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Justifying definitions in mathematics: going beyond Lakatos

Werndl, Charlotte (2009) Justifying definitions in mathematics: going beyond Lakatos. Philosophia Mathematica, 17 (3). pp. 313-340. ISSN 0031-8019

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Abstract

This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world justification, condition justification, and redundancy justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show how various kinds of justification can be found and can be reasonable, and they fail to acknowledge the interplay among the different kinds of justification.

Item Type: Article
Official URL: http://philmat.oxfordjournals.org/
Additional Information: © 2009 The Author
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Philosophy, Logic and Scientific Method
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 Jan 2011 13:42
URL: http://eprints.lse.ac.uk/31097/

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