Chapter

‘The Form of a Relation’: Peirce and Mathematical Structuralism

Christopher Hookway

in The Pragmatic Maxim

Published in print November 2012 | ISBN: 9780199588381
Published online January 2013 | e-ISBN: 9780191745089 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199588381.003.0007
‘The Form of a Relation’: Peirce and Mathematical Structuralism

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Mathematics raises a number of problems for pragmatist philosophers: how can pragmatists tolerate concepts such as numbers?; how can we apply the pragmatic maxim to clarify mathematical concepts?; of abstract objects and our knowledge of them?; and how can we obtain mathematical knowledge using the method of science? Peirce argues that the objects of mathematical propositions are abstract structures (the ‘form of a relation’), and, since these abstract structures can have concrete instantiations, we can obtain mathematical knowledge by experimenting on diagrams which are such concrete instantiations. This is explained through Pierce’s views about the natural numbers, showing how the primary uses of numerical expressions are adjectival but that terms for mathematical objects can be obtained through hypostatic abduction.

Keywords: mathematics; natural numbers; pragmatism; structuralism; metaphysics; Peirce; form of a relation; hypostatic abduction

Chapter.  10093 words. 

Subjects: History of Western Philosophy

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