Philosophia Mathematica 28 (3):347-359 (2020)

Authors
Mary Leng
University of York
Abstract
Stewart Shapiro’s ante rem structuralism recognizes the structural or ‘algebraic’ aspects of mathematical practice while still offering a face-value semantics. Fictionalism, as a purely ‘algebraic’ approach, is held to be at a disadvantage, as compared with Shapiro’s structuralism, in not interpreting mathematics at face value. However, the face-value reading of mathematical singular terms has difficulty explaining how we can use such terms to pick out a unique referent in cases where the relevant mathematical structures admit non-trivial automorphisms. Shapiro offers a solution to this difficulty, but his solution, I argue, evens the score between Shapiro’s structuralism and fictionalism.
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DOI 10.1093/philmat/nky005
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References found in this work BETA

The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Mathematics and Reality.Mary Leng - 2011 - Bulletin of Symbolic Logic 17 (2):267-268.
Philosophical and Mathematical Correspondence. [REVIEW]A. Reix - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.

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