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Philosophy Behind Mathematics

In: Handbook of the History and Philosophy of Mathematical Practice

Author

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  • Ken’ichi Ohshika

    (Gakushuin University, Department of Mathematics)

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.

Suggested Citation

  • Ken’ichi Ohshika, 2024. "Philosophy Behind Mathematics," Springer Books, in: Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, pages 881-895, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-40846-5_70
    DOI: 10.1007/978-3-031-40846-5_70
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