Structuralism as a philosophy of mathematical practice

Synthese 163 (2):119 - 131 (2008)
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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.

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
Frege.Michael Dummett - 1973 - Cambridge, Mass.: Harvard University Press.

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