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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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    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 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
    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 11:17
    Item ID: 4537
    URI: http://philsci-archive.pitt.edu/id/eprint/4537

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