Abstrakt
DOI: http://doi.org/10.26333/sts.xxxii2.03
THOMAS BEDÜRFTIG,ROMAN MURAWSKI
PHENOMENOLOGICAL IDEAS IN THE PHILOSOPHYOF MATHEMATICS. FROM HUSSERL TO GÖDEL
SU M M A R Y: The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker andGödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the philosophy of mathematics, namely Hermann Weyl and Oskar Becker, will be briefly discussed. Lastly, the connections between Husserl’s ideas and the philosophy of mathematics of Kurt Gödel will be studied.
ThomasBedürftig
Leibniz Universität Hannover
Institut für Didaktik der Mathematik und Physik
E-mail: th.beduerftig@gmx.de
Roman Murawski
Adam Mickiewicz University
Faculty of Mathematics and Comp. Sci
E-mail: rmur@amu.edu.pl
ORCID: 0000-0002-2392-4869
Bibliografia
Becker, O. (1927). Mathematische Existenz. Untersuchungen zur Logik und Ontologie mathematischer Phänomene. Jahrbuch für Philosophie und phänemenologische Forschung, 8, 439–809.
Bedürftig, Th., Murawski, R. (2015). Philosophie der Mathematik (3rd edition). Berlin/Boston: Walter de Gruyter.
Bedürftig, Th., Murawski, R. (2018), Philosophy of Mathematics. Berlin/Boston: Walter de Gruyter.
Cantor, G. (1895). Beiträge zur Begründung der transfiniten Mengenlehre. Mathematische Annalen, 46, 481–512.
Føllesdal, D. (1995). Gödel and Husserl. In: J. Hintikka (Ed.), Essays on the Development of the Foundations of Mathematics (pp. 427–446). Dordrecht: Kluwer Academic Publishers.
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I. Monatshefte für Mathematik und Physik, 38, 173–198.
Gödel K. (1944). Russell’s Mathematical Logic. In: P. A. Schilpp (Ed.), The Philosophy of Bertrand Russell (pp. 123–153). Evanston: Northwestern University. Reprinted in: K. Gödel, Collected Works, vol. II, ed. by S. Feferman et al., New York-Oxford 1990: Oxford University Press, 119–141.
Gödel, K. (1947/1964). What is Cantor’s Continuum Problem? The American Mathematical Monthly, 54, 515–525. Second revised version in: P. Benacerraf and H. Putnam (Eds.), Philosophy of Mathematics. Selected Readings (pp. 258–273). Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
Gödel, K. (1951/1995). Some Basic Theorems on the Foundations of Mathematics and Their Implications, first published in: S. Feferman et al. (Eds.), Collected Works, vol. III (pp. 304–323). New York and Oxford: Oxford University Press.
Gödel, K. (1953/1995). Is Mathematics Syntax of Language? (unfinished contribution), first published in: S. Feferman et al. (Eds.), Collected Works, vol. III (pp. 334–362). New York and Oxford: Oxford University Press.
Gödel, K. (1961/1995). The Modern Development of the Foundations of Mathematics in the Light of Philosophy, first published (German text and English translation) in: S. Feferman et al. (Eds.), Collected Works, vol. III (pp. 374–387). New York and Oxford: Oxford University Press.
Grattan-Guinness, I. (2000). The Search for Mathematical Roots 1870–1940. Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton and London: Princeton University Press.
Hartimo, M. (2017). Husserl and Gödel’s Incompleteness Theorems. Review of Symbolic Logic, 10(4), 638–650.
Husserl, E. (1891). Philosophie der Arithmetik. Psychologische und logische Untersuchungen, Halle-Saale: C. E. M. Pfeffer.
Husserl, E. (1900–1901), Logische Untersuchungen (Vol. 1–2). Halle: Niemeyer.
Husserl, E. (1970). Philosophie der Arithmetik. Mit Ergänzenden Texten (1890–1901). The Hague: Martinus Nijhoff.
Husserl, E. (1994). Edmund Husserl Briefwechsel. Band VII: Wissenschaftskorrespondenz. Dordrecht: Kluwer Academic Publishers.
Husserl, E. (2003). Philosophy of Arithmetic. Psychological and Logical Investigations with Supplementary Texts from 1887–1901. Collected Works, vol. X. Dordrecht: Kluwer Academic Publishers.
Kauferstein, C. (2006). Transzendentalphilosophie der Mathematik. Stuttgart: ibidem-Verlag.
Kaufmann, F. (1930). Das Unendliche in der Mathematik und seine Ausschaltung. Leipzig and Vienna: Franz Deuticke.
Kirby L., Paris J. (1982). Accessible Independence Results for Peano Arithmetic. Bulletin of London Mathematical Society, 14(4), 285–293.
Maddy, P. (1980). Perception and Mathematical Intuition. The Philosophical Review, 89(2), 163–196.
Mancosu, P., Ryckman Th. (2005). Geometry, Physics and Phenomenology: Four Letters of O. Becker to H. Weyl. In: V. Peckhaus (Ed.), Oskar Becker und die Philosophie der Mathematik (pp. 229–243). München: Fink Verlag, 229–243.
Murawski, R. (1984). Matematyczna niezupełność arytmetyki. Roczniki Polskiego Towarzystwa Matematycznego. Seria II: Wiadomości Matematyczne, 26, 47–58.
Paris J., Harrington L. (1977). A Mathematical Incompleteness in Peano Arithmetic. In: J. Barwise (Ed.), Handbook of Mathematical Logic (pp. 1133–1142). Amsterdam: North-Holland Publ. Comp.
Parsons, Ch. (1980). Mathematical Intuition. Proceedings of the Aristotelian Society, 80, 145–168.
Tieszen, R. (1988). Phenomenology and Mathematical Knowledge. Synthese, 75(3), 373–403.
Tieszen, R. (1994). The Philosophy of Arithmetic: Frege and Husserl. In: L. Haaparanta (Ed.), Mind, Meaning and Mathematics (pp. 85–112). Dordrecht: Kluwer Academic Publishers.
Wang, Hao (1974). From Mathematics to Philosophy. London: Routledge and Kegan Paul.
Wang, Hao (1996). A Logical Journey: From Gödel to Philosophy. Cambridge, Mass., and London, England: The MIT Press.
Weyl, H. (1918). Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis. Leipzig: Veit.
Weyl, H. (1922). Raum, Zeit, Materie. Vorlesungen über allgemeine Relativitätstheorie (5th ed.). Wien: Springer.
Weyl, H. (1967). Comments on Hilbert’s Second Lecture on the Foundations of Mathematics. In: J. van Heijenoort (Ed.), From Frege to Gödel. A Source Book in Mathematical Logic 1879–1930 (pp. 480–484). Cambridge, Mass.: Harvard University Press.