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Brouwerian intuitionism

Mind 99 (396):501-534 (1990)

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  1. Poincaré Against the Logicians.Michael Detlefsen - 1992 - Synthese 90 (3):349 - 378.
    Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...)
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  • Undecidability, Epistemology and Anti-Realist Intuitionism.Sanford Shieh - 1997 - Nordic Journal of Philosophical Logic 2:55-67.
  • Gestalt Switches in Poincaré׳s Prize Paper: An Inspiration for, but Not an Instance of, Chaos.Lena Christine Zuchowski - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:1-14.
    I analyse in detail the construction of asymptotic surfaces in Sections 16–19 of Poincaré , also known as the prize paper. There are two prime reasons for doing so. Firstly, this part of the prize paper contains an interesting argumentative strategy, which I call Poincaré׳s gestalt switch. Secondly, it has been claimed that the prize paper contains one of the first descriptions of chaotic motion. I will argue that the latter claim is false, although both the gestalt switches and the (...)
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  • Why Did Weyl Think That Formalism's Victory Against Intuitionism Entails a Defeat of Pure Phenomenology?Iulian D. Toader - 2014 - History and Philosophy of Logic 35 (2):198-208.
    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 (...)
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  • Against Against Intuitionism.Dirk Schlimm - 2005 - Synthese 147 (1):171-188.
    The main ideas behind Brouwer’s philosophy of Intuitionism are presented. Then some critical remarks against Intuitionism made by William Tait in “Against Intuitionism” [Journal of Philosophical Logic, 12, 173–195] are answered.
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