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 |
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| 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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