Dialectics, Mathematics and the Cavaillès-Hyppolite Encounter

This essay utilises Suzanne Bachelard's essay ‘Forme et Contenu’ as an entry point to sketch out the possibility (or impossibility) of a dialectic of mathemata following the work of Jean Cavaillès and Jean Hyppolite. Firstly, I outline what Bachelard sees as a ‘dialectic’ of form and content in the history of abstract algebra, highlighting a parallel between Bachelard's reading of algebra and Hyppolite reading of the relation of the human subject to logos. Secondly, I move towards Jean Hyppolite's discussion of Lautman in ‘Mathematical Thought’ which allows for a revealing of convergences between the work of Hyppolite and Cavaillès. I conclude by noting that the similarities between Cavaillès and Hyppolite – despite possible protestations by Hyppolite – go against Hegel's understanding of mathematics, leading to the possibility of opening up a ‘Hegelian mathematics against Hegel’.