18 Aug 2015

Somers-Hall, (4.11), Deleuze’s Difference and Repetition, ‘4.11 The Origin of Negation (202–4/253–5, 206–8/257–60)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 4. Ideas and the Synthesis of Difference


4.11 The Origin of Negation (202–4/253–5, 206–8/257–60)



Brief summary: 

Negation for Deleuze is not fundamental to the genesis of things; however, it can result from that genesis. There is no negation inherent to the problematic situations on whose basis we form Ideas, nor is negation found within those Ideas formed from and in response to the problems, since both the problems and the Ideas affirmatively interrelate differential relations. There is also no negation when those Ideas are actualized into solutions, since these solutions affirm one of the actualizable instantiations implied in the Idea. But when we incorrectly understand problems in propositional terms, we might affix to one proposition ‘this is not the case’, since we affirm some opposite proposition to in fact instead be the case. However, the problems really do not lend themselves to propositional explanations, since they exist on a sub-representational level. So this notion of propositional denial is one origin of negation, but it leads to the false understanding of reality that negation is inherent to it. The other origin of negation is the process of differenciation, which generates actual distinct states of affairs that could have been many other actualizations. But this negation is secondary to their genesis and to their more fundamental structures, and thus still negation is not fundamental to reality, for Deleuze.


Deleuze has been telling us that “the existence of the negative is an illusion” (161). Now on the basis of what we have said regarding Ideas, we can give an account of the origin of negation. We will find that it rests “on a confusion between seeing transcendental problems and empirical solutions” (161). [It seems we first put aside the notion of the negative and instead concern ourselves with the notion of non-being. In Deleuze’s philosophy, non-being would not be the negative, but instead it seems to be the non-extensive being of the infinitesimal magnitudes that make up differential reciprocal relations that have an intensive magnitude.] “As Deleuze writes, ‘There is a non-being which is by no means the being of the negative, but rather the being of the problematic. The symbol for this (non)-being or ?-being is 0/0’ (DR 202/253). The problematic is therefore non-being | in the sense that it is not extensive being, in the same way that the differential was not actual (it did not have a magnitude) without on that basis not existing (it was, in Wronski’s terms, an intensive quantity)” (SH 161-162). [We noted before that problems and the Ideas related to them are complete since they are fully real and they express all actualizable solutions.] “As we have seen, Deleuze takes problems to be interpenetrative multiplicities which determine all possible actual states of the object. In this sense, the problem does not contain any negation” (162). [Recall also how when learning we move first from actual states of affairs to the Idea. Here it is a matter of fields of differential relations. So this is a process of differentiation. Then, we choose one determinate solution rather than another, and thus it is a process of differenciation. Now, when we form the Idea through differentiation, the negative is not involved, since we are adding together the Idea fragments affirmatively. And, when we devise a solution, we are affirming one actualizable outcome implied in the Idea. Thus negation is not a part of differentiation or differenciation.] “Learning and solving problems involve a move from the actual state of affairs to the Idea and back again to a different possible solution. They thus involve differentiation to determine the Idea followed by differenciation to reach an alternative solution. Now, as Deleuze notes, ‘the negative appears neither in the process of differentiation nor in the process of differenciation’ (DR 207/258). We can see that differentiation does not lead us to posit the negative, as differentiation involves contracting together actual states of affairs to form an affirmation. Similarly, differenciation is the process whereby we extract a state of affairs from the Idea, and as such is also an affirmation of the Idea” (SH 162). But if negation is not a part of either of these processes, then how does it come about in the first place? Deleuze says it results when we regard the problem as being structured like a proposition. To clarify how this is so, SH turns to Bergson’s example of looking for a poetry book on a book shelf, picking one up at random, and seeing that it is prose. We then say, “this is not verse,” and thus it seems to be the experience of negation. However, we do not actually experience an absence of verse. We experience a presence of prose. Only because our expectations were unfulfilled do we think it is negative. This is similar for Deleuze’s understanding of problems. If we understand problems propositionally, that means we might be able to say “this is not the case” for some given proposition, since some other proposition is the case (162-163). In this way, negation “becomes an ontological feature of the world”. But this ultimately is incorrect, since the problem is not propositional and thus does not admit of propositional negation. In Deleuze’s analysis, at the heart of this error is the assumption that negation is the way that something is determined, or put another way, that opposition and limitation are interchangeable (SH 163, citing DR 203/253). Instead for Deleuze, determination does not come about through reciprocal negation and limitation (this is not that and vice versa) but rather through the reciprocal determination of differentials [this is such on account of its (individually undetermined) differential relations, perhaps, but I am not sure how to rephrase this notion in a parallel way.] [And since actualization does differenciate actual distinct entities or states of affairs,] “Negation thus only appears when we understand all determination as determination through opposition: ‘Forms of the negative do indeed appear in actual terms and real relations, but only in so far as these are cut off from the virtuality which they actualise, and from the movement of their actualisation’ (DR 207/258)” (SH 163).




Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Bergson, Henri (1998), Creative Evolution, trans. Arthur Mitchell, Mineola, NY: Dover Publications.







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