Philosophia Mathematica 23 (1):116-125 (2015)

I raise an objection to Stewart Shapiro's version of ante rem structuralism: I show that it is in conflict with mathematical practice. Shapiro introduced so-called ‘finite cardinal structures’ to illustrate features of ante rem structuralism. I establish that these structures have a well-known counterpart in mathematics, but this counterpart is incompatible with ante rem structuralism. Furthermore, there is a good reason why, according to mathematical practice, these structures do not behave as conceived by Shapiro's ante rem structuralism
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Reprint years 2014, 2015
DOI 10.1093/philmat/nku034
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References found in this work BETA

Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.

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Citations of this work BETA

Ante Rem Structuralism and the No-Naming Constraint.Teresa Kouri - 2016 - Philosophia Mathematica 24 (1):117-128.

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