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REREADING TARSKI ON LOGICAL CONSEQUENCE

Published online by Cambridge University Press:  09 July 2009

MARIO GÓMEZ-TORRENTE
MARIO GÓMEZ-TORRENTE*
Affiliation:
Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México
*
*INSTITUTO DE INVESTIGACIONES FILOSÓFICAS, UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO, MÉXICO DF 04510, MEXICO. E-mail: [email protected]
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Abstract

I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical correctness of certain omega-arguments, on the Tarskian proof that Etchemendy took to be modal and fallacious, and on Tarski’s appeals to the “common concept of consequence”.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 2 , June 2009 , pp. 249 - 297
Copyright
Copyright © Association for Symbolic Logic 2009

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References

BIBLIOGRAPHY

Ackermann, W. (1928). Über die Erfüllbarkeit gewisser Zählausdrücke. Mathematische Annalen, 100, 638–649.CrossRefGoogle Scholar
Bays, T. (2001). On Tarski on models. Journal of Symbolic Logic, 66, 1701–1726.CrossRefGoogle Scholar
Benacerraf, P., & Putnam, H. (editors.). (1983). The Philosophy of Mathematics (second edition). Cambridge: Cambridge University Press.Google Scholar
Bernays, P., & Schönfinkel, M. (1928). Zum Entscheidungsproblem der mathematischen Logik. Mathematische Annalen, 99, 342–372.CrossRefGoogle Scholar
Carnap, R. (1934). Logische Syntax der Sprache. Vienna: Julius Springer.CrossRefGoogle Scholar
Carnap, R. (1937). The Logical Syntax of Language. London: Routledge & Kegan Paul.Google Scholar
Carnap, R. (1942). Introduction to Semantics. Cambridge, MA: Harvard University Press.Google Scholar
Church, A. (1956). Introduction to Mathematical Logic I. Princeton, NJ: Princeton University Press.Google Scholar
De Rouilhan, P. (forthcoming). Carnap on logical consequence for languages I and II. In Wagner, P., editor. Carnap’s Logical Syntax of Language. New York: Palgrave-Macmillan.Google Scholar
Editorial Office of Fundamenta Mathematicae. (1934). Bemerkung der Redaktion. Fundamenta Mathematicae, 23, 161.Google Scholar
Edwards, J. (2003). Reduction and Tarski’s definition of logical consequence. Notre Dame Journal of Formal Logic, 44, 49–62.CrossRefGoogle Scholar
Etchemendy, J. (1988). Tarski on truth and logical consequence. Journal of Symbolic Logic, 53, 51–79.CrossRefGoogle Scholar
Etchemendy, J. (1990). The Concept of Logical Consequence. Cambridge, MA: Harvard University Press.Google Scholar
Garcìa-Carpintero, M. (1993). The grounds for the model-theoretic account of the logical properties. Notre Dame Journal of Formal Logic, 34, 107–131.Google Scholar
Garcìa-Carpintero, M. (2003). Gómez-Torrente on modality and Tarskian logical consequence. Theoria (San Sebastián), 18, 159–170.CrossRefGoogle Scholar
Gödel, K. (1930). Die Vollständigkeit der Axiome der logischen Funktionenkalküls. Monatshefte für Mathematik und Physik, 37, 349–360. Reprinted in Gödel (1986, pp. 102–122). Translated as “The completeness of the axioms of the functional calculus of logic” in van Heijenoort (1967, pp. 583–591) and in Gödel (1986, pp. 103–123).CrossRefGoogle Scholar
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173–198. Reprinted in Gödel (1986, pp. 144–194). Translated as “On formally undecidable propositions of Principia Mathematica and related systems I” in van Heijenoort (1967, pp. 596–616) and in Gödel (1986, pp. 145–195).CrossRefGoogle Scholar
Gödel, K. (1986). Collected Works, Vol. I. New York: Oxford University Press.Google Scholar
Gómez-Torrente, M. (1996a). Tarski on logical consequence. Notre Dame Journal of Formal Logic, 37, 125–151.CrossRefGoogle Scholar
Gómez-Torrente, M. (1996b). Tarski’s Definition of Logical Consequence. Historical and Philosophical Aspects (PhD dissertation, Princeton University). Ann Arbor, MI: University Microfilms.CrossRefGoogle Scholar
Gómez-Torrente, M. (1998). On a fallacy attributed to Tarski. History and Philosophy of Logic, 19, 227–234.CrossRefGoogle Scholar
Gómez-Torrente, M. (1998/1999). Logical truth and Tarskian logical truth. Synthèse, 117, 375–408.CrossRefGoogle Scholar
Gómez-Torrente, M. (2000). A note on formality and logical consequence. Journal of Philosophical Logic, 29, 529–539.CrossRefGoogle Scholar
Gómez-Torrente, M. (2004). The indefinability of truth in the Wahrheitsbegriff. Annals of Pure and Applied Logic, 126, 27–37.CrossRefGoogle Scholar
Hanson, W. H. (1997). The concept of logical consequence. Philosophical Review, 106, 365–409.CrossRefGoogle Scholar
Hempel, C. G. (1945). On the nature of mathematical truth. The American Mathematical Monthly, 52, 543–556. Reprinted in Benacerraf and Putnam (1983, pp. 377–393).CrossRefGoogle Scholar
Herbrand, J. (1930). Recherches sur la théorie de la démonstration. Travaux de la Société des Sciences et des Lettres de Varsovie, Classe III. Sciences mathématiques et physiques, no. 33. Chapter 5 translated as “Investigations in proof theory: The properties of true propositions” in van Heijenoort (1967, pp. 525–581).Google Scholar
Hilbert, D., & Ackermann, W. (1928). Grundzüge der theoretischen Logik. Berlin: Julius Springer.Google Scholar
Jané, I. (2006). What is Tarski’s common concept of consequence? Bulletin of Symbolic Logic, 12, 1–42.CrossRefGoogle Scholar
Lewis, C. I. (1918). A Survey of Symbolic Logic. Berkeley, CA: University of California Press.CrossRefGoogle Scholar
Lewis, C. I., & Langford, C. H. (1932). Symbolic Logic. New York: Century Company.Google Scholar
Löwenheim, L. (1915). Über Möglichkeiten im Relativkalkül. Mathematische Annalen, 76, 447–470. Translated as “On possibilities in the calculus of relatives” in van Heijenoort (1967, pp. 228–251).CrossRefGoogle Scholar
Mancosu, P. (2006). Tarski on models and logical consequence. In Ferreirós, J., and Gray, J. J., editors. The Architecture of Modern Mathematics. Oxford: Oxford University Press, pp. 209–237.CrossRefGoogle Scholar
Prawitz, D. (1985). Remarks on some approaches to the concept of logical consequence. Synthèse, 62, 153–171.CrossRefGoogle Scholar
Ramsey, F. P. (1925). The foundations of mathematics. Proceedings of the London Mathematical Society, 2nd series, 25, 338–384. Reprinted in Ramsey (1931, pp. 1–61).Google Scholar
Ramsey, F. P. (1931). The Foundations of Mathematics and Other Logical Essays. London: Kegan Paul.Google Scholar
Ray, G. (1996). Logical consequence: A defense of Tarski. Journal of Philosophical Logic, 25, 617–677.CrossRefGoogle Scholar
Shapiro, S. (1998). Logical consequence: Models and modality. In Schirn, M., editor. The Philosophy of Mathematics Today. Oxford: Oxford University Press, pp. 131–156.CrossRefGoogle Scholar
Sher, G. (1991). The Bounds of Logic. Cambridge, MA: M.I.T. Press.Google Scholar
Sher, G. (1996). Did Tarski commit ‘Tarski’s fallacy’? Journal of Symbolic Logic, 61, 653–686.CrossRefGoogle Scholar
Skolem, T. (1919). Untersuchungen über die Axiome des Klassenkalküls und über Produktations- und Summationsprobleme, welche gewisse Klassem von Aussagen betreffen. Videnskapsselskapets Skrifter, I Mat.-nat. Klasse, no. 3.Google Scholar
Skolem, T. (1920). Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theorem über dichte Mengen. Videnskapsselskapets Skrifter, I Mat.-nat. Klasse, no. 4. Section 1 translated as “Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Löwenheim and generalizations of the theorem” in van Heijenoort (1967, pp. 252–263).Google Scholar
Skolem, T. (1929). Über einige Grundlagenfragen der Mathematik. Skrifter utgitt av Det Norske Videnskaps-Akademi I Oslo, I Mat.-nat. Klasse, no. 4.Google Scholar
Soames, S. (1999). Understanding Truth. New York: Oxford University Press.CrossRefGoogle Scholar
Stroińska, M., & Hitchcock, D. (2002). Introduction to Tarski (2002, pp. 155–175).Google Scholar
Tarski, A. (1931). Sur les ensembles définissables de nombres réels. I. Fundamenta Mathematicae, 17, 210–239.CrossRefGoogle Scholar
Tarski, A. (1933). Einige Betrachtungen über die Begriffe der ω-Widerspruchsfreiheit und der ω-Vollständigkeit. Monatshefte für Mathematik und Physik, 40, 97–112.CrossRefGoogle Scholar
Tarski, A. (1935a). Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica, 1, 261–405.Google Scholar
Tarski, A. (1935b). Einige methodologische Untersuchungen über die Definierbarkeit der Begriffe. Erkenntnis, 5, 80–100.CrossRefGoogle Scholar
Tarski, A. (1936a). O pojęciu wynikania logicznego. Przegląd Filozoficzny, 39, 58–68. References to the English translation Tarski (2002).Google Scholar
Tarski, A. (1936b). Über den Begriff der logischen Folgerung. In Actes du Congrès International de Philosophie Scientifique, fasc. 7 (Actualités Scientifiques et Indus-trielles, Vol. 394). Paris: Hermann et Cie, pp. 1–11.Google Scholar
Tarski, A. (1936c). O logice matematycznej i metodzie dedukcyjnej. Lvov-Warsaw: Ksiażnica-Atlas.Google Scholar
Tarski, A. (1936d). Grundzüge des Systemenkalküls, Zweiter Teil. Fundamenta Mathematicae, 26, 283–301.CrossRefGoogle Scholar
Tarski, A. (1937a). Einführung in die mathematische Logik und in die Methodologie der Mathematik. Vienna: Springer.CrossRefGoogle Scholar
Tarski, A. (1937b). Sur la méthode déductive. In Travaux du IXeCongrès International de Philosophie, tome 6 (Actualités Scientifiques et Industrielles, Vol. 535). Paris, France: Hermann et Cie, pp. 95–103.Google Scholar
Tarski, A. (1940). On the completeness and categoricity of deductive systems. Unpublished typescript, Alfred Tarski Papers, Carton 15, Bancroft Library, U.C. Berkeley. A version of the typescript edited by Paolo Mancosu is to appear as an archival appendix to Mancosu’s book The Adventure of Reason, forthcoming from Oxford University Press.Google Scholar
Tarski, A. (1941). Introduction to Logic and to the Methodology of Deductive Sciences. New York: Oxford University Press.Google Scholar
Tarski, A. (1946). Introduction to Logic and to the Methodology of Deductive Sciences (second edition). New York: Oxford University Press.Google Scholar
Tarski, A. (1953). “A general method in proofs of undecidability” in Tarski et al. (1953, pp. 1–35).Google Scholar
Tarski, A. (1965). Introduction to Logic and to the Methodology of Deductive Sciences (third edition). New York: Oxford University Press.Google Scholar
Tarski, A. (1983a). Logic, Semantics, Metamathematics (second edition, Corcoran, J., editor). Indianapolis, IN: Hackett.Google Scholar
Tarski, A. (1983b). On the concept of logical consequence. Translation of Tarski (1936b) by Woodger, J.H. in Tarski (1983a, pp. 409–420).Google Scholar
Tarski, A. (2002). On the concept of following logically. Translation of Tarski (1936a) by Stroińska, M., & Hitchcock, D. History and Philosophy of Logic, 23, 155–196.CrossRefGoogle Scholar
Tarski, A., & Lindenbaum, A. (1935). Über die Beschränktheit der Ausdrucksmittel deduktiver Theorien. Ergebnisse eines mathematischen Kolloquiums, fasc. 7, 1934–1935, 15–22.Google Scholar
Tarski, A., Mostowski, A., & Robinson, R. (1953). Undecidable Theories. Amsterdam, The Netherlands: North-Holland.Google Scholar
van Heijenoort, J. (editor). (1967). From Frege to Gödel. A Source Book in Mathematical Logic, 1879-1931. Cambridge, MA: Harvard University Press.Google Scholar
Whitehead, A. N., & Russell, B. (1925–1927). Principia Mathematica (second edition, 3 vols). Cambridge: Cambridge University Press.Google Scholar