Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T07:34:35.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Logique mathématique et philosophie des mathématiques1

Published online by Cambridge University Press:  01 June 1971

Yvon Gauthier
Yvon Gauthier
Affiliation:
Université de Sudbury
Get access Rights & Permissions [Opens in a new window]

Extract

Pour le philosophe intéressé aux structures et aux fondements du savoir théorétique, à la constitution d'une « méta-théorétique «, θεωρíα., qui, mieux que les « Wissenschaftslehre » fichtéenne ou husserlienne et par-delà les débris de la métaphysique, veut dans une intention nouvelle faire la synthèse du « théorétique », la logique mathématique se révèle un objet privilégié.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 10 , Issue 2 , June 1971 , pp. 243 - 275
Copyright
Copyright © Canadian Philosophical Association 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

SOURCES

1Addison, Henkin, Tarski, (eds) The Theory of Models. Proceedings of the 1963 Symposium on Model Theory in Berkeley, California, North-Holland, Amsterdam, 1965.Google Scholar
2Barwise, J. (ed.) The syntax and semantics of infinitary languages. Lectures Notes in Mathematics, vol. 72, Springer, Berlin, 1968.Google Scholar
3Beth, E. W.The Foundations of Mathematics, North-Holland, Amsterdam, 1959.Google Scholar
4Cohen, P. J.“The Independence of the Continuum Hypothesis” Proceedings of the National Academy of Sciences of the U.S.A., I vol. 50 (1963), pp. 1143–1148, II, vol. 51 (1964), pp. 105–110.Google Scholar
5Cohen, P. J. Set Theory and the Continuum Hypothesis, W. A. Benjamin, New York and Amsterdam, 1966.Google Scholar
6Curry, H. B. et Feys, R.Combinatory Logic, vol. I, North-Holland, Amsterdam, 1958.Google Scholar
7Curry, H. B.Foundations of Mathematical Logic, McGraw-Hill, New York, 1963.Google Scholar
8Daigneault, A.La theorie des modeles en logique mathimatique, Presses de l'Universite de Montreal, Montreal, 1964.Google Scholar
9Desanti, J. T.Les idéalités mathématiques, Editions du Seuil, Paris, 1968.Google Scholar
10Feferman, S.“Systems of Predicative Analysis” in The Journal of Symbolic Logic, I, vol. 29 (1964), pp. 1–30, II, vol. 33 (1968), pp. 193–220.Google Scholar
11Feferman, S. “Lectures on proof theory” in Proceedings of the Summer School in Logic, Leeds 1967, Lectures Notes in Mathematics, vol. 70, Springer, Berlin, 1968.Google Scholar
12Feferman, S. “Set-theoretical Foundations of Category Theory” in [48] pp. 201–232.Google Scholar
13Fraenkel, A. et Bar-Hillel, Y.Foundations of Set Theory, North-Holland, Amsterdam, 1958.Google Scholar
14Fraissé, R.Cours de logique mathématique, T. I. Relation, formule logique, compacité, complétude, Gauthier-Villars, Paris, 1967.Google Scholar
15Gauthier, Y.« Logique hégélienne et formalisation » in Dialogue, vol. VI, no 2, 1967, pp. 151–165.Google Scholar
16Gauthier, Y. “The Use of the Axiomatic Method in Quantum Physics” à paraitre dans Philosophy of Science, Sept. 1971.Google Scholar
17Gauthier, Y.« La notion theoretique de structure » in Dialectica, vol. 23, nos. 3–4, 1969, pp. 217–227.CrossRefGoogle Scholar
18Gauthier, Y. «Phénoménologie et Mathématiques » à paraître dans Dialogue.Google Scholar
19Gödel, K. The Consistency of the Axiom of Choke and the Generalized Hypothesis with the Axioms of Set Theory, Princeton University Press, Princeton, N. J., 1940.Google Scholar
20Gödel, K. “Remarks before the Princeton Bicentennial Conference on Problems in Mathematics (1946)” in The Undecidable, ed. by Davis, M., Raven Press, New York, 1965, pp. 84–88.Google Scholar
21Gödel, K. “What is Cantor's Continuum Hypothesis?” in Philosophy of Mathematics, ed. by Benacerraf, P. and Putnam, H., Prentice-Hall, Engle-wood Cliffs, N. J., 1964.Google Scholar
22Hintikka, J. (ed.) The Philosophy of Mathematics, Oxford University Press, London, 1969.Google Scholar
23Karp, C. R.Languages with expressions of infinite length, North-Holland, Amsterdam, 1964.Google Scholar
24Kleene, S. C.Introduction to Metamathematics, North-Holland, Amsterdam, 1952.Google Scholar
25Körner, S.The Philosophy of Mathematics, Harper, New York, 1960.Google Scholar
26Kreisel, G.“A variant to Hilbert's theory of the foundations of arithmetic” in The British Journal for the Philosophy of Science, vol. IV (1953–1954) pp. 107–129.Google Scholar
27Kreisel, G. Compte-rendu de Remarks on the Foundations of Mathematics de L. Wittgenstein in The British Journal for the Philosophy of Science, ix (1958), pp. 135–158.Google Scholar
28Kreisel, G.“Hilbert's Programme” in Dialectica, vol. 12, nos 3–4, 1958, pp. 346–372.CrossRefGoogle Scholar
29Kreisel, G.« La prédicativité », Bulletin de la Société mathématique de France, vol. 88 (1960), pp. 101–128.Google Scholar
30Kreisel, G. “Set-theoretical problems suggested by the notion of potential totality” in Infinistic Methods, Pergamon Press and PWN, Oxford and Warszawa, 1961, pp. 103–140.Google Scholar
31Kreisel, G. “Informal rigour and Completeness Proofs” in [42] [22].Google Scholar
32Kreisel, G.“Mathematical Logic” in Lectures on Modern Mathematics, vol. III, ed. by Saaty, Wiley, N. Y., 1965, pp. 95–195.Google Scholar
33Kreisel, G. “Mathematical Logic: what has it done for the philosophy of mathematics?” in Bertrand Russell: Philosopher of the Century, Allen Unwin, London, 1967, pp. 201–272.Google Scholar
34Kreisel, G.“A Survey of Proof Theory” in The Journal of Symbolic Logic, vol. 33, no. 3, Sept. 1968, pp. 321–388.Google Scholar
35Kreisel, G. “Appendix II” à Particle de S. Feferman in [48] pp. 232–245.Google Scholar
36Kreisel, G. et Krivine, J. L.Eléments de logique mathématique. Théorie des modèles, Dunod, Paris, 1967.Google Scholar
37Kreisel, G. “Appendices I et II” a [36].Google Scholar
38Kreisel, G. and Krivine, J. L.Elements of Mathematical Logic. Model Theory, North-Holland, Amsterdam, 1967.Google Scholar
39Krivine, J. L.Théone axiomatique des ensembles, P.U.F., Paris, 1969.Google Scholar
40Lacombe, D.« La théorie des fonctions récursives et ses applications» Bulletin de la Société mathématique de France, vol. 88, 1960, pp. 393–468.Google Scholar
41Ladrière, J.Les limitations internes des formalismes, Béatrice Nauwelaerts, Paris-Louvain, 1957.Google Scholar
42Lakatos, I, (ed.) Problems in the Philosophy of Mathematics, North-Holland, Amsterdam, 1967.Google Scholar
43Lawvere, W. F. “The Category of Categories as a foundation for Mathematics” in Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer, Heidelberg and New York, 1966.Google Scholar
44Levy, A.“Principles of Reflection in Axiomatic Set Theory”, Fund. Math., XLIX (1960), no. 1, Warszawa, pp. 1–10.Google Scholar
45Lévy, A.“Axiom Schemata of strong infinity in Axiomatic Set Theory” in Pacific Journal of Mathematics, vol. 10 (1960), pp. 223–238.Google Scholar
46Lorenzen, P.Metamathematik, Bibliographisches Institut, Mannheim, 1962.Google Scholar
47MacLane, S.Homology, Springer, Berlin, 1963.Google Scholar
48MacLane, S. (ed.) Reports of the Midwest Category Seminar III, Lectures Notes in Mathematics, Springer, Berlin, 1969.Google Scholar
49MacLane, S. “One universe as a foundation for Category Theory” in [48].Google Scholar
50Montague, R. “Set Theory and higher-order logic” in Formal Systems and Recursive Functions, North-Holland, Amsterdam, 1965, pp. 131–148.Google Scholar
51Mostowski, A.Thirty years of Foundational Studies, Basil Blackwell, Oxford, 1966.Google Scholar
52Mostowski, A. “Recent results in Set Theory” in [42] pp. 82–96.Google Scholar
53Papert, S. “Structures et Catégories” in Logique et connaissance scientifique, publié sous la direction de J. Piaget, Gallimard, 1967, pp. 486–511.Google Scholar
54Putnam, H.“Mathematics without Foundations” in the Journal of Philosophy, vol. 64, no 1 (1967), pp. 5–22.Google Scholar
55Quine, W.v.O.Mathematical Logic, Harper and Row, New York, revised edition (1951).Google Scholar
56Rasiowa, H. et Sikorski, R.The Mathematics of metamathematics, PWN, Warszawa, 1963.Google Scholar
57Robinson, A.Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam, 1963.Google Scholar
58Rogers, H.Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
59Rootselaar, B. van et Staal, F. (eds) Logic, Methodology and Philosophy Science III, North-Holland, Amsterdam, 1968.Google Scholar
60Scott, D.“Measurable cardinals and constructible sets” in Bulletin de L'Académic Polonaise des Sciences, vol. 9 (1961), pp. 521–524.Google Scholar
61Scott, D.“A proof of the independence of the Continuum Hypothesis” in Mathematical Systems Theory, vol. I, 1966, pp. 89–111.Google Scholar
62Shoenfield, J. R.Mathematical Logic, Addison-Wesley, Reading, Mass, 1967.Google Scholar
63Schütte, K.Beweistheorie, Springer, Berlin, 1960.Google Scholar
64Smullyan, R. M.Theory of Formal Systems, (revised edition), Princeton University Press, Princeton, N. J., 1961.Google Scholar
65Tarski, S. “Some problems and results relevant to the foundations of set theory” in Logic, Methodology and Philosophy of Science I, Stanford Press, Stanford, Cal., 1962, pp. 125–136.Google Scholar
66Wang, H.A Survey of Mathematical Logic, North-Holland, Amsterdam, 1963.Google Scholar
67Weyl, H.Philosophy of Mathematics and Natural Science, Princeton, Princeton University Press, N. J., 1949.Google Scholar