Formal Theories of Truth
In eight lectures I will provide an introduction to formal theories of truth.
The slides (at least some) for the lectures can be found here on WebLearn.
I shall start with an account of the diagonal lemma and the liar paradox. The main emphasis of the lectures will be on developments after 1975, that is after Kripke's Outline of the Theory of Truth. The relevance of the formal results with respect to truth-theoretic deflationism will be discussed.
I intend to cover the following topics:
- The theory of sytax and diagonalisation
- Kripke's theory
- Axiomatisations of Kripke's theory
- Revision semantics
- Other axiomatic theories
- Truth and necessity
Cantini, Andrea (1996), Logical Frameworks for Truth and Abstraction. An Axiomatic
Study, vol. 135 of Studies in Logic and the Foundations of Mathematics, Elsevier,
Feferman, Solomon (1991), ‘Reflecting on incompleteness’, Journal of Symbolic Logic 56, 1–49.
Gupta, Anil and Nuel Belnap (1993), The Revision Theory of Truth, MIT Press, Cambridge (Mass.) and London.
Halbach, Volker (2001), ‘How innocent is deflationism?’, Synthese 126, 167–194.
Halbach, Volker (2006b), ‘How not to state the T-sentences’, Analysis 66, 276–280. Correction of printing error in vol. 67, 268.
Halbach, Volker (Spring 2006a), Axiomatic theories of truth, in E. N.Zalta, ed., ‘Stanford Encyclopedia of Philosophy’. URL = http://plato.stanford.edu/archives/spr2006/entries/truthaxiomatic/.
Heck, Richard G. (2004), ‘Truth and disquotation’, Synthese 142, 317–352.
Herzberger, Hans G. (1982), ‘Notes on naive semantics’, Journal of Philosophical Logic 11, 61–102.
Ketland, Jeffrey (1999), ‘Deflationism and Tarski’s paradise’, Mind 108, 69–94.
Kripke, Saul (1975), ‘Outline of a theory of truth’, Journal of Philosophy 72, 690–712. reprinted in Martin (1984).
Leitgeb, Hannes (2001), ‘Theories of truth which have no standard models’, Studia Logica 21, 69–87.
Leitgeb, Hannes (2005), ‘What truth depends on’, Journal of Philosophical Logic 34, 155–192.
Leitgeb, Hannes (2007), What theories of truth should be like (but cannot be), in ‘Blackwell Philosophy Compass 2/2’, Blackwell, pp. 276–290.
Martin, Robert L., ed. (1984), Recent Essays on Truth and the Liar Paradox, Clarendon Press and Oxford University Press, Oxford and New York.
McGee, Vann (1985), ‘How truthlike can a predicate be? A negative result’, Journal of Philosophical Logic 14, 399–410.
McGee, Vann (1991), Truth, Vagueness, and Paradox: An Essay on the Logic of Truth, Hackett Publishing, Indianapolis and Cambridge.
McGee, Vann (1992), ‘Maximal consistent sets of instances of Tarski’s
schema (T)’, Journal of Philosophical Logic 21, 235–241.
Shapiro, Stewart (1998), ‘Proof and truth: Through thick and thin’, Journal of Philosophy 95, 493–521.
Sheard, Michael (1994), ‘A guide to truth predicates in the modern era’, Journal of Symbolic Logic 59, 1032–1054.
Tarski, Alfred (1956), The concept of truth in formalized languages, in ‘Logic, Semantics, Metamathematics’, Clarendon Press, Oxford, pp. 152–278.
Yablo, Stephen (1993), ‘Paradox without selfreference’, Analysis 53, 251–252.