From the entry on "Gilles Deleuze" in the Stanford Encyclopedia of Philosophy:
"In his magnum opus Difference and Repetition, he tries to develop a metaphysics adequate to contemporary mathematics and science—a metaphysics in which the concept of multiplicity replaces that of substance, event replaces essence and virtuality replaces possibility."
"In Bergsonism (1966), Deleuze develops the ideas of virtuality and multiplicity that will serve as the backbone of his later work. From Maimon's reading of Kant, we know that Deleuze needs to substitute the notion of the condition of the genesis of the real for the notion of conditions of possibility of representational knowledge. The positive name for that genetic condition is the virtual, which Deleuze adopts from the following Bergsonian argument. The notion of the possible, Bergson holds in Creative Evolution, is derived from a false problem that confuses the “more” with the “less” and ignores differences in kind; there is not less but more in the idea of the possible than in the real, just as there is more in the idea of nonbeing than in that of being, or more in the idea of disorder than in that of order. When we think of the possible as somehow “pre-existing” the real, we think of the real, then we add to it the negation of its existence, and then we project the “image” of the possible into the past. We then reverse the procedure and think of the real as something more than possible, that is, as the possible with existence added to it. We then say that the possible has been “realized” in the real. By contrast, Deleuze will reject the notion of the possible in favor of that of the virtual. Rather than awaiting realization, the virtual is fully real; what happens in genesis is that the virtual is actualized.
The fundamental characteristic of the virtual, that which means it must be actualized rather than realized, is its differential makeup. Deleuze always held the critical axiom that the ground cannot resemble that which it grounds; he constantly critiques the “tracing” operation by which identities in real experience are said to be conditioned by identities in the transcendental. For instance, Deleuze criticizes Kant for copying the transcendental field in the image of the empirical field. That is, empirical experience is personal, identitarian and centripetal; there is a central focus, the subject, in which all our experiences are tagged as belonging to us. Kant says this empirical identity is only possible if we can posit the Transcendental Unity of Apperception, that is, the possibility of adding “I think” to all our judgments. Instead of this smuggled-in or “traced” identity, Deleuze will want to have the transcendental field be differential. Deleuze still wants to work back from experience, but since the condition cannot resemble the conditioned, and since the empirical is personal and individuated, the transcendental must be impersonal and pre-individual. The virtual is the condition for real experience, but it has no identity; identities of the subject and the object are products of processes that resolve, integrate, or actualize (the three terms are synonymous for Deleuze) a differential field. The Deleuzean virtual is thus not the condition of possibility of any rational experience, but the condition of genesis of real experience.
As we have seen, the virtual, as genetic ground of the actual, cannot resemble that which it grounds; thus, if we are confronted with actual identities in experience, then the virtual ground of those identities must be purely differential. Deleuze adopts “multiplicity” from Bergson as the name for such a purely differential field. In this usage, Deleuze later clarifies, “multiplicity” designates the multiple as a substantive, rather than as a predicate. The multiple as predicate generates a set of philosophical problems under the rubric of “the one and the many” (a thing is one or multiple, one and multiple, and so on). With multiplicity, or the multiple as substantive, the question of the relation between the predicates one/multiple is replaced by the question of distinguishing types of multiplicities (as with Bergson's distinction of qualitative and quantitative multiplicities in Time and Free Will). A typological difference between substantive multiplicities, in short, is substituted for the dialectical opposition of the one and the multiple."
"Deleuze pushes Leibniz's thought to a point where Leibniz could never have taken it, given his theological presuppositions. This is the point where one begins to consider the virtual domain on its own account, freed from its actualization in a world and its individuals. On this score, Deleuze often likes to cite Jorge Luis Borges's famous story, “The Garden of the Forking Paths,” in which such a virtual world is described in the labyrinthine book of a Chinese philosopher named Ts'ui Pên: “In all fiction, when a man is faced with alternatives, he chooses one at the expense of others. In the almost unfathomable Ts'ui Pên, he chooses—simultaneously—all of them… In Ts'ui Pên's work, all the possible solutions occur, each one being the point of departure for other bifurcations.” Leibniz had in fact given a similar presentation of the world at the conclusion of the Theodicy. In Deleuze's transformation of the Leibnizian / Borgesian image, the three Kantian transcendent Ideas of God, World, and Self all take on a completely different demeanor. First, God is no longer a Being who compares and chooses the richest compossible world; he has now become a pure Process that affirms incompossibilities and passes through them. (As the notion of “process” here attests, Deleuze's relation to Whitehead is one of the most important contemporary issues for students of his thought; although the points of comparison are many, Deleuze himself rarely discussed Whitehead, save for several important pages in The Fold.) Second, the world is no longer a continuous world defined by its pre-established harmony; instead, divergences, bifurcations, and incompossibles must now be seen to belong to one and the same universe, a chaotic universe in which divergent series trace endlessly bifurcating paths, and give rise to violent discords and dissonances that are never resolved into a harmonic tonality: a “chaosmos,” as Deleuze puts it (borrowing a word from Joyce) and no longer a world. In contrast, Leibniz could only save the “harmony” of this world by relegating discordances and disharmonies to other possible worlds—this was his theological sleight of hand. Third, selves or individuals, rather than being closed upon the compossible and convergent world they express from within, are now torn open, and kept open through the divergent series and incompossible ensembles that continually pull them outside themselves. The “monadic” subject, as Deleuze puts it, becomes the “nomadic” subject. In other words, if Deleuze is Leibnizian, it is only by eliminating the idea of a God who chooses the best of all possible worlds, with its pre-established harmony and well-established selves; in Deleuze, incompossibilities and dissonances belong to one and the same world, the only world, our world. But they belong to our world as its virtual register; developing the thought of the virtual is one of the great challenges of Deleuze's masterpiece, Difference and Repetition, to which we now turn."
"In isolating the conditions of genesis, Deleuze sets up a tripartite ontological scheme, positing three interdependent registers: the virtual, intensive, and actual. Overlooking many important nuances, we can say that Deleuze's basic notion is that in all realms of being intensive morphogenetic processes follow differential virtual multiplicities to produce localized and individuated actual substances with extensive properties. Simply put, the actualization of the virtual proceeds by way of intensive processes. For orientation purposes, it's useful to consider Gilbert Simondon's theory of individuation as a very simple model for what Deleuze calls “actualization.” For Simondon, crystallization is a paradigm of individuation: a supersaturated solution is metastable; from that pre-individuated field, replete with gradients of density that are only implicit “forms” or “potential functions,” individual crystals precipitate out. The crucial difference is that crystals form in homogenous solutions, while the Deleuzean virtual is composed of “Ideas” or “multiplicities” involving differential relations among heterogeneous components, linked rates of change of, for instance, cell division and gene expression in embryogenesis as mediated by “positional information.”"
"To see how Ideas are transcendental and immanent, we have to appreciate that an Idea is a concrete universal, unlike Kantian concepts of the understanding. In an early article on Bergson (“The Conception of Difference in Bergson” [1956]), Deleuze gave a particularly helpful example of this distinction. In La Pensée et le Mouvant, Bergson had shown that there are two ways of determining what the spectrum of “colors” have in common. (1) You can extract from particular colors an abstract and general idea of color (“by removing from the red that which makes it red, from the blue what makes it blue, from the green what makes it green”). Or, (2) you can make all these colors “pass through a convergent lens, bringing them to a single point,” in which case a “pure white light” is obtained that “makes the differences between the shades stand out.” The former case defines a single generic “concept” with a plurality of objects; the relation between concept and object is one of subsumption; and the state of difference remains exterior to the thing. The second case, on the contrary, defines a differential Idea in the Deleuzean sense: the different colors are no longer objects under a concept, but constitute an order of mixture in coexistence and succession within the Idea; the relation between the Idea and a given color is not one of subsumption, but one of actualization and differenciation; and the state of difference between the concept and the object is internalized in the Idea itself, so that the concept itself has become the object. White light is still a universal, but it is a concrete universal, and not a genus or generality. The Idea of color is thus like white light, which “perplexes” within itself the genetic elements and relations of all the colors, but which is actualized in the diverse colors and their respective spaces. (Like the word “problem,” Deleuze uses the word “perplexion” to signify, not a coefficient of doubt, hesitation, or astonishment, but the multiple and virtual state of Ideas. Indeed, Deleuze adopts a number of neoplatonic notions to indicate the structure of Ideas, all of which are derived from the root word ‘pli’ [fold]: perplication, complication, implication, explication, and replication.) Similarly, the Idea of sound could be conceived of as a white noise, just as there is also a white society or a white language, which contains in its virtuality all the phonemes and relations destined to be actualized in the diverse languages and in the remarkable parts of a same language."
"A Thousand Plateaus maintains the tripartite ontological scheme of all of Deleuze's work, but, as the title indicates, with geological terms of reference. Deleuze and Guattari call the virtual “the Earth,” the intensive is called “consistency,” and the actual is called “the system of the strata.” As the latter term indicates, one of the foci of their investigations is the tendency of some systems to head toward congealment or stratification. More precisely put, any concrete system is composed of intensive processes tending toward the (virtual) plane of consistency and/or toward (actual) stratification. We can say that all that exists is the intensive, tending towards the limits of virtuality and actuality; these last two ontological registers do not “exist,” but they do “insist,” to use one of Deleuze's terms. Nothing ever instantiates the sheer frozen stasis of the actual nor the sheer differential dispersion of the virtual; rather, natural or worldly processes are always and only actualizations, that is, they are processes of actualization structured by virtual multiplicities and heading toward an actual state they never quite attain. More precisely, systems also contain tendencies moving in the other direction, toward virtuality; systems are more or less stable sets of processes moving in different directions, toward actuality and toward virtuality. In still other words, Deleuze and Guattari are process philosophers; neither the structures of such processes nor their completed products merit the same ontological status as processes themselves. With this perspective, Deleuze and Guattari offer a detailed and complex “open system” which is extraordinarily rich and complex. A useful way into it is to follow the concepts of coding, stratification and territorialization. They are related in the following manner. Coding is the process of ordering matter as it is drawn into a body; by contrast, stratification is the process of creating hierarchal bodies, while territorialization is the ordering of those bodies in “assemblages,” that is to say, an emergent unity joining together heterogeneous bodies in a “consistency.”"
"We will deal with Deleuze and the arts in some detail below. In discussing What is Philosophy?, let us concentrate on the treatment of the relation of philosophy and science. We should remember at the outset that the nomad or minor science evoked in A Thousand Plateaus is not the Royal or major science that makes up the entirety of what Deleuze and Guattari call ‘science’ in What is Philosophy?. The motives for this conflation are unclear; in the eyes of some, this change considerably weakens the value of the latter work. Be that as it may, in What is Philosophy? Deleuze and Guattari vigorously deny that philosophy is needed to help science think about its own presuppositions (“no one needs philosophy to reflect on anything” [WP 6]). Instead, they emphasize the complementary nature of the two. First, they point out a number of similarities between philosophy and science: both are approaches to “chaos” that attempt to bring order to it, both are creative modes of thought, and both are complementary to each other, as well as to a third mode of creative thought, art. Beyond these similarities, Deleuze and Guattari distinguish between philosophy as the creation of concepts on a plane of immanence and science as the creation of functions on a plane of reference. Both relate to the virtual, the differential field of potential transformations of material systems, but in different ways. Philosophy gives consistency to the virtual, mapping the forces composing a system as pure potentials, what the system is capable of. Meanwhile, science gives it reference, determining the conditions by which systems behave the way they actually do. Philosophy is the “counter-effectuation of the event,” abstracting an event or change of pattern from bodies and states of affairs and thereby laying out the transformative potentials inherent in things, the roads not taken that coexist as compossibles or as inclusive disjunctions (differentiation, in the terms of Difference and Repetition), while science tracks the actualization of the virtual, explaining why this one road was chosen in a divergent series or exclusive disjunction (differenciation, according to Difference and Repetition). Functions predict the behavior of constituted systems, laying out their patterns and predicting change based on causal chains, while concepts “speak the event” (WP 21), mapping out the multiplicity structuring the possible patterns of behavior of a system—and the points at which the system can change its habits and develop new ones. For Deleuze and Guattari in What is Philosophy?, then, science deals with properties of constituted things, while philosophy deals with the constitution of events. Roughly speaking, philosophy explores the plane of immanence composed of constellations of constitutive forces that can be abstracted from bodies and states of affairs. It thus maps the range of connections a thing is capable of, its “becomings” or “affects.” Science, on the other hand, explores the concretization of these forces into bodies and states of affairs, tracking the behavior of things in relation to already constituted things in a certain delimited region of space and time (the “plane of reference”). How do concepts relate to functions? Just as there is a “concept of concept” there are also “concepts of functions,” but these are purely philosophical creations “without the least scientific value” (WP 117). Thus concrete concepts like that of “deterritorialization” are philosophical concepts, not scientific functions, even though they might resonate with, or echo, scientific functions. Nor are they metaphors, as Deleuze and Guattari repeatedly insist:
"Of course, we realize the dangers of citing scientific propositions outside their own sphere. It is the danger of arbitrary metaphor or of forced application. But perhaps these dangers are averted if we restrict ourselves to taking from scientific operators a particular conceptualizable character which itself refers to non?scientific areas, and converges with science without applying it or making it a metaphor (Deleuze 1989: 129).
Deleuze and Guattari's refusal to recognize that their work contains metaphors is due to their struggle against the “imperialism” of the signifying regime, a major theme in both Anti-Oedipus and A Thousand Plateaus: not every relation between different intellectual fields can be grasped by the most common notions of “metaphor,” reliant as they are on the notion of a transfer of sense from primary to secondary signification.""
"5. Deleuze and the Arts
Kant had dissociated aesthetics into two halves: the theory of sensibility as the form of possible experience (the “Transcendental Aesthetic” of the Critique of Pure Reason), and the theory of art as a reflection on real experience (the “Critique of Aesthetic Judgment” in the Critique of Judgment). In Deleuze's work, these two halves of aesthetics are reunited: if the most general aim of art is to “produce a sensation,” then the genetic principles of sensation are at the same time the principles of composition for works of art; conversely, it is works of art that are best capable of revealing these conditions of sensibility. Deleuze therefore writes on the arts not as a critic but as a philosopher, and his books and essays on the various arts—including the cinema (Cinema I and II), literature (Essays Critical and Clinical), and painting (Francis Bacon: The Logic of Sensation)—must be read as philosophical explorations of this transcendental domain of sensibility. The cinema, for instance, produces images that move, and that move in time, and it is these two aspects of film that Deleuze set out to analyze in The Movement-Image and The Time-Image: “What exactly does the cinema show us about space and time that the other arts don't show?” Deleuze thus describes his two-volume Cinema as “a book of logic, a logic of the cinema” that sets out “to isolate certain cinematographic concepts,” concepts which are specific to the cinema, but which can only be formed philosophically. Francis Bacon: The Logic of Sensation likewise creates a series of philosophical concepts, each of which relates to a particular aspect of Bacon's paintings, but which also find a place in “a general logic of sensation.” In general, Deleuze will locate the conditions of sensibility in an intensive conception of space and a virtual conception of time, which are necessarily actualized in a plurality of spaces and a complex rhythm of times (for instance, in the non-extended spaces and non-linear times of modern mathematics and physics)."
http://plato.stanford.edu/entries/deleuze/
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