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A UNIFIED THEORY OF TRUTH AND PARADOX

  • LORENZO ROSSI (a1)

Abstract

The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language, as in (Kripke, 1975). In this article, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory of truth and paradox, that is a theory of truth that also provides a unified account of paradoxical sentences. The theory I propose here yields a threefold classification of paradoxical sentences—liar-like sentences, truth-teller–like sentences, and revenge sentences. Unlike existing treatments of semantic paradox, the theory put forward in this article yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model.

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Corresponding author

*DEPARTMENT OF PHILOSOPHY (KGW) UNIVERSITY OF SALZBURG FRANZISKANERGASSE 1 5020 SALZBURG, AUSTRIA E-mail: lorenzo.rossi@sbg.ac.at

References

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Asenjo, F. G. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 7(1), 103105.
Barwise, J. & Etchemendy, J. (1987). The Liar: An Essay on Truth and Circularity. Oxford: Oxford University Press.
Beall, J. (2001). Is Yablo’s paradox noncircular? Analysis, 61(3), 176187.
Beall, J. (2006). True, false and paranormal. Analysis, 66(2), 102114.
Beall, J. (2007a). Prolegomenon to future revenge. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 130.
Beall, J. (editor) (2007b). Revenge of the Liar. Oxford: Oxford University Press.
Beall, J. (2009). Spandrels of Truth. Oxford: Oxford University Press.
Beringer, T. & Schindler, T. (2017). A graph-theoretic analysis of the semantic paradoxes. Bulletin of Symbolic Logic, 23(4), 442492.
Billon, A. (2013). The truth-tellers paradox. Logique et Analyse, 56(224), 371389.
Blamey, S. (2002). Partial logic. In Gabbay, D. M. and Guenthner, F., editors. Handbook of Philosophical Logic, Second Edition, Vol. V. Dordrecht: Kluwer Academic Publishers, pp. 261353.
Bondy, A. & Murty, U. (2008). Graph Theory. London: Springer.
Bueno, O. & Colyvan, M. (2003). Paradox without satisfaction. Analysis, 62(2), 152156.
Burgess, J. (1986). The truth is never simple. Journal of Symbolic Logic, 51(3), 663681.
Burgess, J. (1988). Addendum to ‘The truth is never simple’. Journal of Symbolic Logic, 53(2), 390392.
Chemla, E. & Égré, P. (2019). Suszko’s problem: Mixed consequence and compositionality. The Review of Symbolic Logic, to appear.
Chemla, E., Égré, P., & Spector, B. (2017). Characterizing logical consequence in many-valued logic. Journal of Logic and Computation, 27(1), 21932226.
Chierchia, G. & McCconnell-Ginet, S. (2000). Meaning and Grammar: Introduction to Semantics (second edition). Cambridge, MA: MIT Press.
Cieśliński, C. (2007). Deflationism, conservativeness and maximality. Journal of Philosophical Logic, 36(6), 695705.
Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347385.
Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2013). Reaching transparent truth. Mind, 122(488), 841866.
Cook, R. (2004). Pattern of paradox. The Journal of Symbolic Logic, 69(3), 767774.
Cook, R. (2006). There are noncircular paradoxes (but Yablo’s isn’t one of them!). The Monist, 89(1), 118149.
Cook, R. (2007). Embracing revenge: On the indefinite extensibility of language. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 3152.
Cook, R. (2009). What is a truth value, and how many are there? Studia Logica, 92, 183201.
Cook, R. (2014). The Yablo Paradox: An Essay on Circularity. Oxford: Oxford University Press.
Cook, R. & Tourville, N. (2016). Embracing the technicalities: Expressive completeness and revenge. The Review of Symbolic Logic, 9(2), 325358.
Davidson, D. (1967). Truth and meaning. Synthese, 17, 304323.
Davis, L. (1979). An alternate formulation of Kripke’s theory of truth. Journal of Philosophical Logic, 8(1), 289296.
Diestel, R. (2010). Graph Theory (fourth edition). Berlin: Springer.
Dyrkolbotn, S. & Walicki, M. (2014). Propositional discourse logic. Synthese, 191(5), 863899.
Eldridge-Smith, P. (2015). Two paradoxes of satisfaction. Mind, 124(493), 85119.
Field, H. (2002). Saving the truth schema from paradox. Journal of Philosophical Logic, 31(1), 127.
Field, H. (2003). A revenge-immune solution to the semantic paradoxes. Journal of Philosophical Logic, 32(2), 139177.
Field, H. (2007). Solving the paradoxes, escaping revenge. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 53144.
Field, H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.
Field, H. (2013). Naive truth and restricted quantification: Saving truth a whole lot better. The Review of Symbolic Logic, 7(1), 147191.
Fine, K. (2017). Truthmaker semantics. In Hale, B., Wright, C., and Miller, A., editors. A Companion to the Philosophy of Language, Second Edition, Oxford: Wiley-Blackwell, pp. 556577.
Fischer, M., Halbach, V., Kriener, J., & Stern, J. (2015). Axiomatizing semantic theories of truth? The Review of Symbolic Logic, 8(2), 257278.
Friedman, H. & Sheard, M. (1987). An axiomatic approach to self-referential truth. Annals of Pure and Applied Logic, 33, 121.
Gaifman, H. (1988). Operational pointer semantics: Solution to self-referential puzzles I. In Vardi, M., editor. Theoretical Aspects of Reasoning about Knowledge. Los Angeles: Morgan Kauffman, pp. 4359.
Gaifman, H. (1992). Pointers to truth. Journal of Philosophy, 89(5), 223261.
Gaifman, H. (2000). Pointers to propositions. In Chapuis, A. and Gupta, A., editors. Circularity, Definition, and Truth. Indian Council of Philosophical Research.
Gottwald, S. (2001). A Treatise on Many-valued Logics. Studies in Logic and Computation. Baldock, Hertfordshire, England: Research Studies Press LTD.
Greenough, P. (2011). Truthmaker gaps and the no-no paradox. Philosophy and Phenomenological Research, 82(3), 547563.
Gupta, A. (1982). Truth and paradox. Journal of Philosophical Logic, 11(1), 160.
Gupta, A. & Belnap, N. (1993). The Revision Theory of Truth. Cambridge (MA): MIT Press.
Hájek, P., Paris, J., & Shepherdson, J. (2000). The liar paradox and fuzzy logic. Journal of Symbolic Logic, 65(1), 339346.
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge: Cambrdige University Press.
Halbach, V. & Horsten, L. (2006). Axiomatizing Kripke’s theory of truth. Journal of Symbolic Logic, 71(2), 677712.
Halbach, V., Leitgeb, H., & Welch, P. (2003). Possible-worlds semantics for modal notions conceived as predicates. Journal of Philosophical Logic, 32(2), 179223.
Halbach, V. & Visser, A. (2014a). Self-reference in arithmetic I. The Review of Symbolic Logic, 7(4), 671691.
Halbach, V. & Visser, A. (2014b). Self-reference in arithmetic II. The Review of Symbolic Logic, 7(4), 692712.
Halbach, V. & Zhang, S. (2017). Yablo without Gödel. Analysis, 77(1), 5359.
Hansen, C. (2015). Supervaluation on trees for Kripke’s theory of truth. The Review of Symbolic Logic, 8(1), 4674.
Hazen, A. (1981). Davis’s formulation of Kripke’s theory of truth: A correction. Journal of Philosophical Logic, 10(3), 309311.
Herzberger, H. (1982a). Naive semantics and the liar paradox. Journal of Philosophy, 79(9), 479497.
Herzberger, H. (1982b). Notes on naive semantics. Journal of Philosophical Logic, 11(1), 61102.
Horsten, L. (2009). Levity. Mind, 118(471), 555581.
Horsten, L. (2012). The Tarskian Turn. Deflationism and Axiomatic Truth. Cambridge (MA): MIT Press.
Ketland, J. (2003). Can a many-valued language functionally represent its own semantics? Analysis, 63(4), 292297.
Ketland, J. (2004). Bueno and Colyvan on Yablo’s paradox. Analysis, 64(2), 165172.
Ketland, J. (2005). Yablo’s paradox and ω-inconsistency. Synthese, 145(3), 295302.
Kleene, S. C. (1952). Introduction to Metamathematics. New York: van Nostrand.
Kremer, P. (2009). Comparing fixed-point and revision theories of truth. Journal of Philosophical Logic, 38(4), 363403.
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72(19), 690716.
Leitgeb, H. (2002). What is a self-referential sentence? Critical remarks on the alleged (non)circularity of Yablo’s paradox. Logique et Analyse, 177–178, 314.
Leitgeb, H. (2005). What truth depends on. Journal of Philosophical Logic, 34(2), 155192.
Leitgeb, H. (2007). On the metatheory of Field’s ‘Solving the paradoxes, escaping revenge’. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 159183.
Maudlin, T. (2004). Truth and Paradox: Solving the Riddles. New York: Oxford University Press.
Maudlin, T. (2007). Reducing revenge to discomfort. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 184196.
McCarthy, T. (1988). Ungroundedness in classical languages. Journal of Philosophical Logic, 17(1), 6174.
McGee, V. (1985). How truthlike can a predicate be? A negative result. Journal of Philosophical Logic, 14(4), 399410.
McGee, V. (1991). Truth, Vagueness, and Paradox. Indianapolis: Hackett Publishing Company.
Montague, R. (1974). Formal Philosophy. Selected Papers of Richard Montague. New Haven: Yale University Press.
Mortensen, C. & Priest, G. (1981). The truth teller paradox. Logique et Analyse, 95–96, 381388.
Moschovakis, Y. (1974). Elementary Induction on Abstract Structures. Amsterdam, London and New York: North-Holland and Elsevier.
Murzi, J. & Rossi, L. (2019). Generalised revenge. Australasian Journal of Philosophy, to appear.
Nicolai, C. & Rossi, L. (2018). Principles for object-linguistic consequence: From logical to irreflexive. Journal of Philosophical Logic, 47(3), 549577.
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1), 219241.
Priest, G. (1997). Yablo’s paradox. Analysis, 57(4), 236242.
Priest, G. (2006). In Contradiction (expanded edition). Oxford: Oxford University Press.
Priest, G. (2007). Revenge, Field, and ZF. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 225233.
Rabern, L., Rabern, B., & Macauley, M. (2013). Dangerous reference graphs and semantic paradoxes. Journal of Philosophical Logic, 42(5), 727765.
Restall, G. (1992). Arithmetic and truth in Lukasiewicz’s infinitely valued logic. Logique et Analyse, 139–140, 303312.
Restall, G. (2007). Curry’s revenge: The costs of nonclassical solutions to the paradoxes of self-reference. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 262271.
Rogers, H. (1987). Theory of Recursive Functions and Effective Computability (second edition). Cambridge (MA) and London: MIT Press.
Rossi, L. (2016). Adding a conditional to Kripke’s theory of trugh. Journal of Philosophical Logic, 45(5), 485529.
Rossi, L. (2019). Model-theoretic semantics and revenge paradoxes. Philosophical Studies, to appear.
Scharp, K. (2007). Aletheic vengeance. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 272319.
Scharp, K. (2013). Replacing Truth. Oxford: Oxford University Press.
Schlenker, P. (2007). The elimination of self-reference: Generalized Yablo-series and the theory of truth. Journal of Philosophical Logic, 36(3), 251307.
Schlenker, P. (2010). Super-liars. The Review of Symbolic Logic, 3(3), 374414.
Shapiro, L. (2011). Expressibility and the liar’s revenge. Australasian Journal of Philosophy, 89(2), 118.
Simmons, K. (2007). Revenge and context. In Beall, J., editor. Revenge of the Liar. Oxford: Oxford University Press, pp. 345367.
Smith, J. (1984). A simple solution to Mortensen and Priest’s truth teller paradox. Logique et Analyse, 27(106), 217220.
Sorensen, R. (2001). Vagueness and Contradiction. Oxford: Oxford University Press.
Urquhart, A. (2001). Basic many-valued logic. In Gabbay, D. and Guenthner, F., editors. Handbook of Philosophical Logic, Second Edition, Vol. 2. Dordrecht: Kluwer Academic Publishers, pp. 249295.
Visser, A. (1984). Four valued semantics and the liar. Journal of Philosophical Logic, 13(2), 181212.
Visser, A. (1989). Semantics and the liar paradox. In Gabbay, D. and Günthner, F., editors. Handbook of Philosophical Logic, Vol. 4. Dordrecht: Reidel, pp. 617706.
Walicki, M. (2009). Reference, paradoxes and truth. Synthese, 171, 195226.
Walicki, M. (2017). Resolving infinitary paradoxes. Journal of Symbolic Logic, 82(2), 709723.
Wen, L. (2001). Semantic paradoxes as equations. The Mathematical Intelligencer, 23(1), 4348.
Yablo, S. (1982). Grounding, dependence, and paradox. Journal of Philosophical Logic, 11, 117137.
Yablo, S. (1985). Truth and reflection. Journal of Philosophical Logic, 14(3), 297349.
Yablo, S. (1993). Paradox without self-reference. Analysis, 53(4), 251252.
Yablo, S. (2006). Circularity and paradox. In Bolander, T., Hendricks, V., and Pedersen, S., editors. Self-Reference. Stanford: CSLI Publications, pp. 139157.
Yi, B. (1999). Descending chains and the contextualist approach to paradoxes. Notre Dame Journal of Formal Logic, 40(4), 554567.
Zardini, E. (2011). Truth without contra(di)ction. Review of Symbolic Logic, 4(4), 498535.
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