Lecture Twenty: Conclusions

Introduction

                  For this final lecture, I want to summarise some of the results of Deleuze’s investigations in the first two chapters of Difference and Repetition before presenting some of the themes that will occupy Deleuze in the later chapters of the text. We have covered a fair bit of ground during the course, but there are still some outstanding questions that need to be answered. First, given the possibility of a philosophy of difference, why is it that philosophers have previously constructed their philosophies on the basis of a concept of identity? Second, Deleuze makes it clear that difference cannot be understood for him on the basis of negation, so the question is, how do we understand difference without negation? A question that follows from this is, in what way does the notion of difference actually provide an explanation of phenomena? Finally, I want to look at the question of intensity and the phenomenal world. Deleuze has argued that the extensive world is understood as grounded in intensity. As we saw last week, Deleuze also privileges the perspectivism of the simulacrum over the objectivity of the icon. This raises the question of how different perspectives can be generated from a field of intensive difference (in other words, is there a synthesis of space that parallels the synthesis of time in chapter two of Difference and Repetition?).

Deleuze’s Results

                  In providing a brief summary of the first half of Difference and Repetition, the place to begin, I think, is to present the problems, or perhaps symptoms is a better word, which lead Deleuze to put forward his own metaphysics. I think we can see Deleuze’s project as responding to four specific challenges to a philosophy built upon identity in the first part of DR. These problems are:

  • The Underdetermination of resemblance

This difficulty emerges when we try to present an account of the law that operates purely in terms of resemblance, that is, in terms of the universal and the particular. When we want to show that something operates according to a given law, we are faced with a problem. As Deleuze notes, ‘everything reacts on everything else, and everything resembles everything else.’ (DR 3) In that sense, we need some kind of criterion by which to select which objects a law will range over. If we take law (determination by particulars and universals) to be completely determinative of the world, then there is nothing that will allow us to decide what are ‘natural joints’ of the world, and what are arbitrary connections. The same problem emerges in chapter two of Difference and Repetition: if memory is defined purely in terms of actuality as a passed present, why does recollection bring this memory to the fore rather than that one, given that they are all alike in some way and different in some way?

  • The exception to the law

The second problem is provided by analyses such as Kierkegaard’s. The figure of Abraham, for instance, simply falls outside of the law, and so cannot be adequately characterised by an analysis in terms of the universal and the particular. Abraham, from the perspective of the moral law, should be seen as a murderer, but he is also the champion of faith: ‘Yet no one is as great as Abraham; who is able to understand him?’ (FT, 48) We could relate this to Kant’s argument from incongruent counterparts: even if we can provide a complete list of the conceptual relations of a glove, we could still not completely determine it – the complete list does not determine whether it is left or right handed.

  • The inexplicability of repetition

On this basis, we can see that there is a third problem. Repetition obviously occurs – we see it all the time, but yet we cannot provide a coherent conceptual explanation of it. Either the second object is the same as the first object, but then there is no repetition, as the two cases are indiscernible, or it differs, in which case we once again do not have a true repetition,

  • The equivocity of judgement

The big problem that we dealt with last term was the problem of the equivocal nature of judgement. If we describe the world in terms of subjects and predicates, then we seem to be forced to posit a fundamental distinction between substances and properties. Now, this distinction between different (and incommensurate) types of being is not in itself a criticism, but it does go against our intuitions that the world is constituted of one kind of ‘stuff’.

  • The limited conception of synthesis

Finally, taking judgement to be central to the organisation of the world presents a problem, in that it seems that creatures that are not capable of forming judgements about the world are still able to inhabit the world, and ‘make sense’ of it. In the case of Kant, this problem shows itself by the fact that Kant attempts to explain the notion of habit through judgement, rather than realising that habit is the broader phenomenon exhibited by creatures not capable of judging.

As we have seen, Deleuze’s response to these problems involved showing the strong connection between an equivocal ontology, and a concept of difference which was subordinated to identity. Deleuze’s project in the first part of Difference and Repetition can therefore be seen to revolve around generating an alternative conception of difference which does not function extensively, but rather intensively (the difference between Aquinas’ distinction of the finite and infinite, and Scotus’ distinction, for instance). Deleuze’s characterisation of intensive difference basically sees it as operating on the level of a quasi-Spinozist substance. Given that there we do not relate to substance directly, and that there are two different ways of understanding the determinations of substance, either through intensive or extensive difference, Deleuze’s project involves a large genealogical component. The difficulty is deciding whether a given entity is grounded in difference or identity, or in Deleuze’s terms, whether it operates according to a sedentary or a nomadic distribution. As we have seen in the last few sessions, Deleuze sees this genealogical project as operating according to an ‘inverted Platonism’, whereby difference is selected according to a myth, the myth of the Eternal Return. This philosophical schema led to the following answers to the problems with representation:

In place of a conception of synthesis based on notions of a subject and an object (the Kantian notion of synthesis), Deleuze developed a concept of passive synthesis that constituted centres of subjectivity rather that emanating from them. As passive synthesis was pre-predicative, it explained how habits were contracted without relying on the ‘higher’ form of synthesis defined by judgement. This in turn allowed us to see why judgement appears to be such a successful way of characterising the world (it is a surface effect of a deeper process), while also explaining why an extra element was needed to explain why judgement or law was able to operate. Repetition therefore becomes, not the bare repetition of a state of affairs, but rather the play of the same intensive differences in difference situations.

Further Questions for Difference and Repetition

I now want to briefly go through what occurs in the rest of the book. Apologies for the rather schematic nature of these comments.

The Image of Thought and Representation as Transcendental Illusion (Chapter 3)

Chapter three of Difference and Repetition deals with what Deleuze calls the ‘Image of Thought’. The main questions which Deleuze deals with in this chapter is, I think, why is it that thinking does not naturally develop the kind of account of the world which Deleuze has put forward, and why does it remain caught in an understanding of the world in terms of judgement? To sketch Deleuze’s answer to this question, we can begin by noting that when thinking goes wrong, this is normally because of assumptions which underlie our thinking which are false. For instance, Aristotle argued that the Earth had to be stationary, because if it were in motion would be left behind by the Earth once they left the ground. Now this argument is false because Aristotle falsely assumes that the motion of the birds should be understood in relation to an absolute frame of reference, whereas in fact, the motion of the bird can be understood as relative to the motion of the Earth. If it were assumptions that led one to ‘go wrong’ in one’s reasoning, then something like Descartes’ model of philosophical enquiry would be appropriate. That is, one should strive to remove all assumptions from one’s thinking through the method of doubt. If one only reasoned from absolutely certain assumptions, one could not go wrong: ‘reason now leads me to think that I should hold back my assent from opinions that are not completely certain and indubitable just as carefully as I do from those which are patently false’ (Descartes, 1996, p. 12). What is important about this move by Descartes is that it is reason itself which instigates a method of doubt. Whereas classical doubt often related various faculties to each other in order to undermine all of their claims to primacy in the search for truth, Descartes installs reason as the arbiter of the process of doubt itself. The aim of methodological doubt is therefore to create a space for reason to conduct its enquiries into the nature of the world, as ‘deduction of one thing from another can never be performed wrongly by an intellect which is in the least degree rational’ (Descartes, 1985a, p. 12). If the intellect is incapable of error, however, we have the difficulty of explaining how error can and does occur. Descartes’ solution to this central problem of his method is to situate error in the relations between the faculties. In the Meditations, it is the mismatch between the large domain of the will, which has no concern over truth, and the smaller domain of reason which leads to error. Likewise, in the Rules for the Direction of the Mind, Descartes writes, ‘while it is the intellect alone which is capable of knowledge [scientia], it can be helped or hindered by three other faculties, viz, imagination, sense-perception, and memory’ (Descartes, 1985a, p. 32).

                  Deleuze instead takes up Kant’s radical suggestion that reason itself is subject to internal illusions that lead it to go astray. That is, that reason itself is responsible for thought ‘going wrong’. Kant’s claim emerges from the fact it is ‘set as a task’ (Kant, 1929, A498/B526) to understand empirical phenomena as a totality, as ‘human reason is by nature architectonic.’ (Kant, 1929, A474/B502) It does this by determining the conditions that lead to a particular phenomenon arising. The difficulty is that the totality of conditions cannot be given, as not all of the conditions for empirical phenomena are themselves empirical (some of the conditions will be transcendental, or will derive from the noumenal nature of things prior to our imposition of space and time on them). So reason takes what is given as a legitimate task, the systematisation of knowledge, but it makes the false assumption that because its task is to understand empirical phenomena as a totality, such a totality can actually be given. Rather, the idea that knowledge can be given as a totality is an imaginary focal point that allows the unending and incompletable process of systematising knowledge to proceed:

This is an illusion which can no more be prevented than we can prevent the sea appearing higher at the horizon than at the shore, since we see it through higher light rays; or to cite a still better example, than the astronomer can prevent the moon from appearing larger at its rising, although he is not deceived by this illusion. (Kant, 1929, A297/B355)

This is what is known as a ‘transcendental illusion’, and explains why reason sometimes falls into contradictions when, for instance, it tries to determine whether the universe has a beginning in time, or is eternal. Neither option can be definitively proved, because verifying one or other of the hypotheses would require us going beyond the given. In the sense that reason holds all conditions of phenomena to be in principle accessible to it, it is therefore subject to error, not in the Cartesian sense of external interference or false assumptions, but according to its very nature. Deleuze’s claim will similarly be that the failure of representation is that its very structure contains within it the transcendental illusion that everything is susceptible to representation. In fact, the domain of representation is limited to actuality (in fact, it is further limited than this, but determining exactly why would draw us into some rather tangential issues), as it is not able to adequately represent the virtual.

Difference without negation/the structure of the Idea (Chapter 4)

The central questions which I take to be addressed in chapter four of Difference and Repetition are, how can we develop a positive account of intensive difference, and how does this account of difference serve as an explanatory principle? Deleuze here talks about the Idea as the way in which we characterise intensive difference, and uses the calculus to provide an example of what a difference that isn’t understood in terms of spatial separation might look like. Basically, the differential calculus allows us to determine the gradient of a line. Now, with a straight line, the gradient is the same along the whole length of a line, so we can determine the gradient by simply seeing how much it rises or falls along a given stretch. That is, on a graph, we would divide the increase in height on the y axis by the distance that increase takes place over: y/x. So if a line rises on the y axis by six units as over a two unit stretch of the x axis, the gradient is (6/2) = 3. If we want to determine the gradient of a curved line, the situation is more complex, however, because what makes a curve a curve is the fact that the gradient of the line is constantly changing. This means that we cannot simply determine the gradient by drawing a line between two points, because this would give us the average gradient, not the gradient itself. Leibniz’s solution to this problem was to determine the gradient by assuming that the distance between the two points was infinitesimal (hence the term, infinitesimal calculus). While this solved the problem de facto, it didn’t solve the justificatory problem of why the calculus works, as we are still determining the gradient on the basis of an average between two points (albeit two points infinitesimally close to one another). The difficulty, is, in a sense, that with a curve, we are attempting to determine the gradient of a point, but a gradient is traditionally understood as a ratio between two distances. Deleuze’s solution (which is somewhat similar to Newton’s) is to posit the difference between the two elements of the ratio as intensive. Thus, while they do truly allow us to determine the gradient at a given point of a curve, the differential ratio, (dy/dx) cannot be represented extensively – each of the elements, dy and dx are equal to 0, but when put into a ratio form, they give us a determinate gradient for the point. For this reason, Deleuze claims that ‘just as we oppose difference in itself to negativity, so we oppose dx to not-A, the symbol of difference to that of contradiction.’ (DR 217)

Deleuze introduces the notion of the Idea as what is supposed to provide an explanation of phenomena without relying on simply repeating the structure of these phenomena at a higher level. So, for instance, Deleuze uses it to oppose the Kantian style of explanation that we looked at in chapter two of DR where the operations of the empirical imagination were explained by positing a transcendental imagination in the case of habit. Deleuze sets up three criteria that the Idea must meet:

  • ‘The elements of the multiplicity [of the Idea] must have neither sensible form nor conceptual signification, nor therefore any assignable function.’ (DR 231)

If it is going to explain actual states of affairs, it has to be different in kind from them, otherwise the explanation will be tautologous.

  • ‘These elements must in effect be determined, but reciprocally, by reciprocal relations which allow no independence whatsoever to subsist.’

If the Idea is going to be different in kind from states of affairs, it cannot be made up of elements which maintain themselves through self-identity. Rather, the being of the elements is purely defined by their relations to other elements.

  • ‘A multiple ideal connection, a differential relation, must be actualised in diverse spatiotemporal relationships.’

If the Idea is going to explain situations, then clearly it cannot apply to just one situation – it has to have a greater degree of generality in order to allow us to select in what way given phenomena are alike and dissimilar.

We can see how this works by looking at one of Deleuze’s examples: the use of homologies in biology. For traditional (and pre-evolutionary) comparative anatomy, the names of the parts of animals are, to a certain extent, derived analogically with other animals, archetypally with man. When the function or form of the parts differ 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 man, on a teleological account, the functional and structural differences mean that different terms must be applied to each. Now, because an organism was defined as a unity of these parts defined by their functional roles, the transformation of species became problematic. This is because deviations in the structure of the parts had to be understood as accompanied by a reduction in functional performance. In effect, deviation could only be understood as lacking the functional unity of the species in question (as deformity).

                  So we have a situation in which a conceptual understanding does not cut reality at the joints, hence preventing us from properly understanding a key natural phenomenon – evolution. Now, one of the key conceptual developments that made the theory of evolution possible was Geoffroy St. Hillaire’s positing of homologies between different parts of organisms. That is, rather than seeing an organism as defined by the form or function of parts, Geoffroy saw it as defined by the relations between parts. By focusing on relations rather than functions, Geoffroy was able to provide an account that explains one of the key results of evolutionary theory, that the same structure can change its function in different organisms (fins becoming arms, for instance). Now Geoffory didn’t relate organisms to one another directly to generate his account of homologies, but rather posited a transcendental structure of an ideal organism that other organisms were instantiations of (he called his approach ‘transcendental anatomy’).

Deleuze’s interpretation of Geoffroy’s work rests on what he calls Geoffroy’s dream, ‘to be the Newton of the infinitely small, to discover ‘the world of details’ or ‘very short distance’ ideal connections beneath the cruder play of sensible and conceptual differences and resemblances’ (DR, 185). He argues that what Geoffroy is aiming at with his emphasis on connections is a field of differential elements (the ideal correlates of the bones) forming specific types of relations (the connections which are central to Geoffroy’s account). On this basis, Deleuze claims that Geoffroy’s transcendental anatomy functions like a Deleuzian Idea, with its three characteristics. The elements of the Idea ‘must have neither sensible form nor conceptual signification,’ and transcendental anatomy fulfils this requirement due to the fact that it is essentially non-metric and topological, therefore differing from the actual structures which express it. Second, ‘these elements must be determined reciprocally,’ which in the case of the unity of composition, Deleuze takes to mean that what is central is not the bones themselves, but the connections they hold with other bones. Third, ‘a multiple ideal connection, a differential relation, must be actualised in diverse spatio-temporal relationships, at the same time as its elements are actually incarnated in a variety of terms and forms.’ emphasises that homologies do not exist directly between actual terms, ‘but are understood as the actualisation of an essence, in accordance with reasons and at speeds determined by the environment, with accelerations and interruptions’ (DR, 184). That is, we note a homology by recognising that the actual parts of both organisms are actualisations of the same transcendental essence, the unity of composition, rather than by a direct correlation of actual terms, as in comparative anatomy. The Idea in this case therefore allows us to determine in what way diverse phenomena are related to one another.

Depth and Intensity (Chapter 5)

I don’t want to go into much detail about the final chapter, but its main concern is to explain how we can understand perspectivism without these perspectives being correlated with a central identity that generates them. Now, in this chapter, Deleuze draws upon a central distinction that Merleau-Ponty makes in the Phenomenology of Perception, and his last published work, Eye and Mind. The reason why we might consider perspectives to be related to an identity which generates them is because we normally see the dimensions of a perspective as interchangeable. So we feel that what is depth from one perspective will be seen as width from another. So even though objects obscure one another from our own perspective, ‘another man, situated elsewhere – or better, God, who is everywhere – could penetrate [the objects] hiding place and see them openly deployed’ (EM, 173). Different perspectives are therefore situated within a common space that co-ordinates them. In this case, each perspective can be explained purely in terms of extensity. Deleuze claims rather that depth therefore forms the generative space from which extensive space is generated. Following Merleau-Ponty once again, in his claim that ‘a first dimension which contains all the others is no longer a dimension’ (EM, 180), Deleuze argues that ‘once depth is grasped as an extensive quantity, it belongs to engendered extensity, and ceases to include in itself its own heterogeneity in relation to the other two’ (DR, 229). In this sense, for Deleuze, we see intensity, rather than extension as generative of perspective in relation to a field of depth. We can compare these two approaches by noting the two different ways in which perspective has been represented in art. In the renaissance, perspective was represented through projective geometry, which essentially involved deforming the scene in such a way as to allow the brain to reconstruct depth information from the two visible dimensions. In modern artists such as Cezanne or Klee, however, we find that depth is constructed through the interplay, and interpenetration, of colour that doesn’t rely on a prior sharply determined geometry of objects or identities. In this sense, in making depth as a field of intensity the ground for perspective, Deleuze takes up Merleau-Ponty’s claim that ‘any theory of painting is a metaphysics.’ (EM, 171)

Conclusion

                  Each of those summaries is, of course, far too short to do justice to Deleuze’s arguments in those chapters, but they do, I hope give an indication of the themes of the rest of the book.

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