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Tim Räz, Say My Name: An Objection to Ante Rem Structuralism, Philosophia Mathematica, Volume 23, Issue 1, February 2015, Pages 116–125, https://doi.org/10.1093/philmat/nku034
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Abstract
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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