Structuralism as a philosophy of mathematical practice

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

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.
Keywords structuralism   mathematics   WAYS
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DOI 10.1007/s11229-007-9169-6
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References found in this work BETA

Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Harvard University Press.

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Citations of this work BETA

Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.

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