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Justifying Definitions in Mathematics—Going Beyond Lakatos

Werndl, Charlotte (2009) Justifying Definitions in Mathematics—Going Beyond Lakatos. [Preprint]


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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 that various kinds of justification can be found and can be reasonable, and they fail to acknowledge the interplay between the different kinds of justification.

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Item Type: Preprint
Werndl, Charlotte
Additional Information: Forthcoming in: Philosophia Mathematica
Keywords: definitions in mathematics, justification of definitions, Lakatos, mathematical reasoning, chaos, dynamical systems theory, ergodic theory
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Complex Systems
Specific Sciences > Probability/Statistics
Specific Sciences > Mathematics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Charlotte Werndl
Date Deposited: 31 Mar 2009
Last Modified: 07 Oct 2010 15:17
Item ID: 4537

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