In a recent talk at COIN I argued that Meillassoux's argument from ancestrality in his book After Finitude against strong correlationism fails. But later on in his book he presents another argument against strong correlationism. It is called the argument from factiality. Let me quote the crucial passage. In this passage Meillassoux addresses the strong correlationist directly: "When you think of [realism and idealism] as "possible", how are you able to access this possibility? How are you able to think this "possibility of ignorance" which leaves [both] eventualities open? The truth is that you are only able to think this possibility of ignorance because you have actually thought the absoluteness of this possibility, which is to say, its non-correlational character. Let me make myself clear, for this is the crux of the matter. So long as you maintain that your scepticism towards all knowledge of the absolute is based upon an argument, rather than upon mere belief or opinion, then you have to grant that the core of any such argument must be thinkable. But the core of your argument is that we can access everything's capacity-not-to-be, or capacity-to-be-other, our own as well as the world's. But once again, to say that one can think this is to say that one can think the absoluteness of the possibility of every thing" (After Finitude, p. 58).
This argument fails. For, indeed, the strong correlationist thinks the absoluteness of both possibilities. After all, the strong correlationist is thinking about a possibility with respect to the in-itself and not with respect to the correlation. But this absolute has to be understood correctly. What is the strong correlationist actually saying? For all we know, the strong correlationist says, realism about the in-itself is true. Similarly, as the strong correlationist has it, for all we know idealism about the in-itself is true. Now, as the 'for all we know' already indicates, both assertions of the strong correlationist about the in-itself are claims about the absence of knowledge of the in-itself. More specifically, the strong correlationist merely affirms that realism and idealism are epistemic possibilities. He or she is not affirming that these possibilities are ontological possibilities. For that would entail that he or she knows something about the in-itself, which contradicts strong correlationism. So the strong correlationist is affirming nothing more than possibilities of ignorance. He or she is thus not saying anything positive about the in-itself. No knowledge of the in-itself is claimed, which is entirely consistent with strong correlationism. Meillassoux has therefore not broken the circle. He has not regained access to the absolute.