Review of: Hilary Putnam on Logic and Mathematics, by Geoffrey Hellman and Roy T. Cook (eds.) [Book Review]

Mind 129 (516):1327-1337 (2019)
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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, focusses mostly on Putnam’s 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 do my best to tease out some connections between the paper; and there are some really interesting connections to be made.

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Hilary Putnam on Logic and Mathematics.Roy T. Cook & Geoffrey Hellman (eds.) - 2018 - Cham, Switzerland: Springer Verlag.
Extendability and Paradox.Roy Cook & Geoffrey Hellman - 2018 - In Roy Cook & Geoffrey Hellman (eds.), Hilary Putnam on Logic and Mathematics. Springer Verlag.
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Tim Button
University College London

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References found in this work

What good are our intuitions: Philosophical analysis and social kinds.Sally Haslanger - 2006 - Aristotelian Society Supplementary Volume 80 (1):89-118.
Philosophy and Model Theory.Tim Button & Sean P. Walsh - 2018 - Oxford, UK: Oxford University Press. Edited by Sean Walsh & Wilfrid Hodges.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
Mathematics without foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.

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