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Justifying definitions in mathematics: going beyond Lakatos

By Charlotte Werndl

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

Topics: QA Mathematics
Publisher: Oxford University Press
Year: 2009
DOI identifier: 10.1093/philmat
OAI identifier: oai:eprints.lse.ac.uk:31097
Provided by: LSE Research Online

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