Philosophy of Mathematics Seminar


Philosophy of Mathematics seminar


Dan Isaacson, Oxford

Kreisel’s philosophy of mathematics


Kreisel has described how his interest in foundations of mathematics arose early: “Since my school days I had had those interests in foundations that force themselves on beginners when they read Euclid's Elements (which was then still done at school in England), or later when they are introduced to the differential calculus.” At the same time, he had a mathematician’s distrust of philosophers of mathematics, though he was one himself, in the way in which other mathematicians such as Cantor, Dedekind, Hilbert, Brouwer, Weyl, and Gödel were philosophers of mathematics, motivating and justifying the way in which they did their mathematics. Among Kreisel’s more than 200 publications, a relatively small number are explicitly philosophical, but these grow out of and at the same time inform the whole body of his work. But even recognizing Kreisel as a philosopher of mathematics, it’s not easy to say which philosophy of mathematics is his. My talk will be a preliminary attempt to do this.