Volker Halbach
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Formal Theories of Truth

Volker Halbach & Carlo Nicolai

In the eight classes we will provide an introduction to formal theories of truth. Truth plays a crucial role in many areas of philosophy including moral philosophy, epistemology, metaphysics and philosophy of language. However, the semantic paradoxes such as the liar paradox pose a threat to any analysis of truth. Consequently these paradoxes occupy a central place in the dicussion about truth. However, we will also look at other topics, for instance, formal accounts of truth-theoretic deflationism, primitivism about truth, and the interplay of truth with modal notions. If time permits, we will also cover some paradoxes for necessity, knowledge and further notions.

This class is intended for B.Phil. and M.St. students in Philosophy, but others, including undergraduates and DPhil students, are welcome to attend and to participate in discussion. In the first half of the two-hour session, Volker Halbach will give a lecture. This will be followed by a discussion. Philosophy graduate students are welcome to give a short presentation of 10 to 15 minutes.

Participants should have a good grasp of predicate logic including a proof system such as the system of Natural Deduction as covered, e.g, in the Logic Manual. We do not assume familiarity with more advanced topics such as the Gödel incompleteness theorems, which is sometimes assumed in textbooks on the topic.

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.

We intend to cover the following topics. Depending on the preferences and background knowledge of the participants, we may revise our plan.


Week 1: Syntax, Diagonalization and Paradoxes.

Here are the slides.

Complementary Readings:

1) Vann McGee (1991), Truth, Vagueness and Paradox, Hackett: Chapter 1.

2) Volker Halbach (2014), Axiomatic Theories of Truth, Revised Edition, Cambridge University Press: Chapter 13.


Week 2: The T-sentences

Focus of the Discussion: The Impact of the Liar Paradox on Disquotationalism

Recommended Readings:

1) Paul Horwich (1998), Truth, Second Edition. Clarendon Press: Chapters 1-2.

2) Leon Horsten (2012), The Tarskian Turn: Deflationism and Axiomatic Truth, MIT Press 2012, Chapters 4 and 5.

3) Volker Halbach (2014), Axiomatic Theories of Truth, Revised Edition, Cambridge University Press: Chapter 7 and 19 (up to 19.3 excluded).

Week 3: Tarskian Truth

Focus of the Discussion: Understanding the nonconservativeness of Tarskian truth over the base theory

Recommended readings

1) Stewart Shapiro (1998), "Truth and Proof: through thin and thick", Journal of Philosophy 93, 493-521

2) Hartry Field (1999), "Deflating the conservativeness argument", Journal of Philosophy 96, 533-540

3) Leon Horsten (2012), The Tarskian Turn: Deflationism and Axiomatic Truth, MIT Press 2012: Chapter 7.

4) Carlo Nicolai (2015), "Deflationary Truth and the Ontology of Expressions", Synthese, online first version.

Week 4: Kripke's Theory of Truth

Focus of the discussion: Kripke's fixed point construction.

Recommended readings

1) Saul Kripke (1975), "Outline of a theory of truth", Journal of Philosophy 72, 690-712

Complementary Readings

2) Vann McGee (1991), Truth, Vagueness and Paradox, Hackett: Chapter 5.

Week 5: Kripke-Feferman

Focus of the discussion: Comparing KF, its internal logic, and Kripke's semantic construction.

Recommended readings:

1) Volker Halbach (2014), Axiomatic Theories of Truth, Revised Edition, Cambridge University Press: Chapter 15.

2) Vann McGee (1991), Truth, Vagueness and Paradox, Hackett: Chapter 4.

3) Harty Field (2008), Saving Truth from Paradox, Oxford University Press: Chapter 3.

Week 6: The revision theory of truth

Focus of the discussion: Rules of revision, limit stages, stable and nearly stable truths.

Recommended readings:

1) Anil Gupta and Nuel Belnap (1993), The revision theory of truth, MIT Press: Chapter 4.

2) Philip Welch (2001). "On Gupta-Belnap revision theories of truth, Kripkean fixed-points, and the next stable set". Bulletin of Symbolic Logic 7(2001), 345-360.

Week 7: Symmetric Truth

Focus of the discussion: Is FS sound?

Recommended readings:

1) Volker Halbach (2014), Axiomatic Theories of Truth, Revised Edition, Cambridge University Press: Chapter 14.

2) Volker Halbach and Leon Horsten (2005), "The deflationist's axioms for truth", in Beall, J.C and Armour-Garb (2005), Deflationism and Paradox, Clarendon Press, 203-217.

Week 8: The real culprit

Focus of the discussion: From truth to necessity. Predicate approaches to modalities.

Recommended readings:

1) Halbach, Leitgeb, Welch (2003), "Possible-Worlds semantics for modal notions conceived as predicates", Journal of Philosophical Logic 32(2): 179-223.

2) Volker Halbach and Philip Welch (2009), "Necessities and necessary truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions". Mind 118: 71-100.

Complementary readings:

1) P. Schweizer (1992). "A syntactical approach to modality", Journal of Philosophical Logic 21: 1-31.

2) Johannes Stern (2013), "Montague's Theorem and Modal Logic", Erkenntnis 79(3) 551-570.


Cantini, Andrea (1996), Logical Frameworks for Truth and Abstraction. An Axiomatic Study, vol. 135 of Studies in Logic and the Foundations of Mathematics, Elsevier, Amsterdam.

Feferman, Solomon (1991), ‘Reflecting on incompleteness’, Journal of Symbolic Logic 56, 1–49.

Field, Hartry (2008), Saving Truth From Paradox, Oxford University Press.

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/.

Halbach, Volker (2011), Axiomatic Theories of Truth, Cambridge University Press

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.