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Logical Consequence Revisited

Published online by Cambridge University Press:  15 January 2014

José M. Sagüillo
José M. Sagüillo*
Affiliation:
Department of Logic, University of Santiago De Compostela, Santiago de Compostela 15701, SpainE-mail: , [email protected]
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Extract

Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: (1) terminological and conceptual preliminaries, (2) Tarski's definition of the concept of logical consequence, (3) Tarski's discussion of omega-incomplete theories, and (4) concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves subsidiary issues, such as Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.

§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P (the premise-set) and a single proposition c (the conclusion). The expression ‘c is a [logical] consequence of P’ is used with the same meaning as the expression ‘c is [logically] implied by P’. The expressions ‘is a logical consequence of’ and the converse ‘implies’ are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 3 , Issue 2 , June 1997 , pp. 216 - 241
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1] Carnap, R., The logical syntax of language, 8th ed., London, Routledge and Kegan Paul, 1937/1971.Google Scholar
[2] Carnap, R., Foundations of logic and mathematics., International encyclopedia of unified science (Neurath, O. et al., editors), University of Chicago Press, 1938, Section 7, pp. 139–213.Google Scholar
[3] Church, A., Introduction to mathematical logic, 6th ed., Princeton University Press, Princeton, 1956/1970.Google Scholar
[4] Corcoran, J., Conceptual structure of classical logic, Philosophy and Phenomenological Research, vol. 33 (1972), pp. 25–47.CrossRefGoogle Scholar
[5] Corcoran, J., Gaps between logical theory and mathematical practice, The methodological unity of science (Bunge, M., editor), Reidel Publishing Company, Dordrecht-Holland, 1973, pp. 23–50.CrossRefGoogle Scholar
[6] Corcoran, J., Meanings of implication, Dialogos, vol. 9 (1973), pp. 59–76, Spanish translation by José M. Sagüillo in Agora , vol. V (1985), pp. 279–294; reprinted in [15, pp. 85–100].Google Scholar
[7] Corcoran, J., Categoricity, History and Philosophy of Logic, vol. 1 (1980), pp. 187–207.CrossRefGoogle Scholar
[8] Corcoran, J., Argumentations and logic, Argumentation, vol. 3 (1989), pp. 17–43, Spanish translation by Rubén Blanco in Agora , vol. XIII/1 (1994), pp. 27–55.Google Scholar
[9] Corcoran, J., Information recovery problems, Theoria, vol. 24 (1995), pp. 55–78.Google Scholar
[10] Corcoran, J., Information-theoretic logic, Truth in perspective. Proceedings of the international congress “Truth: logic, representation and world”, Ashgate Publishing Limited, Aldershot, England, United Kingdom, 1997, forthcoming.Google Scholar
[11] Etchemendy, J., The concept of logical consequence, Harvard University Press, Cambridge, Massachusetts, 1990.Google Scholar
[12] Moreno, L. Fernández, Neutralidad temática y la delimitación de las constantes lógicas en Carnap, Tarski y Quine, Contextos, vol. XI (1993), nos. 21–22, pp. 59–75.Google Scholar
[13] García-Carpintero, M., The grounds for the model-theoretic account of the logical properties, Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 107–131.Google Scholar
[14] Hodges, W., Truth in a structure, Proceedings of the Aristotelian Society, vol. 86 (1986), pp. 135–151.CrossRefGoogle Scholar
[15] Hughes, R. I. G., A philosophical companion to first order logic, Hackett, Indianapolis & Cambridge, 1993.Google Scholar
[16] Mellor, D. H., F. P. Ramsey. Philosophical papers, Cambridge University Press, 1990.Google Scholar
[17] Prawitz, D., Remarks on some approaches to the concept of logical consequence, Synthese, vol. 62 (1985), pp. 153–171.CrossRefGoogle Scholar
[18] Quine, W. v. O., The problem of interpreting modal logic, Journal of Symbolic Logic, vol. 12 (1947), pp. 43–48.CrossRefGoogle Scholar
[19] Quine, W. v. O., Immanence and validity, included in [20, pp. 242–50], 1991.Google Scholar
[20] Quine, W. v. O., Selected logic papers, Harvard University Press, Cambridge, Massachusetts & London, England, 1995.Google Scholar
[21] Ramsey, F., The foundations of mathematics., included in [16, pp. 164–224], 1925.Google Scholar
[22] Russell, B., Introduction to mathematical philosophy, 3rd ed., Dover Publications, New York, 1919/1993.Google Scholar
[23] Sagüillo, J. M., Validez y semántica representacional, Theoria, vol. 24 (1995), pp. 103–120.Google Scholar
[24] Sher, G., The bounds of logic, MIT Press, Cambridge, Massachusetts, 1991.Google Scholar
[25] Tarski, A., Fundamental concepts of the methodology of the deductive sciences, included in [36, pp. 60–109], 1930.Google Scholar
[26] Tarski, A., The concept of truth in formalized languages, included in [36, pp. 152–278], 1933.Google Scholar
[27] Tarski, A., On some fundamental concepts of metamathematics, included in [36, pp. 30–37], 1933.Google Scholar
[28] Tarski, A., Some observations on the concepts of ω-consistency and ω-completeness, included in [36, pp. 279–295], 1933.Google Scholar
[29] Tarski, A., On the concept of logical consequence, included in [36, pp. 409–20], 1936.Google Scholar
[30] Tarski, A., Introduction to logic, Oxford University Press, 1941/1994, 4th ed. by Tarski, J..Google Scholar
[31] Tarski, A., A general method in proofs of undecidability, included in [41, pp. 3–35], 1953.CrossRefGoogle Scholar
[32] Tarski, A., Contributions to the theory of models I, included in [37, pp. 515–526], 1954.CrossRefGoogle Scholar
[33] Tarski, A., Contributions to the theory of models II, included in [37, pp. 527–535], 1954.CrossRefGoogle Scholar
[34] Tarski, A., Contributions to the theory of models III, included in [37, pp. 537–547], 1955.CrossRefGoogle Scholar
[35] Tarski, A., Truth and proof, Scientific American, vol. 220 (1969), no. 6, pp. 63–77, reprinted in [15, pp. 101–125].CrossRefGoogle ScholarPubMed
[36] Tarski, A., Logic, semantics, metamathematics, Hackett Publishing Company, Indianapolis, 1983, 2nd ed. edited with an introduction by Corcoran, John.Google Scholar
[37] Tarski, A., Alfred Tarski: Collected papers. Volumen 3, 1945–1957 (Givant, S. R. and Mckenzie, R. N., editors), Birkhäuser, Basel, Boston, Stuttgart, 1986.Google Scholar
[38] Tarski, A., What are logical notions, (introduced and edited by Corcoran, John), History and Philosophy of Logic, vol. 17 (1986), pp. 143–154.Google Scholar
[39] Tarski, A., A philosophical letter of Alfred Tarski, Journal of Philosophy, vol. 84 (1987), pp. 28–32, from 1944.Google Scholar
[40] Tarski, A. and Lindenbaum, A., On the limitations of the means of expression of deductive theories, included in [36, pp. 384–392], 1934–1935.Google Scholar
[41] Tarski, A., Mostowski, A., and Robinson, R., Undecidable theories, North-Holland Publishing Company, Amsterdam, 1953.Google Scholar
[42] Thompson, P., Bolzano's deducibility and Tarski's logical consequence, History and Philosophy of Logic, vol. 2 (1981), pp. 11–20.CrossRefGoogle Scholar
[43] Vega, L., Alfred Tarski (1936): sobre el concepto de consecuencia lógica, 1984, included in [44].Google Scholar
[44] Vega, L. and Castrillo, P. (editors), Lecturas de lógica II, UNED, Madrid, 1984.Google Scholar