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Induction and Explanatory Definitions in Mathematics

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
Creators:
CreatorsEmailORCID
Lehet, Ellenelehet@nd.edu0000-0002-5102-1990
Keywords: Mathematical Explanation, Mathematical Practice, Induction, Mathematical Definition
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Practice
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
Date: January 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15587

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