Meillassoux on Hume

The splash that Quentin Meillassoux's After Finitude has made seems to be going through stages. Initially, at least in the blogosphere, the concern was largely with Meillassoux's idea of the arche fossil. Recently, I've started to see some engagement with his absolute contingency and divinology - Martin Hägglund's comments actually made Derrida sound attractive to me.

Still, I haven't come across commentary on my favorite section of the book, the take down of Hume. It seems to me that this chapter is the lynchpin - this is the chapter that secures what I see as a genuine realism - for my own reasons, reasons I will get to another time, I would also say this chapter secures a solid empiricism.

As far as I know, most strategies for dealing with Hume's problem of causal necessity involve dissolving it (ie, ignoring it) or shifting the terms of the problem without actually solving it. Hence, Hume's own skeptical tactic of changing the question to the origins of the belief in causal necessity, or Kant's transcendental move of claiming that, given the consistency of representation, causation could not be otherwise. Phenomenologists throw their hat into the ring by radicalizing Kant via the hermenutics of finitude.

As Meillassoux points out, all of these strategies still presuppose the necessity of causal necessity. Each of these strategies sidesteps the question of why causation itself is not simply random - if there is no necessity, then there is also no reason why wine should not spontaneously become water, or why the moon should not suddenly fly away from the Earth, etc. His goal is to evacuate existence of all necessity, while maintaining a place for the world's manifest stability.

So what is the fourth option? Meillassoux calls it the speculative option. Instead of showing the necessity of laws or God, "we must ask how we are to explain the manifest stability of physical laws given that we take them to be contingent." (p.91,92)

Why assume the necessity of the laws of nature? The standard argument goes that if the laws could change, (say, if light could change its speed) they would do so, with whatever degree of frequency you wish to claim. It is this "frequentalist implication" (FI) that must go.

Let's expand on the FI. If I were playing a game of dice, and the six side came up a thousand times in a row, I'd begin to suspect the die was loaded. If you're smarter than me, you'd begin to assume that much earlier. What about a more extreme possibility? Why doesn't the die transform into a potted plant? Why doesn't the die negate gravity and float into the air? There is no way to eliminate these possibilities, based entirely on experience. Just because X follows from Y today, does not mean it will follow tomorrow. Hence the belief in causal necessity - sooner or later, you have to assume enemy action.

This is a version of apriori reason - we know there is no aposteriori reason why the 6 six shouldn't come up a thousand times in a row - that'd be the gambler's fallacy. And we know there is no apriori reason why your die should not become a potted plant. Here is the flaw: what the FI does is conflate the possible and the whole - as Meillassoux says of the FI, "what is apriori possible [is] thinkable in terms of a numerical totality." When we say the propability of your die becoming a plant is 1:X, that X is a number in a calculable totality, known apriori, however infinite in a cardinal sense.

So the FI is an element of apriori reason. What we have to show is that apriori reasoning is illegitimate here - in fact, that the FI is a fallacy. What is the condition of refuting the FI, and therefore securing the manifest stability of nature while at the same time claiming absolute ontological contingency? We eliminate that X by showing that the absolute contingency of the world is inaccessible to probabalistic reasoning.

They key is refuting this equating of the thinkable with the possible. We can think, without contradiction, an infinite number of outcomes when we roll the die. The result could be a one, or a six, or a magically appearing seven, or a miniature unicorn. Meillassoux borrows from Alain Badiou's reading of set theory, and the upshot here is the detotalization of number. The universe, or being as such, is not totalized by an apriori thinkable set of infinite cardinals.

What in set theory is capable of doing is showing is that this numerical whole is a chimera? This is where Alain Badiou's just-translated book comes in. The argument isn't all that difficult, and is a spiritual descendant of Russell's Barber paradox. The short version - being as such is turtles all the way up, down and around. Take a set - (A, B, C). Set theory says that A, B and C are all themselves sets - A is made up of (X, Y, Z), and Z is made up of its own sets. The question that concerns us here, is there a set that encompasses all other sets? In other words, the numerical totality that would supply the X of 1:X?

The answer is no. There are two kinds of sets - reflexive and non-reflexive. Reflexive sets include themselves as an element in their set - for example, reflexive set A includes A in itself - (A, X, Y). A is an element there. Non-reflexive sets do no include themselves - take B, whose elements are (C, D). B is not an element of itself.

If there is a set of the whole, it obviously must include itself. If A includes all sets, it must include itself.

However, if we divide all sets into reflexive and non-reflexive, a problem emerges. If the set of the whole, A, includes all non-reflexive sets, B, then there must be a complete subset of non-reflexive sets. Let's call this set of all non-reflexive sets the Chimera. To quote two paragraphs from page 110 of Logics of Worlds:

"Is the Chimera reflexive or non-reflexive?. . . . Now, if the Chimera is reflexive, this means that it presents itself. It is within its own multiple-composition. But what is the Chimera? The multiple of all non-reflexive multiples. if the Chimera is among these multiples, it is because it is not-reflexive. But we have just supposed that it is. Inconsistency.

"Therefore, the Chimera is not reflexive. However, it is by definition the multiple of all non-reflexive multiples. If it is not reflexive, it is in this 'all', this whole, and therefore presents itself. It is reflexive. Inconsistency, once again."

So the Chimera can neither be reflexive or non-reflexive, and if all sets must be one or the other, then the Chimera simply is not.

What this means for our argument is that there is no numerical totality of possibilities. The FI completely depends on such a totality, and this totality does not exist. In other words, probabilistic reasoning - either apriori or aposteriori - is incapable of supplying the X that 1:X requires. There is no grand set of possibilities to choose from. The only possiblities are those that are given - the one, the two, the three, etc. The miniature unicorn and the potted plant are not given possibilies.

The admittedly strange upshot: we know that absolutely everything is absolutely contingent, but we have no valid reasons to believe that everyday relations (pool games, combustion engines, scientific experiments) will be thrown into chaos.

Ok, so why did I say at the beginning that this is the real condition for a realism? Leaving aside my allusion to empiricism, what this does is continue the Enlightenment project of demystifying the world. In other words, I think any realism must be a continuous project of seeing the world as an ever more prosaic place.

It may appear that Meillassoux's absolute contingency is anything but prosaic, as I think it is easy to latch onto it in a heroic way, such as "anything is possible," or "where there is a will, there is a way." Meillassoux himself nods in this direction when he claims that contingency is the basis of all critique of ideology. However, I think what his project does is really to throw us back onto the given world as a banal place where there are no gods to save us. These gods take many forms, especially in theory - the openness of the future, the inbreaking of an Event, or anarchic sensible becoming. I think Meillassoux shows us why we can and must dismiss these gods as attempts not to go beyond the given, but as attempts to deny or escape it. This post already seems long enough, so I'll leave it there now.