Justifying definitions in mathematics—going beyond Lakatos

Philosophia Mathematica 17 (3):313-340 (2009)
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
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DOI 10.1093/philmat/nkp006
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References found in this work BETA
Charlotte Werndl (2009). What Are the New Implications of Chaos for Unpredictability? British Journal for the Philosophy of Science 60 (1):195-220.

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Citations of this work BETA
Charlotte Werndl (forthcoming). On Defining Climate and Climate Change. British Journal for the Philosophy of Science:axu048.
Lena Christine Zuchowski (2014). Gestalt Switches in Poincaré׳s Prize Paper: An Inspiration for, but Not an Instance of, Chaos. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:1-14.

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