terms that conjunction, which really means the juxtaposition of the two things which are never combined. But if they are combined, they produce a paradox. So the way I see it is that in Anti-Oedipus this aim of creating a deviant logic that could incorporate paradox, but also as contrast with super rationality, is kind of realized there. And what we’re getting here in Logic of Sense is a whole lot of different attempts to say what that might be like, and to try to use Lewis Carroll to try to come up with a formalization of that, to the extent that he can.

Terence Blake 1:28:18

Yes it seems to me that the project of the book comes out straight away in the preface, where he says “The work of Lewis Carroll has everything required to please the modern reader”. So already it is coded, there’s a difference between pleasure and something else, that comes out later. So it has “everything required to please the modern reader”, and he spells it out:

“children’s books, or rather books for little girls, splendidly bizarre and esoteric words, grids, codes and decodings; drawings and photographs, a profound psychoanalytic content; and an exemplary logical and linguistic formalism”.

So I think lots of things there are already said, but you only realize later. So, for example, he mentions “a profound psychoanalytic content”. The form is logical and linguistic, and it is the form that he’s going to develop into something else. Psychoanalysis is a content, it is only interesting insofar as it exhibits this sort of logical grammar that he’s trying to find. And then when finally he decides that it doesn’t exhibit it enough, he jettisons it, and he goes on to Anti-Oedipus.

And he goes on to say “Over and above the immediate pleasure, there is something else, a play of sense and nonsense, a chaos-cosmos”. This play of sense and nonsense, this chaos-cosmos is “over and above”. I don’t think he’s talking about the heights there. I think he’s just talking about a value that’s more important than pleasure itself. And that’s the play of sense and nonsense, the chaos-cosmos. Then he says, as if it’s the same thing, that since “the marriage of language and the unconscious has already been consummated and celebrated in so many ways, it is necessary to examine the precise nature of this union in Carroll’s work”.

So the program is the marriage or the union of language and the unconscious, perhaps of the depths. And he’s envisaging that there are many different ways to create that marriage or union. And the sort of signature of a work in the sort of tradition that he’s looking at will be the precise way that the author or the thinker realizes that marriage of language and the unconscious. So for me he’s saying that basically he’s looking for a new logic and a new logical grammar, that’s the ”exemplary logical and linguistic formalism”.

He’s looking for a new logical grammar wherever sketches or little parts of it can be found. And at the same time this logical grammar maybe you can’t state it, maybe it’s sort of like Wittgenstein’s logical grammar, which you’ve got to learn by example, case by case, and it can’t come out in a theoretical form, because automatically, the theory would distort it. But I don’t think that’s a necessary consequence of his search for logical grammar.

And one of the things that I think is lacking even when Deleuze gets to Anti-Oedipus and he develops these syntheses of the unconscious, which are logical syntheses, logical grammars or parts of regions of logical grammar, is that he never gets round to the logic of negation, that he rejects negation. He rejects negativity, he rejects the dialectic when it’s based on negativity, or contradiction. And at the same time, all over the place in his work, in his vocabulary, he’s got lots of negative suffixes:

“de” – de-territorialization, “a” – a-signifying; “im” – im-personal

He’s also got negativity in the sorts of emotions and affects that he’s willing to consider. He’s got lots of polemic and he’s got lots of de-structuration. But he never gets around to creating a concept of the sort of negation that is virtually everywhere in his work. I don’t think he ever does.

So I think it’s a work in progress that has made lots of contributions to theorizing that sort of logic, he’s made lots of contributions to a practice of reasoning or thinking according to a different sort of logic. But well, you can’t do everything. And for me, one of the lacuna of his system is the never created a new concept of negation. And then he was just satisfied with debunking the old concept of negation.

This is a point that I made years ago on Andrew Culp’s blog, that he took up from me (he even thanked me for it) and elaborated n his book DARK DELEUZE. Unfortunately, Culp does not understand that it is a logical point, and conflates it with totally unrelated considerations.

Negation is not dark. The logic of negation in Deleuze’s work has been explicated creatively, with great talent and in great detail, in Corry Shores’ brilliant and indispensable new book THE LOGIC OF GILLES DELEUZE.

Kent Palmer 1:33:42

Yeah, I think that’s right. The weakness in his reconsideration of logic is he didn’t transform negation, like he transformed the “and” by repeating it and the “or” by repeating it. And by adding in conjunction, or juxtaposition as an operator. He’s neglected negation; he’s added another operator, but he has neglected the negation operator, because it is possible to change it, because, for instance, Zizek talks about the difference between the “anti-” and the “non-”, and so they’re an obvious transformation of negation from anti to non that Zizek makes a lot of, but I don’t think Deleuze tried that, I don’t think he explained that.

Terence Blake 1:34:31

Oh, Badiou as well in “Immanence of Truths”, which still hasn’t been translated, but at a certain point, he discusses the different concepts of negation that you get in the standard accounts of negation: two-valued logic that respects the law of non contradiction, and he discusses negation in intuitionist logic and in paraconsistent logic And he says that the difference between the three logics could be laid out in terms of the different force that you give to negation – a weak negation that allows intermediate cases or third values, and a strong negation, which repels the two terms, and then a more paradoxical negation, as in paraconsistent logic.

And Badiou says that when you’re thinking about politics you need all three sorts of negation. There’s a difference between seeking for consensus, seeking for negotiation, and seeking for war, for example, and there are different aspects or phases of negation. And the same applies to love: he gives a quite amusing description of a conjugal quarrel, where you can start up with something which is on the way to being negotiated, and it can blow up and lead to the rupture of the couple or can be brought back from “either you do this or else” to a third solution or a more intuitionist solution.

So regardless of that anecdotal approach, Badiou does explicitly theorize the role of negation within the truth procedures that he wants to discuss. And this is something that Deleuze didn’t do. Deleuze didn’t consider different senses and the different enunciative forces that could be given to negation.

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