Let me begin with a good quote:
My thesis is that Deleuze’s commitment to the strong principle of univocity – the claim that there is only one kind of existence – precludes him from grounding the principle of sufficient reason in such an onto-theological way. This is because in both cases [i.e. Spinoza and Leibniz], there is a being with a unique ontological status (i.e God, which consists in the existence of all other beings being thought in terms of it), which implies that it exists in a different way to other beings, and the infinite intellect of this being is used to ground the complete intelligibility of causation. The strong principle of univocity precludes the reconciliation of the order of thinking and the order of Being through a special kind of being.
What is especially good about this passage is the focus on univocity. Univocity here just means that we are positing a single sort of existence. (Ignore for now the apparent implication here, that univocity just is the collapse of modalities, which it would then be question-begging to posit rather than argue for.) Without univocity as a premise, we are left trying (in Findlay’s words) to catch the analogical eel (i.e. God) in our dialectical net. So let’s go ahead and help ourselves to it.
Wolfendale’s basic thesis is then this: Deleuze takes univocity more seriously than Spinoza or Leibniz, but without wanting to abandon the PSR. Whereas Spinoza and Leibniz meet the requirements of the PSR in terms of necessary existence, Wolfendale points out that this is “horribly unsatisfactory” from the viewpoint of the atheist, and “indeed for anyone who accepts the strong principle of univocity”. Thus the atheist needs to give up the PSR, or else find an alternative way of satisfying it.
Thus according to Wolfendale, if we think of causation (read: whatever plays the role of sufficiency) in terms of possibility and actuality, we are forced to choose between God and indeterminacy, between the PSR and brute contingency, where the latter is linked to Badiou and Meillassoux. Wolfendale complains that the latter amounts to negative theology
taken to its proper conclusion: some aspect of Being (not a being), shed of all theistic predicates (perfection, benevolence, understanding, etc.), pushed to the point of sheer unintelligibility (as either absolute Nothing or absolute Chaos respectively) is taken to select what actually occurs…
Wolfendale then positions Deleuze as passing between the horns of God and negative theology (i.e. God again), where this is once again equated with rendering the PSR compatible with univocity.
[Note: in the passage just quoted Wolfendale seems to infer the unthinkability of x from the premise that x has been shorn of all its predicates. This inference is question-begging against the nominalist (e.g. Azzouni), for whom the predicates of nothing belong to other things.]
The schematic solution we are given, to pass between the horns of God and negative theology (the PSR and brute contingency), is to replace the possible/actual distinction with that between the virtual and the actual. Deleuzians typically have high hopes for this distinction, though frankly I have yet to see it solve anything to my satisfaction.
In any case, Wolfendale proceeds almost immediately to say that Deleuze affirms Spinozist necessity in some sense. The immediate interpretative problem here is that, since possibility and necessity are inter-definable, one cannot reject the former without rejecting the latter, which is to say that Wolfendale owes us an account of what Deleuze means by ‘necessity’ – if it is not the negation of impossibility.
The second-order point I want to make here is that whatever the virtual/actual distinction ends up amounting to, nothing prevents us from thinking of it as an alternative account of possibility and contingency. (For the record: it is by no means unduly temerous to propose such an alternative account.)
Wolfendale does give some detail that is supposed to flesh out the schematic proposal he attributes to Deleuze. In particular, he says that it involves jettisoning “full blown possible worlds”, a claim I will comment on (obliquely) below. Beyond this, however, he loses me a bit.
Skipping over some material, we arrive at the following slogan:
We must understand how the world is both completely determined at each point, and yet how chance enters into this determination at every instant.
Reading this over gives a sense of the challenge: as Lewis once said in a different context, it just sounds contradictory. Wolfendale provides a useful contrast: whereas Leibniz satisfies the PSR in terms of an actual infinity, Deleuze is said to do so in terms of a potential infinity, the idea being that “we can always regress further to find a reason” for something apparently contingent or contingent given only a proper part of reality.
Two objections that can be raised here are as follows. First there is the response on Leibniz’s behalf: a potential infinite is inadequate to the requirements of the PSR. You can regress as far as you like, but only the actual infinite can provide the sufficient reason of the whole series.
A second objection is that in order to avoid the collapse of the potential infinite into the actual infinite, you have to deny that the potential infinite can be actualised (since it would then be necessary), or else opt for something weaker than S5 (but then is that all the virtual/actual distinction accomplishes?). Supposing we opt for the former, we end up with a potential that corresponds to no possible world, a robust impossible world if you like (this is my oblique comment promised above). But then this potentiality either has its own sort of being (in which case you lose univocity), or else it has no sort of being whatever (in which case you are back with Badiou and Meillassoux).
So what does Wolfendale actually say here? He says that potential infinity is merely the unthinkable sum of the parts of reality, not non-being per se or a different sort of being. I am not sure how to read this so that it avoids saying either that the Whole lacks being or else that it subsists in some pseudo-Meinongian sense.
Perhaps the answer is to be found in this passage from a bit earlier in his discussion:
[S]omething counts as an entity precisely if it has a degree of power, i.e., precisely insofar as it is able to do something that its parts alone cannot. This is a very Spinozan thought.
Della Rocca proposes to treat existence itself as admitting of degrees, and it might be thought that this suggestion has probative force in rendering the PSR and univocity consistent. This is indeed an ingenious move to make, but here as elsewhere I remain dubious that it can succeed. It is as if Deleuze, following Spinoza in this way, wants to avoid equivocity by smashing existence into dust, pulverising it like Leibniz pulverised spirit. However, for me this can only yield an infinite swarm of microscopic equivocations.