Why did Weyl think that formalism's victory against intuitionism entails a defeat of pure phenomenology?

History and Philosophy of Logic 25:198-208 (2014)
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Abstract

It has been contended that it is unjustified to believe, as Weyl did, that formalism's victory against intuitionism entails a defeat of the phenomenological approach to mathematics. The reason for this contention, recently put forth by Paolo Mancosu and Thomas Ryckman, is that, unlike intuitionistic Anschauung, phenomenological intuition could ground classical mathematics. I argue that this indicates a misinterpretation of Weyl's view, for he did not take formalism to prevail over intuitionism with respect to grounding classical mathematics. I also point out that the contention is false: if intuitionism fails, in the way Weyl thought it did, i.e. with respect to supporting scientific objectivity, then one should also reject the phenomenological approach, in the same respect.

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Citations of this work

Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics?Iulian D. Toader - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11.
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References found in this work

Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton, N.J.: Princeton University Press. Edited by Olaf Helmer-Hirschberg & Frank Wilczek.
Naturalism Without Mirrors.Huw Price - 2011 - New York, US: OUP Usa.

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