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The fundamental characteristic of the virtual, that which means it must be actualized rather than realized, is its differential makeup.

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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. 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.

A typological difference between substantive multiplicities, in short, is substituted for the dialectical opposition of the one and the multiple.

Foucault and critique: Kant, humanism and the human sciences

To these he added a trio of pre-Kantians, Spinoza, Leibniz and Hume, but read through a post-Kantian lens. There are many Spinozist inheritances in Deleuze, but one of the most important is certainly the notion of univocity in ontology. The result is a Spinozism minus substance, a purely modal or differential universe.

In univocity, as Deleuze reads Spinoza, the single sense of Being frees a charge of difference throughout all that is. In univocal ontology being is said in a single sense of all of which it is said, but it is said of difference itself. What is that difference? In social terms, puissance is immanent power, power to act rather than power to dominate another; we could say that puissance is praxis in which equals clash or act together rather than poiesis in which others are matter to be formed by the command of a superior, a sense of transcendent power that matches what pouvoir indicates for Deleuze.

In the most general terms Deleuze develops throughout his career, puissance is the ability to affect and to be affected, to form assemblages or consistencies, that is, to form emergent unities that nonetheless respect the heterogeneity of their components. 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.

The Wound Before the Blow: Fascicles X and XI

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. 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. 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.

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First, rather than seeking the conditions for possible experience, Deleuze wants to provide an account of the genesis of real experience, that is, the experience of this concretely existing individual here and now. Second, to respect the demands of the philosophy of difference, the genetic principle must itself be a differential principle. However, despite these departures, Deleuze maintains a crucial alignment with Kant; Difference and Repetition is still a transcendental approach.

Transcendental philosophy in fact critiques the pretensions of other philosophies to transcend experience by providing strict criteria for the use of syntheses immanent to experience. Three further preliminary notes are in order here. First, as we will discuss in section 4 below, the Capitalism and Schizophrenia project of Deleuze and Guattari will bring to the fore naturalist tendencies that are only implicitly present in the still-Kantian framework of Difference and Repetition. It is the experience by human subjects of this individual object in front of it, and it is the experience enjoyed by the concretely existing individual itself, even when that individual is non-human or even non-living.

Second, then, in the demand for genetic principles to account for the real experience of concrete individuals, Deleuze is working in the tradition of the Principle of Sufficient Reason.

The unconditioned in philosophy of religion

We are now ready to discuss the book itself. Deleuze inverts this priority: identity persists, but is now a something 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 for example, it is the difference of electrical potential between cloud and ground that constitutes the sufficient reason of the phenomenon of lightning.

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. Here difference is submitted to a fourfold structure that renders difference subordinate to identity: 1 identity in the concept; 2 opposition of predicates; 3 analogy in judgment; and 4 resemblance in perception.

Finally, the relation of substance to the other categories is analogical, such that being is said in many ways, but with substance as the primary way in which it is said.

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Here we see the dynamic genesis from intensity in sensation to the thinking of virtual Ideas. Each step here has a distinct Kantian echo. Intensity is the characteristic of the encounter, and sets off the process of thinking, while virtuality is the characteristic of the Idea. 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.

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. 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. 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. 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.

An immanent transcendental

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. 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. Simply put, the actualization of the virtual proceeds by way of intensive processes. 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.

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. 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 singular individuations or actualizations of that structure.

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While Difference and Repetition ranges over a wide field of philosophical topics, Logic of Sense focuses on two aspects of a single issue, the structure and genesis of sense. The genius of Frege and Russell was to have discovered that the condition of truth denotation lies in the domain of sense.

In order for a proposition to be true or false it must have a sense; a nonsensical proposition can be neither true nor false. Yet they betrayed this insight, Deleuze argues, because they—like Kant before them—remained content with establishing the condition of truth rather than its genesis.