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Mathematical Representation: Playing a Role

Hodesdon, Kate (2013) Mathematical Representation: Playing a Role. [Preprint]

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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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Hodesdon, Katekate@hodesdon.com
Keywords: Mathematical Structuralism, Representation, Modelling, Van Fraassen,
Subjects: Specific Sciences > Mathematics
General Issues > Models and Idealization
Depositing User: Kate Hodesdon
Date Deposited: 01 Jun 2013 15:24
Last Modified: 01 Jun 2013 15:24
Item ID: 9809
Subjects: Specific Sciences > Mathematics
General Issues > Models and Idealization
Date: 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/9809

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