Paolo Mancosu


UC Berkeley

Definitions by abstraction: From stable practice to global foundations

One of the most influential programs in contemporary philosophy of mathematics is the neo-logicist program. At the core of neo-logicism are a technical result and a set of philosophical considerations. The technical result is called Frege's theorem: second-order Peano arithmetic can be derived from Hume's principle and second order logic. The cluster of philosophical considerations are aimed at showing that Hume's principle is analytic and that second order logic does not take us out of the realm of analyticity.