Assuming that you are well versed in Hegel, Deleuze, and the history of philosophy thereof, the key benefit to reading this book is the analysis and comparison of Hegel and Deleuze’s thoughts on calculus and the philosophy of nature, as opposed to a critique of representationalism per se, which followers of one, the other, or both would be likely to agree that they are both successful to somewhat successful in this attempt. HSH does at times seem to think that Hegel did not successfully overturn representationalism, rather that he created a system of infinite representation. This is because he thinks that for Hegel thought is a universal as opposed to a singular, and thus anything thinkable is subject to being expressed through a universal medium as opposed to determined as a singularity. I am not sure if I quite agree with this conception and following argument, largely because I am not sure that this is still representation as conceived of by Kant.
HSH is wise to realize that both are for the most part internally consistent and offer both valid and fruitful thoughts on each, and likewise that it is only a comparison through another medium as opposed to a direct comparison that we can really tease out the differences in their philosophies and see which is true. He also does a good job of drawing on the thinkers who both Hegel and Deleuze draw from in determining their respective views.
In this sense, the main question that he is concerned with is whether or not Hegel can think Deleuze’s sense of difference. If so, then it would be the case that Deleuze had not thought a genuinely non dialectical notion of difference, and that Deleuze would simply be another “beautiful soul” only another step along the path to absolute knowing. I liked his breakdown of Deleuze’s difference into the sub-unary parts of opposition and determination, and only expressed in a non neutral medium. However, these sub-unary parts can be determined without the reciprocal determination of another exterior element. This is different from Hegel who thinks that difference cannot be thought of in itself, and only as a epiphenomena of contrasting identities. This is a byproduct of his thinking which remains squarely grounded in Aristotle. This is also why HSH says that Hegel only has an epiphenomenal logic.
For calculus, the implication that this has is that for Deleuze, both parts of the differential can be determined in themselves and without respect to an other, while for Hegel they can only be determined reciprocally to each other and, analogous to the Perception stage in the PoS, are only extant as a unity because of the force or condition of thought that they are expressed in. Deleuze gets around this by arguing for a non Euclidean notion of space (phase space) whereby space and its structure is also a conditioned and not an intuitive feature of our cognition or a given empirical element. If space is as such, then the elements that determine it are sub representational. This circumvents the issues that HSH brings up with Hegel’s Newtonian calculus, which struggles to account for the status of fluxions/derivatives as having their own determinate being. Deleuze, borrowing from Leibniz and doing a little bit of his own magic, evades this problem with that same sub representational element.
For the philosophy of nature, Hegel prefers Cuvier’s comparative anatomy that relies on a relatively crude means of direct identification between body parts of differing species. Each identity is constructed out of contraries, emerging as a third term or point of mediation between the two that both really were all along. Deleuze on the other hand prefers Geoffroy’s homologous relations which argued that the same set of transcendental principles are constructive of various species. Similar problems and solutions emerge as in calculus - because Hegel relies on differentiation through identity, he cannot adequately approach the genesis of the subrepresentational in the way that Deleuze can.
Solid book. Will definitely return to it in the future. Would be curious to learn more about what HSH thinks about the role of depth in Deleuze’s thought in particular, as he seems to think that its a key element drawing from Merleau Ponty but doesn’t really explain why or go into much detail about that, and also his thoughts about Hegel’s infinite representation.