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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 and Definitions

Mathematical Concepts and Definitions

(p.256) 9 Mathematical Concepts and Definitions
The Philosophy of Mathematical Practice

Jamie Tappenden

Oxford University Press

This chapter lays some preliminary groundwork for answering the question: What kind of success have we attained when we introduce a ‘good’ mathematical concept or definition? What sort of contribution is this to our mathematical knowledge? It develops two mathematical examples from algebraic number theory: the Legendre symbol and the definition of prime number. The question is studied in connection with the contrast of ‘real’ versus ‘nominal’ definitions in general, and with current philosophical theories of natural properties.

Keywords:   concept, definition, mathematical knowledge, Legendre symbol, prime number, real definition, nominal definition, natural properties

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