Philosophia Mathematica 6 (1):63-84 (1998)
Abstract |
A response is given here to Benacerraf's (1965) non-uniqueness (or multiple-reductions) objection to mathematical platonism. It is argued that non-uniqueness is simply not a problem for platonism; more specifically, it is argued that platonists can simply embrace non-uniqueness—i.e., that one can endorse the thesis that our mathematical theories truly describe collections of abstract mathematical objects while rejecting the thesis that such theories truly describe unique collections of such objects. I also argue that part of the motivation for this stance is that it dovetails with the correct response to Benacerraf's other objection to platonism, i.e., his (1973) epistemological objection.
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
DOI | 10.1093/philmat/6.1.63 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
View all 16 references / Add more references
Citations of this work BETA
Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
Pluralism in Mathematics: A New Position in Philosophy of Mathematics.Michèle Friend - 2013 - Dordrecht, Netherland: Springer.
Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
For Better and for Worse. Abstractionism, Good Company, and Pluralism.Andrea Sereni, Maria Paola Sforza Fogliani & Luca Zanetti - forthcoming - Review of Symbolic Logic:1-30.
View all 9 citations / Add more citations
Similar books and articles
Embedding and Uniqueness in Relationist Theories.Brent Mundy - 1991 - Philosophy of Science 58 (1):102-124.
Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - New York, NY, USA: Oxford University Press.
Against (Maddian) Naturalized Platonism.Mark Balaguer - 1994 - Philosophia Mathematica 2 (2):97-108.
Analytics
Added to PP index
2009-01-28
Total views
117 ( #98,798 of 2,499,305 )
Recent downloads (6 months)
4 ( #169,627 of 2,499,305 )
2009-01-28
Total views
117 ( #98,798 of 2,499,305 )
Recent downloads (6 months)
4 ( #169,627 of 2,499,305 )
How can I increase my downloads?
Downloads