Perhaps unsurprisingly, the central step in Meillassoux's After Finitude is the step through which he claims to have gotten beyond finitude. It is the move whereby he turns the recognition of the limits of human knowledge which is fairly widely accepted in today's philosophical environment into a discovery of an absolute ontological truth. Also perhaps unsurprisingly, one of my main worries about his work is whether he can make such a move.
How does he think he has done this? It is interesting that his move resembles a move made by Husserl. Husserl, following from Descartes and others, claims that there is a connection between what is imaginable and what is possible. The practice of imagination, or eidetic variation, provides us with an experience of the limits and laws of the transcendental ego's constituting activities. For example, we can't imagine color without it taking up space and this reveals a potential universal truth.
Interestingly, Meillassoux takes a different tone when discussing imagination (or rather, thought). He suggests, inspired by Hume's concern that our grasp of causality is based entirely on repeated observations of matters of fact, that there is a potential infinity of different ways in which we can imagine any specific event occurring (i.e. we can imagine any number of things occurring when one billiard ball rolls into another). Generally this has been taken to demonstrate that reason tells us nothing about what causal connections exist between things, and that thus all our causal reasoning is at best probabilistic. When you throw in the realization that reason also reveals that we don't know whether the future need conform to the past we are left with no sure foundation for future predictions. We have no reason not to think that tomorrow all the laws of the universe may be different.
This ability to think everything as different includes, of course, the ability to think ourselves as not existing. It is from this point that Meillassoux takes off: "... we are able to think - by dint of the absence of any reason for our being - a capacity-to-be-other capable of abolishing us, or of radically transforming us. But if so, then this capacity-to-be-other cannot be conceived as a correlate of our thinking, precisely because it harbours the possibility of our own non-being. In order to think myself as mortal, as the atheist does - and hence as capable of not being - I must think my capacity-not-to-be as an absolute possibility, for if I think this possibility as a correlate of my thinking, if I maintain that the possibility of my not-being only exists as a correlate of my act of thinking the possibility of my not-being, then I can no longer conceive the possibility of my not-being, which is precisely the thesis defended by the idealist." (p. 57).
The idea here is that the skeptic (correlationist) is trapped in a dilemma. Either we admit that we have access to some truth not relative to, and dependent upon, our thought, specifically we admit the truth that our thought could stop at any moment (i.e. we could cease to exist), or we must fall into idealism and admit that the dependence of the thought of our non-existence on thought itself makes the thought of non-existence an illusion. If we admit our access to a non-thought correlated possibility, however, we are admitting getting out of the correlationist box or, to put it differently, we are getting beyond the "finitude claim" that our knowledge and thought is always constrained within its own limits such that we can't "think beyond thought".
Meillassoux also formulates this point, see pages 58-59, by pointing out that the very tool the skeptic uses to get out of idealism and argue against the certainty of the theist or naive realist, the distinction between reality as thought and reality as it is in-itself, is accessible only insofar as we have gotten beyond it and thought SOMETHING absolute independent of human thought: "Your general instrument of de-absolutization only works by conceding that what the speculative philosopher considers to be absolute is actually thinkable as an absolute; or better still, is actually thought - by you - as absolute, since were this not the case, it would never have occurred to you not to be a subjective (or speculative) idealist." (p. 59)
The conclusion, then, is that the mind has access to one absolute truth, namely universal contingency. All things could be otherwise. Thus we are not caught in the skeptical position of stating that the idealist, theist and realist positions are all equally possible, rather we can firmly state that each of these positions is false to the extent that they assert any "reason" or grounding cause for things being the way they are and not otherwise.
Let me say that the inversion, here, of the Hegelian response to Kant is brilliant. Rather than assert that the thinkability of the distinction between phenomena and thing-in-itself demonstrates our surpassing of the distinction towards the realization of the necessary correlation of thought and being, he asserts that it demonstrates our realization of the non-correlation of thought and being and the absolute truth of universal contingency. I adore this conclusion, but I don't think the argument gets us there.
As my mention of Hegel should make clear, Meillassoux also rejects the Kantian claim that thought can recognize its own limits without surpassing them. The post-Kantian correlationist spin on this is the claim that thought can recognize the possibility, and perhaps even current formation, of its own limits without knowing, as Kant seems to think he can, their absolute necessity and stability.
It seems to me that, despite Meillassoux's use of the reflexive paradox here to demonstrate that the skeptic must assume the thinkability of the non-thought-correlated in order to craft his correlationist arguments, the inconsistency of the correlationist's argument, if indeed this has been demonstrated, does not constitute ontological knowledge.
What we need is a reason to think that the fact that we can think things as being different constitutes ontological knowledge of their contingency. This would require a rather extensive investigation of the nature of thought. What is thought such that it can provide knowledge of absolute truth, rather than simply taking (fallibly) various possibilities to be absolute?
Phenomenologically we do indeed experience various things as universal, particulars can show up in the mode of universality. But this appearance-as-universal does nothing to establish actual knowledge of universal truth. In the same way, the fact that my reasoning depends upon a certain assumption tells me nothing about the truth or falsity of that assumption. Even were it possible to demonstrate that all reasoning rests on a certain assumption it would not justify the claim that this assumption is universally true. A similar point can be made in relation to the supposed connection between imagination and possibility. Let me make this fairly basic point in a schematic way: in order to justify a claim to universal ontological knowledge we would first need indubitable ontological knowledge concerning the relation of human thought and reality.
There is obviously much more I want to say, and this is admittedly a fairly gut level response to Meillassoux's very impressive book. It also strikes me, for example, that the focus on understanding correlationism in terms of "thought" smuggles in quite a lot and is not necessarily an accurate depiction of a large class of supposed correlationists (including, I would claim, Heidegger).