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Construction of Truth Predicates: Approximation Versus Revision

Published online by Cambridge University Press:  15 January 2014

Juan Barba
Juan Barba*
Affiliation:
Departamento de Filosofía, Lógica y Filosofía de la Ciencia, Universidad de Valladolid, Plaza de la Universidad, E-47002 Valladolid, Spain.E-mail: [email protected]
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Extract

§1. Introduction. The problem raised by the liar paradox has long been an intriguing challenge for all those interested in the concept of truth. Many “solutions” have been proposed to solve or avoid the paradox, either prescribing some linguistical restriction, or giving up the classical true-false bivalence or assuming some kind of contextual dependence of truth, among other possibilities. We shall not discuss these different approaches to the subject in this paper, but we shall concentrate on a kind of formal construction which was originated by Kripke's paper “Outline of a theory of truth” [11] and which, in different forms, reappears in later papers by various authors.

The main idea can be presented as follows: assume a first order language ℒ containing, among other unspecified symbols, a predicate symbol T intended to represent the truth predicate for ℒ. Assume, also, a fixed model M = 〈D, I〉 (the base model)where D contains all sentences of ℒ and I interprets all non-logical symbols of ℒ except T in the usual way. In general, D might contain many objects other than sentences of ℒ but as that would raise the problem of the meaning of sentences in which T is applied to one of these objects, we shall assume that this is not the case.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 4 , December 1998 , pp. 399 - 417
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Barwise, J. and Etchemendy, J., The liar: An essay on truth and circularity, Oxford University Press, Oxford, 1987.Google Scholar
[2] Belnap, N. D., Gupta's rule of revision theory of truth, Journal of Philosophical Logic, vol. 11 (1982), pp. 103–116.CrossRefGoogle Scholar
[3] Fitting, M., Notes on mathematical aspects of Kripke's theory of truth, Notre Dame Journal of Formal Logic, vol. 27 (1986), pp. 75–88.CrossRefGoogle Scholar
[4] Fitting, M., Bilattices and the theory of truth, Journal of Philosophical Logic, vol. 18(1989), pp. 225–256.CrossRefGoogle Scholar
[5] Gabbay, D. and Guenthner, F. (editors), Handbook of philosophical logic, vol. IV, Reidel, Dordrecht, 1989.CrossRefGoogle Scholar
[6] Gupta, A., Truth and paradox, Recent essays on truth and the liar paradox (Martin, R. L., editor), Clarendon Press, Oxford, 1984, pp. 175–235.Google Scholar
[7] Gupta, A., Two theorems concerning stability, Truth or consequences: Essays in honor of Nuel Belnap (Dunn, J. M. and Gupta, A., editors), Kluwer, 1990, pp. 49–60.CrossRefGoogle Scholar
[8] Gupta, A. and Belnap, N., The revision theory of truth, MIT Press, Cambridge, Massachusetts, 1993.CrossRefGoogle Scholar
[9] Herzberger, H. G., Notes on naive semantics, Journal of Philosophical Logic, vol. 11 (1982), pp. 61–102.CrossRefGoogle Scholar
[10] Kremer, M., Kripke and the logic of truth, Journal of Philosophical Logic, vol. 17 (1988), pp. 225–278.CrossRefGoogle Scholar
[11] Kripke, S., Outline of a theory of truth, Journal of Philosophy (1975), pp. 690–716, reprinted in [13].CrossRefGoogle Scholar
[12] Martin, D. A., Review of Barwise and Etchemendy's ‘the liar’, this Journal, vol. 57 (1992), pp. 252–254.Google Scholar
[13] Martin, R. L., Recent essays on truth and the liar paradox, Clarendon Press, Oxford, 1984.Google Scholar
[14] McGee, V., Truth, vagueness and paradox: An essay on the logic of truth, Hackett, Indianapolis, 1991.Google Scholar
[15] McLarty, C., Anti-foundation and self-reference, this Journal, vol. 22 (1993), no. 1, pp. 19–28.Google Scholar
[16] Priest, G., The logic of paradox, Journal of Philosophical Logic, vol. 8 (1979), pp. 219–241.CrossRefGoogle Scholar
[17] Priest, G., Logic of paradox revisited, Journal of Philosophical Logic, vol. 13 (1984), pp. 13–179.CrossRefGoogle Scholar
[18] Sheard, M., A guide to truth predicates in themodern era, this Journal, vol. 59 (1994), no. 3, pp. 1032–1054.Google Scholar
[19] Visser, A., Four valued semantics and the liar, Journal of Philosophical Logic, vol. 13 (1984), pp. 181–212.CrossRefGoogle Scholar
[20] Visser, A., Semantics and the liar paradox, Handbook of philosophical logic (Gabbay, D. and Guenther, F., editors), vol. IV, Reidel, Dordrecht, 1989, pp. 617–706.CrossRefGoogle Scholar
[21] Woodruff, P. W., Paradox, truth and logic part I: Paradox and truth, Journal of Philosophical Logic, vol. 13 (1984), pp. 213–232.CrossRefGoogle Scholar
[22] Yablo, S., Truth and reflection, Journal of Philosophical Logic, vol. 14 (1985), pp. 297–349.CrossRefGoogle Scholar