Phenomenological Foundations of Mathematics

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Phenomenological Foundations of Mathematics

META: Research in Hermeneutics, Phenomenology, and Practical Philosophy – XI (2) / 2019 META: RESEARCH IN HERMENEUTICS, PHENOMENOLOGY, AND PRACTICAL PHILOSOPHY VOL. XI, NO. 2 / DECEMBER 2019: 322, ISSN 2067-3655, www.metajournal.org Editorial After Husserl: Phenomenological Foundations of Mathematics First and foremost, I would like to express my gratitude to all contributors for all of the hard work they put into writing their pieces of original work to show the lasting vibrancy and vitality of Edmund Husserl‟s ideas and to encourage further investigations. From the outset it was my intention to open up a way of research on different interpretative perspectives on Edmund Husserl and his interlocutors (Gottlob Frege, Oskar Becker, David Hilbert, Hermann Weyl, J. Klein, L.E.J. Brouwer, Kurt Gödel, Bourbaki, Marc Richir), which does not end up either in the naive celebration of Husserl‟s investigations of das Mathematisierendes Dasein or in its brute rejection. Professor Ilie Pârvu, my doctoral supervisor and an exemplary philosopher, was an inspiration: his erudition and analytical creativity spurred me on. This special issue would have been a very different project without his philosophical support. Also, I benefitted greatly from conversations on Oskar Becker‟s opus magnum from 1927, Mathematical Existence (Mathematische Existenz), and David Hilbert‟s „transcenden- talism‟ exposed in his metamathematics, with Constantin C. Brîncuş, with whom I worked in the project “The Phenomenological Analysis of Axiomatic Mathematics.” Brigitte Parakenings, the archivist at the Philosophical Archive of the University of Konstanz, helped me enormously with archival materials from The Oskar Becker collection. I am very grateful to George Bondor for his constructive suggestions and excellent editorial support. Thanks go also to the representatives and the production team of Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy. Guest Editor: Iulian Apostolescu (University of Bucharest & Phenomenological Reviews) December 15th, 2019 Bucharest, Romania 322 .

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1 Radical Besinnung in Formale Und Transzendentale Logik (1929)
1 Radical Besinnung in Formale und transzendentale Logik (1929)1 This is a pre-print of an article published in Husserl Studies. The final authenticated version is available online at: https://doi.org/DOI: 10.1007/s10743- 018-9228-5 ABSTRACT. This paper explicates Husserl’s usage of what he calls ‘radical Besinnung’ in Formale und transzendentale Logik (1929, henceforth FTL). Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical Besinnung and transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological framework within which transcendental phenomenological descriptions are used to criticize historically given goal- directed practices. KEYWORDS: Husserl, Formal and Transcendental Logic, Besinnung, mathematics, apophantic logic, phenomenological method, criticism. Introduction This paper explicates Husserl’s usage of what he calls ‘radical Besinnung’ in Formale und transzendentale Logik (1929, henceforth FTL). Husserl started to emphasize the importance of Besinnung already in the early in the 1920s,2 but, for the sake of a clear argument, I limit myself 1 This paper has been greatly improved thanks to the detailed criticisms and useful and generous suggestions of George Heffernan. I am particularly thankful for him for drawing my attention to FTL §§102-105, where Husserl discusses transcendental Selbst-Besinnung. 2 The term is mentioned already in Logical Investigations (e.g., Hua1/1, 24-25; 304).
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