Putnam on foundations

models, modals, muddles

John P. Burgess

pp. 129-143

in: Geoffrey Hellman, Roy T. Cook (eds), Hilary Putnam on logic and mathematics, Berlin, Springer, 2018

Abstract

Putnam has famously offered a sketch of a mathematics without foundations, existing in two equivalent descriptions, set-theoretic and modal-logical. Here his proposal is critically examined, with attention to difficulties surrounding both the modal-logical description itself and especially the notion of equivalence of descriptions.