Lehet, Ellen (2019) Induction and Explanatory Definitions in Mathematics. [Preprint]
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Abstract
In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory
definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of
explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics
--- CW-complexes --- and argue that it is explanatory. With this, we see that there are cases of explanatory induction.
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Item Type: | Preprint | ||||||
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Keywords: | Mathematical Explanation, Mathematical Practice, Induction, Mathematical Definition | ||||||
Subjects: | Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Practice |
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Depositing User: | Ellen Lehet | ||||||
Date Deposited: | 16 Jan 2019 01:19 | ||||||
Last Modified: | 22 Jan 2019 13:36 | ||||||
Item ID: | 15587 | ||||||
Subjects: | Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Practice |
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Date: | January 2019 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/15587 |
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