Abstract
In this paper, I present a summary of the philosophical relationship betweenWittgenstein and Brouwer, taking as my point of departure Brouwer's lecture onMarch 10, 1928 in Vienna. I argue that Wittgenstein having at that stage not doneserious philosophical work for years, if one is to understand the impact of thatlecture on him, it is better to compare its content with the remarks on logics andmathematics in the Tractactus. I thus show that Wittgenstein's position, in theTractactus, was already quite close to Brouwer's and that the points of divergence are the basis to Wittgenstein's later criticisms of intuitionism. Among the topics of comparison are the role of intuition in mathematics, rule following, choice sequences, the Law of Excluded Middle, and the primacy of arithmetic over logic.
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REFERENCES
Alexandroff, P.: 1961, Elementary Concepts of Topology, Dover, New York.
Brouwer, L. E. J.: 1975, in A. Heyting (ed.), Collected Works, volume 1, North-Holland, Amsterdam.
Brouwer, L. E. J.: 1981, in D. van Dalen (ed.), Brouwer's Cambridge Lectures on Intuitionism, Cambridge University Press, Cambridge.
Brouwer, L. E. J.: 1996a, ‘Mathematics, Science, and Language’, in Ewald (1996), vol. 2, pp. 1175–1185.
Brouwer, L. E. J.: 1996b, ‘The Structure of the Continuum’, in Ewald (1996), vol. 2, pp. 1186–1197.
Church, A.: 1932, ‘A Set of Postulates for the Foundation of Logic’, Annals ofMathematics 33, 346–366; 34, 839-864.
Crary, A. and R. Read (eds.): 2000, The New Wittgenstein, Routledge, London.
Dubucs, J.: 1988, ‘L. E. J. Brouwer: Topologie et Constructivisme’, Revue d'Histoire des Sciences 41, 133–155.
Hancock, P. and P. Martin-Löf: 1975, ‘Syntax and Semantics of the Language of Primitive Recursive Functions’, preprint no. 3, Department of Mathematics, University of Stockholm.
Hindley, J. R. and J. P. Seldin: 1986, Introduction to Combinators and λ-Calculus, Cambridge University Press, Cambridge.
Ewald, W. (ed.): 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Oxford, Clarendon Press.
Feigl, H.: 1981, ‘The Wiener Kreis in America’, in R. S. Cohen (ed.), Inquiries and Provocations. Selected Writings 1929-1974, Dordrecht, D. Reidel, pp. 57–94.
Finch, H. Le Roy: 1977, Wittgenstein-The Later Philosophy, Humanities Press, Atlantic Highlands, N.J.
Frascolla, P.: 1994, Wittgenstein's Philosophy of Mathematics, Routledge, London.
Frascolla, P.: 1997, ‘The Tractatus System of Arithmetic’, Synthese 112, 353–378.
Gödel, K.: 1986, ‘On Intuitionistic Arithmetic and Number Theory’, in S. Feferman et al. (eds.), Collected Works, Oxford University Press, Oxford, vol. 1, pp. 287–295.
Hacker, P.M. S.: 1972, Insight & Illusion.Wittgenstein on Philosophy and the Metaphysics of Experience, Clarendon Press, Oxford.
Hacker, P. M. S.: 1986, Insight & Illusion. Themes in the Philosophy of Wittgenstein, revised edition, Clarendon Press, Oxford.
Hilbert, D.: 1998, ‘The New Grounding of Mathematics. First Report’, in Mancosu (1998), pp. 198–214.
Hintikka, M. B. and J. Hintikka: 1986, Investigating Wittgenstein, Blackwell, Oxford.
Hintikka, J.: 1992, ‘“Die Wende der Philosophie’: Wittgenstein's New Logic of 1928', reprint in Hintikka (1996), pp. 79–105.
Hintikka, J.: 1996, Selected Papers, Volume 1. Ludwig Wittgenstein. Half-Truths and Oneand-a-Half Truths, Kluwer, Dordrecht.
Körner, S.: 1960, The Philosophy of Mathematics. An Introduction, Harper Torchbooks, New York.
Kreisel, G. and M. H. A. Newman: 1969, ‘Luitzen Egbertus Jan Brouwer 1881-1966’, Biographical Memoirs of the Fellows of the Royal Society, pp. 39–68.
Latraverse, F.: 2002, ‘Signes, Propositions, Situations. Éléments pour une lecture du Tractatus Logico-Philosophicus’, Revue Internationale de Philosophie m. 219, 124–140.
Mancosu, P. (ed.): 1998, From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press, Oxford.
Marion, M.: 1998, Wittgenstein, Finitism, and the Foundations of Mathematics, Clarendon Press, Oxford.
Marion, M.: 2000, ‘Operations and Numbers in the Tractatus’, Wittgenstein Studien 2, 105–123.
Marion, M.: 2001, ‘Qu'est-ce que l'inférence? Une relecture du Tractatus Logico-Philosophicus’, Archives de Philosophie 64, 545–567.
Martin-Löf, M.: 1982, ‘On the Meanings of the Logical Constants and the Justifications of the Logical Laws’, in C. Bernardi and P. Pagli (eds.), Atti Degli Incontri di Logica Matematica, Scuola di Specializzazione in Logica Matematica, Dipartimento di Matematica, Universita di Siena, vol. 2, pp. 203–281.
McGuinness, B. F.: 1991, ‘Wittgensteins Beziehungen zum Schlick-Kreis’, in P. Kruntorad, R. Haller and W. Hochkeppel (eds.), Jour fixe der Vernunft. Der Wiener Kreis und die Folgen, Hölder-Pichler-Tempsky, Vienna, pp. 108–126.
Menger, K.: 1994, in L. Golland, B. McGuinness and A. Sklar (eds.), Reminiscences of the Vienna Circle and the Mathematical Colloquium, Kluwer, Dordrecht.
Monk, R.: 1990, Ludwig Wittgenstein. The Duty of Genius, Jonathan Cape, London.
Pitcher, G.: 1964, The Philosophy of Wittgenstein, Prentice-Hall, Englewood Cliffs, N.J.
Ramsey, F. P.: 1978, in D. H. Mellor (ed.), Foundations, Routledge & Kegan Paul, London.
Rose, H. E.: 1988, ‘Obituary: R. L. Goodstein’, Bulletin of the London Mathematical Society, 20, 155–166.
Sundholm, G.: 1985, ‘Brouwer's Anticipation of the Principle of Charity’, Aristotelian Society Proceedings 85, 263–276.
Tait, W. W.: 1981, ‘Finitism’, Journal of Philosophy 78, 524–546.
van Atten, M. S. P. R.: 1999, Phenomenology of Choice Sequences, Quaestiones Infinitae 31, Zeno, The Leiden-Utrecht Institute of Philosophy, Utrecht.
van Dalen, D.: 1990, ‘The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen’Mathematical Intelligencer 12(4), 17–31
van Peursen, C. A.: 1970, Ludwig Wittgenstein. An Introduction to his Philosophy, Dutton, New York.
Wittgenstein, L.: 1922, Tractatus Logico-Philosophicus, Routledge & Kegan Paul, London.
Wittgenstein, L.: 1974, Philosophical Grammar, Blackwell, Oxford.
Wittgenstein, L.: 1975, Philosophical Remarks, Blackwell, Oxford.
Wittgenstein, L.: 1976, Lectures on the Foundations of Mathematics, Cambridge 1939, University of Chicago Press, Cambridge.
Wittgenstein, L.: 1979a, Notebooks 1914-1916, second edition, Blackwell, Oxford, 1979.
Wittgenstein, L.: 1979b, Ludwig Wittgenstein and the Vienna Circle, from the notes of F. Waismann, Blackwell, Oxford.
Wittgenstein, L.: 1980, Wittgenstein's Lectures, Cambridge 1930-1932, from the notes of J. King and D. Lee, Blackwell, Oxford.
Wittgenstein, L.: 1994a, Wiener Ausgabe, Band 1, Philosophische Bemerkungen, Springer Verlag, Wien/New York.
Wittgenstein, L.: 1994b, Wiener Ausgabe, Band 2, Philosophische Betrachtungen/ Philosophische Bemerkungen, Springer Verlag, Wien/New York.
Wittgenstein, L.: 1995, Wiener Ausgabe, Band 4, Philosophische Betrachtungen/ Philosophische Bemerkungen, Springer Verlag, Wien/New York.
Wrigley, M.: 1989, ‘The Origins ofWittgenstein's Verificationism’, Synthese 78, 265–290.
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Marion, M. Wittgenstein and Brouwer. Synthese 137, 103–127 (2003). https://doi.org/10.1023/A:1026230917748
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DOI: https://doi.org/10.1023/A:1026230917748