Structuralism as a philosophy of mathematical practice |
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Authors: | Jessica Carter |
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Institution: | (1) Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark |
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Abstract: | 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.
I wish to thank Colin McLarty as well as the anonymous referees for helpful comments on earlier versions of this paper. |
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Keywords: | Philosophy of mathematics Structuralism Mathematical practice |
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