Revisiting Brouwer - Minimal Intuitionism

(Logik & Philosophie der Mathematik, Englisch)

he aim of this work is to show that a new reading of Brouwer's philosophical thought could be useful to fulfill the necessity of a philosophical account of intuition for intuitionism. To avoid the circularity argument formulated by Richard Dedekind an intuitionist is compelled to claim that in his definition of natural numbers the idea of keeping going, i.e. keeping following the arrows of the counting algorithm, is immediately intelligible and does not presuppose any grasp of eternity. To make this statement true a philosophical account of intuition is needed: the idea of keeping going can be immediately understandable only if we have the intuition that the process of construction can be continued infinitely. Brouwer tried to explain this in terms of temporal intuition but his philosophy is often rejected due to some structural problems such as irreflexivity, solipsism, psychologism and subjectivism. In the past twenty years attempts have been made to use the phenomenological method to overcome these difficulties. Philosophers like Richard Tieszen and Mark van Atten, using the Husserlian notion of intuition, answer the critics by interpreting Brouwer's creative subject as the phenomenological transcendental subject. In this work I will try to show that this kind of intuition, in which to intuit something means to present directly and immediately the object, is not suitable for intuitionism, since it makes it impossible to state a precise limit between constructive and non-constructive objects. Therefore, it is necessary to return to Brouwer's conception of intuition, which is a productive one, trying to solve all the problems exposed earlier. This is precisely what my efforts aim to. I believe that it is possible to read Brouwer in transcendental terms without using the Husserlian notion of intuition. Interpreting the intuition productively the minimal intuitionism answers easily to the charges of psychologism, subjectivism and solipsism. It also succeeds in solving the problem of irreflexivity modifying Brouwer's notion of two-ity: this is no more read in terms of temporal relation between sensations but in terms of an act-content relationship, thematized through an intentional act of reflection.

Chair: Christine Schurz

Zeit: 11:45-12:15, 14. September 2013 (Samstag)

Ort: HS 104

Andrea Tenuta

(Catholic University of Milan, Italien)

Andrea Tenuta (MA phil.). Catholic University of Milan. 2010 baccalaureate in Philosophy, thesis about the infinity in mathematics; 2013 master of arts in Logic and Philosophy of Science; thesis about the foundation of intuition in the intuitionism.

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Letzte Aktualisierung: 2013-02-14.