Title < 特別寄稿 > 数学の無尽蔵性 と二つの哲学 -- カヴァイエスとゲーデル -- Author(s) 中村, 大介 Citation 哲学論叢 (2016), 43: 27-39 Issue Date 2016 URL http://hdl.handle.net/2433/219150 Right Type Departmental Bulletin Paper Textversion publisher Kyoto University
特別寄稿 1931 Kurt Gödel, 1906-1978 inexhaustibility Jean Cavaillès, 1903-1944 1 2 3 1. 27
1931 1936 J B A A A A A (1) 1920 1931 (2) 1947 (3) ZF 1963 (4) 1953 1959 28
数学の無尽蔵性 と二つの哲学 (5) 1959 1961 (Gödel, 1995a, p. 383) Cassou-Noguès (2005, p. 213) 1920 1933 (6) van Atten & Kennedy (2003, pp. 430 434) 29
2. 1938 19 1947 19 30
数学の無尽蔵性 と二つの哲学 (Cavaillès, 1981, pp. 143 144) (7) (Cavaillès, 1981, p. 144) 0 Sinaceur (1999, pp. 301 333) 1930 31
1937 (Cavaillès, 1994a, p. 577) (8) 32
数学の無尽蔵性 と二つの哲学 3. 1947 3 1913 1929 tertium non datur (Husserl, 1974, p. 100,, 106 ) (9) 33
Tertium datur (Cavaillès, 1997, pp. 84 85,, 63 ) 1901 L M L M L L M (10) L (11) (Husserl, 1974, p. 196,, 209 ) 34
数学の無尽蔵性 と二つの哲学 L L M L L L M L M L (Cavaillès, 1997, p. 84,, 62 ) 35
(12) (13) 36
数学の無尽蔵性 と二つの哲学 (Cavaillès, 1994b, p. 603) (1) (2006, pp. 139 141) 1951 incompletability (Gödel, 1995b, p. 309,, 11 ) (2) XI M A P M, A (Gödel, 1986, p. 194,, 61 ) (3) Gödel (1990, pp. 261 264,, 26 30 ) (4) (Gödel, 1990, pp. 269 270,, 38 39 (5) (Gödel, 1995c, pp. 343 344,, 37 ) (6) (Gödel, 1995d, p. 50) (7) Zach (2001, pp. 83 85) (2006, 225 231 ) (8) (9) (1997) (10) Husserl (1970, p. 441) (11) (1987) Okada (2013) (12) (Cavaillès, 1997, p. 90,, 67 ) 37
(13) Gödel (1990, p. 260,, 25 ) Gödel (1995b, p. 321,, 19 ) (1995, 292 293 ) van Atten, M., Kennedy, J. (2003). On the philosophical development of Kurt Gödel, The Bulletin of Symbolic Logic, 9, 4, 425 476. Cassou-Noguès, P. (2005). Gödel and the objective existence of mathematical objects, History and Philosophy of Logic, 26, 211 228. Cavaillès, J. (1981). Méthode axiomatique et formalisme. Essai sur le problème du fondement des mathématiques, Paris: Hermann. (1994a). Réflexions sur le fondement des mathématiques, in B. Huisman (Ed.), Œuvres complètes de philosophie des sciences (pp. 577 580), Paris: Hermann. (1994b). La pensée mathématique, (en collaboration avec Albert Lautman) in B. Huisman (Ed.), Œuvres complètes de philosophie des sciences (pp. 593 630), Paris: Hermann. (1997). Sur la logique et la théorie de la science, Paris: Vrin. (2013,,,.) Gödel, K. (1986). Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I, in S. Feferman, J. W. Dawson, S. C. Kleene, G. H. Moore, R. M. Solovay & J. v. Heijenoort (Eds.), Collected Works, vol. 1 (pp. 144 195), New York: Oxford University Press-Clarendon Press. (2006,, I,, (15 72 ),.) (1990). What is Cantor s continuum problem?, in S. Feferman, J. W. Dawson, S. C. Kleene, G. H. Moore, R. M. Solovay & J. v. Heijenoort (Eds.), Collected Works, vol. 2 (pp. 254 270), New York: Oxford University Press-Clarendon Press. (1995,,,, (17 55 ),.) (1995a). The Modern Development of the Foundations of Mathematics in the Light of Philosophy, in S. Feferman, J. W. Dawson, W. Goldfarb, C. Parsons & R. M. Solovay (Eds.), Collected Works, vol. 3 (pp. 374 387), New York: Oxford University Press-Clarendon Press. (1995b). Some Basic Theorems on the Foundations of Mathematics and their Implications, in S. Feferman J. W. Dawson, W. Goldfarb, C. Parsons & R. M. Solovay (Eds.), Collected Works, vol. 3 (pp. 304 323), New York: Oxford University Press-Clarendon Press. (2007,,,, 35 3, 8 27. ) (1995c). Is Mathematics Syntax of Language?, in S. Feferman, J. W. Dawson, W. Goldfarb, C. Parsons & R. M. Solovay (Eds.), Collected Works, vol. 3 (pp. 334 356), New York: Oxford University Press-Clarendon Press. (2007,,,, 35 3, 28 51.) (1995d). The Present Situation in the Foundations of Mathematics, in S. Feferman, J. W. Dawson, W. Goldfarb, C. Parsons & R. M. Solovay (Eds.), Collected Works, vol. 3 (pp. 45 53), New York: Oxford University Press-Clarendon Press., (2006).,, (73 305 ),. Husserl, E. (1970). Das Imaginäre in der Mathematik, in Lothar Eley (Ed.), Husserliana, vol. 12 (pp. 430 451), Den Haag: Martinus Nijhoff. (1974). Formale und Transzendentale Logik : Versuch einer Kritik der logischen Vernunft, in P. Janssen (Ed.), Husserliana, vol. 17 (pp. 1 298), Den Haag: Martinus Nijhoff. (2015,,,.) (2006).,, 20 20 (111 169 ),. (1987).,, 37, 210 221. (1997).,,, 38
数学の無尽蔵性 と二つの哲学 101, 1 43. Okada, M. (2013). Husserl and Hilbert on Completeness and Husserl's Term Rewrite-based Theory of Multiplicity, 24th International Conference on Rewriting Techniques and Applications (RTA2013), 21, 4 19. Sinaceur, H. (1999). Corps et modèles. Essai sur l'histoire de l'algèbre réelle, seconde édition corrigée, Paris: Vrin. (1995).,,. Zach, R. (2001). Hilbert s Finitism: Historical, Philosophical, and Metamathematical Perspectives, Dissertation, University of California: Berkeley. 39