Philosophy of Mathematics seminar

A.C. Paseau and Fabian Pregel, Oxford

Deductivism: a new appraisal  

Our talk is a survey of deductivism in the philosophy of mathematics. Deductivism understands a mathematical sentence s as expressing the claim that s deductively follows from appropriate axioms. For instance, deductivists might construe ‘2 + 2 = 4’ as “the sentence ‘2 + 2 = 4’ deductively follows from the axioms of arithmetic”. Deductivism was popular in the late 19th and early 20th centuries, and was endorsed at some point by Russell, Hilbert, Pasch and Curry. It is often seen as philosophically ‘clean’ (Rheinwald) or as a way to ‘avoid philosophical quicksand’ (Maddy), and indeed, in dicussion, one may encounter mathematicians professing to be deductivists. But following its early 20th-century heyday, it fell out of favour before arguably being reinvented as structuralism, a philosophy which in some form or other claims many adherents today. Our aim will be to offer an up-to-date and detailed survey and appraisal of deductivism. The talk is based on a paper we are currently reworking into an entry on this topic for the Stanford Encyclopedia of Philosophy.