This chapter is turning into quite a compressed history of philosophy. First we had Aristotle. Then the rebel tradition of Scotus-Spinoza-Nietzsche. Now we get a whole long section (pg. 42-50) on Hegel and Leibniz. Unfortunately, my knowledge of Leibniz is borderline zero, and my knowledge of Hegel is the cartoon understanding one gleans from scraps of undergraduate reading about the "master-slave dialectic". I suspect my knowledge of Hegel is destined to remain forever in its current state. Never did care much for the dialectic, whether in Hegel or in the more messianic aspects of Marx. It always struck me as explaining things ass-backwards by starting with the conclusion and so turning all of history into a just-so story to justify the present (or near future, in the case of Marx). Leibniz, however, I'm interested in exploring further. The monad seems related to Whitehead's "actual occasion". I'm also curious about the philosophy of the co-inventor of calculus and one of the first people to cotton on to binary numbers. But man, I can't read everything. At least not all at once. Which means that we're going to have leave this section with only a fairly vague understanding of Delueze's comments about these guys.
I think it's okay to stay with the 30,000 foot view of this section because the takeaway is very clear. Hegel and Leibniz both come up with a concept of difference that goes beyond the finite organic representation Aristotle constructed with his genus and species system. Deleuze calls this new system "infinite orgiastic representation". It comes in two flavors depending on your starting point: starting from the infinitely large (Hegel) we find that difference or determination is fundamentally contradiction, or starting from the infinitely small (Leibniz) we find that difference is "vice-diction". Both schemes change our way of thinking about the part-whole relationship. With Aristotle, the parts were related to the whole as organs are related to a body, that is, as parts of an organic or organized whole. Hegel and Leibniz come up with two different ways of saying essentially that the part is the whole. For Hegel, the infinitely large whole differentiates itself into a finite "part" which contradicts that infinity, but is then reabsorbed, as it were, into the infinity when it meets the contradiction of the contradiction. This is the boring concentric circle of the dialectic where thesis meets antithesis and annihilates itself in a burst of light and neutrinos to leave us with a synthesis that is identical to where we started. If this sounds like a wordy double negative, that's because it is. Leibniz, by contrast, starts with the infinitely small, and is somehow the opposite of Hegel. Frankly, I don't understand the Leibniz section well enough to even summarize it yet.
But all of this is a bit academic, because the punchline is that neither Leibniz nor Hegel offers us a concept of difference in itself that does not ultimately derive from identity. That's why Deleuze continues to call their schemes "representations". The basic issue is the concentric circles in the case of Hegel and the way all the series of infinitesimals in Leibniz always converge on his belief in the "best of a all possible worlds".
The point is that in the last resort infinite representation does not free itself from the principle of identity as a presupposition of representation. That is why it remains subject to the condition of the convergence of series in the case of Leibniz and to the condition of the monocentring of circles in the case of Hegel. Infinite representation invokes a foundation. While this foundation is not the identical itself, it is nevertheless a way of taking the principle of identity particularly seriously, giving it an infinite value and rendering it coextensive with the whole, and in this manner allowing it to reign over existence itself.
Like I said, I'm not clear how this critique applies to Leibniz, but it makes sense to me in the case of Hegel. If everything is destined for a certain endpoint development of "Absolute Spirit" (or commie utopia in Marx) then there's no real history or development or movement at all. All particular things or moments in history become like virtual particles popping in and out of existence and getting us nowhere -- in fact, there's even a Feynman diagram for the dialectic. Any difference that would limit or mark off some part of the whole is produced by a contradiction and then reabsorbed as the contradiction of that contradiction. The whole negates itself and negates the negation of itself, and unsurprisingly, we get back the identity of the whole.
Hegelian contradiction does not deny identity or non-contradiction: on the contrary, it consists in inscribing the double negation of non-contradiction within the existent in such a way that identity, under that condition or on that basis, is sufficient to think the existent as such. Those formulae according to which 'the object denies what it is not', or 'distinguishes itself from everything that it is not', are logical monsters (the Whole of everything which is not the object) in the service of identity.
Anyhow, the point of the section is clear. Neither Hegel nor Leibniz produce the concept of difference in itself that Deleuze is looking for. Both of them still start with the premise of identity, though this time phrased in the form of a double negative.
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