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The Pragmatic MaximEssays on Peirce and pragmatism$
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Christopher Hookway

Print publication date: 2012

Print ISBN-13: 9780199588381

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199588381.001.0001

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

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

(p.115) 6 ‘The Form of a Relation’: Peirce and Mathematical Structuralism
The Pragmatic Maxim

Christopher Hookway

Oxford University Press

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

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