Deleuzian Supervenience

In his account of necessity David Lewis proposes that given two worlds that are exactly alike at time1, W and W*, and in which the same natural laws apply, then at any later time these two worlds will continue to be exactly alike. As a good Humean, however, Lewis encountered what he claimed to be a damning problem, the problem of undermining futures. On Lewis’s reading of Hume, any claims or truths we make regarding the world, including claims concerning necessary laws, supervene upon a given distribution of qualities. There cannot be a change in this distribution without there also being a change in the claims or truths that supervene upon them. Given the laws of probability, the chances of a dice coming up showing a six is one in six. Three or four sixes may show up in a row, but given a large enough number of throws the number of times it shows up sixes approaches one in six. These laws of probability therefore supervene upon a given distribution of qualities in the world up to and including time1. If there is a non-zero chance, however, that after time1 sixes come up every time then that would effect the chance distribution at W at time1—it would be something higher than one in six, but this contradicts Humean supervenience. Given the case of an undermining future we would assign a probability value x and non-x to the throw of the dice at time1. In his response to this problem, Lewis proposes modifying the laws, but many have been unhappy with Lewis’s proposal. In his analysis of Hume in After Finitude, Meillassoux, following Badiou, would argue that the very laws themselves presuppose a totalized whole, an All, in order for there to be the regularities upon which these necessary laws supervene. If mathematics thinks the not-All, however, then there is no reason why Humean supervenience needs to stay the same or be different at a later time. The notion of an undermining future would be vacated of sense. We may continue to axiomatize and mathematize the distribution of qualities in the world, but there is no All which assures their necessity, and hence no necessity to be undermined. The only necessity for Meillassoux is the necessity of contingency. In his response to the problem of undermining futures, John Roberts argues that what gives rise to the problem is the idealization of our knowledge of chance at time1. It is only under the assumption that we can specify a particular value to the chance of a particular event happening whereby we are led to a contradictory belief when the undermining future entails a different value and result. ‘But real evidence,’ Roberts claims, ‘never constrains these credences by specifying the objective chances of such events.’ (“Undermining Undermined,” p. 104) As Roberts clarifies, ‘if HS is correct, there could be such evidence only if there were no problem of induction,’ meaning that this evidence would have to ‘entail…contingent information about the future, something no evidence in principle available to creatures like us could ever do.’ (ibid.). By constraining evidence concerning chance and supervenience to ‘finite empirical cognizers,’ Roberts is able to block the reduction that results from undermining futures. In other words, people like us, finite cognizers, are simply unable to process all the evidence necessary to get the appropriate value, much less the undermining futures which we cannot even access, and thus we would be unable to generate the contradictory value. In doing this, however, Roberts fails to avoid the central critique of Meillassoux’s book. By calling upon the mathematical thinking of the not-All associated with Cantorian set-theory, Meillassoux sought to address the correlationist trap that has been in place since Kant—namely, we cannot know an object as it is in itself except for how it appears in its relationship to us as finite empirical cognizers. This is precisely what Roberts does, however, and the fact that Lewis himself was not attracted to the solution Roberts offers should give us pause. The reason for this is that Lewis sought, with the tools of modal logic, to do much what Meillassoux and Badiou would like to do—break free from the limiting cages of finite cognizers and arrive at truths about an autonomous reality that is not correlated to a finite cognizer. As a good Humean, however, Lewis would no doubt not accept Meillassoux’s rejection of the problem of undermining futures, the problem of induction, and similarly Meillassoux would reject Lewis’s approach since Humean supervenience continues the correlationsist legacy—knowledge of reality in itself is correlated to the various qualities of the world as they are related to a presupposed totality. This last claim I think is debatable since Lewis’s metaphysics may well involve a reality of possible worlds that are non-totalizable. Lewis nonetheless continued to believe in the necessity of natural law, thus even if there is a transfinite set of possible worlds (a not-All), the laws, whatever they are in each world, would hold as a consequence of the totality of that world; and hence Meillassoux’s argument would resurface.

At this point we can turn to Deleuze’s understanding of mathematics to clarify our take on Lewis’s position. As Daniel Smith has shown in his essay on the importance of mathematics in understanding Deleuze’s theory of multiplicities, and how this theory in turn differs from Badiou’s theory of the multiple-without-One, Smith shows that Deleuze’s theory is informed by a tradition of problematics in mathematics in contrast to the axiomatic approach favored by Badiou. (“Mathematics and the Theory of Multiplicities”). The difference becomes clear in Deleuze and Guattari’s very definition of the nondenumerable: ‘What characterizes the nondenumerable is neither the set nor its elements; rather, it is the connection, the “and” produced between elements, between sets, and which belongs to neither, which eludes them and constitutes a line of flight.’ (TP 518). The nondenumerable is problematic, for Deleuze, precisely because it constitutes problems that have, as Smith puts it, ‘an objectively determined structure, apart from its solution,’ and this objectively determined structure entails ‘a zone of objective indetermination’ that precludes being reduced to demonstrative and axiomatic methods in mathematics. The ‘genetic and problematic aspect of mathematics…remains inaccessible to set theoretical axiomatics,’ and yet, through continual movements and translations, the problematic in mathematics gives way to axiomatic innovations and recodings (Smith offers the example of the translation of infinitesimals and approaching the limit in calculus [an example of the problematics tradition] into the axiomatic epsilon-delta method as developed by Weierstrass). We have in short what you might call Deleuzian supervenience, whereby the discretization of the axiomatic maps or supervenes upon the continuity of the problematic, but the problematic forever exceeds the axiomatic, it is the ‘power of the continuum, tied to the axiomatic but exceeding it.’ (ibid. 466). Axiomatics, or what Deleuze will also call major or royal science, thus draws from problematics the necessity of inventing and innovating in response to the ‘objectively determined structure’ of the problem. Similarly problematics, minor or nomad science, calls upon axiomatics to actualize the solutions it lays out, if only indeterminately so. Deleuze and Guattari are clear on this point: ‘Major science has a perpetual need for the inspiration of the minor; but the minor would be nothing if it did not confront and conform to the highest scientific requirements.’ (ibid. 486). We can thus rethink Lewis’ problem of induction not as a problem intrinsic to the relationship between a finite cognizer and the distribution of qualities as they relate to this cognizer, but rather as an ‘objectively determined’ problem that exceeds the tools of modal realism and axiomatic logic. Lewis, in short, is encountering the necessity and insufficiency of invention. In the next post we’ll see that one interpretation of why Spinoza abandoned his Treatise on the Emendation of the Intellect was precisely because he, like Lewis, encountered the necessity and insufficiency of invention.

Is Deleuze a Speculative Realist?

At first it might seem he is. If Bruno Latour is on the right track with respect to speculative realism, as Graham Harman and others would argue, then it might seem that Deleuze is on the right track as well for there are a number of areas where their philosophies converge in significant ways – especially concerning events, multiplicity, and their embrace of an ontological monism. I cover much of this in Deleuze’s Hume. It would also seem that Deleuze would not be a “hyper-incommensurable” postmodern philosopher as Latour discusses this in We Have Never Been Modern. Not only does Lyotard, for example, continue to embrace the incommensurability between humans and nonhumans, but will go even further and claim that ‘there is nothing human about scientific expansion,’ thus radicalizing the incommensurability (hence the ‘hyper-‘). Deleuze, by contrast, moves with ease in discussing human and nonhuman assemblages. The frequently used example of an assemblage – man-horse-stirrup – is a case and point of Deleuze (and Deleuze and Guattari’s) readiness to at the very least blur if not eliminate the incommensurability between humans and nonhumans.

Then there is Quentin Meillassoux’s critique of the correlationists. One of the central planks of the SR platform is the critique of correlationism. Kant is frequently singled out as the subtle grandmaster of correlationism (the final chapter of After Finitude sets out to undermine [and correctly so I might add] Kant’s Copernican revolution). But Meillassoux doesn’t simply have his sights set on Kantians; rather, he sees much if not all of the post-Kantian philosophical tradition as beholden to certain correlationist assumptions, or to what Harman calls a ‘philosophy of access.’ Most notably, the correlationist philosopher thinks that our only access to objects is through thought. Thus, we cannot think the thing in itself but only as given to thought, as a correlate of thought. As Meillassoux points out, however, a correlationist is not necessarily tied to a subject-object metaphysics, to a hypostasized subject and object in the manner of Descartes; rather, what is central to correlationism, at least since Kant, is ‘not a metaphysics,’ but rather ‘it invokes correlation to curb every hypostatization, every substantialization of an object of knowledge which would turn the latter into a being existing in and of itself.’ (After Finitude, p. 11). Correlationists, in short, cannot think an object as it is in itself and correlationism assures the impossibility of ever thinking an object in itself.

With Deleuze, for Meillassoux, we have a classic example of an attempt to ‘curb every hypostatization,’ and moreover we have in Deleuze and Nietzsche ‘the vitalist hypostatization of the correlation’ as an integral aspect of their critique of metaphysics (ibid. p. 37). Without addressing the fact that Deleuze never saw himself as part of the ‘critique of metaphysics’ tradition, the question remains: is Deleuze hypostatizing the correlation with his notion of life and his emphasis upon process and becoming? In other words, if there are for Deleuze no objects, if objects are merely abstractions of a flux, much like Bergson’s snapshot photographs were abstractions of duration (duree), then objects would indeed simply be correlates and abstractions of becoming. Deleuze would thus be a strong correlationist, as Meillassoux argues, or a hyper-correlationist as Latour might argue. As for Kant it is impossible to think the object in itself but only as a phenomenal correlate of thought, is Deleuze a strong correlationist who, as Meillassoux argues, that ‘it is unthinkable that the unthinkable is impossible’? (ibid. 41). If there remains something that is unthinkable, namely becoming, and if it is indeed unthinkable that this unthinkable is impossible, then Deleuze would most definitely not be a speculative realist since a central task of SR is to think objects in themselves.

But what does it mean to think an object in itself, or as Meillassoux puts the problem, an object that is anterior to givenness itself? Put simply, it is to think the absolute, to think that which is not limited by being given to a consciousness, to a historical situation, discourse, etc., but to think the absolute in itself. This absolute, however, is not to be an absolute becoming, life, or will to power, for then we would be back in correlationism. Rather, the absolute, for Meillassoux, is contingency itself, or, as he puts it: ‘The absolute is the absolute impossibility of a necessary being.’ (Ibid. 60). It might seem that Deleuze would agree on this point, but it is precisely here where Deleuze would stumble, for in absolutizing becoming he ultimately calls upon a necessary being, a contradictory, paradoxical being. Meillassoux is quite clear on this point (as he is with most of the points he makes): ‘the utterly Immutable instance against which even the omnipotence of contingency would come to grief, would be a contradictory entity. And this for the precise reason that such an entity could never become other than it is because there would be no alterity for it in which to become.’ (ibid. 69). It would already include its contradictory other and thus such an entity would be a necessary being and hence undermine contingency itself. It is for this reason that to think the absolute one must not think it as becoming, if for becoming ‘things must be this, then other than this; they are, then they are not.’ (ibid. 70). ‘The only possibility of introducing difference into being, and thereby a conceivable becoming, would be by no longer allowing oneself the right to make contradictory statements about an entity.’ (ibid. 71). In the end, it is only through mathematics that one can think the absolute as the contingent without contradiction, and philosophers of becoming such as Deleuze, Bergson, and Nietzsche continue to affirm the right to utter contradictions, much as did their intellectual progenitor Heraclitus.

Deleuze’s philosophy, however, is not to be confused with Bergson’s and Nietzsche’s, despite the influence of the latter two on Deleuze’s own thought, and for Deleuze to think difference in-itself, as he claims is the central task of his philosophy in the early pages of Difference and Repetition, is not to think or to affirm a contradictory entity. As alluded to in my earlier post on Badiou and Spinoza, Deleuze rejects the idea that there is an identifiable difference, much less an identifiable contradiction, between two entities that it is the task of philosophy to think. This is not what it means to think difference in itself according to Deleuze. At the same time, identity for Deleuze is not merely a correlate of difference. Deleuze, however, does speak of the impossibility of thought, of an unconscious that is understood to be ‘something that cannot be thought in finite thought.’ (Fold, p. 89), or he will write in Cinema 2, in reference to Artaud and Blanchot, that “what forces us to think is ‘the inpower [impouvoir] of thought’, the figure of nothingness, the inexistence of a whole which could be thought.” (C2, 162). This impossibility and unconscious that thought itself cannot think but forces thought is not a necessary being (e.g., duration, becoming, will to power, a life etc.) relative to which what can be thought would merely be correlates of this necessary being. To the contrary, and much in line with Meillassoux, that which ‘cannot be thought in finite thought’ is ‘the absolute impossibility of a necessary being’, to quote Meillassoux again. It is ‘the inexistence of a whole which could be thought,’ or as Meillassoux understands it, adopting Cantor’s definition of transfinite numbers, ‘the (quantifiable) totality of the thinkable is unthinkable.’ (AF, 104). And the unthinkable nature of the totality is key to avoiding correlationism, for it is mathematics, especially Cantorian set theory, that is able to theorize the non-totalizable, the ‘non-All’ – hence Meillassoux’s conclusion that ‘what is mathematizable cannot be reduced to a correlate of thought.’ (ibid. 117). To the extent that Deleuze too theorizes the ‘inexistence of the whole,’ what Deleuze and Guattari will also refer to as the ‘nondenumerable,’ then it would seem that we would be too hasty to exclude Deleuze from the speculative realist camp. Moreover, as was argued in the Spinoza post, the non-denumerable, the ‘inexistence of a whole’ (i.e., or the attributes as discussed there) is not separable and distinct from the denumerable (the modes) and that which is thought. There is nothing but objects and events, both human and nonhuman, and there is no incommensurability between them nor are they totalizable in a way that would return us to claiming that objects and events are correlates of a necessary being. Deleuze is not a correlationist. But is he a realist? That will have to wait for another post.