Somers-Hall, (3.9), Deleuze’s Difference and Repetition, ‘3.9 The Postulate of Modality or Solutions (156–64/195–204)’, summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[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 3. The Image of Thought

3.9 The Postulate of Modality or Solutions (156–64/195–204)

Brief summary:
The seventh postulate of the problematic image of thought is of solutions or of modality. Here problems are understood in terms of propositions and the possibility of the problems being solved. For example, a referendum is based on a possible policy change, which can be stated as a proposition or as a question like, “Yes or no, should the possible change be made?” Deleuze’s criticism is that understanding problems this way only helps us grasp what conditions them and not what generates them, and therefore it does not provide an adequate model for accounting for thinking itself.

 

 

 

Summary

 

Since, [as we saw in the previous section] sense cannot be given in terms of a proposition, Deleuze considers the possibility that it can be given in terms of a question. SH writes: “It is clearly the case that we can see a proposition as in some way expressing a question, and it is also the case that a question differs from a statement, in that it is not itself true or false” (SH 125) [Later we will learn more about how propositions express questions.] So the question is different in kind from the statement. But “The extent to which we are able to understand the ground of the proposition as different in kind from it will depend on how we understand questioning” (125). One way of understanding questioning seems merely to take a proposition and formulate it as a question or a “problem” by considering it as a possibility. So a government referendum proposes a possible policy change, and formulates it as a question like, “Yes or No, should this possible change be made?” Deleuze refers to how Aristotle notes that a problem can be made from a proposition by modifying its syntax. Also, a problem can obtain its value depending on whether it is solvable or not. So, “Here, what makes the problem false is purely the fact that it does not have any (propositional) solutions” (126). The seventh postulate of the image of thought, then, is “that ‘truth and falsehood only begin with solutions or only qualify responses’ (DR 158/197)” (126). So recall that a proposition is false if it fails to designate an actual state of affairs. Yet, problems or questions can go wrong if “They can circumscribe too narrow or too broad a domain to capture properly the point at issue.  In these cases, they are false through overdetermination or indeterminacy, regardless of whether they generate true propositions” (126). The difficulty here, according to Deleuze, is that problems are defined in terms of possibility. In the case of the referendum, the problem is understood purely in terms of its possible solutions [the solution being either to enact or to not enact the policy]. “A problem in this sense can be seen as simply a disjunction of propositions, one of which is true. As such, it fails to escape from the image of thought” (126).

[Recall Kant’ notion of transcendental illusion:]

As we have seen, Kant at first glance appears to provide something of an exception to this conception of the problem by introducing the notion of transcendental illusion. Kant’s claim is that reason’s task of systematising knowledge leads it to introduce what are known as transcendental Ideas. These are concepts of unconditioned totality that arise naturally when reason goes beyond the bounds of experience, and provide a focal point (focus imaginarius) for reason. As such, reason generates false problems not simply in the sense of problems with no true solutions, but as necessary moments in its operation. In introducing the Idea in the Critique of Pure Reason, Kant explicitly claims to take up the Platonic notion of the Idea as ‘something which not only can never be borrowed from the senses but far surpass the concepts of the understanding . . . inasmuch as in experience nothing is ever met with that is coincident with it’ (Kant 1929: A313/B370). As modes of thinking of totality, the Ideas emerge when reason considers all possible relations between our representations.
(126)

Since for Kant there are three forms of relations encompassing all things, he proposes three transcendental Ideas: 1) the relation to the subject (which contains the absolute, unconditioned unity of the thinking subject), 2) the relation to objects (which contains the absolute unity of the series of conditions of appearance), 3) the relation to all things (which contains the absolute unity of the condition of all objects of thought in general). (SH 126-127, citing Kant 1929: A334/B391) [I am not sure how all this works, so I cannot say more to elaborate]. These concepts go beyond experience and for that reason Kant considers them problematic. But they are what allow us systematize knowledge by making use of concepts not found in nature. “Ultimately, therefore, for Deleuze they sustain the image of thought precisely at the moment when reason goes beyond experience” (SH 127) [Perhaps this is because the image of thought privileges reason, where Deleuze wants a model of thinking that takes into account raw experience that cannot be processed by reason]. Also, these transcendental Ideas merely “play a regulative role rather than a truly genetic role” (127). [Perhaps the idea here is that the transcendental ideas do not produce new knowledge but only help organize knowledge we already possess, but I am not sure.] For Deleuze, recall, sense does more than condition the proposition, since it in fact generates it; “what is needed is a model that recognises the intrinsic relationship between representations and their non-representational ground. Rather than being interested in what regulates the image of thought, Deleuze is interested in those structures that underlie it.  In this way, sense is what makes possible the proposition.” (127). The Idea for Deleuze is likewise related more to the structures that underlie thought. “Similarly, the Idea is what makes possible the structure of recognition that we encounter in the image of thought. The two processes operate concurrently, just as the passive syntheses operated underneath active syntheses” (127).

 

 

Citations from:

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

Or if otherwise noted:

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

 

Kant, Immanuel (1929), Critique of Pure Reason, trans. Norman Kemp Smith, London: St. Martin’s Press.

 

 

Pt2.Ch4.Sb4 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Deleuze and the Structure of the Problem.’ summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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.