Philosophical Studies 168 (3):769-782 (2014)

Kate Hodesdon
University of Bristol
The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the attributes them to the mathematical practice of representing numbers using more concrete tokens, such as sets, strokes and so on
Keywords Mathematical structuralism  Representation  Ontological relativity  Model-theoretic arguments  Empiricist structuralism  Van Fraassen
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DOI 10.1007/s11098-013-0160-4
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Laws and Symmetry.Bas C. van Fraassen - 1989 - Oxford University Press.
Reason, Truth and History.Hilary Putnam - 1981 - Cambridge University Press.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.

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