Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-09T15:41:18.674Z Has data issue: false hasContentIssue false
  • English
  • Français

The Problem of Logical Constants

Published online by Cambridge University Press:  15 January 2014

Mario Gómez-Torrente
Mario Gómez-Torrente*
Affiliation:
Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, México, D. F. 04510, MexicoE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

There have been several different and even opposed conceptions of the problem of logical constants, i.e., of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 8 , Issue 1 , March 2002 , pp. 1 - 37
Copyright
Copyright © Association for Symbolic Logic 2002

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

REFERENCES

[1] Aristotle, , Posterior analytics, Clarendon Press, Oxford, 1975, (translation by Barnes, J.).Google Scholar
[2] Belnap, N. D., Tonk, plonk andplink, Analysis, vol. 22 (1962), pp. 130–134.Google Scholar
[3] Bolzano, B., Theory of science, Basil Blackwell, Oxford, 1972, (translation by R. George of selections of Wissenschaftslehre, Seidel, Sulzbach, 1837).CrossRefGoogle Scholar
[4] Carnap, R., The logical syntax of language, Routledge & Kegan Paul, London, 1937, (expanded English translation by A. Smeathon of Logische Syntax der Sprache, Julius Springer, Vienna, 1934).Google Scholar
[5] Carnap, R., Replies and systematic expositions, The philosophy of Rudolf Carnap (Schilpp, P. A., editor), Open Court, La Salle, Illinois, 1963, pp. 859–1013.Google Scholar
[6] Coffa, J. A., The semantic tradition from Kant to Carnap, Cambridge University Press, Cambridge, 1991.CrossRefGoogle Scholar
[7] Dummett, M., The logical basis of metaphysics, Harvard University Press, Cambridge, Massachusetts, 1991.Google Scholar
[8] Etchemendy, J., The concept of logical consequence, Harvard University Press, Cambridge, Massachusetts, 1990.Google Scholar
[9] Frege, G., Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought, From Frege to Godel (van Heijenoort, J., editor), Harvard University Press, Cambridge, Massachusetts, 1967, (translation by S. Bauer-Mengelberg of Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Nebert, Halle, 1879).Google Scholar
[10] Gentzen, G., Investigations into logical deduction, The collected papers of Gerhard Gentzen (Szabo, M. E., editor), North-Holland, Amsterdam, 1969, (translation of Untersuchungen über das logische Schliessen, Mathematische Zeitschrift , vol. 39, 1934, pp. 176–210, 405–431), pp. 68–131.Google Scholar
[11] Gómez-Torrente, M., Logical truth and Tarskian logical truth, Synthese, vol. 117 (1998/1999), pp. 375–408.Google Scholar
[12] Hacking, I., What is logic?, Journal of Philosophy, vol. 76 (1979), pp. 285–319.Google Scholar
[13] Hanson, W. H., The concept of logical consequence, Philosophical Review, vol. 106 (1997), pp. 365–409.Google Scholar
[14] Kneale, W., The province of logic, Contemporary British philosophy, 3rd series (Lewis, H. D., editor), Allen & Unwin, London, 1956, pp. 237–261.Google Scholar
[15] McCarthy, T., The idea of a logical constant, Journal of Philosophy, vol. 78 (1981), pp. 499–523.Google Scholar
[16] McCarthy, T., Modality, invariance, and logical truth, Journal of Philosophical Logic, vol. 16 (1987), pp. 423–443.CrossRefGoogle Scholar
[17] McCarthy, T., Logical form and radical interpretation, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 401–419.Google Scholar
[18] McGee, V., Logical operations, Journal of Philosophical Logic, vol. 25 (1996), pp. 567–580.CrossRefGoogle Scholar
[19] Mostowski, A., On a generalization of quantifiers, Fundamenta Mathematicae, vol. 44 (1957), pp. 12–36.Google Scholar
[20] Peacocke, C., What is a logical constant?, Journal of Philosophy, vol. 73 (1976), pp. 221–240.CrossRefGoogle Scholar
[21] Popper, K. R., New foundations for logic, Mind, vol. 56 (1947), pp. 193–235.Google Scholar
[22] Prior, A. N., The runabout inference-ticket, Analysis, vol. 21 (1960), pp. 38–39.Google Scholar
[23] Quine, W.V., Carnap and logical truth, The philosophy of Rudolf Carnap (Schilpp, P. A., editor), Open Court, La Salle, Illinois, 1963, pp. 385–406.Google Scholar
[24] Ray, G., Logical consequence: a defense of Tarski, Journal of Philosophical Logic, vol. 25 (1996), pp. 617–677.CrossRefGoogle Scholar
[25] Russell, B., The principles of mathematics, Cambridge University Press, Cambridge, 1903.Google Scholar
[26] Russell, B., Introduction to mathematical philosophy, 2 ed., Allen & Unwin, London, 1920, the first edition is of 1919.Google Scholar
[27] Sainsbury, M., Logical forms, Basil Blackwell, Oxford, 1991.Google Scholar
[28] Sher, G., The bounds of logic, Massachusetts Institute of Technology Press, Cambridge, Massachusetts, 1991.Google Scholar
[29] Tarski, A., Einführung in die mathematische Logik und in die Methodologie der Mathematik, Julius Springer, Vienna, 1937.CrossRefGoogle Scholar
[30] Tarski, A., What is elementary geometry?, The axiomatic method, with special reference to geometry and physics (Henkin, L., Suppes, P., and Tarski, A., editors), North-Holland, Amsterdam, 1959, pp. 16–29.Google Scholar
[31] Tarski, A., Logic, semantics, metamathematics, 2 ed., Hackett, Indianapolis, 1983.Google Scholar
[32] Tarski, A., What are logical notions?, History and Philosophy of Logic, vol. 7 (1986), pp. 143–154, (the text of a lecture originally delivered by Tarski in 1966, edited by John Corcoran).CrossRefGoogle Scholar
[33] Tarski, A., A philosophical letter of Alfred Tarski, Journal of Philosophy, vol. 84 (1987), pp. 28–32, (a 1944 letter of Tarski to Morton White, published with a preface of the latter).Google Scholar
[34] Tarski, A., The concept of truth in formalized languages, in [31], (translation by J. H. Woodger of Der Wahrheitsbegriff' in den formalisierten Sprachen, Studia Philosophica , vol. 1, 1935, pp. 261-405), pp. 152–278.Google Scholar
[35] Tarski, A., On the concept of logical consequence, in [31], (translation by J. H. Woodger of Über den Begriff der logischen Folgerung,in Actes du Congrès International de Philosophie Scientifique , fasc. 7 (Actualités Scientifiques et Industrielles, vol. 394), Hermannet Cie, Paris, 1936, pp. 1-11), pp. 409–420.Google Scholar
[36] Tarski, A. and Givant, S., A formalization of set theory without variables, American Mathematical Society, Providence, Rhode Island, 1987.Google Scholar
[37] Tarski, A. and Lindenbaum, A., On the limitations of the means of expression of deductive theories, in [31], (translation by J. H. Woodger of Über die Beschranktheit der Ausdrucksmittel deduktiver Theorien, in Ergebnisse eines mathematischen Kolloquiums, fasc. 7, 1934-1935, pp. 15-22), pp. 384–392.Google Scholar
[38] Warmbrōd, K., Logical constants, Mind, vol. 108 (1999), pp. 503–538.CrossRefGoogle Scholar