I have been unable to put together a continental connections post of late due to a study abroad program in Scotland I was heading up. The timing of the program worked out well, however, for I was able to attend the Hume Society conference in Edinburgh and meet up with Eric (all of which was very nice). Now that I'm back in sultry Louisiana I should be able to post more regularly. Sticking with Hume, and following up on the discussions of PSR from my previous post (here), I'll connect Quentin Meillassoux's arguments against PSR with the arguments of David Lewis's defense of the same, showing how Deleuze, with his notion of the impossibility of thought (and his concept of concrete universals), differs from both.
In his book After Finitude: an essay on the necessity of contingency, Meillassoux devotes an entire chapter to what he calls Hume's Problem. The central arguments of this chapter are intended to address objections to the claim, and preciesly the claim Meillassoux seeks to defend, that "not only things but also physical laws are really contingent...these laws could actually change at any moment for no reason whatsoever." Meillassoux's strategy in avoiding the objections is to solve "Hume's problem," which he states as follows: "is it possible to demonstrate that the same effects will always follow from the same causes ceteris paribus, i.e. all other things being equal?" For Hume, and for Meillassoux, the answer is "no," and Meillassoux ushers Hume's famous billiard-ball passage from EHU to the center of his argument:
When I see, for instance, a Billiard-ball moving in a straight line towards another; even suppose motion in the second ball should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from that cause? May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? All our reasonings a priori will never be able to shew us any foundation for this preference. (EHU section IV)
In David Lewis’s Humean understanding of necessity, or what he calls Humean Supervenience, he argues that any claims we make regarding the world supervene upon a given distribution of particular facts. Given any two worlds, for example, if they are identical in every way and share the same laws of nature then they will remain identical at any and all later times. There cannot be a change in the distribution of particular facts, or a divergence between the two worlds, without a simultaneous change in the laws that supervene upon these worlds and facts. Given the laws of probability, for example, the chance a single throw of the dice will give me a six are 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 I throw a six approaches one in six. These laws of probability therefore supervene upon a given distribution of particular facts (rolls of the dice) in the world, W, 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 for the world, W, at time1 would both be and not be in accordance with the laws of probability up to and including time1. Lewis refers to this as an undermining future.
In his analysis of Hume, however, Meillassoux argues that what makes Hume’s understanding of necessity possible, or why we eventually come to the strong and lively beliefs we do, and this is also what gives for Meillassoux the principle of sufficient reasons its explanatory power, is precisely that there is a totality relative to which the particular facts are compared. If I roll a pair of dice and it comes up sixes 30 times in a row I will no doubt begin to think there must be a reason why this is happening – e.g., loaded dice. Similarly, if a student happens to see their professor at the store they would likely think nothing of it (a mere chance encounter), and they may continue to think so even if they happen to run into them again later that day; but if this continues then at some point they will no doubt begin to think there is a reason that explains these encounters – namely, they are being stalked. For Meillassoux what gives these reasons their explanatory power is that they are held in relationship to a set or totality of instances. Relative to the totality of past instances, dice do not come up sixes 20 times in a row, nor does one run into one’s professor more than once or twice on any given day outside the classroom. Much the same argument could be extended to Lewis’s account – it is the totality of a given distribution of facts at a given world, W, at all possible worlds, upon which the laws supervene. It is thus the totality of facts at W at time1 relative to the totality of facts at time2 that gives rise to undermining futures. Following Badiou and Cantor, however, Meillassoux argues for the non-All that cannot be totalized (or the nondenumerable, which I discuss here) and which therefore undermines the necessary laws that would supervene upon a given totality. The notion of an undermining future would not even arise on this reading. This is not to say that there are no particular facts or regularities between facts. Within a large set of observations the odds of sixes appearing may indeed be one in six, or there may be countless other regularities, but the ‘laws’ that supervene upon these regularities are, Meillassoux argues, ‘contingent. They are not necessary. As Hume said, we are unable to demonstrate any such necessity.’ In short, there is no reason why these laws could not "change at any moment for no reason whatsoever," and from here Meillassoux argues against the principle of sufficient reason (PSR) as well for it too relies upon a presupposed totality that he rejects.
Turning to Deleuze now, we find a similar rejection of totality, but for Deleuze this does not lead to the rejection of PSR. In his book on Leibniz, for instance, Deleuze refers to the impossibility of thought, or an unconscious 'that cannot be thought in finite thought.’ (Fold, p. 89), and in Cinema 2, in reference to Artaud and Blanchot, this impossibility is described as “what forces us to think [and] 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, self-identical being (e.g., duration, becoming, will to power, a life etc.) relative to which what can be thought would merely be modes 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 Meillassoux’s arguments against PSR (and it is also crucial to his efforts to avoid correlationism [a discussion for another time]), and it is mathematics, especially Cantorian set theory, that justifies these arguments for it is able to theorize the non-totalizable, the ‘non-All’. 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 Deleuze too would end up rejecting PSR, but as I argued in an earlier post (here), if one understands the PSR in terms of concrete universals (such as white noise/light, for example), then they are neither totalizable in terms of a language or logic of representation (the reliance upon which is the basis for my critique of Meillassoux, and as an aside Graham Priest's criticism of Cantor in Beyond the Limits of Thought can equally well be applied to Meillassoux), but such universals are nonetheless the concrete condition for, or the PSR for, the determinate instances and facts of the language and logic of representation, the very language and logic we are unable to totalize. Deleuze thus remains a strong proponent of PSR.