Philosophy of Mathematics Seminar Week 4 TT17

Philosophy of Mathematics

Speaker: Ian Rumfitt (All Souls College, Oxford)

Title: Neo-Fregeanism and the Burali-Forti Paradox

Abstract: This paper considers what form a neo-Fregean account of ordinal numbers might take.  The natural abstraction principle for ordinals yields a contradiction (the Burali-Forti Paradox) when combined with impredicative second-order logic.  I argue that the fault lies in the use of impredicative logic rather than in the abstraction principle per se.  Focusing on a form of predicative logic which reflects a philosophical diagnosis of the source of the paradox, I consider how far Hale and Wright’s neo-logicist programme in cardinal arithmetic can be carried out in that logic.

Convenors: James Studd (University of Oxford)Daniel Isaacson (University of Oxford),  Volker Halbach (University of Oxford)

Website: Philosophy of Mathematics Seminar