Induction and explanatory definitions in mathematics

Synthese 198 (2):1161-1175 (2019)
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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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ CW}$$\end{document}-complexes—and argue that it is explanatory. With this, we see that there are cases of explanatory induction.

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Ellen Lehet
Lees-McRae College

Citations of this work

Mathematical Explanation in Practice.Ellen Lehet - 2021 - Axiomathes 31 (5):553-574.
Explicação Matemática.Eduardo Castro - 2020 - Compêndio Em Linha de Problemas de Filosofia Analítica.

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References found in this work

Mathematical concepts and definitions.Jamie Tappenden - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 256--275.
Mathematical concepts: Fruitfulness and naturalness.Jamie Tappenden - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 276--301.

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