As noted a few days ago, Dan Smith and I are revising our Stanford Encyclopedia of Philosophy entry on Deleuze. We are completely rewriting the Difference and Repetition section. Here is the draft. Some of the technical terms we use (e.g., "virtual") are discussed in the preceding section of the piece.
This kind of reference article is very tricky to write. You have to be technical enough for the specialists and yet accessible for interested non-specialists. So we'd be very grateful for suggestions for additions, deletions, clarifications, expansions, and so on, either here in comments or by email.
3.1 Difference and Repetition
Deleuze's historical monographs were, in a sense, preliminary sketches for the great canvas of Difference and Repetition (1968), which marshaled these resources from the history of philosophy in an ambitious project to construct a "philosophy of difference." Following Maimon's critique, which we mentioned above, Difference and Repetition produces a two-fold shift from the Kantian project of providing the universal and necessary conditions for possible experience. First, Deleuze wants to provide an account of the genesis of “real experience” – the experience of this concretely existing individual here and now – and second, to respect the demands of "philosophy of difference," the genetic principle must be differential so that the conditions of the genesis of an individual cannot themselves be individuated.
We are now ready to discuss the book itself, beginning with the table of contents.
Introduction: Repetition and Difference
1: Difference in Itself
2: Repetition for Itself
3: The Image of Thought
4: Ideal Synthesis of Difference
5: Asymmetrical Synthesis of Sensibility
Conclusion: Difference and Repetition
Following Murphy 1992, we see that the first part of the book (the Introduction and Chapters 1 and 2) is Deleuze's treatment of the history of philosophy while the second part of the book (Chapters 4, 5, and Conclusion) is Deleuze "doing philosophy" in his "own name." Chapter 3, on the "image of thought," then plays a pivotal role, taking us from Deleuze's treatment of the history of philosophy to Deleuze's philosophy itself. This transitional role of Chapter 3 is confirmed elsewhere when Deleuze says that the study of the image of thought is the "prolegomena to philosophy" (Negotiations, 149).
In Chapters 1 and 2, to find a differential genetic principle, Deleuze works through the history of philosophy to isolate the concepts of "difference in itself" and "repetition for itself" that previous philosophies had prevented. "Difference in itself" is difference that is freed from identities that are metaphysically primary. Normally, difference is conceived of as an empirical relation between two terms each of which has a prior identity of its own (“x is different from y”). In Deleuze, this primacy is inverted: identity persists, but it is now a secondary principle produced by a prior relation between differentials (dx rather than not-x). Difference is no longer an empirical relation but becomes a transcendental principle that constitutes the sufficient reason of empirical diversity as such (for example, it is the difference of electric potential between cloud and ground that constitutes the sufficient reason of the phenomenon of lightning).
In Chapter 2, "repetition for itself" is repetition that is freed from being a repetition of an original self-identical thing so that it can be repetition of difference; following the formula of Nietzsche's eternal return, repetition is the return of the differential genetic condition of real experience each time there is an individuation of a concrete entity. Ultimately, then, Difference and Repetition will show that the individuation of entities is produced by the actualization, integration, or resolution (the terms are synonymous) of a differentiated virtual field of "Ideas" or "multiplicities" that are themselves changed, via "counter-effectuation," in each individuating event.
Chapter 3 lays out 8 postulates of the "dogmatic image of thought." Between the first four and last four postulates we find a "theory of the faculties," which is thus at the crossroads of both the book and the chapter.
Let us take up the first four postulates. The first postulate concerns our supposed natural disposition to think; the denial of this is what necessitates our being forced to think. The second and third postulates concern subjective and objective unity: the notion of "common sense" such that our faculties of sensation, memory, imagination and thought work in harmony and the notion of "recognition" such that it is the same object that is sensed, remembered, imagined and thought. The fourth postulate concerns "representation," in which difference is submitted to a fourfold structure that renders difference subordinate to identity: 1) identity in the concept; 2) opposition in the predicate; 3) analogy in judgment; and 4) resemblance in perception. A good way to approach the structure of representation is via Aristotle and Porphyry. Specific differences are the "opposed predicates" that function on a horizon of identity in the concept under division; thus "animal" is the genus that is divided into "rational" and "irrational" as specific differences to isolate the species "human." Then, we find that the differences between individuals of the same species is infra-conceptual and can only be made via perception of resemblances: Theaetetus looks like Socrates but not so much that they cannot be distinguished. Finally, the relation of substance to the other categories is analogical or "pros hen equivocation," such that being is said in many ways, but "substance" is the primary way in which it is said.
After the first four postulates, we find the theory of the faculties, which will be Deleuze's account of what it means to be "forced" to think in differential rather than identitarian terms. To free a notion of "difference in itself" such that difference need not be thought on the basis of a prior horizon of identity, Deleuze looks for an "encounter," a sensation that cannot be thought, that cannot find the empirical category under which an object can be recognized, and thus forces the “transcendent exercise” of the faculty of sensibility, when something can only be sensed. (Deleuze is here pushing the Kantian notion of reflective judgment from the Third Critique to its limits.)
Here we see the dynamic genesis from intensity in sensation to the thinking of virtual Ideas. Each step here has a distinct Kantian echo. The faculties are linked in order; here Deleuze as well as Kant looks to the privilege of sensibility as the origin of knowledge—the “truth of empiricism.” With sensibility, pure difference in intensity is grasped immediately in the encounter as the sentiendum, that which can only be sensed. In the differential theory of the faculties, sensibility, imagination, memory, and thought all “communicate a violence” from one to the other – here Deleuze works with the Kantian notion of the sublime as discordant accord of the faculties. The “free form of difference” in intensity moves each faculty and communicates its violence to the next, though in this case there is no supernatural vocation that will redeem the conflict of imagination and reason, as there is in the resolution to the discussion of the sublime in the Critique of Judgment. Rather than a reconciliation of the faculties, with thought, a "fractured self" – here Deleuze takes up Kant's notion of the split between the empirical ego and the Transcendental subject – is constrained to think “difference in itself” in Ideas.
We won't discuss the last four postulates in detail, as they concern the theory of Ideas, the topic of Chapter 4, which we will shortly discuss. For now, let us note that two of Deleuze's technical terms, intensity and virtuality, occupy two different places on this line of dynamic genesis. Intensity is the characteristic of the encounter, and sets off the process of thinking, while virtuality is the characteristic of the Idea, that which is thought at the end of the genetic line.
With the notions of intensive and extensive we come upon a crucial distinction for Deleuze that is explored in Chapters 4 and 5 of Difference and Repetition. Extensive differences, such as length, area or volume, are intrinsically divisible. A volume of matter divided into two equal halves produces two volumes, each having half the extent of the original one. Intensive differences, by contrast, refer to properties such as temperature or pressure that cannot be so divided. If a volume of water whose temperature is 90º is divided in half, the result is two volumes at the original temperature, not two volumes at 45º. However, the important property of intensity is not that it is indivisible, but that it is a property that cannot be divided without involving a change in kind. The temperature of a volume of water, for instance, can be “divided” by heating the container from below, causing a temperature difference between the top and the bottom. In so doing, however, we change the system qualitatively; moreover, if the temperature differences reach a certain threshold (if they attain a certain “intensity” in Deleuze's terms), the system will undergo a “phase transition,” losing symmetry and changing its dynamics, entering into a periodic pattern of motion—convection—which displays extensive properties of size: X centimeters of length and breadth. Drawing on these kinds of analyses, Deleuze will assign a transcendental status to the intensive: intensity, he argues, constitutes the genetic condition of extensive space. Intensive processes are themselves in turn structured by Ideas or multiplicities.
An Idea or multiplicity is really a process of progressive determination of differential elements, differential relations, and singularities. Let us take these step-by-step. "Elements" must have no independent existence from the system in which they inhere; phonemes as the elements of the virtual linguistic Idea are an example Deleuze uses in Difference and Repetition. When phonemes are actualized they enter into differential relations that determine the patterns of individual languages; thus the English phoneme /p/ is reciprocally determined by its differences from /t/, /b/, /d/, and so on. Finally, these differential relations of an individual language determine singularities or remarkable points at which the pattern of that language can shift: the Great Vowel Shift of Middle English being an example, or more prosaically, dialect pronunciation shifts.
For another example – and here, in the applicability of his schema to widely divergent registers, is one of the aspects of Deleuze as metaphysician – let us try to construct the Idea of hurricanes. The differential elements would be material "flows" driven by intensive differences in temperature and pressure but undetermined in form (neither smooth nor turbulent, neither big nor small) and function (neither forming nor destroying of weather events). These flows qua differential elements enter into relations of reciprocal determination linking changes in any one element to changes in the others; thus temperature and pressure differences will link changes in air and water currents to each other: updrafts are related to downdrafts even if the exact relations (the tightness of the links, the velocity of the flows) are not yet determined. Finally, at singular points in these relations singularities are determined that mark qualitative shifts in the system, such as the formation of thunderstorm cells, the eye wall, and so on. But this is still the virtual Idea of hurricanes; real existent hurricanes will have measurable values of these variables so that we can move from the philosophical realm of sufficient reason to that of scientific causation. A hurricane is explained by its Idea, but it is caused by real wind currents driven by real temperature supplied by the sun to tropical waters.
To see how Ideas are transcendental and immanent, we have to appreciate that an Idea is a concrete universal. In an early article on Bergson (“The Conception of Difference in Bergson” ), Deleuze gave a particularly helpful example of this notion. 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.
We can now move to discuss Chapter 5, on the individuation of concretely existing real entities as the actualization of a virtual Idea. In isolating the conditions of genesis, Deleuze sets up a tripartite ontological scheme, positing three interdependent registers: the virtual, intensive, and actual. 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. Beneath the actual (any one state of a system), we find "impersonal individuations" or intensive morphogenetic processes that produce system states and beneath these we find "pre-individual singularities" (that is, the key elements in virtual fields, marking system thresholds that structure the intensive morphogenetic processes). We thus have to distinguish the intense "impersonal" field of individuation and its processes from the virtual "pre-individual" field of differential relations and singularities that make up an Idea or multiplicity.
Tying together the themes of difference, multiplicity, virtuality and intensity, at the heart of Difference and Repetition we find a theory of Ideas (dialectics) based neither on an essential model of identity (Plato), nor a regulative model of unity (Kant), nor a dialectical model of contradiction (Hegel), but rather on a problematic and genetic model of difference. Ideas define the being of a thing, but one cannot attain an Idea through the Socratic question “What is … ?” (which posits Ideas as transcendent and eternal), but rather through “minor” questions such as “Which one?” “Where?” “When?” “How?” “How many?” “In which case?” “From which viewpoint?”— all of which allow one to define the differential Ideas immanent in the intensive processes they structure.
From these examples we can see that Ideas structure the intensive processes that give rise to the behavior patterns of systems, and their singularities mark the thresholds at which systems change behavior patterns. In a word, the virtual Idea is the transformation matrix for material systems or bodies. Bodies are determined "solutions" to the "problem" that lays out the manifold options for incarnating bodies of that nature. Ideas then respond to the question "who?" (who is it that incarnates the Idea in this case?) rather than the essentialist "what is?" (what are the properties of the substance that provide the necessary and sufficient conditions for membership in the class of which the object is a member?)
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, whose rates of change are connected with each other. For an example of such heterogeneity, let us return to hurricane formation, the Idea of which we sketched above. Here it should be intuitively clear that there is no central command, but a self-organization of multiple processes of air and water movement propelled by temperature and pressure differences. All hurricanes form when intensive processes of wind and ocean currents reach singular points. These singular points, however, are not unique to any one hurricane, but are virtual for each actual hurricane, just as the boiling point of water is virtual for each actual pot of tea on the stove. In other words, all hurricanes share the same virtual structure even as they are individuations or actualizations of that structure.
In this treatment, we have concentrated on only some of the metaphysics in Difference and Repetition; much more could be said about the role that Nietzsche's thought of the eternal return plays therein, in addition to Deleuze's remarks on a dizzying array of figures from Plato and Scotus to Freud and Artaud. In the interests of space, however, let us move to a brief treatment of Deleuze's second major work of the late 1960s, Logic of Sense.