I would like to write a book entitled ANTI-LARUELLE, which would be just as much for Laruelle’s non-philosophy as against it, and which would include a defence of Badiou against Laruelle’s critiques. In effect, most of the book has already been written and has been posted, in fragments, on this blog and on my academia.edu page. A key idea would be that Laruelle’s ANTI-BADIOU is not really directed against Badiou himself, but against Laruelle’s own tendencies to philosophical sufficiency.
To interpret the prefix « anti- » one should take into account Badiou’s theory of the three negations. The negative prefix is not necessarily a sign of ressentiment, which is based on monist exclusion and foregrounds strong, classical negation. My treatise ANTI-LARUELLE would be pluralist, and it would work with intuitionist and paraconsistent negation.
This approach does not assume that critique has « run out of steam », but only that it must be transformed. Nor does it presuppose the death of « strong » or classical negation. I don’t think it is dead, just not absolute. Many other types of negation exist, and the supposedly binding rules of classical propositional logic are far from capturing our habitual, and even less our creative, modes of reasoning.
The mathematics of non-classical negation are just a very late formalisation of what many have been saying for ages. For example, Hegel, Nietzsche, Wittgenstein, and Feyerabend emphasise the heuristic value of negation and of contradictions. Laruelle’s concept of « non- » as a relativising and a pluralising prefix goes in the same direction, as does his concept of « superposition ».