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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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What Structuralism Achieves

What Structuralism Achieves

Chapter:
(p.354) 13 What Structuralism Achieves
Source:
The Philosophy of Mathematical Practice
Author(s):

Colin McLarty

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199296453.003.0014

Mathematicians in practice use a quite different idea of structure than is discussed by many philosophers of mathematics. Great work in geometry and number theory made category theory the standard structure concept in textbooks and research. Categorical tools produce an ontology similar to the various philosophical structuralisms, but not identical to any one. While some philosophers feel abstraction detracts from intuition or from the unity of mathematics, experience shows categorical structure often gives the most transparent link of intuition to rigorous proof and the most productive unity between many branches.

Keywords:   isomorphism, structuralism, ontology, topology, number theory

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