In Difference and Repetition, Deleuze proposes what we may be permitted to term a differential phenomenology capable at last of setting mathematics and logic themselves upon a proper “ground” — that of difference, and multiplicity… Not only is it possible to overturn representation, but we can begin right away — if we immediately cease to encode relationships between singularities as identities, oppositions, analogies, and so on — but instead in terms of constitutive inequalities.
Deleuze’s project, as always, is pure affirmation without negativity or contradiction. Here he challenges all of us to affirm a Difference capable of constructing the very system which then cancels it — precisely by explicating it! — so that, strictly speaking, difference ought to be (and always will have been) inexplicable. What does this mean? How does this affirmation work?
Difference resists inclusion within the symbolic network which it produces as its destination and even “discovers” as its origin. Qualities, especially when taken as signs, present us with these same two faces. For on the one hand, they indicate “an implicated order of constitutive differences”; but on the other hand, the quality “tends to cancel out those differences in the extended order in which they are explicated.” (Difference and Repetition 228) It is also in this sense that signification is at once an origin and a destination (or directing agency, an “ordering” machine.) But the two functions are uneasily fused together: the destination denies the origin. Difference cancels itself by extending itself, covering itself with a quality. What happened? What is this uncanny “empirical” effect of qualitative distortion?
For Deleuze, “[t]he peculiarity of ‘effects,’ in the causal sense, is to have a perceptual ‘effect’ and to be able to be called by a proper name (Seebeck effect, Kelvin effect…), because they emerge in a properly differential field of individuation which the name symbolises. The vanishing of difference is precisely inseparable from an ‘effect’ of which we are victims.” (D&R 228) The unblinking (or “indifferent”) victims of a vanished Difference which nonetheless lives on, in itself, even as it is being evacuated, cancelled, and mutilated by its own explication. Deleuze returns again and again to the the two distinct “faces” of pragmatics, characterized by the fixation upon a particular “extensity” guaranteed by an illusory functionalization of difference (for example, the empirical or sensible as opposed to the transcendental.)
Nonetheless, there are always extensive and ultimately illusory factors (like entropy, which cannot be measured using any procedure outside of energetics) which are also an extension or explication implicated as such ‘in intensity,’ that is, factors which do not exist outside the implication, precisely because they have the function of making possible the general movements by which the object of the implication explicates itself, or becomes extended:
“It is therefore unnecessary, in order to save the universe from heat death or to safeguard the chances of eternal return, to imagine highly ‘improbable’ extensive mechanisms supposedly capable of restoring difference. For difference has never ceased to be in itself, to be implicated in itself even while it is explicated outside itself. Therefore, not only are there sensory illusions but there is also a transcendental physical illusion…” (228)
One way to frame the problem with extensity is that it persistently fails to account for the individuation which it is always already capable of (and indeed which occur unceasingly within it.) Individuating factors have only a relative value since they take place within an extensity already developed — whereas in fact they flow from a deeper source altogether; Deleuze argues they escape, not just from any abyss, but from “depth itself, which is not an extension but a pure implex.” (229) But can’t we “grasp” depth in terms of an extensive quantity? But then it would already belongs to an engendered extensity; that is, it would cease to “include in itself its own heterogeneity…” (229)
What, then, are depth and extensity? “Extensity as a whole comes from the depths. Depth as the (ultimate and original) heterogeneous dimension is the matrix of all extensity… The ground as it appears in a homogeneous extensity is notably a projection of something ‘deeper’: only the latter may be called ungrund or groundless. The law of figure and ground would never hold for objects distinguished from a neutral background or a background of other objects unless the object itself entertained a relation to its own depth. The relation between figure and ground is only an extrinsic plane relation which presupposes an internal, voluminous relation between surfaces and the depth which they envelop. This synthesis of depth which endows the object with its shadow, bears witness to the furthest past and to the coexistence of the past with present… Depth is like the famous geological line from NE to SW, the line which comes diagonally from the heart of things and distributes volcanoes: it unites a bubbling sensibility and a thought which ‘rumbles in its crater.’ Shelling said that depth is not added from without to length and breadth, but remains buried, like the sublime principle of the differend which creates them.” (228-9)