29 Mar 2015

Somers-Hall, (1.8), Deleuze’s Difference and Repetition, ‘1.8 Infinite Representation (42–4/52–4, 48–54/59–65)’, summary

Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH.]

[UPDATE: My lack of knowledge, cleverness, and time prevent me in some cases from being able to re-explain in my own way some ideas in Somers-Hall's text. We are fortunate that the author has taken the time to remedy these gaps in my summary. Please see his clarifications in the comments section.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text


Chapter 1. Difference in Itself

1.8 Infinite Representation (42–4/52–4, 48–54/59–65)

Brief summary:

Representational systems may be classified either as finite or infinite. In finite ones, finite forms are limited  by the matter they inform. But in infinite representation, all things are somehow expressions of one infinite concept. (This distinction will be clarified in forthcoming sections.)



[We had been dealing with the problems of Aristotle’s manner of understanding difference and being. He had a representational, identity-based conception of beings, with negation as a determinant of definitional limits, that in the end had to have an equivocal conception of being in order for it to be able to have sense within his system. We saw then how a univocal conception of being could remedy the problems of Aristotle’s system. But] Deleuze also says that there is a way other than a univocal understanding of being. So we have philosophies based on the notion of judgment [perhaps an example would be philosophies like Aristotle’s which regard things themselves as having a subject-predicate judgment structure. In Aristotle’s system, the genus is a predicate to a species, such that we might say, ‘a man (species) is an animal (genus) that reasons (specific difference).’] Deleuze distinguishes two ways to characterize such judgment-based systems. (44a). [The following is very complicated and yet brief. I will try to work through it, but I will be unable to articulate it very clearly. We first note Aquinas’ definition of limit. I am not sure if everything mentioned here was already said before. Previously we saw how Aquinas defines finite and infinite on the basis of limit, with the finite being limited and the infinite not limited. And we also saw how for him, matter on its own and form on its own are unlimited. Matter can unlimitedly take on any form, but as soon as it does, it is limited to that form. Form, however, is unlimited in that it can be instantiated in infinitely many cases, but as soon as it is instantiated in matter, it is limited to that instance (or that limited number of instances). I cannot connect that very well with SH’s point here that “Aquinas’ definition of limit […] showed that finite things failed to properly express their form because they were limited by matter” (44). I am not exactly sure why this would be. Perhaps the form itself has features that are not expressible in the matter they inform, maybe because the matter has physical limitations that restrict its ability to express those formal features. I am just guessing. Then SH says that this situation leads to a distinction between something’s essence and its appearance (perhaps because its essence somehow has features not found in its appearance, but I am not sure). And, perhaps the appearance can be more or less fitting to the essence (somehow), since “something expresses its essence to the degree that its actual finite form embodies its essence” (SH 44). This is finite representation, I am guessing because something finite somehow in a limited way expresses or represents its essence. Now we move to infinite representation, which I also have trouble grasping. First we are to recognize that in finite representation, there are finite forms which occur in matter. I did not in the prior text understand the difference between a finite form and an infinite form. Is the infinite form one that is not instantiated in a matter, and forms that are informing matter are finite given that matter somehow limits them? At any rate, in infinite representation, this is no longer the case. Instead, “everything that is exists as a moment of an infinite concept which encompasses everything” (SH 44). I am not sure how to grasp this. How would a concept be infinite? How would a concept encompass everything? If it is not like the highest genus, then how do we conceive it?

I am a bit confused at this point. But SH says he will elaborate, so we should at this stage be patient. I quote SH in the following:]

At this point, he makes a distinction between two different ways in which we can characterise philosophies that are based on the notion of judgement. The first form, which we have been dealing with, is finite representation. This is based on the idea that judgements describe the essential structure of things. In other words, they set out the essential determinations which make up something. What makes it finite is the notion of limit. Aquinas’ definition of limit, for instance, showed that finite things failed to properly express their form because they were limited by matter. This led to a distinction between the essence of something and its appearance, in that something expresses its essence to the degree that its actual finite form embodies its essence (‘their degree of proximity or distance from a principle’ [DR 37/46]). Deleuze’s claim is that infinite representation replaces the notion of matter with a broader notion of representation. Rather than finite forms occurring in matter, everything that is exists as a moment of an infinite concept which encompasses everything. In effect, this is the claim that the world is therefore conceptual ‘all the way down’: ‘Instead of animating judgements about things, orgiastic representation makes things themselves so many expressions, or so many propositions: infinite analytic or synthetic propositions’ (DR 43/53). I want to spend a bit of time outlining how these approaches might function. In relation to the discussion of representation so far, the following comment by Deleuze sums up the difference between finite and infinite representation [the following quotes Deleuze]:

The signification of the very notion of limit changes completely; it no longer refers to the limits of finite representation, but on the contrary to the womb in which finite determination never ceases to be born and to disappear, to be enveloped and deployed within orgiastic representation. (DR 42–3/53)
(SH 44)


Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

[Deleuze] Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.





  1. The point about Aquinas is more that when forms are instantiated in matter, there is often a limit to how well that form is instantiated in matter, due to the play of contingency, or the intransigence of matter itself (we might think of cases of deformity, or when beings lack characteristics which they should have according to their form/essence – in these cases, the lack is due to issues in the way the form has been realised in a particular material structure). For Aristotle, these aspects of contingency limit our ability to talk rationally about the external world – deformity has to be understood as a failure of form to express itself, and the being is measured (negatively) in accordance to its distance from essence. This is the point I deal with in the last chapter of the Hegel-Deleuze book where I talk about the failure of representation to develop an adequate conception of teratology. Hegel and Leibniz both see conceptual determinations as not simply imposed on matter, but they see the world itself as (in a sense) reason/the conceptual itself. Hence, Leibniz will say that the phenomenal world is simply a confused vision of conceptual determinations, and Hegel will say that all determination is (conceptual) mediation. In extending reason/judgement to everything, Hegel and Leibniz aim to think totality in terms of judgement.

    1. I wanted to place some relevant quotations from your Hegel-Deleuze book, since you are referencing a very interesting and compelling part of your argument. The following is quotation from: Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

      "Rather than arguing that comparisons between organisms should be grounded in an analysis of the form or function of their parts, Geoffroy instead proposed that anatomical classification should proceed along morphological lines. In rejecting form and function, Geoffroy argued that what was key was the relations between parts themselves. Parts were therefore understood in terms of their connections with other parts and their genesis, according to an abstract schema. Such an account presented a radical break with teleology." (Somers-Hall, Hegel, Deleuze, and the Critique of Representation, page 224)

      "For the comparative anatomist, the names of the parts of animals are, to a certain extent, derived analogically with those of other animals, archetypally with man. Thus, for instance, we can apply the term legs to other animals as they share certain characteristics of form and function with human legs. When the function or form of parts differs from those of man, however, a different term must be assigned to the part in question. Thus, although there is a similarity between the fins of a fish and the arm of a man, on a teleological account, the functional and structural differences mean that different terms must be applied to each." (Somers-Hall, Hegel, Deleuze, and the Critique of Representation p.225)

      "The principle that Geoffroy employs for this role is the principle of the unity of composition. In order to posit similarities, Geoffroy posited an underlying abstract structure for particular animal forms. This structure was not to be understood in teleological terms, the function of the structure emerging depending on the particular form this strucn1re took in the animal in question. The underlying plan allows the homology to be defined without reference to teleology. The British comparative anatomist Richard Owen was later to define it as "the same organ in different animals under every variety of form and function," whereas Cuvier's analogies were defined as "a part or organ in one animal which has the same function as another part or organ in another animal." Thus, to use Appel's example, the legs of a crab are analogous to those of a quadruped, as they share the same function, but they are not homologous to them. Fins and arms, on the contrary, would be homologous without being analogous." (Somers-Hall, Hegel, Deleuze, and the Critique of Representation p.225)

    2. Continuing quotations from: Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

      "The classic example of Geoffroy's method was his application of the principle to the skeletal structure of the fish. Whereas under the teleological account, the specific nature of the various structures of different organisms is not of particular importance, since we are there concerned with identity of function, Geoffroy's account requires that the same connections of parts are expressed in different organisms. Whereas for a teleological reading, for instance, it does not matter precisely how many bones make up the skull, provided the function and form are similar in the two cases, on a morphological account such as Geoffroy's, it is essential that he is able to show | how each bone is connected to another. In order to show that both man and fish, both of which are vertebrates, are constructed according to the same plan, each bone within the structure of the fish must have a correlate within the structure of the mammal. Geoffroy actually attempted to prove this fact. He showed that, despite the fact that fish had a greater number of bones than mammals, by looking at the embryos of the two classes of vertebrates, equivalences could be found. Despite the differences in the final number of bones, the same number of centers of ossification were found in both types of embryos, although these fused together as mammalian embryos developed. Using this approach, Geoffroy was able to explain all but one key set of bones in the fish, the gill cover, which aids the fish in respiring. Eventually, Geoffroy concluded that the gill cover was homologous with the four bones of the inner ear. That is, the bones that provided the function of hearing within mammals were part of the respiratory system of fishes . Thus, the field of homologies extended beyond those that could be discovered by teleological means. Once the rejection of the teleological criterion had been accepted, it was possible to describe homologies between other parts of organisms, such as the fins and arms of our initial example . In Geoffroy's work in these cases, he was once again able to demonstrate identity of the connection of parts persisting through dissimilarity of function." (Somers-Hall, Hegel, Deleuze, and the Critique of Representation, p.225-226)

    3. Again, continuing quotations from: Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

      "Cuvier's teleological approach did not lead to him rejecting variation in the organism, but it was limited. In particular, variation became more common as one departed from the major organs and considered those of less importance to the organism as a whole. Deviations in minor organs were less likely to affect the optimal functioning of the organism as a whole and could therefore be sustained. As we saw in chapter 2, however, for Aristotle's teleological account, differences were largely understood as a lack, that is, as a deviation from the essence of the species. Prior to Geoffroy, little progress had been made on this reading beyond recognizing "monsters by excess" and "monsters by defect." By providing a positive account of deformity in terms of the arrest of the development of a part of the organism leading to the actualization of the unity of composition in a different form, Geoffroy was able to explain contingency in terms other than merely as an absence of organization. Thus, he attempted to show that aberrations still followed the principle of the unity of composition: "Monstrosity exists, but not, however, exceptions to the ordinary laws [of nature]." Furthermore, as the form of the organism was not understood in purposive terms, Geoffroy was able to give a positive description of these changes that allowed the organ either to no longer function in the new organism or to change its function. Thus, while we might argue teleologically that the bones in the human skull are separate in infants and later fuse together by claiming that this aids parturition, a teleological account seems implausible of the separation of the same bones in birds, which peck their way out of a shell." (Somers-Hall, Hegel, Deleuze, and the Critique of Representation p.230)

      See more discussion: