Justifying definitions in mathematics—going beyond Lakatos

Philosophia Mathematica 17 (3):313-340 (2009)
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
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References found in this work BETA
Joseph Berkovitz, Roman Frigg & Fred Kronz (2006). The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (4):661-691.
D. Corfield (1997). Assaying Lakatos's Philosophy of Mathematics. Studies in History and Philosophy of Science Part A 28 (1):99-121.
Roman Frigg (2006). The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. Studies in History and Philosophy of Science Part B 37 (4):661-691.

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