# Mathematical representation: playing a role

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

**Abstract**

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

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2014

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HODMRP-3

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Archival date: 2014-11-14

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References found in this work BETA

Word and Object.Quine, Willard Van Orman

Laws and Symmetry.van Fraassen, Bas C.

What is Structural Realism?Ladyman, James

Scientific Representation: Paradoxes of Perspective.van Fraassen, B. C.

Mathematics as a Science of Patterns.Resnik, Michael D.

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Citations of this work BETA

The Epsilon-Reconstruction of Theories and Scientific Structuralism.Schiemer, Georg & Gratzl, Norbert

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