# 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

**PhilPapers/Archive ID**

HODMRP-3

**Revision history**

Archival date: 2014-11-14

View upload history

View upload history

References found in this work BETA

Word and Object.Quine, W. V.

What is Structural Realism?Ladyman, James

Laws and Symmetry.van Fraassen, Bas C.

Philosophy of Mathematics: Structure and Ontology.Shapiro, Stewart

Mathematics as a Science of Patterns.Resnik, Michael D.

View all 22 references / Add more references

Citations of this work BETA

The Epsilon-Reconstruction of Theories and Scientific Structuralism.Schiemer, Georg & Gratzl, Norbert

**Added to PP index**

2013-06-30

**Total views**

141 ( #18,258 of 38,963 )

**Recent downloads (6 months)**

16 ( #23,831 of 38,963 )

How can I increase my downloads?

**Monthly downloads since first upload**

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