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Why DidWeyl Think that Formalism’s Victory Against Intuitionism Entails a Defeat of Pure Phenomenology?

机译:魏尔为什么认为形式主义对直觉主义的胜利必然导致纯粹现象学的失败?

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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 wayWeyl thought it did, i.e. with respect to supporting scientific objectivity, then one should also reject the phenomenological approach, in the same respect.
机译:有人认为,像韦尔一样,认为形式主义对直觉主义的胜利必然会导致数学现象学方法的失败,这是没有道理的。保罗·曼科苏(Paolo Mancosu)和托马斯·里克曼(Thomas Ryckman)最近提出这种争论的原因是,与直觉主义的Anschauung不同,现象学的直觉可以成为古典数学的基础。我认为这表明对魏尔的观点有误解,因为就古典数学的基础而言,他并未使形式主义胜于直觉主义。我还指出这一论点是错误的:如果直觉主义以魏尔认为的方式失败,即在支持科学客观性方面,那么人们也应该在同一方面拒绝现象学方法。

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