Mind | 2019
Hilary Putnam on Logic and Mathematics, edited by Geoffrey Hellman and Roy T. Cook
Abstract
Putnam’s most famous contribution to mathematical logic was his role in investigating Hilbert’s Tenth Problem: Putnam is the ‘P’ in the MRDP Theorem. This volume, though, focuses mostly on his work on the philosophy of logic and mathematics. It is a somewhat bumpy ride. Of the twelve papers, two scarcely mention Putnam. Three others focus primarily on Putnam’s ‘Mathematics without Foundations’ (1967), but with no interplay between them. The remaining seven papers apparently tackle unrelated themes. Some of this disjointedness would doubtless have been addressed if Putnam had been able to compose his replies to these papers; sadly, he died before this was possible. In this review, I shall do my best to tease out some connections between the papers; and there are some really interesting connections to be made. Ultimately, though, my review will be only a little less bumpy than the volume itself.