reply to wolfendale

Pete Wolfendale has written a good response to my post on his draft paper ‘Ariadne’s Thread: Temporality, Modality, and Individuation in Deleuze’s Metaphysics’. I certainly appreciate the (by now trademark) time and care he puts into his blogging. As another recently minted PhD with no stable employment, I am sympathetic with his biographical comments – in any case, I don’t want to pressure him into making the details of his account “magically appear” before they are ready. Nor could I, even if I wanted to, since my objections are also preliminary in nature. In any case, this will be my last post in this series, though I look forward to interacting more with Pete in the future.

1. The Existence of the Plane of Immanence

Wolfendale suggests that I misunderstand his position regarding the existence of the plane of immanence (POI), and I think he is right, though perhaps not exactly in the sense he thinks. According to Wolfendale, there is something fundamentally problematic about asking whether the POI exists, analogous to how there is something fundamentally wrong with asking where space is. Rather, “to exist is in some sense to be situated in the world, or space of some kind.” Wolfendale continues:

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.

Let us see how this understanding of existence and individuation works in the case of numbers, which are paradigmatically abstract objects. Referring to Levi Bryant, Wolfendale writes in an earlier post on the plane of immanence:

Take for example his concern with whether numbers exist. Of course, he has himself said that he is not sure whether numbers exist, whereas Harman explicitly affirms the existence of numbers. However, for Deleuze, this would not even be a legitimate question. For anything to exist it must be theoretically possible to situate it within the causal-mereological network that criss-crosses the plane. For numbers to be candidate entities one would not only have to be able to posit the parts out of whose interactions [numbers] are constituted, but one would have to show how it is that there could possibly be indirect causal interactions between numbers and other entities, and importantly, this means being able to show in principle that these interactions can be manifest in the interactions of their parts with other things (all the way down, as in our bank teller example).

Now, how does this characterisation of existence, together with what Wolfendale says about individuation and self-individuation, underwrite his charge of misunderstanding?

I take it that the misunderstanding Wolfendale attributes to me is something like this: I erroneously read him as asserting that the POI is an existent, absolutely infinite individualWhat specifically is the error here? Not, surely, the description of the POI as absolutely infinite, since on Wolfendale’s account there is, for Deleuze, an “actually infinite chain of causes” (italics removed).

Putting this aside, is the problem with only one of the remaining characterisations, or both? It seems to be both, as they are connected. Hence, on the one hand, the POI is not an individual – or at least not a non-self-individuating individual. It is rather a self-individuating condition of existence within the world. On the other hand, Wolfendale thinks it is fundamentally problematic to ask whether the POI exists, the reason being that existence means something like being situated or being a space of some kind.

With both of these hands we can then reach for the conclusion that the POI is not the right sort of thing whose existence we ought to inquire into – which in turn has two readings, simple and subtle.*

The simple reading, which I return to in a moment, is that the POI does not, strictly speaking, exist. This comes in two flavours: (a) the POI does not exist at all, and (b) the POI does not exist in the world.

According to the subtle reading, Wolfendale is saying that we lack the ability to mean anything determinate when we talk about whether the POI exists or not. Without meaning we lack truth-value, hence strictly speaking the POI neither exists nor does not exist.

Against this reading we can marshal two points:

(1) Wolfendale himself tells us briefly what it might or could mean for it to be either true or false that the POI exists:

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.

(2) He gives a characterisation of ‘exists’ that allows us to say that the POI does not, given that characterisation, exist.

A final difficulty for the subtle reading is that the sort of semantic claim it involves is hard to defend. Nevertheless, supposing these points can be set aside, the benefit of the subtle reading is that it avoids, or seems to avoid, the antinomic consequences of the simple reading, which I shall describe presently.

In trying to understand my own misunderstanding of Wolfendale’s position (and it is clear to me that I did not grasp it properly), I am led to highlight the following ambiguity in his description of that misunderstanding. First we are given what looks like a definition: “to exist is in some sense to be situated in the world, or space of some kind.” Given this definition, the POI does not exist. Yet what Wolfendale actually says is that the POI does not exist within the world, as if there is some other sort of existence for it to have. Now, I’m uncertain what the significance of this ambiguity is, but it seems to me that if the POI is the sort of thing that can be rightfully said to exist in some sense, then it is also the sort of thing whose existence can be legitimately inquired into in that sense. Whereas it is prima facie ad-hoc to deny the legitimacy of this inquiry tout court whilst issuing a merely qualified denial of the existence of the POI.

As I see it, my real misunderstanding was this: I read Wolfendale as working with an unrestricted concept of existence. By ‘unrestricted’ I mean that if x does not exist then there is no x, i.e. x is nothing at all. In this sense of existence, we cannot say that x does not exist and is the sufficient reason of y, since if x is the sufficient reason of y then (plausibly) x is something, and hence exists (in the unrestricted sense).

As Williamson notes (2013: 18-9), ‘exists’ also has various restricted uses, which can create confusion.

For example, one might naturally say ‘Events do not exist; they occur’. In saying so, one does not imply that there are no events, as one would on an unrestricted use of ‘exist’.

For Williamson, the logically interesting sense of ‘exists’ is the unrestricted one, and this is something I suppose I have taken over more or less unreflectively.

As I see it, what is problematic is the very distinction between being and existence that appears to underwrite Wolfendale’s account. This distinction is functioning when Wolfendale characterises existence in terms of situatedness, unless he is prepared to assert that things that are not situated are nothing at all. But since the POI is for him a sort of structural feature of reality, it is clearly not nothing at all.

Thus when I say that the POI exists for Wolfendale, I mean that it has being per se, i.e. it is something rather than nothing. Proceeding univocally from this starting point, I take it that modernising Spinoza requires denying that Substance has being – and not only that it exists (in the restricted sense) – as well as refusing to replace Substance with anything, even a non-existent (in the restricted sense) thing. It is actually quite possible that I am just mistaken on this point. Anyway, this line of thought provokes an interesting reframing of my guiding question: does Deleuze intend a univocity of being? Or does he intend a univocity of existence premised on an underlying equivocity of being?

2. Potential Infinity and Sufficient Reason

Wolfendale has helpfully clarified his position and corrected my misunderstanding of it. I had taken him to be saying that actual infinity is to be replaced by potential infinity both ontologically and epistemically, whereas it turns out that he has only the latter replacement in mind. However, notice that in the above I gave myself the means of reformulating my core objection, according to which there is a violation of PUB in Wolfendale’s account of the POI, such that it does not depend upon characterising the latter in terms of (ontological) potential infinity. The objection is this: whether or not POI exists in Wolfendale’s restricted sense, it clearly exists in the unrestricted sense, i.e. it has being. As far as I can see (and perhaps here we have unearthed a substantial disagreement), this distinction between being and existence is forbidden by the PUB. From my perspective, Deleuze employs a restricted use of ‘exists’ in order to give the illusion of compatibility between univocity, immanence and sufficient reason.

3. Time and Emergence

Wolfendale explains that he does not understand Aion to be emergent “in any useful sense”. Upon reflection this is obvious, and I was not being careful enough when I wrote that time is emergent. I wrote principally on the basis of two bits of information: (1) in an earlier post on the plane of immanence mentioned above, Wolfendale writes several passages suggestive of a strong (or strongish) account of emergence, for example:

The important point is that athough the individual interactions between higher-level entities are always manifest in particular interactions of their parts, the general form of such interactions is not easily (or even possibly) modelled in terms of those kinds of interactions. This is what emergence consists in: the genesis of new general forms of systematic interaction which are irreducible to the general forms of systematic interaction that they are manifest in.

(2) I find it hard to draw a sharp, general distinction between Leibniz and Kant without saying that relational or phenomenal properties are contingently held or instantiated (by things in themselves).

Putting these together, I glossed the unity of time, as that which constitutes Deleuze’s siding with Kant over Leibniz, in terms of the emergence referred to by Wolfendale in (1), and posited by me (following e.g. Langton) in (2).

*Sorry about the complexity here.


  • Timothy Williamson, Modal Logic as Metaphysics, (OUP: 2013).
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2 Responses to reply to wolfendale

  1. deontologistics says:

    Great post again, and I think you’re right that we should probably leave the exchange here. I’ll respond to a few of your points briefly though, as I think there’s some worthwhile things to be said quickly:-

    1. I’m definitely advocating a *subtle* position. Retrospectively I see how the confusion can emerge here regarding restricted and unrestricted notions of existence. This is something I’ve worked on so much that I’m sometimes forget to make all of my prior commitments explicit, especially in the context of exegetical work such as my interpretation of Deleuze. I’ve elsewhere developed a distinction between a generic notion of existence (belonging to logic) and a real notion of existence (belonging to metaphysics). I briefly gloss this idea at the beginning of the Deleuze paper, but I discuss this in much more depth in my Essay on Transcendental Realism ( I also deal with some of the more complex philosophy of logic issues in the last chapter of my thesis on Heidegger ( The real upshot of this is that I have a story about mathematical objects such as numbers which allows us to say that they exist in the generic sense, but that they are not real in the strong metaphysical sense. This applies to other things such as fictional objects, propositions, and numerous other so called pseudo-existents.

    2. This point being made, I don’t think it’s relevance to my points about the difference between conditions of individuation and individuals is quite what you make of it. I should explicitly state that when I’m talking about the ‘plane of immanence’, I’m talking about ‘the world’, or at least a fundamental aspect of its structure. There is obviously room to debate the whole appropriateness of this Deleuzian metaphysical viewpoint, but my subtle semantic point is that this is a debate about whether the world has this particular structure, rather than whether this or that particular posit exists in a manner that is usefully analogous to the existence of individuals. Perhaps a better way of phrasing the question, given my larger semantic story, would be: is the plane of immanence real? But this involves recognising the complicated equivocal structure of ‘real’, as opposed to the univocal structure of ‘existence’. Given the connection I draw between the notion of ‘reality’ and the notion of ‘being’ this might raise potential concerns about my advocacy of PUB, but I think such worries are overblown, insofar as I explicitly define the strong version of univocity in terms of the addition of a univocity of existence to a univocity of predication. I don’t think pushing univocity any further really makes much sense here, once you understand the issues at play in providing an account of Being (again, see my dissertation).

    3. I can’t blame you for any misunderstanding regarding my use of the term emergence. I left it out in the Deleuze paper because, although I think it’s a crucial issue which is definitely connected to all this, it’s such a loaded theoretical term, which can be interpreted in so many specific ways, that I’m not sure how best to describe the position I’m articulating in those terms. Nevertheless, I think the terrain of the PSR is the correct place to address these issues, insofar as it is the crucial connecting point between the relevant metaphysical and epistemological issues.

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