wolfendale, ariadne and deleuze’s song

In this post I (selectively) exposit and discuss Pete Wolfendale’s unfinished paper ‘Ariadne’s Thread: Temporality, Modality, and Individuation in Deleuze’s Metaphysics’. Although rich and well worth reading, I struggled to see where it addresses my worries about combining sufficient reason and univocity (and immanence).

Wolfendale’s paper has two main parts with a hinge connecting them and a brief introduction. The first part introduces three metaphysical problems: universals, modality and individuation. The hinge quickly situates Deleuze historically and gives a telling thumbnail sketch of his core motivation, which prefaces description of his contribution to each metaphysical problem in part two of the essay. The format works well, but here on my blog I’m going to mix it all together, beginning with the following characterisation of the basic problem-landscape as Wolfendale and I both evidently see it (p. 8):

The metaphysical debate regarding the nature of probability tends to focus upon whether or not it is reducible to our ignorance of the totality of causal constraints, or whether there is something like real chance over and above this ignorance. The core issue here is the question of whether every determinate state has a sufficient reason (PSR). If one accepts PSR, then it is much easier to maintain that chance is purely epistemic, even if it is based upon an ignorance that only an infinite intellect could overcome (e.g. Spinoza’s Substance or Leibniz’s God), but this threatens to collapse into and undermine the metaphysics of possibility on which it is founded. Once one acknowledges that there is always a reason why the actual world is in one state rather than another, it becomes hard to defend the thesis that possible states are any more real than probable ones. This is the fine line across which Spinoza and Hume stare at one another. If one denies PSR, then it is much easier to maintain that chance is properly metaphysical, even if it is something extrinsic to possible states that selects which ones to actualise, but this threatens to collapse the various local points of chance into a single global chaos which determines everything. One risks trading an epistemology of ignorance for a theology of contingency.

Wolfendale endeavours to give a reconstruction of Deleuze’s metaphysics that would allow us to pass between these two horns.

We must treat Deleuze in the same way he treated Spinoza, Kant, Nietzsche and especially Bergson: we must aim to present him in a more accessible and consistent fashion than he himself ever managed.

As just noted, the guiding thread of Wolfendale’s reconstructive efforts is the attempt to calibrate the Principle of Sufficient Reason (PSR) with the Principle of the Univocity Being (PUB) and the Principle of Immanence (PIM). (It is implied on p. 14 that Deleuze infers immanence from sufficient reason and univocity, or else saw in some looser sense that the former follows naturally from the latter.) 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.

Regarding the historical background of Deleuze’s project, Wolfendale writes that Deleuze’s system represents an “attempt to rewrite Spinoza’s metaphysics after Heidegger’s critique of onto-theology.” (p. 12) Following this is a good characterisation of Deleuze’s core motivation in terms of the three principles mentioned in the previous paragraph: “…it is no exaggeration to say that Deleuze takes his philosophical task to be to make [sufficient reason] compatible with atheism.” (p. 13)

The explanation that follows of what Deleuze takes to be missing from Spinoza’s position is also very good: Spinoza views Substance and modes as distinct types of existent, to which certain logical categories apply analogically, specifically the categories of quantity, causation and time (pp. 13-4). Following Spinoza and Leibniz we reach very quickly the “metaphysical essence of theism” that Heidegger critiqued.

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. Here the distinction between actual and potential infinities is introduced. However, it is hard to identify the ingredients of an answer to my objection to the use of this distinction, formulated here.

Here is a restatement of that objection. 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.

Moving on, the first problem Wolfendale discusses in his paper is that of universals. Do universals exist, and if so in what sense? If doghood exists, is this in the same sense that a particular dog exists, or some analogous sense? Given PUB, analogy is the enemy here, but obviously doubts about Platonism can be independently motivated. So say we reject the premise that universals exist in some special Platonic heaven. As Wolfendale notes (p. 5), this alone doesn’t quite get us out of the woods. If the universals do not exist in some intelligible realm, then where? Aristotle brought them into the sensible realm, but his account does no better than Plato’s in explaining how the universals are themselves individuated. What we should instead be asking, according to Wolfendale, is “whether universals are conditions of individuation in a way similar to space.” (p. 14)

Wolfendale mentions the famous debate over the identity of indiscernibles, which is a disagreement over what is sufficient for complete individuation. Here is his characterisation of Leibniz’s position (p. 4):

Leibniz’s really challenging claim is that the thing’s spatio-temporal location is unnecessary for individuating it, and that it can be deduced entirely from the list of its non-spatio-temporal properties.

This should presumably be read as saying that Leibniz reduces spatio-temporal properties to non-spatio-temporal ones. This reduction seems to be both epistemic, meaning the former are scrutable from the latter, and ontological, meaning that the former are epiphenomenal. Kant’s position is then glossed as asserting that we need spatio-temporal information to individuate something.

On Wolfendale’s reading, Deleuze splits the difference between Leibniz and Kant in the case of space, and sides with Kant in the case of time. That is, (1) Deleuze agrees with Kant that individuation requires supplementary spatial information, so that individuals are inscrutable without the latter – but that nevertheless (2) there is no “single system of spatial dimensions common to all concrete universals”, meaning that space ends up being epiphenomenal, or almost epiphenomenal, after all (p. 19). Finally, (3) Kant get’s the last laugh: whereas there is a “plurivocal metaphysics of space”, there is a “univocal metaphysics of time” (p. 21). This key point only receives one paragraph of discussion, and it is to be hoped that Wolfendale elaborates upon it in future drafts of the paper.

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. To understand this point, consider the distinction Wolfendale proposes between Leibniz’s ambition and Deleuze’s adaptation of it. Leibniz thought that the individuation of monads could be understood in terms of the individuation of numbers: the natural numbers do not occupy points along the line of succession, “as if their mathematical properties could somehow be pulled apart from their location. They simply are the points along the line of succession, and nothing more.” The ambitious suggestion is that “our propositions (monads) may be individuated in precisely the same way that numbers are, and that this may be done without appeal to either space or time as they are traditionally understood.” (p. 15)

What does Deleuze have to say about this, according to Wolfendale? As for Leibniz so for Deleuze: the actual world is to be thought of as a sort of informational surface. But on Wolfendale’s reading (p. 16), Deleuze learnt from Bergson that there are types of analog information that are not convertible to digital information, which at least blocks the inference of scrutability (unless the latter is taken to mean only what a Turing machine could compute at infinity). Whether it is fair to read Leibniz as denying this is not presently important. What is important is how this disagreement should be articulated in the case of time, since here Deleuze denies not only the scrutability of individual concepts from non-spatial information, but also the reducibility of temporal information to non-temporal information. The reason why I want to press this is because irreducibility and emergence, if understood strongly enough, entail the falsity of the PSR, and my basic suspicion is that Deleuze cannot preserve univocity (PUB) and immanence (PIM) without understanding the pure and empty form of time in such strong terms.* Does Ariadne’s thread really lead us out of the labyrinth, or are we merely sweeping the problem of calibrating sufficient reason with univocity and immanence under the rug of Aion?

* That Wolfendale does have something like emergence in mind is clear from an earlier post on Deleuze’s notion of the plane of immanence over at his blog, here.

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One Response to wolfendale, ariadne and deleuze’s song

  1. Pingback: More Atheology on Deleuze | Deontologistics

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