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Structuralism and Its Ontology
2015
Ergo, An Open Access Journal of Philosophy
A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious
doi:10.3998/ergo.12405314.0002.001
fatcat:s24fxqxf3vbkhi5sn5h52zqgp4