Structuralism as a philosophy of mathematical practice
 Jessica Carter
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This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the second case, from algebraic topology, one point is that an object can be a place in different structures. Which structure one chooses to place the object in depends on what one wishes to do with it. Overall the paper argues that mathematics certainly deals with structures, but that structures may not be all there is to mathematics.
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 Title
 Structuralism as a philosophy of mathematical practice
 Journal

Synthese
Volume 163, Issue 2 , pp 119131
 Cover Date
 20080701
 DOI
 10.1007/s1122900791696
 Print ISSN
 00397857
 Online ISSN
 15730964
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Philosophy of mathematics
 Structuralism
 Mathematical practice
 Industry Sectors
 Authors

 Jessica Carter ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark