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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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Mathematical Concepts: Fruitfulness and Naturalness

Mathematical Concepts: Fruitfulness and Naturalness

(p.276) 10 Mathematical Concepts: Fruitfulness and Naturalness
The Philosophy of Mathematical Practice

Jamie Tappenden

Oxford University Press

This chapter addresses the question of when one concept or definition is properly regarded as more ‘natural’ than another with reference to the principle that a mark of good definitions is their theoretical fruitfulness, especially as incorporated in the methodology implicit in the work of Riemann and Dedekind. It explores the suggestion that the objectivity of imputations of ‘naturalness’ of concepts/definitions/properties can be underwritten at least in part by quasi-empirical mathematical practices of conjecture and verification, in a mathematical analogue of Goodman's ‘New Riddle of Induction’.

Keywords:   concept, definition, natural property, fruitfulness, methodology, Bernhard Riemann, Richard Dedekind, conjecture, verification

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