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Did Tarski commit “Tarski's fallacy”?

Published online by Cambridge University Press:  12 March 2014

G. Y. Sher
G. Y. Sher*
Affiliation:
Department of Philosophy, The University of California, San Diego, La Jolla, CA 92093-0302, USA, E-mail: [email protected]
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Extract

In his 1936 paper, On the Concept of Logical Consequence, Tarski introduced the celebrated definition of logical consequence: “The sentenceσ follows logically from the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentence σ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentence σ is false. Moreover, … we are concerned here with the concept of logical, i.e., formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 2 , June 1996 , pp. 653 - 686
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Barwise, J. and Cooper, R., Generalized quantifiers and natural language, Linguistics and Philosophy, vol. 4 (1981), pp. 159–219.CrossRefGoogle Scholar
[2]Barwise, J. and Feferman, S., Model-theoretic logics, Springer-Verlag, New York, 1985.Google Scholar
[3]Bolzano, B., Theory of science, D. Reidel, Dordrecht, 1973.Google Scholar
[4]Boolos, G., On second-order logic, Journal of Philosophy, vol. 72 (1975), pp. 509–27.Google Scholar
[5]Boolos, G., Nominalist platonism, Philosophical Review, vol. 94 (1985), pp. 327–44.Google Scholar
[6]Chihara, C., Constructibility and mathematical existence, Oxford, 1990.Google Scholar
[7]Enderton, H. B., A mathematical introduction to logic, Academic Press, New York, 1972.Google Scholar
[8]Etchemendy, J., Tarski on truth and logical consequence, this Journal, vol. 53 (1988), pp. 51–79.Google Scholar
[9]Etchemendy, J., The concept of logical consequence, Harvard, Cambridge, 1990.Google Scholar
[10]Forbes, G., The metaphysics of modality, Clarendon, Oxford, 1985.Google Scholar
[11]Frege, G., The foundations of arithmetic, Northwestern, Evanston, 1884, translated by Austin, J. L., 1986.Google Scholar
[12]García-Carpintero, M. S.-M., The grounds for the model-theoretic account of the logical properties, Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 107–31.Google Scholar
[13]Gardenfors, P. (editor), Generalized quantifiers: Linguistic and logical approaches, Reidel, 1987.Google Scholar
[14]Gottlieb, D., Ontological economy, Oxford, 1980.Google Scholar
[15]Hellman, G., Mathematics without numbers, Oxford, 1989.Google Scholar
[16]Higginbotham, J. and May, R., Questions, quantifiers and crossing, Linguistic Review, vol. 1 (1981), pp. 41–79.Google Scholar
[17]Hodges, W., Truth in a structure, Proceedings of Aristotelian Society (1986), pp. 135–51.Google Scholar
[18]Keenan, E. L. and Stavi, J., A semantic characterization of natural language determiners, Linguistics and Philosophy, vol. 9 (1986), pp. 253–329.Google Scholar
[19]Keisler, H.J., Logic with the quantifier ‘there exist uncountably many’, Annals of Mathematical Logic, vol. 1 (1970), pp. 1–93.Google Scholar
[20]Kreisel, G., Informal rigour and completeness proofs, Problems in the philosophy of mathematics (Lakatos, I., editor), North-Holland, Amsterdam, 1969, pp. 138–71.Google Scholar
[21]Kripke, S. A., Naming and necessity, Harvard, Cambridge, 1972.Google Scholar
[22]Kripke, S. A., Is there a problem about substitutional quantification?, Truth and meaning (Evans, and McDowell, , editors), Oxford, 1976, pp. 325–419.Google Scholar
[23]Lindenbaum, A. and Tarski, A., On the limitations of the means of expression of deductive theories, in Tarski [1983], pp. 382–92.Google Scholar
[24]Lindstrom, P., First order predicate logic with generalized quantifiers, Theoria, vol. 32 (1966), pp. 186–95.CrossRefGoogle Scholar
[25]Marcus, R. B., Interpreting quantification, Inquiry, vol. 5 (1962), pp. 252–9.Google Scholar
[26]Marcus, R. B., Quantification and ontology, Noûs, vol. 6 (1972), pp. 240–50.Google Scholar
[27]May, R., Interpreting logical form, Linguistics and Philosophy, vol. 12 (1989), pp. 387–435.Google Scholar
[28]McCarthy, T., The idea of a logical constant, Journal of Philosophy, vol. 78 (1981), pp. 499–523.Google Scholar
[29]McGee, V., Review of the concept of logical consequence, this Journal, vol. 57 (1992), pp. 254–5.Google Scholar
[30]McGee, V., Two problems with Tarski's theory of consequence, Proceedings of The Aristotelian Society, vol. 92 (1992), pp. 273–92.Google Scholar
[31]Mostowski, A., On a generalization of quantifiers, Fundamenta Mathematicae, vol. 44 (1957), pp. 12–36.Google Scholar
[32]Parsons, C., A plea for substitutional quantification, 1971, Mathematics in philosophy, Cornell, 1983.Google Scholar
[33]Parsons, C., The structuralist view of mathematical objects, Synthese, vol. 84 (1990), pp. 303–46.CrossRefGoogle Scholar
[34]Peacocke, C., What is a logical constant?, Journal of Philosophy, vol. 73 (1976), pp. 221–40.CrossRefGoogle Scholar
[35]Putnam, H., Mathematics without foundations, 1967, Mathematics, matter and method: Philosophical papers I, Cambridge, 1975, pp. 43–59.Google Scholar
[36]Putnam, H., Philosophy of logic, 1971, Mathematics, matter and method: Philosophical papers I, Cambridge, 1975, pp. 323–57.Google Scholar
[37]Quine, W. V., Word and object, MIT, Cambridge, 1960.Google Scholar
[38]Quine, W. V., Existence and quantification, Ontological relativity and other essays, Columbia, 1969, pp. 91–113.CrossRefGoogle Scholar
[39]Quine, W. V., Philosophy of logic, Prentice Hall, Englewood Cliffs, 1970.Google Scholar
[40]Ray, Greg, Logical consequence: A defense of Tarski, to appear.Google Scholar
[41]Resnik, M. D., Mathematics as a science of patterns: Ontology and reference, Noûs, vol. 15 (1981), pp. 529–50.CrossRefGoogle Scholar
[42]Russell, B., Introduction to mathematical philosophy, Allen and Unwin, London, 1919.Google Scholar
[43]Russell, B., The principles of mathematics, second ed., Norton, New York, 1938.Google Scholar
[44]Shagrir, O., Computation and its relevance to cognition, Ph.D. thesis, UCSD, 1994.Google Scholar
[45]Shapiro, S., Foundations without foundationalism: A case for second-order I, Oxford, 1991.Google Scholar
[46]Sher, G., A conception of Tarskian logic, Pacific Philosophical Quarterly, vol. 70 (1989), pp. 341–69.CrossRefGoogle Scholar
[47]Sher, G., The bounds of logic: A generalized viewpoint, Bradford, MIT, Cambridge, 1991.Google Scholar
[48]Sher, G., A new solution to the problem of truth (abstract), Bulletin of Symbolic Logic, vol. 1 (1995), p. 131.Google Scholar
[49]Sher, G., On the possibility of a substantive theory of truth, manuscript, 1996.Google Scholar
[50]Sher, G., Semantics and logic, Handbook of contemporary semantic theory (Lappin, S., editor), Blackwell, Oxford, 1996, pp. 511–37.Google Scholar
[51]Simons, P., Bolzano, Tarski, and the limits of logic, Philosophia Naturalis, vol. 24 (1987), pp. 378–405.Google Scholar
[52]Tarski, A., The concept of truth in formalized languages, 1933, in Tarski [1983], pp. 152–278.Google Scholar
[53]Tarski, A., Some observations on the concepts of ω-consistency and ω-completeness, 1933, in Tarski [1983], pp. 279–95.Google Scholar
[54]Tarski, A., The establishment of scientific semantics, 1936, in Tarski [1983], pp. 401–8.Google Scholar
[55]Tarski, A., On the concept of logical consequence, 1936, in Tarski [1983], pp. 409–20.Google Scholar
[56]Tarski, A., (Corcoran, J., editor), Hackett, second ed., 1983, translated by Woodger.Google Scholar
[57]Tarski, A., What are logical notions?, 1966, History and philosophy of logic 7 (Corcoran, J., editor), 1986, pp. 143–54.Google Scholar
[58]van Benthem, J., Essays in logical semantics, Reidel, Dordrecht, 1986.Google Scholar
[59]van Benthem, J., Polyadic quantifiers, Linguistics and Philosophy, vol. 12 (1989), pp. 437–64.Google Scholar
[60]Vaught, R. L., Model theory before 1945, Proceedings of the Tarski Symposium (Henkin, et al., editors), AMS, 1974, pp. 153–72.Google Scholar
[61]Westerståhl, D., Quantifiers in formal and natural languages, Handbook of philosophical logic (Gabbay, and Guenthner, , editors), vol. 4, Reidel, Dordrecht, 1989.Google Scholar
[62]Wittgenstein, L., Tractatus logico-philosophicus, Routledge and Paul, 1921, translated by Pears, and McGuinness, , 1961.Google Scholar