Philosophia Mathematica 2 (2):148-160 (1994)

Stewart Shapiro
Ohio State University
The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.
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DOI 10.1093/philmat/2.2.148
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References found in this work BETA

Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
Russell's Mathematical Logic.Kurt Gödel - 1944 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Northwestern University Press. pp. 119--141.

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Citations of this work BETA

Set Theoretic Naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
Phenomenology and Mathematical Practice.Mary Leng - 2002 - Philosophia Mathematica 10 (1):3-14.

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