I think that's the fundamental problem here, with Deleuze, and with the aesthetic approach to epistemology in general. Insofar as it purports to be a sub-representational account of thought, it cannot be represented - it literally cannot be thought or talked about. — Aaron R
The issue is more subtle than this, although I admit that in my haste to distinguish intensive (analog) differences from the Kantian 'thing-in-itself' I moved too quickly. First, sub-representational intensities are meant to
account for extensional magnitudes: in Deleuze's words, they are the
sufficient reason of all phenomena, "the condition of that which appears". Second - and here is where I moved too fast, we don't know intensity 'directly', but rather "we know intensity only as already developed within extensity, and as covered over by qualities."
As far as logical status of intensity goes, intensity thus occupies an
undecidable place
within any system of representation: it can only be known through representation, but is is nonetheless not
of the representational register. It's status is strictly correlative to that of the digital cut itself, which neither belongs to the system of representation nor is merely external to it. Hence the paradoxical status of intensity with respect to the question of knowledge: "[Intensity] has the paradoxical character of the limit ... [It] is both the imperceptible and that which can only be sensed."
Here is where things get complicated, but I'll try and do my best to explicate the ideas. If you recall that what's at stake is a 'critique of pure logic', then the idea is to introduce 'extra-formal’/‘real'
constraints on the the exercise of what might otherwise be purely syntactic logical manipulations which might simply follow transitively from an established set of axioms. For Deleuze, intensive differences are precisely what force 'real life' (extra-formal) constraints of 'existence' on logic, making logic no longer a formal and arbitrary play of symbolic manipulation, but beholden to a specific existential situation, as it were.
Thought - which just is representational - must be ‘forced' to think under the aegis of what Deleuze refers to as an ‘encounter’ with sub-representational intensities which impose 'real constraints' on thought. These constraints shift the modality of thought from the order of the
arbitrary to the
necessary: "if necessity is only ever the necessity of an encounter, and of a relation that this encounter gives rise to within us, a relation whose nature cannot be known prior to the forced movement it induces, then we must reconsider the meaning of the arbitrary. The concern of critical philosophy cannot be bound up with evaluating truth from a position of relative or extrinsic indifference … When truths are separated from the necessity of an encounter they become abstract, which is to say, they are reduced to being merely possible or hypothetical.” (Kieran Aarons,
The Involuntarist Image of Thought).
There’s a lot more to say here. I’ve not really given a full blown account of intensive differences, nor the
manner in which they force us to think, so much as focused on attempting to answering the charge that buying into the notion plunges us into the myth of the given. At most, I’ve focused on the
status of intensive differences with respect to thought, but I’ve already gone on too long. By all means ask any follow up questions though, cause these are bloody good thought-encounters for me. But I don’t want to prattle on too long. In the meantime, I'd direct you to
this paper by Peter Kugler which takes up exactly how to make sense of the above using Ryle's notion of categories. Will probably elaborate in a next post if you want.