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The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos

Werndl, Charlotte (2009) The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos. [Preprint]

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The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable.

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Item Type: Preprint
Werndl, Charlotte
Keywords: definitions in mathematics; justification of definitions; Lakatos; chaos; mathematical reasoning
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Mathematics
Depositing User: Charlotte Werndl
Date Deposited: 30 Jun 2011 11:29
Last Modified: 30 Jun 2011 11:29
Item ID: 8687

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