Alice Nilsson

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’.

Theodor Adorno has been quoted as responding to the Humanist Union stating ‘I might possibly be willing to join if your club had been called an inhuman union, but I could not join one that calls itself “humanist”’. Adorno’s opposition to forms of humanism (both liberal and Marxist) which posit the existence of our humanity is reflected in readings of The Frankfurt Institute’s history such as that produced by Martin Jay. While this is the case, one of Adorno’s highly admired students, Alfred Schmidt, commemorated his teacher by proclaiming him a ‘philosopher of Real Humanism’. In categorising Adorno’s work as embodying a ‘Real Humanism’, Schmidt points towards an understanding and orientation towards the human (and our understanding of it) which cannot be accurately characterised through the philosophies of Humanism and Anti-Humanism as oppositional viewpoints. Rather, the Real Humanism of Adorno (as well as some of his fellow travellers) understands the human as the negative image of our currently existing society’s inhumanity, and urges us to take an ethical orientation towards the constitution of the human through the abolition of our inhumanity. If we, like Adorno, are to believe in the new categorical imperative that we must make sure ‘that Auschwitz never repeats itself, so that nothing similar ever happen[s] again’, then we must fundamentally orient ourselves towards the goal of ‘real humanism’ – a society free from the domination of ourselves and the other.