# 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

**Keywords**

**Categories**

(categorize this paper)

**Reprint years**

2014

**ISBN(s)**

**PhilPapers/Archive ID**

HODMRP-3

**Upload history**

Archival date: 2014-11-14

View other versions

View other versions

**Added to PP index**

2013-06-30

**Total views**

230 ( #31,301 of 69,167 )

**Recent downloads (6 months)**

13 ( #50,397 of 69,167 )

How can I increase my downloads?

**Downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.*