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Alfred Tarski: Semantic Shift, Heuristic Shift In Metamathematics

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REFERENCES

  • Barwise, J., S. Feferman, and P. Suppes: 1989, ‘Commemorative Meeting for Alfred Tarski’ in P. Duren (ed.), 7 November, 1983, Stanford University, pp. 393–404.

  • Beth, E.: 1953, ‘Sur le parallélisme logico-mathématique’ in Les méthodes formelles en axiomatique, Colloques Internationaux du Centre National de la Recherche Scientifique, Vol. 36, Paris, pp. 27–33.

    Google Scholar 

  • Block, W. J. and Don Pigozzi: 1988, ‘Alfred Tarski's Work on General Mathematics’ The Journal of Symbolic Logic 53(1), 36–50.

    Google Scholar 

  • Bochnak, J., M. Coste, and M.-F. Roy: 1987, Géométrie algébrique réelle, Springer-Verlag, Berlin.

    Google Scholar 

  • Carnap, R.: 1942, Introduction to Semantics, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Duren, P. (ed.): 1989, A Century of Mathematics in America, Part III. American Mathematical Society, Providence, RI.

    Google Scholar 

  • Etchemendy J.: 1988, Tarski on truth and logical consequence, The Journal of Symbolic Logic 53(1), 51–79.

    Google Scholar 

  • Feferman, S.: 1999, ‘Tarski and Gödel: Between the Lines’ in J. Wolenski and E. Köhler (eds), pp. 53–63.

  • Gödel, K.: 1986–1995, in S. Feferman et al. (eds), Collected Works, Vols. I, II and III, Oxford University Press.

  • Henkin, L. et al. (eds): 1974, Proceedings of the Tarski Symposium, American Mathematical Society, Proceedings of Symposia in Pure Mathematics, Vol. 25, Providence, RI.

  • Hilbert, D.: 1899, Die Grundlagen der Geometrie, 10th edn, Teubner, Stuttgart, 1968.

  • Hilbert, D.: 1905, ‘Ñber die Grundlagen der Logik und der Arithmetik’ Verhandlungen des dritten internationalen Mathematiker-Kongresses, Heidelberg 1904, Teubner, Leipzig, pp. 174–185. French trans. by H. Sinaceur in Rivenc F. and de Rouilhan Ph. (eds), Logique et Fondements des Mathématiques, Payot, Paris, pp. 245–275.

  • Hilbert, D.: 1918, ‘Axiomatisches Denken’ Mathematische Annalen 78, 405–415; repr. in Hilbert (1935), pp. 146–156.

    Google Scholar 

  • Hilbert, D.: 1922, ‘Neubegründung der Mathematik. Erste Mitteilung’ Abhandlungen math. Sem. Hamb. 1, 157–177; repr. in Hilbert (1935), pp. 157–177.

    Google Scholar 

  • Hilbert, D.: 1923, ‘Die logischen Grundlagen der Mathematik, Mathematische Annalen 88, 151–165; repr. in Hilbert (1935), pp. 178–191.

    Google Scholar 

  • Hilbert, D.: 1930, ‘Probleme der Grundlegung der Mathematik’ Mathematische Annalen 102, pp. 1–9.

    Google Scholar 

  • Hilbert, D.: 1931, ‘Die Grundlegung der elementaren Zahlenlehre’ Mathematische Annalen 104, 485–494; repr. In Hilbert (1935), pp. 192–195.

    Google Scholar 

  • Hilbert, D.: 1935, Gesammelte Abhandlungen, Vol. III, Springer, Berlin. Reprint, Chelsea, New York, 1965.

    Google Scholar 

  • Hilbert, D. and P. Bernays: 1934, Grundlagen der Mathematik, Vol. I, Springer, Berlin.

    Google Scholar 

  • Hintikka, J.: 1988, ‘On the Development of the Model-Theoretic Viewpoint in Logical Theory’ Synthese 77, 1–36.

    Google Scholar 

  • Hintikka, J. (ed.): 1995, From Dedekind to Gödel, Essays on the Development of the Foundations of Mathematics, Vol. 251, Synthese Library, Kluwer, Dordrecht/Boston/London.

    Google Scholar 

  • Kreisel, G: 1954, ‘Applications of Mathematical Logic to Various Branches of Mathematics’ Actes du 2e Colloque International de Logique Mathématique, Paris (1952), Gauthier-Villars, Paris-Nauwelaerts, Louvain, pp. 37–49.

    Google Scholar 

  • Kreisel, G: 1958, ‘Mathematical Significance of Consistency Proofs’ The Journal of Symbolic Logic 23(1), 155–182.

    Google Scholar 

  • Kreisel, G.: 1985, ‘Mathematical Logic: Tool and Object Lesson for Science’ Synthese 62(2), 139–151.

    Google Scholar 

  • £ojasiewicz, S.: 1964, Ensembles Semi-Analytiques, I.H.E.S. (prépublication).

  • Robinson, A.: 1955, Théorie métamathématique des idéaux, Gauthier-Villars, Paris.

    Google Scholar 

  • Sinaceur, H.: 1991, Corps et Modèles. Essai sur l'histoire de l'algèbre réelle, Paris, Vrin (Collection Mathesis), 2nd edn, Paris, 1999. An English translation is forthcoming, Birkhäuser, Boston/Basel/New York.

    Google Scholar 

  • Sinaceur, H.: 1999, ‘L'interprétation en mathématiques: de Descartes à Hilbert et Tarski’ in P. Radelet de Grave et J.-F. Stoffel (eds), Actes du Colloque. Les “enfants naturels” de Descartes, Louvain-la-Neuve 21–22 Juin 1996, Breepols, Collection Réminiscences.

  • Skolem, Th.: 1970, in J. E. Fenstad (ed.), Selected Works, Universitetsforlaget, Oslo.

    Google Scholar 

  • Tarski, A.: 1928, ‘Remarques sur les notions fondamentales de la méthodologie des mathématiques’ Annales de la Société Polonaise de Mathématique 7, 270–272; repr. in Tarski (1986a), Vol. IV, pp. 552–554.

    Google Scholar 

  • Tarski, A.: 1930a, ‘Ñber einige fundamentale Begriffe derMetamathematik’ Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Classe III 23, pp. 23–29; repr. in Tarski (1986a), Vol. I, pp. 311–320. English trans. by H. Woodger in Tarski (1956).

    Google Scholar 

  • Tarski, A.: 1930b, ‘Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften I’ Monatshefte für Mathematik und Physik 37, 361–404; repr. in Tarski (1986a), Vol. I, pp. 341–390. English trans. by H. Woodger in Tarski (1956).

    Google Scholar 

  • Tarski, A.: 1931, ‘Sur les ensembles définissables de nombres réels I’ Fundamenta mathematicae 17, 210–239; repr. in Tarski (1986a), Vol. I, pp. 517–548. Revised text and English trans. by H. Woodger in Tarski (1956); revised French text in Tarski (1972–1974).

    Google Scholar 

  • Tarski, A.: 1935, ‘Einige methodologische Untersuchungen über die Definierbarkeit der Begriffe’ Erkenntnis 5, 80–100; repr. in Tarski (1986a), Vol. II, pp. 637–659. English trans. by H. Woodger in Tarski (1956).

    Google Scholar 

  • Tarski, A.: 1935–1936, ‘Grundzüge des Systemenkalküls I, II’ Fundamenta mathematicae 25, 503–526 and 26, 283–301; repr. in Tarski (1986a), Vol. II, 25–50 and 223–244. English trans. by H. Woodger in Tarski (1956).

    Google Scholar 

  • Tarski, A.: 1936a, ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ Studia Philosophica 1, 261–404; repr. in Tarski (1986a), Vol. II, pp. 51–198. English trans. by H. Woodger in Tarski (1956).

    Google Scholar 

  • Tarski, A.: 1936b, Introduction à la logique, Paris, Gauthier-Villars, Louvain, E. Nauwelarts. 2e éd. augmentée 1969. English trans.: Introduction to Logic and to the Methodology of Deductive Sciences, 4th edn, Oxford University Press, 1994.

    Google Scholar 

  • Tarski, A.: 1936c, ‘Grundlegung der wissenschaftlichen Semantik’ Actes du Congrès International de Philosophie Scientifique, Vol. 3, Paris, Hermann, Actualités scientif. et indus, Vol. 390, pp. 1–8; repr. in Tarski (1986a), Vol. II, pp. 259–268.

    Google Scholar 

  • Tarski, A.: 1936d, ‘Ñber den Begriff der logischen Folgerung’ Actes du Congrès International de Philosophie Scientifique, Vol. 7, Paris, Hermann, Actualités scientif. et indus, Vol. 394, pp. 1–11; repr. in Tarski (1986a), Vol. II, pp. 269–282.

    Google Scholar 

  • Tarski, A.: 1937, ‘Sur la méthode déductive’ Travaux du 9e Congrès International de Philosophie, tome 6, Hermann, Paris, Actualités scientif. et indus, Vol. 535; repr. in Tarski (1986a), Vol. II, pp. 323–334.

    Google Scholar 

  • Tarski, A.: 1939, ‘On Undecidable Statements in Enlarged Systems of Logic and the Concept of Truth’ The Journal of Symbolic Logic 4, 105–112; repr. in Tarski (1986a), Vol. II, pp. 559–568.

    Google Scholar 

  • Tarski, A.: 1939/1967, The Completeness of Elementary Algebra and Geometry, Institut Blaise Pascal, Paris; repr. in Tarski (1986a), Vol. IV, pp. 289–346.

    Google Scholar 

  • Tarski, A.: 1944, ‘The Semantic Conception of Truth and the Foundations of Semantics’ Philosophical and Phenomenological Research 4, 341–376; repr. in Tarski (1986a), Vol. II, pp. 661–699.

    Google Scholar 

  • Tarski, A.: 1946/2000, ‘Lecture at the Princeton Bicentennial Conference on the Problems of Mathematics’ in H. Sinaceur (ed.), The Bulletin of Symbolic Logic, forthcoming.

  • Tarski, A.: 1948/1951, A Decision Method for Elementary Algebra and Geometry, prepared for publication by J. C. McKinsey. Second revised edn (1951), University of California Press, Berkeley and Los Angeles; repr. in Tarski (1986a), Vol. III, pp. 297–368.

    Google Scholar 

  • Tarski, A.: 1952, ‘Some Notions and Methods on the Borderline of Algebra and Metamathematics’ Proceedings of the International Congress of Mathematicians, Cambridge, MA, 1950, American Mathematical Society, Providence, pp. 705–720; repr. in Tarski (1986a), Vol. III, pp. 459–476.

    Google Scholar 

  • Tarski, A.: 1953, Undecidable Theories (co-written with Mostowski and R. M. Robinson), North-Holland, Amsterdam.

  • Tarski, A.: 1956, Logic, Semantics, Metamathematics, Papers from 1923 to 1938, trans. by J. H. Woodger, Clarendon Press, Oxford, 2nd edn with an Introductory Note by J. Corcoran, Hackett, Indianapolis, IN, 1983.

    Google Scholar 

  • Tarski, A.: 1972–1974, Logique, sémantique, métamathématique 1923–1944, Vols. 1 and 2, Armand Colin, Paris.

    Google Scholar 

  • Tarski, A.: 1986a, in S. R. Givant and R. N. McKenzie (eds) Collected Papers, Vols. I–IV, Birkhäuser.

  • Tarski, A.: 1986b, ‘What are Logical Notions?’ History and Philosophy of Logic 7, 143–154.

    Google Scholar 

  • Tarski, A.: 1995, ‘Some Current Problems in Metamathematics’ History and Philosophy of Logic 16, 159–168.

    Google Scholar 

  • Vaught, R. L.: 1974, ‘Model Theory before 1945’ in L. Henkin et al. (eds), pp. 153–172.

  • Wang, H.: 1988, Reflections on Kurt Gödel, A Bradford Book, MIT Press, Cambridge MA.

    Google Scholar 

  • Webb, J.: (1995), ‘Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert’ in Hintikka (1995), pp. 1–20.

  • Woleński, J.: 1989, Logic and Philosophy in the Lvov-Warsaw School, Vol. 198, Synthese Library, Kluwer, Dordrecht.

    Google Scholar 

  • Woleński, J.: 1995, ‘On Tarski's Background’ in Hintikka (1995), pp. 331–342.

  • Woleński, J.: 1999, ‘Semantic Revolution — Rudolph Carnap, Kurt Gödel, Alfred Tarski’ in J. Wolenski and E. Köhler E. (eds), pp. 1–15.

  • Woleński, J. and E. Köhler (eds): 1999, Alfred Tarski and the Vienna Circle. Austro-Polish Connections in Logical Empirism, Vol. 6, Vienna Circle Institute Yearbook, Kluwer, Dordrecht.

    Google Scholar 

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Sinaceur, H. Alfred Tarski: Semantic Shift, Heuristic Shift In Metamathematics. Synthese 126, 49–65 (2001). https://doi.org/10.1023/A:1005268531418

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