Atheology has just put up another post on my interpretation of Deleuze, this time based on my more recent paper ‘Ariadne’s Thread: Temporality, Modality, and Individuation in Deleuze’s Metaphysics’ (available here). It’s a very generous and thorough reading of the paper, in relation to the other things I’ve written about Deleuze on the blog. Though he expresses a certain dissatisfaction with the unfinished character of the essay (it was written for an hour length presentation, and alas, was inevitably consumed by preliminaries) in parallel with his dissatisfaction at the unfinished character of my posts on Deleuze and Sufficient Reason (available here), he also says:
This strikes me as an extremely promising angle of approach and one which could easily yield a book-length treatment, perhaps under the title Ariadne’s Thread: Deleuze and the Song of Sufficient Reason. For me this approach represents tangible progress in the study of Deleuze’s thought.
I can only feel humbled by such praise, and would love to write this book one of these days. Alas, I am stuck in the same position as many of my compatriots, unsure as to which aspects of my work will lead to stable employment, so it’ll have to wait for now. That being said, I do intend to extend the ‘Ariadne’s Thread’ paper for publication at some point, once a few other commitments are out of the way. As such, the comments in Atheology’s post are very helpful and useful. However, there are a number of possible misunderstandings and points that can be addressed quickly, and so I will endeavour to do so here. I’ll try to number the points to keep them brief and organised.
1. The Existence of the Plane of Immanence
Atheology slightly misunderstands my position on this point when he says:
Deleuze’s atheism requires that we remove the last vestiges of equivocity from Spinozism, which means that Deleuze’s equivalent of Substance “cannot under any circumstances be said to exist.” (p. 14) Given this requirement, the first question to ask is this: does the virtual or the plane of immanence exist? The answer, apparently, is that they exist but not qua Whole, i.e. not qua actual infinite.
The problem here is that I think the question of whether the plane of immanence (POI) exists is parallel to the question of whether the world exists, or more specifically, to a question like whether space exists. I think there’s something fundamentally problematic about all these questions, because to exist is in some sense to be situated in the world, or a space of some kind. This is a theme that I work out quite explicitly in the paper, and it’s crucial to my interpretation of how Deleuze transforms the problem of universals. To recapitulate this briefly, Deleuze says that we should cease to think of universals (e.g., doghood) by analogy with individuals (e.g., fido), and instead to think of them as conditions of individuation (i.e., space and time). This is to say that we should think of universals not as existents within the world, but as conditions under which things exist within the world. The plane of immanence is just the limit of this, insofar as it is supposed to encompass all universals and the information that they immanently encode within themselves.
So even if we can sort of make sense of questions as to whether a particular universal exists (e.g., does doghood exist? or does humorousness exist?), analogously to the question of whether a particular space exists (e.g., is there an absolute edge of space?), these are really questions about the structure of the world understood as the set of conditions in which entities are individuated (e.g., are these dimensions (x/y/z) finite in extent, infinite in extant, or do they loop back upon themselves?), rather than questions about discrete entities. Put simply, we are asking ‘is the world like this?’ rather than ‘does the world contain this?’. Once we understand this, it’s clear that there is no analog for the question ‘does the world exist?’ insofar as it doesn’t ask about any structural feature of the world. To make sense of it, one would have to have some set of conditions outside the world in terms of which to locate it (or fail to). One would need to treat the world as contained within a sort of meta-world in order to raise the question of its existence, which is obviously a terrible metaphysical regress.
Another way of thinking about this is to treat it as analogous to the question ‘where is space?’, to which the only sensible answer is ‘here’. The conditions of individuation don’t need to be individuated in terms of some meta-conditions of individuation, but are self-individuating, in precisely the sense that space contains itself. It is understanding this point and developing it properly that I take to be the crucial advance that Deleuze makes upon Spinoza.
2. Potential Infinity and Sufficient Reason
The next problem is in the way my claim that Deleuze moves from understanding the PSR in terms of actual infinity to understanding it in terms of potential infinity is interpreted. I think this is largely my own fault for not making explicit the delicacy of the interface between epistemology and metaphysics that the PSR deals with. Here is the relevant quote from Atheology:
To posit a potentially infinite series is in effect to say that we can approximate to an arbitrary degree the consequences of God’s existence. More prosaically, a potentially infinite series is usually understood as one that could continue. But how to understand the modal term (‘could’) here? My worry is about whether it makes sense to distinguish sharply between potentiality and possibility. That is what you have to do if you are serious about using potential infinity as a surrogate for actual infinity, i.e. if you are serious about replacing Spinoza’s Substance with something that cannot under any circumstances be said to exist qua actual infinite. But then it follows that every potentially infinite series is finite in every possible world, and the potentiality of such series begins to seem ephemeral and dubious. On the face of it, it looks like potentiality has possible being in some other sense than possible existence per se. But that seems to violate PUB. I don’t know – maybe I’m making a mistake somewhere here. In any case, I would like a little more light to be shown on Deleuze’s appropriation of this strategy.
This is a very good objection to a position that, alas, is not mine. To see this it is important to understand what the principle of sufficient reason does: it makes the actual state of the world in principle intelligible. This intelligibility is a matter of providing every state with a ground (metaphysics) that can be understood as a reason (epistemology). These grounds are then understood either temporally as efficient causes or atemporally as immanent causes, though I’m going to sideline this distinction for now and focus principally on efficient causes. All the problems result from how we interpret the ‘in principle’ aspect of the above stated goal. This is because the metaphysical side confronts us with an infinity of causes (at least, Spinoza, Leibniz and Deleuze are agreed on this), while the epistemological side confronts us with a finite procedure for articulating and understanding these causes as reasons. The difficulty of the PSR is reconciling the infinity of the world with the finitude of the mortal mind.
Spinoza and Leibniz overcome this difficulty through ontological equivocity – they insist that thought/mind/reason comes in two flavours: temporal/mortal/finite and atemporal/divine/infinite. It’s important to recognise that this is problematic not just metaphysically, insofar as it falls into the trap of onto-theology, but also epistemologically, insofar as it relies on an implicit understanding of the genus of reason that is not tied to anything like an account of procedures for reasoning. To describe this in another way, Spinoza and Leibniz make the world in principle intelligible by positing an absolutely distinct form of intellect that is capable of grasping the actually infinite chain of causes as an actually infinite chain of reasons. This is an ad hoc posit, because they do not develop their conception of infinite reason out of a conception of finite reason.
I can now frame my interpretation of Deleuze’s transformation of the PSR properly. Unlike the position that Atheology criticises above, I do not think that Deleuze overcomes the above difficulty by simply substituting potential infinity for actual infinity across the board: taking there to be a potentially infinite chain of causes that is graspable as a potentially infinite chain of reasons. He is entirely right that this position is incoherent, insofar as its not clear that we can make sense of a potential infinity on the metaphysical side here. Rather, I interpret Deleuze as taking there to be an actually infinite chain of causes that is graspable in terms of a potentially infinite process of reasoning. This has to be cashed out a bit, because it is a completely different approach to the ‘in principle’ discussed above. The crucial concept is that of limit. This provides the connection between finitely specifiable procedures and actually infinite results. Take the procedure ‘beginning with n=1 add n/2 to n and repeat’. This is the classic example used to introduce the concept of limits to young mathematicians, insofar as, although the procedure will go on indefinitely (a potential infinity), we can understand it as approaching a fixed result (an actual infinity), in this case n=2. This idea can of course be worked out in more detail than I am capable of accounting for, but this should suffice for now. I interpret Deleuze as holding that the finitely specifiable procedure of reason, through which we successively uncover the chains of causation underlying given state of affairs, can be indefinitely iterated in this way, and that, as such, we can conceive it as approaching the actual infinity of causes as a limit. This contrasts to the ad hoc approach of Spinoza and Leibniz insofar as the connection between metaphysical infinity and epistemological finitude is generated out of finitude itself, as an immanent projection of its procedure, rather than a transcendent supplement to it.
This doesn’t answer all the difficult questions by any means. I think that this strategy requires a lot more detailed work on the actual structure of the finite procedures that constitute causal reasoning than Deleuze ever did. However, I do think that it is the right strategy, and that it is a key part of avoiding the metaphysical pitfalls of onto-theology on the one hand and negative theology on the other.
3. Time and Emergence
The questions of time and emergence are where Atheology has the most legitimate concerns. This is largely because the bits of the story that are supposed to deal with the details here haven’t yet appeared, for the above discussed reasons. I’m not going to make them magically appear here, but I will make a few suggestive points:
i) Space and Emergence: One of the crucial things I didn’t really have time to address in the MMU paper was the claim that Deleuze sides with Leibniz on the question of space. The point I was trying to make is that the extensive spaces that must be added to the qualitative dimensions of the phase spaces in order to get a concrete universal (i.e., to adequately individuate the instance of that universal) are not independent of the qualitative dimensions, but are co-determined with them. This is the really tricky stuff that Deleuze gets into in chapters 4 and 5 of Difference and Repetition in talking about the intensive spatium and the generation of extensity. There is so much work to do here it’s almost painful to contemplate it, including some serious exegetical work on Heidegger and Merleau-Ponty on space. However, the basic intuition is very simple: new spaces emerge along with new qualities, as different perspectives upon (or ways of individuating discrete entities within) the same unitary informational surface. This is basically Deleuze’s reinterpretation of Spinoza’s notion of an attribute on the one hand, and his appropriation of Leibniz’s concept of ‘world’ in Logic of Sense on the other. This does not mean that space is an epiphenomenon by any means.
ii) The Unity of Time: I want to council against a certain reading of my account of the pure and empty form of time (Aion) Atheology puts forward:
In a nutshell, unlike space time is not an epiphenomenon or near-epiphenomenon for Deleuze. What is spatially divergent is temporally unified by the enigmatic pure and empty form of time. What this means is that time is not only inscrutable but irreducible or emergent in some sense.
Aion isn’t emergent in any useful sense. The point is that it binds the various universals together insofar as they must lack a time dimension in order to encode the information they encode, both about the virtual potentialities (the pure past) and actual states (the pure present) of systems. It is this single time that opens these systems to external shocks the modality of which is not encoded within them, though demonstrating this point is going to take a lot more work. Regardless, I should probably complicate the single time/many spaces schema I presented at the end of the paper, as it can cause a lot of confusion. In truth, it is more like Deleuze’s metaphysics incorporates a fourfold distinction between plurivocal space (Ideas), plurivocal time (Chronos), univocal space (POI), and univocal time (Aion). The reason I emphasise plurivocal space and univocal time in the paper is that these are the aspects of the schema that seem to have explanatory priority.
Another way of thinking about this (which I owe to discussions with Reza Negarestani) is to understand the plurivocal/univocal distinction in both cases in terms of the discrete/continuous distinction. We start from thinking about how we individuate discrete entities in local contexts (Ideas), and the moves necessary to think the real modal features underlying this individuation then necessitate thinking about a continuous global time (Aion), which forces us to think about the continuous global informational surface (POI) which encodes all of the limited informational viewpoints contained in the discrete local contexts, and its continuous transformation in this global time, which finally leads us to try and understand how the temporally discrete procedures through which we individuate this information are themselves situated (Chronos). This is an awfully complex metaphysical path to follow, but I’ll endeavour to work out a better way through it in the future.
However, I will close with the tantalising suggestion that this path represents the proper approach to the ‘in principle’ of the PSR discussed above. The point is to move from an epistemological understanding of the discrete processes of causal reasoning and the finitely specifiable procedure they instantiate to a metaphysical understanding of the projected limit which these processes approach, and this limit is nothing other than the continuous informational surface of the POI and its continuous transformation in the empty time of Aion. This is an approach to emergence which aims to reconcile it with the PSR by adequately balancing the methodological demands of epistemology and metaphysics that it bridges.