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Philosophy Behind Mathematics

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Handbook of the History and Philosophy of Mathematical Practice

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Abstract

In this chapter, we look at how philosophical standpoints widely held by mathematicians, conventionalism, and logical positivism were brought about through works of mathematicians. Starting from Poincaré’s philosophical ideas, we try to understand philosophical ideas of two mathematicians in the Vienna Circle, Hans Hahn and Karl Menger, through their mathematical works. After that, we also touch upon a problem about the relationship between natural science and mathematics, which the Vienna Circle left unsolved.

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Acknowledgments

This research was supported by the JSPS Fund for the Promotion of Joint International Research 18KK0071.

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Authors and Affiliations

  1. Department of Mathematics, Gakushuin University, Tokyo, Japan

    Ken’ichi Ohshika

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  1. Ken’ichi Ohshika
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Correspondence to Ken’ichi Ohshika .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. University of Strasbourg, Strasbourg, France

    Athanase Papadopoulos

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Ohshika, K. (2021). Philosophy Behind Mathematics. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19071-2_70-1

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  • DOI: https://doi.org/10.1007/978-3-030-19071-2_70-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19071-2

  • Online ISBN: 978-3-030-19071-2

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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