Deleuze on the Negative

Deleuze on The Negative

Part I: Negation and Problems

Deleuze is well known for his 'critique of the negative', but what really, is that critique? One way to answer this is through Deleuze's critique of Hegel, specifically in some passages of Difference and Repetition. There, the Deleuzian complaint is that Hegel mistakes a product for an origin - that product being 'the negative'. Insofar as the negative is the 'motor' of Hegelian dialectics, Deleuze's critique is that there needs to be an account of the genesis of the negative itself, and that this is something missing from Hegel: "The negative is always derived and represented, never original or present: the process of difference and of differenciation is primary in relation to that of the negative and opposition". (D&R 207) To understand why this is the case, one needs to pay attention to the language of 'problematics' or 'problems' and 'solutions' which is key to Deleuze's ontology (at least at the time of D&R):

D&R, 206: "The negative is indeed, therefore, the turning shadow of the problematic upon the set of propositions that it subsumes as cases [...] Each proposition, however, has a double negative which expresses the shadow of the problem in the domain of solutions - in other words, it expresses the manner in which the problem subsists in the distorted image of it given in representation" (my italics).

D&R, 64: "Being (what Plato calls the Idea) 'corresponds' to the essence of the problem or the question as such. ... As for negation, this is only the shadow of the highest principle, the shadow of the difference alongside the affirmation produced. Once we confuse (non)-being with the negative, contradiction is inevitably carried into being; but contradiction is only the appearance or the epiphenomenon, the illusion projected by the problem, the shadow of a question which remains open and of a being which corresponds as such to that question (before it has been given a response) ... Beyond contradiction, difference - beyond non-being, (non)-being; beyond the negative, problems and questions" (D&R 64).

There's alot going on in these passages, but the key here is the relation between what Deleuze calls 'the problematic' and the negative. In each case Deleuze calls the negative 'the shadow' of the problematic, something derivative. This is because Deleuze models Being here on the notion of a 'problem': Being is literally an 'open problem' for Deleuze (like an extended essay question!), as opposed to a 'closed one' (like "1+1=?"). And 'open problems' have multiple, open-ended solutions (you can't 'completely answer' an essay question - there are always other things to consider, other connections to be made). Or to use another example, one might consider biological life as a 'problem' to which corresponds - as a set of 'solutions' - the entire diversity of living beings, in all forms, from plants to birds to humans and so on.

And if you model being as a 'problematic', the whole vocabulary of negation loses its purchase: what is the 'negation' of the bird as a solution to the problem of life? You could say: something that doesn't fly, that doesn't have feathers, etc. But at this point, you're missing the important stuff: life as a problem, which is a primary in relation to the product that is the 'bird form'. This is why for Deleuze 'affirmation' is primary. What comes first is the response to a problem, which is the source of genesis, while negation takes a 'solution' as its starting point and then looks to 'invert' it as it were, in order to work 'backwards' at an origin: "When does the negative emerge? Negation is the inverted image of difference" (D&R 235). And it's only once you take negation as primary does 'contradiction' become the motor of dialectics.

Part II: Dialectics

One of the interesting things about this critique of negation as derivative, is that it does not imply, as is sometimes thought, a critique of dialectics as such. To put it in no uncertain terms: Deleuze is a dialectician! However, Deleuze's dialectics is a dialectics which is not driven by negation (and with it, contradiction). Instead, Deleuze's dialectics is a dialectics of 'problems': "Dialectic is the art of problems and questions, the combinatory or calculus of problems as such" (D&R 157). However, as Deleuze continues, it is precisely when dialectics begins from already-constituted 'solutions' or 'propositions', rather than problems, that dialectics becomes a dialectics of the negative: "Dialectic loses its peculiar power when it remains content to trace problems from propositions [read: "solutions"]: thus begins the history of the long perversion which places it under the power of the negative" (ibid).

In other words, it is only when the dialectic is understood in terms of negation does dialectics become 'bad'. In contrast to this, Deleuze advocates for something like a 'positive' dialectic, a dialectic that takes for its content the correspondence of problems and solutions (the bird as a solution to the problem of life; the eye as a solution to the problem of light...). It's only when one loses sight of the problem-solution complex, out of which the negative derives, that the dialectic can be thought of as a matter of contradictions and their resolutions: "Whenever the dialectic 'forgets' its intimate relation with Ideas in the form of problems, whenever it is content to trace problems from propositions, it loses its true power and falls under the sway of the power of the negative, necessarily substituting for the ideal objectivity of the problematic a simple confrontation between opposing, contrary or contradictory, propositions. This long perversion begins with the dialectic itself, and attains its extreme form in Hegelianism" (D&R 162-164).

One consequence of this 'forgetting of problems' should be noted: that philosophy, rather than dealing with the singular and the concrete - this bird, that eye - becomes a practice of dealing merely with 'generalities': the concept 'bird', or the concept 'eye'. This in turn leads to a mode of conceptaulizing that can never reach the level of actually existing things. As Deleuze put it with respect to Bergson: "It seems that in this type of dialectical method [driven by the negative], one begins with concepts that, like baggy clothes, are much too big. The One in general, the multiple in general, non-being in general ... In such cases the real is recomposed with abstracts; but of what use is a dialectic that believes itself to be reunited with the real when it compensates for the inadequacy of a concept that is too broad or too general by invoking the opposite concept, which is no less broad and general? The concrete will never be attained by combining the inadequacy of one concept with the inadequacy of its opposite. The singular will never be attained by correcting a generality with another generality. ... Negation always involves abstract concepts that are much too general." (Bergsonism, 44).

Part III: Contradiction and Vicediction

That all said, dialectics is not the only thing that Deleuze attempts to 'save' from negation. He also, in a way, attempts to save contradiction too - or rather, he tries to think contradiction in a way that, like his dialectics, is also not driven by negation. In so doing, Deleuze opposes Hegel's movement of 'contra-diction' to what he instead calls 'vice-diction'. Now, what even is contradiction and vicediction? Well, minimally, both are ways of thinking about things which are 'incompatible' with each other, in some way. In which ways? Well, contradiction is a logical incompatibility: it says that one cannot affirm both "A" and its negation, "not-A", at the same time. However, if negation is something derivative and secondary, what would it be like to conceive of (in)compatibility in a way that is not driven by negation?

Deleuze finds just such a model of 'non-negative' incompatibility in what he calls 'vicediction', which, as he specifies, is a matter of 'alogical incompatibility'. What does this mean? Well, it refers first of all to a kind of incompatibility which precedes contradiction, and in turn, makes it possible. And he finds this kind of incompatibility in Leibniz' theory of compossibility. What is compossibility? As the name implies, com-possibility has to do with the compatibility of possibilities. For Leibniz, everything that is possible strives to be actual. However, not all possible things can be actualized together at the same time: some possibilities are compatible with each other, and some are not. However - and this is key - what makes possibilities compatible and incompatible is not their being contradictions with each other (A and not-A), but their being compatible in the same world as each other.

Deleuze uses Leibniz's example of Adam the sinner, and Adam the non-sinner: "The contradiction between Adam-the-sinner and Adam-non-sinner results from the incompossibility of worlds in which Adam sins or does not sin" (LS 111, my emphasis). It is because of the incompossibility between worlds - one in which Adam sins, and another in which Adam does not - that there is, as a secondary effect, a contradiction between Adam-the-sinner and Adam-the-not-Sinner. Again, the interest here is in the way in which contradiction follows from, or is derivative of, a more primary difference (between worlds) which is not defined in terms of negation. Understood in this way, contradiction is not a 'wrong' way of looking at things: things really do contradict each other! Rather, it's that contradiction, like the negative, is something derivative and secondary, parasitic, as it were, on a more primary movement of 'vicediction'.

Post-Script: Logic

Considering that all of the above touches on themes that comes very close to terms dear to logic - issues like 'contradiction' and 'negation' - it's worth saying something quickly about what this might have to do with logic. One of the subterranean threads of Deleuze's thought is it's effort to come to grips with a logic that is not just the logic of - as we know it - 'formal logic'. Briefly put, formal logic is the logic of possibility: it belongs entirely in the realm of the hypothetical. You can't logic your way, as it were, to existence (this is the lesson of Kant's objection to the ontological argument for God). However, part of what Deleuze is trying to do is formulate something like a 'logic of existence': or, what he refers to in D&R as a "transcendental logic or dialectic of existence" as distinct from "logic pure and simple" (D&R 15). This would be a logic of the actual, one that does not work with empty generalities, but takes its starting point from the singular and the concrete.

As such, the distinction above made between 'logical' and 'alogical' compatibility must be seen in a different light: the logic of compossibility is only 'alogical' from the point of view of formal logic. However, from the point of view of a transcendental logic, the alogical compatibility of vicediction belongs to an Other-Logic, a logic of affirmation that does not find its limits in negation or contradiction, which, insofar as they belong to the order of 'logic pure and simple', will never have anything to say about life itself.