There are many different reasons for studying the relationship between the philosophical approaches of Gilles Deleuze and G.W.F. Hegel. Deleuze's deep anti-Hegelianism means that Deleuze scholars need to know something of Hegel in order to grasp the real import of Deleuze's thought; Hegel scholars, on the other hand, intrigued by the claim that we find in Deleuze a non-Hegelian ontology, might want to know whether we do indeed find anything new in Deleuze to challenge the Hegelian dialectic. However, Deleuze's anti-Hegelianism means that it is difficult to compare the thought of Deleuze and Hegel, since Deleuze's rejection of Hegel can often seem so total that there appears to be no shared territory upon which we can construct a comparison of the two thinkers.

Henry Somers-Hall responds to this difficulty by trying to show that the philosophies of Hegel and Deleuze can, after all, be compared on the basis of a ‘common problematic’, namely, the problem of ‘finite representation’ (2). Furthermore, he wants to demonstrate that Deleuze's response to this problematic is superior to that of Hegel. While I want to suggest, in the following, that Somers-Hall does not succeed in the latter task, his success in the former makes this book essential reading for anyone interested in the relationship between the philosophies of Deleuze and Hegel and in efforts at overcoming the (often seemingly infinite) distance between their modes of thinking.

Somers-Hall takes quite a different approach from others who have written on this subject. For example, Michael Hardt seems to rule out the possibility of finding a common problematic between the two philosophers by writing that Deleuze ‘engaged Hegelianism not in order to salvage its worthwhile elements […], but rather to articulate a total critique and a rejection of the negative dialectical framework so as to achieve a real autonomy, a theoretical separation from the entire Hegelian problematic’ (Hardt Reference Hardt1993: xi). On the other hand, writers such as Catherine Malabou and Slavoj Žižek have tried to demonstrate the existence of Hegelian motifs in Deleuze's philosophy (Malabou Reference Malabou1996: 136; Žižek Reference Žižek2004: 55). However, such attempts are quite different in character from Somers-Hall's comparative approach, which consists in showing that Deleuze and Hegel find separate solutions to their shared problematic. Other writers, such as Miguel de Beistegui (Reference de Beistegui2004) and Brent Adkins (Reference Adkins2007), also offer comparative accounts of Hegel and Deleuze, but Beistegui's focus on the Deleuze-Heidegger relation, and Adkins's focus on the concept of ‘desire’, mean that Somers-Hall's approach differs from theirs as well (6).

As I mentioned above, Somers-Hall considers the problem of ‘finite representation’ to be the common problematic of Deleuze and Hegel. For Deleuze, ‘representation’ means ‘philosophy of identity’, and refers to any philosophical practice that involves the ‘privileging of identity’ (1); ‘finite representation’ is a narrower term that refers to the ways of privileging identity that we find in the philosophies of (among others) Kant, Aristotle and Russell.

Interestingly, Somers-Hall's strategy allows us to compare the positions of Deleuze and Hegel by comparing their responses to Kant and to problems that arise in logic. In his view, both Hegel and Deleuze want to ‘overturn the rule of judgement’ that we find in Kant (240), but they do so in very different ways: Hegel attempted to show how the categories of judgement ‘immanently sublated themselves’ (241), while Deleuze tried to show that the categories of judgement must be ‘supplemented by a dimension of virtuality’ that would account for the conditions of the empirical object itself and not just the conditions of knowledge of the object (12–13, 241). Contrary to Hegel, Deleuze thus does not think that the concepts of judgement can be shown to sublate themselves. However, the two philosophers share the problematic of finite representation in that they both think that Kant presupposes a kind of identity between the structure of judgement and the structure of empirical objects, and both believe it is necessary to find a philosophical response to this Kantian presupposition. As for logic, Somers-Hall discusses the logics of Aristotle and Russell and argues that they presuppose movement and differences between individuals rather than explaining these things (61–62) and he tries to show how Hegel and Deleuze get beyond finite representation in order to provide logical explanations of these phenomena.

Somers-Hall insists that both Hegel and Deleuze have coherent solutions to the problem of finite representation. It is vital, in his view, to realise that Hegel as well as Deleuze is truly occupied with the problem of representation, that the problem of ‘finite representation’ is ‘much the same’ as the problem of ‘the finite understanding’ that Hegel is interested in (3), and that we can get a good sense of how Hegel's dialectic works by describing his response to this problem. Somers-Hall follows Deleuze in arguing that Hegel solves the problem of representation by making contradiction the highest principle of his philosophical system and thereby extending finite representation so that it becomes ‘an infinitised form of representation’ (186). While Somers-Hall's project is clearly carried out in Deleuzian terms, he nevertheless attempts to show that the fact that he uses a Deleuzian name to describe the common problematic does not mean that it only has a Deleuzian solution.

Somers-Hall's book contains detailed discussions of mathematical and scientific concepts, including one chapter that draws heavily on the mathematical concept of ‘phase space’ to explain the Deleuzian response to the problem of finite representation as he sees it. In other chapters, Somers-Hall compares the Hegelian and the Deleuzian responses by looking at how they can help us to think about questions that arise with calculus and the modern understanding of the evolution of the organism. Deleuze's response to the problem of finite representation involves sustaining a concept of pure difference, while Hegel always pushes difference ‘to its limit as contradiction’ (157). Somers-Hall tries to show how these different responses to the larger problematic imply different accounts of more specific questions that arise from mathematics and biology.

For those who find the details of such scientific matters sometimes difficult (as I do), Somers-Hall very helpfully supplements the discussion by raising some more straightforwardly philosophical questions, and showing how the two conceptions of difference allow us to deal with these. So, at the end of a chapter on calculus, he shows us how Hegel and Deleuze respond to Kant's antinomies, and after the discussion of phase space mentioned above we get a discussion of Merleau-Ponty on aesthetics that helps to explain Deleuze's conceptions of ‘depth’ and ‘the virtual’. I found the latter discussion particularly excellent, and I think it could serve as a very good introduction to these difficult Deleuzian concepts.

In the final chapter of the book, Somers-Hall argues that the Deleuzian way of thinking about difference can account for the modern, scientific understanding of the structure of the organism while the Hegelian view cannot. Furthermore, he suggests that the incompatibility of Hegelianism with the fact of evolution is not just a quirk of his Philosophy of Nature, but is a result of deeper logical commitments necessarily connected with his conception of difference. It is on this basis that he believes he has shown that the Deleuzian response to the problem of representation is superior to the Hegelian. He suggests that we cannot ‘determine which ontological approach to follow simply by looking at possible incoherencies in their different logical systems’ (211), since his view is that both Hegel and Deleuze offer coherent responses to the problem of finite representation and so they are equally valid taken on their own terms; Somers-Hall believes that it is therefore necessary to look at the way that their different approaches can account for ‘the world itself’ in order to determine whether the Hegelian or the Deleuzian philosophy is superior (210). The exposition of Hegel's account of the world itself—in this case, the structure of the organism in nature—that follows is informed by his ‘ontological rather than … transcendental interpretation’ of Hegel (5). In the introduction to the book, Somers-Hall doesn't explain what he means by this, but in chapter 5 it becomes clear that he is following commentators such as William Maker and Stephen Houlgate in reading Hegel's philosophical system as developing out of the immanent enquiry into being with which the Science of Logic begins (134). Consequently, he reads Hegel's Philosophy of Nature as if it were a continuation of the development of the Science of Logic (212). While I agree that this is indeed the way that Hegel intended his work to be read, Somers-Hall does not really consider the possibility that we might put Hegel's works to use in a better way in order to make some of Hegel's arguments more compelling. That is to say, Somers-Hall has perhaps shown that Hegel as he reads him cannot account for the evolution of the organism; however, we might try to read Hegel in a more charitable way in order that his philosophy might fit with our modern scientific understanding more readily, perhaps by accepting parts of Hegel's account and rejecting others, putting aside some of the letter of Hegel's writing in order to better capture its spirit. Somers-Hall neglects the possibility that a transcendental reading of Hegel might after all be the more faithful reading than the ontological one, as well as the possibility that a better answer to the problematic he is considering might be found in an approach that takes elements from both Hegel and Deleuze (such an approach might take inspiration from the works of Žižek and Malabou mentioned above). In sum, it seems to me that Somers-Hall takes a sort of ‘all or nothing’ approach to Hegel when he argues that the problems with Hegel's Philosophy of Nature prove that there are fundamental problems with Hegelian logic in general (234), and thereby rules out the possibility that the Hegelian philosophy of nature could be corrected, rather than rejected outright, in light of modern scientific evidence.

We should also note the choices that Somers-Hall makes when it comes to his interpretation of Deleuze. For example, he opts to focus on the earlier rather than the later Deleuze, and his reasons for doing so are touched upon only very briefly in the book (see 5, 240). This also holds of his claim that, when reading Deleuze, we must consider ‘both the philosophical and scientific sides of his thinking’ (5). The latter could have used more explanation, as could Somers-Hall's conclusion that Deleuze's philosophy is superior on the basis of its ability to account for modern scientific theories, which seems to presuppose an understanding of the relationship between philosophy and science that Deleuze rejects in his later work. For Deleuze, the task for the philosopher is not to offer accounts of scientific theories, but to ‘cut through’ science in order to extract philosophical concepts from science, a philosophical ‘concept’ being something quite different to a scientific ‘function’, and the task of the philosopher being quite different to that of the scientist (Deleuze and Guattari Reference Deleuze and Guattari1994: 117, 202–215). With a little more explanation, Somers-Hall could have clarified whether he was rejecting the later Deleuze's position on this matter, or whether his approach is, despite appearances, compatible with the later Deleuze.

To sum up: Somers-Hall's study of Deleuze and Hegel presents us with an interesting and fruitful reading of each of the two philosophers. A partial justification for Somers-Hall's chosen methodology can be found in the fact that it allows us to compare Hegel and Deleuze in a productive way. However, the fact that Somers-Hall doesn't do more to defend his methodology means that he has not proven that Deleuze's philosophy is superior to that of Hegel, since a reader who wanted to defend Hegel might do so by arguing for a different method of reading Hegel, or by disputing Somers-Hall's claim that Deleuze offers an account of modern scientific theory. But even those who are unpersuaded by his conclusions are likely to find that they have gained an enriched view of the relationship between Hegelian and Deleuzian philosophy from reading this book.