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What are the major points of Quentin Meillassoux's critique of correlationism?

I am beginning to work through After Finitude and am finding it difficult to grasp exactly what his critique consists in; it feels like there is a considerable degree of finesse here. I am basically trying to establish a concise statement of his criticism, including some help putting correlationism in context.

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QM explains that since Kant, philosophy has become “correlationist”.

The premise of correlationism is that we do not know the matter in itself, but only the connection of thought to the matter. According to the definition of QM, correlationism consists in disqualifying all claims, to consider the spheres of subjectivity and objectivity independently from one another. So intersubjectivity, the consensus of a community, was destined to substitute to the adequacy of representations of a solitary subject to the matter itself, as a case of authentic criteria of objectivity, and more specially of scientific objectivity. Thought can then no longer think anything independent from it, and QM asks the following question: how can science “produce statements” on what existed well before the emergence of all thought? QM, who expresses himself often grandiloquently, names archifossile everything that shows the existence of a reality previous to the emergence of thought.

According to QM, it’s the mathematization of scientific statements that allow them to treat ancestral objects (previous to the emergence of thought in his terminology).
In one passage, Meillassoux describes the way “modern philosophers” interpret the ancestral statements of science: in adding a simple codicil. This allows these philosophers to comfort their belief in possessing a deeper meaning of the scientific statements than their literal sense, qualified naïve.

Correlationism, in tackling all forms of rational discourses on the absolute via the notion of fictiousness, has finally reinforced the fideist position. Indeed, correlationsim destroys all claim to justify as much as critique any religious views. For the modern philosopher, it would be vain to tackle the internal contradictions to a belief, because it possesses an incommensurable meaning in the rational sense.

Correlationism does not root positively a belief, but removes effectively all pretention of the reason to delegitimize a belief in the name of unthinkability of its content. The condemnation of fanatism is done [henceforth] in the only name of its practical effects (ethico-politics), never in the name of the eventual falsehood of its content.

The solution of QM consists not in refuting frontally correlationism, that he holds as impossible, but to absolutize its principle: the absolute contingency of all being.

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