In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort

详细信息    查看全文

• 作者：Philippe de Rouilhan (1)
  
• 关键词：03A05 ; 03 ; 03 ; 03Cxx ; A1A60 ; 01A85 ; Jean van Heijenoort ; philosophy of logic ; history of logic ; logical universalism ; model theory
• 刊名：Logica Universalis
• 出版年：2012
• 出版时间：4 - December 2012
• 年：2012
• 卷：6
• 期：3
• 页码：553-586
• 全文大小：415KB
• 参考文献：1. Ajdukiewicz, K.: Z metodologji nauk dedukcyjnych. Nak艂adem Polskiego Towarzystwa Filozoficznego, Lw贸w (1921)
  2. Bynum, T.W.: Editor鈥檚 Introduction. In: [18], pp. 55鈥?00 (1972)
  3. Carroll, L.: What the Tortoise said to Achilles, Mind (n.s) 4, 278鈥?80 (1895)
  4. Carroll, L.: (Gatt茅gno, J., Coumet, E., trans. & ed.), Logique sans peine. Hermann, Paris (1966)
  5. Coumet, E.: Lewis Carroll logicien. In: [4], pp. 255鈥?88 (1966)
  6. Dedekind, R.: Was sind uns was sollen die Zahlen? Vieweg, Braunschweig (1888)
  7. Enderton, H.B.: A Mathematical Introduction to Logic. Academic Press, London (1972) (2nd edn. 2001)
  8. Feferman, A.B.: Politics, Logic, and Love: The Life of Jean van Heijenoort. Jones and Bartlett, Boston; A K Peters, Wellesley, MA (1993); reprinted as: From Trotsky to G枚del: The Life of Jean van Heijenoort. A K Peters, Natick, Mass (2001)
  9. Feferman, A.B., Feferman, S.: Jean van Heijenoort (1912鈥?986). In: [56], pp. 1鈥? (1987)
  10. Feferman A.B., Feferman S.: Alfred Tarski: Life and Logic. Cambridge University Press, Cambridge (2004)
  11. Fraenkel, A.A.: Der Begriff 鈥渄efinit鈥?und die Unabh盲ngigkeit des Auswahlsaxioms, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 253鈥?57 (1922)
  12. Fraenkel A.A.: Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre. Math. Ann. 86, 230鈥?37 (1922) CrossRef
  13. Frege, G.: Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. L. Nebert, Halle (1879); English translations in: [60], pp. 1鈥?2 (1967) and [18], pp. 101鈥?03 (1972)
  14. Frege, G.: 脺ber den Zweck der Begriffsschrift, Sitzungsberichte der Jenaischen Gesellschaft f眉r Medicin und Naturwissenschaft f眉r das Jahr 1882 16, Suppl.-Heft II, 1鈥?0 (1882-83)
  15. Frege, G.: 脺ber Begriff und Gegenstand, Vierteljahrsschrift f眉r wissenschaftliche Philosophie (N.F.) 16, 192鈥?05 (1892)
  16. Frege, G.: Grundgesetze der Arithmetik begriffsschriftlich abgeleitet, 2 Bde. H. Pohle, Jena (1893鈥?903)
  17. Frege, G.: Letter to Russell dated June 22, 1902 (1902); English translation in: [60], pp. 126鈥?28 (1967)
  18. Frege G.: Conceptual Notation and Related Articles (Bynum, T.W., trans. & ed.). Clarendon Press, Oxford (1972)
  19. Girard, J.-Y.: La mouche dans la bouteille. In: [56], pp. 9鈥?2 (1987)
  20. G枚del, K.: 脺ber die Vollst盲nsdigkeit des Logikkalk眉ls, Dissertation, University of Vienna (1929); reprinted, with English translation, in: [23], vol. I, pp. 60鈥?01 (1986-2003)
  21. G枚del, K.: Die Vollst盲ndigkeit der Axiome des logischen Funktionenkalk眉ls. Monatsh. Math. Phys. 37, 349鈥?60 (1930); English translation in: [60], pp. 582鈥?91 (1967); reprinted in, with English translation, in: [23], vol. I, pp. 102鈥?23 (1986-2003)
  22. G枚del, K.: 脺ber formal unentscheidbare S盲tze der Principia Mathematica und verwandter Systeme I. Monatsh. Math. Phys. 38, 173鈥?98 (1931); English translation in: [60], pp. 596鈥?17 (1967); reprinted with English translation in: [23], vol. I, pp. 144鈥?95 (1986鈥?003)
  23. G枚del K.: Collected Works, 5 vols (Feferman, S., / et聽al., eds.). Oxford University Press, Oxford (1986鈥?003)
  24. Goldfarb W.D.: Logic in the twenties: the nature of the quantifier. J. Symbol. Logic 44, 351鈥?68 (1979) CrossRef
  25. Herbrand J.: 脡crits logiques (van Heijenoort, J., ed.). Presses Universitaires de France, Paris (1968)
  26. Hilbert D., Ackermann W.: Grundz眉ge der theoretischen Logik. Springer, Berlin (1928)
  27. Hintikka, J.: On the development of the model-theoretic viewpoint in logical theory. Synth猫se 77, 1鈥?6 (1988); reprinted in: [28], pp. 104鈥?39 (1997)
  28. Hintikka, J.: Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieth-Century Philosophy. Kluwer, Dordrecht (1997)
  29. Hylton P.: Russell鈥檚 substitutional theory. Synthese 45, 1鈥?1 (1980) CrossRef
  30. Hylton P.: Russell, Idealism and the Emergence of Analytic Philosophy. Clarendon Press, Oxford (1990)
  31. Kripke S.: Outline of a theory of truth. J. Philos. 72, 690鈥?16 (1975) CrossRef
  32. L枚wenheim, L.: 脺ber M枚glichkeiten im Relativkalk眉l, Math. Ann. 76, 447鈥?70; English translation in: [60], pp. 228鈥?51 (1967)
  33. Martin-L枚f P.: Intuitionistic Type Theory. Bibliopolis, Naples (1984)
  34. Partee B.H.: Montague grammar and transformational grammar. Linguist. Inquiry 6, 203鈥?00 (1975)
  35. Peano, G.: Arithmetices principia, nova methodo exposita. Bocca, Turin (1889); English partial translation in: [60], pp. 83鈥?7 (1967)
  36. Quine, W.V.: Letter to Jean van Heijenoort dated December 4, 1974. In: [76], p. 39 (1985)
  37. Rayo, A., Uziquiano, G. (eds.): Absolute Generality. Clarendon Press, Oxford (2006)
  38. Rosser J.B.: Extensions of some theorems of G枚del and Church. J. Symbol. Logic 1, 87鈥?1 (1936) CrossRef
  39. de Rouilhan, Ph.: J.v.H; (speech delivered in memory of Jean van Heijenoort at the Institut Henri Poincar茅 on May 14, 1986). In: [56], pp. 13鈥?6 (1987)
  40. de Rouilhan, Ph.: Frege. Les paradoxes de la repr茅sentation. Les Editions de Minuit, Paris (1988)
  41. de Rouilhan, Ph.: De l鈥檜niversalit茅 de la logique. In: Bouveresse, J. (茅d.) L鈥櫭e de la science. Lectures philosophiques, vol. 4. I: Philosophie de la logique et philosophie du langage, pp. 93鈥?13. 脡ditions Odile Jacob, Paris (1991)
  42. de Rouilhan, Ph.: Tarski et l鈥檜niversalit茅 de la logique. In: Nef, F., Vernant, D. (eds.) Le formalisme en question. Le tournant des ann茅es, vol. 30, pp. 85鈥?02. Vrin Paris (1998)
  43. de Rouilhan Ph.: La th茅orie des mod猫les et l鈥檃rchitecture des math茅matiques. In: Gochet, P., Rouilhan, Ph. (eds.) Logique 茅pist茅mique et philosophie des math茅matiques, pp. 39鈥?14. Vuibert, Paris (2007)
  44. de Rouilhan, Ph.: Generalizing Frege鈥檚 paradox and putting truth to work to solve it. In: Achourioti, D., Fujimoto, K., Galinon, H., Martinez, J. (eds.) Unifying the Philosophy of Truth. Springer, Berlin (forthcoming)
  45. Russell, B.: Letter to Frege dated June 16, 1902. In: [60], pp. 124鈥?25 (1967)
  46. Russell, B.: The Principles of Mathematics. G. Allen & Unwin, London (1903)
  47. Skolem, Th.: Logisch-kombonatorische Untersuchungen 眉ber die Erf眉llbarkeit oder Beweisbarkeit mathematischer S盲tze nebst einem Theoreme 眉ber dichte Mengen, Skrifter utgit av det Norske Videnskapsakademiet i Kristiana, I. Matematisk-naturvidenskapelig klasse 4, 1鈥?6 (1920); English translation in: [60], pp. 252鈥?63 (1967)
  48. Skolem, Th.: Einige Bemerkungen zur axiomatischen Begr眉ndung der Mengenlehre. In: Mathematikerkongressen i Helsingfors den 4鈥? Juli 1922, Den femte skandinaviska mathematikerkongressen, Redog枚relse, pp. 217鈥?32. Akademiska Bokhandeln, Helsinki (1923); English translation in: [60], pp. 290鈥?01 (1967)
  49. Tarski, A.: Poj臋cie prawdy w j臋zykach nauk dedukcyjnych, Prace Towarzystwa Naukowego Warszawskiego, Wydzia艂 III, Nauk matematyczno-fizycznych (Travaux de la Soci茅t茅 des Sciences et des Lettres de Varsovie, Classe III, Sciences Math茅matiques et Physiques), nr. 34 (1933)
  50. Tarski, A.: Der Wahrheitsbegriff in den formalisierten Sprachen. Stud. Philos. 1, 261鈥?05 (1936); English translation in: [54], pp. 152鈥?78 (1956)
  51. Tarski, A.: O pojciu wynikania logicznego, Przegl膮d Filozoficzny 39, 58鈥?8 (1936); German translation: 脺ber den Begriff der logischen Folgerung, Actes du Congr猫s International de Philosophie Scientifique. Sorbonne Paris 1935 (Actualit茅s Scientifiques et Industrielles, vol. 388鈥?95), vol. VII (A.S.I., vol. 394). Hermann, Paris, pp. 1鈥?1 (1936); English translation in: [54], pp. 409鈥?20 (1956)
  52. Tarski, A.: A general method in proofs of undecidability. In: Tarski, A., with Mostowski, A., Robinson, R.M. (eds.) Undecidable Theories, pp. 1鈥?5. North-Holland, Amsterdam (1953; reprinted: Dover Publications, Mineola, N.Y., 2010)
  53. Tarski, A.: Contributions to the theory of models, Koninklijke Nederlandse Akademi van Wetenschappen, Proceedings, series A 57 (= Indagationes mathematicae 16), 572鈥?88, 58 (= Indag. math. 17), 56鈥?4 (1954-1955)
  54. Tarski, A.: Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (Woodger, J.H., trans.). Clarendon Press, Oxford (1956)
  55. Tarski A., Vaught R.: Arithmetical extensions of relational systems. Composit. Math. 13, 81鈥?02 (1957)
  56. The Paris Logic Group (eds.): Logic Colloquium 鈥?5. In: Proceedings of the Colloquium held in Orsay, France, July 1985. North-Holland, Amsterdam (1987)
  57. Tich媒 P.: The Foundations of Frege鈥檚 Logic. Walter de Gruyter, Berlin (1988)
  58. Trotsky L., Trotsky N.: Correspondance 1933鈥?938 (van Heijenoort, J., trans. & ed.). Gallimard, Paris (1980)
  59. van Heijenoort, J.: Friedrich Engels and mathematics (1948). In: [76], pp. 123鈥?51 (1985)
  60. van Heijenoort, J. (ed.): From Frege to G枚del: A source book in mathematical logic, 1879鈥?931. Harvard University Press, Cambridge (1967)
  61. van Heijenoort, J.: Logic as calculus and logic as language. In: Cohn, R.S., Wartofsky, M.W. (eds.) Proceedings of the Boston Studies in the Philosophy of Science, vol. 3, pp. 440鈥?46. D. Reidel, Dordrecht (1967); reprinted in: [76], pp. 11鈥?6 (1985)
  62. van Heijenoort, J.: Subject and predicate in Western logic. Philos. East West 24, 253鈥?68 (1974); reprinted in: [76], pp. 17鈥?4 (1985)
  63. van Heijenoort, J.: On the number of planets. In: [76], p. 35 (1985)
  64. van Heijenoort, J.: On Kripke鈥檚 puzzle. In: [76], pp. 37鈥?8 (1985)
  65. van Heijenoort, J.: Letter to Quine dated December 9, 1974. In: [76], p. 41 (1985)
  66. van Heijenoort, J.: El desarrollo de la teoria de la cuantification. Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones Filosoficas, Mexico City (1976)
  67. van Heijenoort, J.: Set-theoretic semantics. In: Gandy, R.O., Hyland, J.M.E. (eds.) Logic Colloquium 鈥?6. Proceedings of a Conference Held in Oxford in July 1976, pp. 183鈥?90. North-Holland, Amsterdam (1977); reprinted in: [76], pp. 43鈥?3 (1985)
  68. van Heijenoort, J.: Sense in Frege. J. Philos. Logic 6, 93鈥?02 (1977); reprint in: [76], pp. 55鈥?3 (1985)
  69. van Heijenoort, J.: Frege on sense identity. J. Philos. Logic 6, 103鈥?08 (1977); reprinted in: [76], pp. 65鈥?9 (1985)
  70. van Heijenoort, J.: Introduction 脿 脿 la s茅mantique des logiques non classiques. Collection de l鈥櫭塩ole Normale Sup茅rieure de Jeunes Filles, Paris (1978)
  71. van Heijenoort, J.: De Prinkipo 脿 脿 Coyoac谩n: Sept ans aupr猫s de L茅on Trotsky. Les Lettres Nouvelles Maurice Nadeau and Robert Laffont, Paris (1978)
  72. van Heijenoort J.: With Trotsky in Exile: from Prinkipo to Coyoacan. Harvard University Press, Cambridge (1978)
  73. van Heijenoort, J.: Ostension and vagueness. In: [76], pp. 71鈥?3 (1985)
  74. van Heijenoort, J.: Absolutism and relativism in logic. In: [76], pp. 75鈥?3 (1985)
  75. van Heijenoort, J.: L鈥櫯搖vre logique de Jacques Herbrand et son contexte historique. In: Stern, J. (ed.) Logic Colloquium 鈥?1: Proceedings of the Herbrand Symposium held in Marseille, France, July 1981, pp. 111鈥?22. North-Holland, Amsterdam (1982)
  76. van Heijenoort J.: Selected Essays. Biblopolis, Naples (1985)
  77. van Heijenoort, J.: Frege and vagueness. In: Haaparanta, L., Hintikka, J. (eds.) Frege synthetized: studies of the philosophical and foundational work of Gottlob Frege, pp. 31鈥?6. D. Reidel, Dordrecht (1985); reprinted in: [76], pp. 85鈥?7 (1985)
  78. van Heijenoort, J.: Jacques Herbrand鈥檚 work in logic and its historical context. In [76], pp. 99鈥?21 (1985); English translation, with emendations of [75].
  79. van Heijenoort, J.: Syst猫me et m茅tasyst猫me chez Russell. In: [56], pp. 111鈥?21 (1987)
  80. Whitehead, A.N. Russell, B.: Principia Mathematica. Cambridge University Press, Cambridge (1910鈥?913; 2nd edn, 1925鈥?927)
  81. Wittgenstein, L. Logisch-philosophische Abhandlung. Annalen der Naturphilosophie 14. Reinhold Berger, Leipzig (1921)
  82. Zermelo, E.: Untersuchungen 眉ber die Grundlagen der Mengenlehre, I. Math. Ann. 65, 261鈥?81 (1908); English translation in [60], pp. 199鈥?15 (1967)
  
• 作者单位：Philippe de Rouilhan (1)
  
  1. 2, square Grang茅, 75013, Paris, France
  
• ISSN：1661-8300

文摘

Van Heijenoort鈥檚 main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schr枚der, and L枚wenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2).