Philosophia Mathematica 9 (2):184-211 (2001)
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| Abstract |
Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality of MS or a close cousin appears at crucial junctures in both STS and SGS, so that the above outcome is not obviously tendentious.
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| Keywords | structuralism WAYS |
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| DOI | 10.1093/philmat/9.2.184 |
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References found in this work BETA
Counterpart Theory and Quantified Modal Logic.David K. Lewis - 1968 - Journal of Philosophy 65 (5):113-126.
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
It’s a kind of magic: Lewis, magic and properties.Daniel Nolan - 2020 - Synthese 197 (11):4717-4741.
Everything You Always Wanted to Know About Structural Realism but Were Afraid to Ask.Roman Frigg & Ioannis Votsis - 2011 - European Journal for Philosophy of Science 1 (2):227-276.
The Interdependence of Structure, Objects and Dependence.Steven French - 2010 - Synthese 175 (S1):89 - 109.
Structuralism and the Notion of Dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.
Identity, Indiscernibility, and Ante Rem Structuralism: The Tale of I and –I.Stewart Shapiro - 2008 - Philosophia Mathematica 16 (3):285-309.
View all 41 citations / Add more citations
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