An image of the alternative doxa, or non-correlationist “counter-image” of thought, favoured by Wolfendale can supposedly be found in the dialogue between Deleuze and Badiou, where he praises their substantial and “non-metaphorical” use of mathematics (353-354). He seems to see in this purported shared feature a criterion for demarcating between correlationism and noncorrelationism. As Wolfendale himself explicitly endorses “mathematical structuralism” (352), one may wonder whether this proposed criterion of demarcation is as objective as Wolfendale would like us to think.
It is not at all obvious why the “central and crucially non-metaphorical role played within [this dialogue] by mathematics” (353-354) should provide any guarantee of non-correlationism. Harman, on the contrary, sees such mathematical scientism as a sign of undermining, i.e; of reductionism, and thus of correlationism. Just positing that mathematics is a non-correlational language or discipline is not very convincing as an argument.
Badiou is contradictory on this point. He poses that mathematics is ontology, and so seems committed to the stability of mathematics, if Being is to be regarded as stable. At the same time he treats the “matheme” (i.e. mathematics and the sciences) as a truth-procedure on a par with poetry, love, and politics. This would seem to open mathematics, the same as for the other procedures, to revolutionary paradigm change. Following Latour and Laruelle we could extend this list of truth-procedures to include religion, an extension that Badiou himself considers, only to reject.
Certainly, much of mathematics is stable, or generally treated as stable. Further, it’s only a small number of specialists who change things. On the other hand, religions, even Christianity, evolve a lot. If one includes the gnostics and other heretics, there is quite a lot of multiplication of axioms, of their variation, replacement, subtraction, and destruction going on. Religion is not to be confused with its institutions, which precisely try to maintain stability. Thus there is no necessary primacy of mathematics in terms of quantity of invention.
As to quality or depth of invention, it is not clear how much deep change and discontinuity there is in mathematics. Little work has been done on this subject. Michel Serres in his HERMES volumes sketched out a periodisation of very general epistemes that included mathematics alongside other domains. In this model, there are informal paradigms that most research, of whatever domain, fits into in a particular epoch, and that are only recognised after we leave them behind.
But even if mathematics is freer and more deterritorialised than other regional ontologies, this is no reason to make it the anchor for a new realism. That is, or should be, a quite separate argument. This freedom to make and break axioms is for Harman a sign that maths is “sensual” rather than real. So we are witnessing an opposition between two philosophical sensibilities in the Harman-Wolfendale dispute, and the status of mathematics is itself part of the dispute, not the decisive criterion for resolving it.
Nor do I see any reason to accept at face value the thesis that “phenomenology” is inherently correlationist. Bernard Stiegler has often remarked that Husserl’s “Origins of Geometry” introduces a new epoch in his thought, that breaks open the subject-object enclosure by making writing as tertiary retention enter essentially into the constitution of mathematics. Hubert Dreyfus and Charles Spinosa argue convincingly that Heidegger’s thing-paradigm breaks with the potential closure and correlationism inherent in his earlier understandings of being paradigm.
As we have seen, the spectre of “orthodox correlationism” presiding as the dominant paradigm of post-Kantian philosophy, enslaving thought and paralysing action, is a chimera that has no foundation if one consults the works of the major post-structuralist French thinkers. The remedies proposed for this imaginary illness, both Harman’s absolutism and Wolfendale’s universalism, represent a regression compared to these works. The two sides share much that is questionable, and disagree only over the general orientation within that common vision. I think we must reject Meillassoux’s whole scenography of the encounter between subject and object, which constitutes a false problem, so that his solution to that problem is of no interest. One has only to recall Popper’s “epistemology without a knowing subject” to see the conceptual regression embodied in setting up the problem in the way that Mellassoux does in AFTER FINITUDE.
(Note: I am particularly indebted to a facebook discussion with Joshua Comer for helping me gain clarity on the problematic status of mathematics in Wolfendale’s polemic with Harman).