Mathematical truth revisited: Mathematics as a toolbox

Reinhard Kahle

doi:10.1007/978-3-319-51608-0_22

Mathematical truth revisited: Mathematics as a toolbox

Reinhard Kahle

DM - Departamento de Matemática

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We discuss the notion of truth in Mathematics as relative to certain structures, very much in line with Bernays’s conception of “bezogene Existenz”. Looking to some concrete examples, we argue that even so-called non-standard structures may have their own rationale. As a result, and in accordance with Bourbaki, structures turn out to be tools and have to be judged with respect to their usefulness rather than with respect to a concept of mathematical truth simpliciter.

Original language	English
Title of host publication	Varieties of Scientific Realism
Subtitle of host publication	Objectivity and Truth in Science
Publisher	SPRINGER INTERNATIONAL PUBLISHING AG
Pages	395-406
Number of pages	12
ISBN (Electronic)	978-331951608-0
ISBN (Print)	978-331951607-3
DOIs	https://doi.org/10.1007/978-3-319-51608-0_22
Publication status	Published - 1 Jan 2017

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10.1007/978-3-319-51608-0_22

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Kahle, R. (2017). Mathematical truth revisited: Mathematics as a toolbox. In Varieties of Scientific Realism: Objectivity and Truth in Science (pp. 395-406). SPRINGER INTERNATIONAL PUBLISHING AG. https://doi.org/10.1007/978-3-319-51608-0_22

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