Philosophy of Mathematics seminar

Chris Scambler, Oxford

The Possibility of Potentialism  

The potentialist program in the foundations of mathematics is centered around the suggestion that regimentations of mathematical theories that employ modalised quantification offer certain advantages over their more familiar purely quantificational counterparts, especially with respect to the handling of certain paradoxes or counterintuitive results. But the question of what kind of modality can or should be used here remains a source of much disagreement. In this talk I’ll outline my preferred answer, focusing on the case of set theory and Russell’s paradox.