Poststructuralism and Deconstruction: A Mathematical History

Examples are not lacking of philosophers whose outlook was inspired or in some way influenced by thinking about meaning of mathematics: Wittgenstein, Husserl, Russell, before them Peirce, and more recently Badiou, to name only clearest cases in point. Philosopher and logician Jean Cavailles was undoubtedly influential on post-war philosophy in France, and effects of his critique of philosophy of subject, especially of Kant and Husserl, carried an important impulse from formalist mathematics to twentieth-century French Even Heidegger, although critical of formal logic and technical reason (like some of his day), followed debate on nature of knowledge and may have been provoked by it--especially by controversy regarding time-continuum--to attempt in his Being and Time (1927) to destroy traditional metaphysics and thus transgress philosophical options that found themselves at loggerheads over question of foundations of mathematics. The link works in other direction, too, although it has become something of a rarity to find articles that contain references to Kant, Fichte, Schopenhauer and Nietzsche. During foundational debate in 1920s, one could see this in articles of Hermann Weyl and L.E.J. Brouwer; Weyl was actively interested in phenomenology and maintained correspondence with Husserl, while Kurt Godel is known to have been a serious reader of Kant and Husserl. Much earlier, Hermann Grassmann (a major influence on Alfred North Whitehead) had built on ideas of his father, Justus Grassmann, who wrote under influence of Schelling.(1) These links have not been severed, even if they remain unstated. Thus, for example, philosophically reticent Bourbaki collective was, according one of its members, a brainchild of German philosophy. One finds influence of Husserl and Heidegger in essays of Gian-Carlo Rota, and at least implicitly in work of Petr Vopenka on alternative set theory. It may not be norm, but examples of cross-fertilization are not as difficult to find as oversimplified binarism of cultures would have us believe. My goal here is to indicate relevance of mathematics to several important points made by Jacques Derrida. A number of Derrida's arguments bear resemblance to critiques of logic and excesses of formalist mathematics. These objections hark back to ideas of intuitionist who--some, I think, under influence of German romantic idealism--rebelled in early 1900s against hegemony of formal logic and symbolic reduction of all thought to computation. The situation is not quite that simple, since Derrida apparently also employs certain ideas of formalist mathematics in his critique of idealist metaphysics: for example, he is on record saying that the effective progress of notation goes along with deconstruction of metaphysics.(2) Derrida's position can, I think, be interpreted as a sublation of two completely opposed schools in For this reason it is not possible to reduce it to a readily available philosophy of mathematics. One could perhaps say that Derrida continues and critically reworks Heidegger's attempt to deconstruct traditional metaphysics, and that his method is more mathematical than Heidegger's because he has at his disposal entire pseudo-mathematical tradition of structuralist thought. He has implied in an interview given to Julia Kristeva that mathematics could be used to challenge logocentric theology, and hence it does not seem unreasonable to try looking for analogies in his A word of caution, though. The similarities I will outline here are similarities of argumentative techniques, not of philosophical outlooks. The analogies--which are informed and limited by my own interpretive ability and my belief that mathematics and continental philosophy are deeply related--are not to be confused with gross misstatement that mathematicians have done it all. …

Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.