Title: Zermelo’s 1930 axiomatisation of set theory and the Kantian Antinomy

Abstract: Kant’s treatment of the infinite, and with it his Antinomy, was not received with enthusiasm in early analytic philosophy and (post)Cantorian mathematics. According to Cantor himself, Kant only managed to formulate his antinomies because of a “vague and distinctless” use of the concept of infinity. Many distinguished philosophers followed his judgement (cf. Russell 2009, Bennett 1974, Priest 1995). A notable exception to this is the set theorist Ernst Zermelo. His 1930 paper on the foundations of set theory is known for giving a first formulation of the axiomatisation of set theory that we use today, and for isolating the so-called inaccessible cardinals as demarcating the size of its models (which also feature in his proposed solution to the Burali-Forti paradox).  At the end of his paper (in a much quoted passage) he identifies the principles motivating his reasoning with the forces at play in Kant’s antinomy. The aim of the talk is to appreciate this connection.