by Corry Shores
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]
Henry Somers-Hall
Hegel, Deleuze, and the Critique of Representation.
Dialectics of Negation and Difference
Part 2: Responses to Representation
Chapter 4: The Virtual and the Actual
Subdivision 4: Deleuze and the Structure of the Problem
Very Brief Summary:
For Deleuze, a problem is virtual, and it is structured as a topographical phase portrait telling us the infinite incompossible paths toward solving the problem. The task in philosophy is to know how to select the problems whose solutions will be of value to us, and this cannot be accomplished if we only examine sets of propositions that call for resolution.
Brief Summary:
For Deleuze, the problem is like the Idea and the topological phase space portraits. A problematic is like a field of possible virtual incompossible routes to being solved. [The problematic of sensing things at distance for evolving organisms is solved with eyes in some creatures and hearing in bats for example.] Seeing problems solely in terms of its propositional formulations as Aristotle and Russell see them misses their value and what makes the problematic what it is. Solving some set of propositions might provide a solution to a problem of no value for the circumstances of that analysis. So we select the problem on the basis of the context of our inquiry. Problems as virtual topographical fields of incompossible solutions are based on a logic of difference rather than on a logic of identity.
Summary
Previously we saw how Merleau-Ponty’s concept of depth in painting can help us characterize Deleuze’s depth as intensive difference, which is the virtual, intensive, intrinsically-related differential variations that actualize by explicating into various actual, extensive, extrinsically-related things. All objects are a mixture of virtual and actual.
Now we turn to the topic of problems. For Aristotle, any proposition can be turned into a question, so there are equally many propositions and problems. In fact, the problem’s nature derives from its propositional formulation. A problem in Russel’s axiomatic philosophy is the “set of propositions or axioms from which a conclusion is derived.” (119) These approaches focus on the propositions and the process of solving their problems. But Deleuze notes that when we only are able to evaluate a problem’s solubility, we cannot evaluate the value of the problem itself.
Indeed, for Deleuze, while one is concerned purely with the actual, the resources for a proper examination of the problematic itself are not present. Instead, it is only possible to evaluate the problem in terms of the possible solubility of the problem itself. The result of this is that the value of the problem itself cannot be adequately determined, leading to a philosophy built on "puerile examples taken out of context and erected into models" (DR, 158).
Russell’s and Aristotle’s systems are based on atomic parts with external relations made in a homogeneous sort of space (recall Bergson’s multiplicities with regard to Russell’s and Aristotle’s systems). But this means that they are evaluated outside their context. We cannot then judge the adequacy of the problematic itself.
If the proposition is made up of self-sufficient entities arbitrarily conjoined through their subsistence within a homogeneous space, then the possibility of judging the adequacy of the problematic itself is impossible. In the model taken up by Russell and Aristotle, determination is not made possible by the reciprocity of interacting elements, but rather by inherence in a logical space, meaning that the context of a proposition does not determine its content. This "infantile" focus on the ability to respond to the problematic, rather than on its formulation, leads to "the grotesque image of culture that we find in examinations and government referenda as well as in newspaper competitions" (DR, 158) . [119]
Something different in kind needs to be added to the propositional formulations. In Kant this is the noumena, and for Deleuze the differential. But if the problem is more than just the propositions, then error can come from something other than from just making incorrect propositional deductions. Somehow “thought itself can be led astray by its own nature.” (199) Recall the phase portraits for dynamic systems. The structure of the phase space differed from the structure of the space it models. This difference provides the foundation for [Deleuze’s? Kant’s] his philosophy. (120) We cannot draw every trajectory for how the system can develop. But we can integrate all of them to describe a topological space where attractor states are like low ground that water drains into. This topological phase space, which is defined using differential geometry, is different in kind from the [Euclidean] space of the system it models. The problem for Deleuze is like this topographical phase portrait, because, “ ‘the problem is at once both transcendent and immanent in relation to its solutions’ (DR, 163). It is transcendent in that it represents an entirely different geography to that of the actualized states of affairs, but at the same time it is immanent due to the fact that the operations of differentiation and integration are reversible.” (120) [I do not know what the reversibility of integration and differentiation have to do with the immanence of the problem and its solutions. Perhaps the fact that from the actualization of line line of development we might be able to derive the whole map, so that from one solution we might be able to obtain the entire problematic field.] So we do not define the problem in terms of its propositions [but rather in terms of its topology of paths of solubility]. Our eyes are evolutionary solutions to a light problem. [So there are different solutions to the problematic needs of the organism. The development of eyes was the one actualization of a course of solubility. It could not have come about through a chain of random mutations. Its course was guided toward an attractor state in accordance with the terrain of the problem of living as an organism without sight.]
Thus, the nature of the problematic is not defined in terms of the proposition. Indeed, "an organism is nothing if not the solution to a problem, as are each of its differenciated organs, such as the eye which solves a light 'problem' " (DR, 211). In this sense, the problematic is another name for the transcendental field. The example of the eye in particular illustrates the advantages of moving to a morphogenetic conception of the problematic, that is, an understanding of the problematic as the emergence of form. While understanding the transformations necessary for the eye to evolve through the standard metric account require a seemingly insurmountable number of modifications that would have to be carried out virtually simultaneously in order not to prejudice the organism's chances of survival through being suboptimally adapted to the environment, an analysis in terms of the morphogenetic processes of folding that generate the structure reveal that the eye can be generated through the iteration of a low number of basic topological transformations. Thus, viewing the development of the eye in terms of the virtual field of singularities which generate it reveals a large attractor capable of explaining the eye's seemingly improbable actual evolution. (120)
The problematic is like a dynamic system then. We are trying to understand the tendencies of this system. [When analysizing a problematic, we need to determine the appropriate system for this analysis. If we do not, then we find solutions of no value to us. So,] a problematic can be noble or base [depending on the value of its solutions for the purposes of our particular analysis] and “ ‘A solution always has the truth it deserves according to the problem to which it is a response’ (DR, 159) .” (120d) Consider if we analyze the behavior of organism on its cellular level. The problematic that this analysis provides [would be something like how do all its cells interact to maintain the organism, and as such this analysis] would be inappropriate for understanding how populations of this organism interact. The system’s context is important for characterizing its problems. So there must be some process of selecting the right problems. Deleuze calls this a dialectics that is the “combinatory calculus of problems as such” (DR 57) [121a]. Deleuze’s dialectics here do not extract problems from propositions but rather is concerned with “the generation of structure itself, rather than its transformation.” (121) The problem is related to virtual space, which is differential like Riemannian space. The rules of classical logic are more related to Euclidean space. The logic of problems however is a logic based on difference rather than identity. “The virtual Idea of a system is a differential field that contains every possible trajectory of the system. All of these trajectories maintain themselves as equally real, although it will only be one such trajectory that is actualized.” (122) Because the virtual itself has no exclusions, it is a pure affirmation. The coincidence of incompossible trajectories is based on a logic of difference and not on the ‘this is not that’ logic of actuality. (122)
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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