The Politics of Logic: Chapter 3 Notes and Comments

You can find the notes to chapter 1 here and chapter 2 here.

Deleuze, Plato, and the Paradox of Sense

In “How Do We Recognize Structuralism” Deleuze shows some common features that are definite of structuralism. The first is the recognition of a specific domain of signification. This is distinct from the domains of the real and the imaginary. This recognition advances beyond the methods of classical philosophy and the movements of Romanticism, Symbolism, and Surrealism (these tried to comprehend the real by seeing it in relation to imagination). Deleuze suggests that structuralism carves out a third regime in language. It is distinct from the real but also distinct from the imaginary. It is at the point of the sign and its action that we discern the “transcendent point where the real and the imaginary interpenetrate and unite.”

Two years later Deleuze published a book called The Logic of Sense which was concerned with the theorization of the structural basis of language. Deleuze calls this “sense”. Sense is the result of the structural deployment of signs in speech and the precondition for total structure of signs. It is a dimension of language presupposed by all of its function but cannot be understood simply in terms of any one of them. Sense is whatever underlies and determines the definition, inference, and reference that sign represents. But sense also underlies the instability of meaning, the phenomena of change, flux, and becoming. Because sense can be understood in both ways it cannot be said to be outside the possibility of sense. Deleuze argues, using Lewis Carrol’s word, that this bidrectionality  is key to understanding change and becoming. Sense is conceived as the domain of “pure becoming” which is the basis of all kinds of change, transformation, or manifestation.

For example, as Alice becomes taller than she was before, she is also smaller than she will be. Alice is characterized by contradictory predicates and this sort of opposition is at the root of becoming and is inherent to all becoming and change. So language as a totality of the possible signification determines sense as meaning or reference to being but the linguistic determination of sense makes it the condition for transcendence of the limits of language in the excessive dimension. Deleuze characterizes this excessive dimension of sense using paradoxes from Lewis Carroll. The first paradox he uses is “What the Tortoise Said to Achilles” where there is an infinite regress of justifications. The solution Deleuze suggests is to either accept the paradox as unsolvable or affirm that sense is a constitutive dimension of the unconditioned which is the foundation for the possibility of significative meaning. This means that the gap between rules and their application results from any attempt to ground language in the unity of a complete system of logical laws.

The second paradox Deleuze uses is the passage where Alice discusses songs and names with the White Knight. Here, the paradox is that if everything real has a name and if no name can name itself, then the provision of any real name for anything requires a name for that name and so on. There is an infinite chain of names. The problem lies in the regress of conditions for intelligible use of the names. If this regress is not blocked then the use of any term, knowledge, and reality lie on an infinite chain of conditions.

Deleuze uses this second paradox to develop yet a third paradox. In the infinite regress there is a necessity of alternation between signifiers and the signifieds. The signification of a signified results in the creation of a new signifier which is then a signified entity, and so on. Deleuze suggests that the only way to understand the possibility of language is to affirm this paradox of regress. But, if we are to accept this paradox, what are the consequences of it for language? The most important one is that language has a fundamental excess of signification over the signified that must always go beyond what is signified. This returns us to the “floating signifier” of previous chapters, which Levi-Strauss says is the foundation of all art, poetry, and aesthetics, to which Deleuze adds it is the promise of all revolutions.

He says that we can use these paradoxes to understand the general conditions of structure. The first condition is the existence of two series–the signfied and the signifier. The relationship between the two is necessary for making sense of the dynamism of structure. The second condition is that these series relate two each other and produce particular events called “singularities” within the structure. These points are the turning points of all points of inflection. They are the bottlenecks, the points of fusion, condensation, and boiling, the points of tears and joy, hope and anxiety, etc. These singularities are neutral because they represent sense prior to the linguistic order of reference and signification. They both escape and precede oppositions between the one and the many, the personal and the impersonal. This led Deleuze to think that structure and event are linked together. These events are both ideal (because they correspond to the structure of language as a whole) and real (because they account for the actual process of change and becoming).

The relationship at hand isn’t based in conditions of possibility but a dimension of the virtual that, rather than being opposed to, is a part of the real. The sense, only by being real and a part or dimension of the objects themselves, can articulate their meaning and determine their properties. This is not done by replicating their form. It is through the effects of the structure. This sense is a paradoxical, two-sided element. It is an excess and a lack. A floating signifier and a floating signified. It also has its own proper sense that is unique and exceptional according to Deleuze. Sense denotes exactly what it expresses and expresses what it denotes. It says its own sense. This sounds mighty similar to Russell’s paradox and Deleuze says that it implies a structural violation of the regression law and the disjunctive law (which says a property cannot refer to itself). Deleuze’s response is different than Russell’s. Deleuze argues that if we take the laws prohibiting self-membership and disjunction without denying that the paradoxical elements violate the laws of “proper” signification, they are grounded in the ordinary logical laws and axioms. 

Deleuze and Plato

Sense, for Deleuze, is a paradoxical virtual structure producing becoming as a result of singularities. This grounds Deleuze’s next claims which are rethinking the relationship of Ideas to things. Plato viewed this relationship as one of resemblance or representation. Deleuze sees this in another way. He argues that the virtual is the characteristic state of Ideas and the basis for the production of existence. Sense is the original domain of constitution. It is relational itself and independent of any opposition between the possible and real. This is ordered by the sense and what it conditions. The goal for him is to not exclude the changing and becoming of phenomena. In contrast to Plato, this is not the relationship of two static beings (the idea and the participant) but a question of relationality as such. This second dimension is not present in classical interpretations but is in the Platonic dialogues. Deleuze sees this not as a relationship between a static Idea and a static participant but of a split in the participant between what allows the participant to participate and “receive” the forms as it moves from one state to another. Thinking through this allows us to think about Ideas beyond or outside of representation. This introduces a simulacrum.

A simulacrum is an image without resemblance. It isn’t built on similarities but on difference. While it produces an effect of resemblance, it isn’t founded on resemblance. Classical philosophical interpretations of Plato built an order of representation that was founded on an essential relation to the model or foundation. Deleuze argues that the simulcra allows us to discern behind this order another, more chaotic one. One that is based on pure differences but precedes and constitutes all identity and representation. (Chaos theory or quantum theory?) So, Deleuze would argue that within the constitutive relationships that define the meaning of the sign and the possibility of its usage can be found the circulation of the simulcra which precedes and produces the order of representation and similitude. This can only be understood through the paradoxical structure of sense.