From philosophical traditions to scientific developments: reconsidering the response to Brouwer’s intuitionism

Author:

Kish Bar-On KatiORCID

Abstract

AbstractBrouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline.

Funder

Massachusetts Institute of Technology

Publisher

Springer Science and Business Media LLC

Subject

General Social Sciences,Philosophy

Reference78 articles.

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3. van Atten, M. (2020). Luitzen Egbertus Jan Brouwer. The Stanford Encyclopedia of Philosophy. 2020. https://plato.stanford.edu/archives/win2017/entries/brouwer/

4. van Atten, M., Boldini, P., Bourdeau, M., & Heinzmann, G. (2008). One Hundred Years of Intuitionism (1907–2007). Birkhäuser Basel: Publications of the Henri Poincaré Archives

5. van Atten, M., van Dalen, D., & Tieszen, R. (2002). Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuum. Philosophia Mathematica, 10(2), 203–226

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