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Philosophia Mathematica Advance Access originally published online on May 8, 2009
Philosophia Mathematica 2009 17(3):313-340; doi:10.1093/philmat/nkp006
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© The Author [2009]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Justifying Definitions in Mathematics—Going Beyond Lakatos{dagger}

Charlotte Werndl*

* Faculty of Philosophy, University of Cambridge, Sidqwick Avenue, Cambridge CB3 9DA U.K. csw39{at}cam.ac.uk

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.

{dagger} I am indebted to Jeremy Butterfield and Peter Smith for valuable feedback on previous versions of this manuscript. Many thanks to Roman Frigg, Franz Huber, Brendan Larvor, Mary Leng, Paul Weingartner, two anonymous referees and the audiences at the 1st London-Paris-Tilburg Workshop in Logic and Philosophy of Science and the 1st Conference of the European Philosophy of Science Association for helpful comments. I am grateful to St John's College, Cambridge, for financial support.


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