Journal of Philosophical Logic 45 (5):485-529 (2016)

Authors
Lorenzo Rossi
University of Salzburg
Abstract
Kripke’s theory of truth, 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the new conditional and on the status of the principles so successfully recovered. Subsequently, I develop a semantics that improves on Kripke’s theory following Field’s program of adding a conditional to it, using some inductive constructions that include Kripke’s one and feature a strong evaluation for conditionals. The new theory overcomes several problems of Kripke’s one and, although weaker than Field’s proposals, it avoids the difficulties that affect them; at the same time, the new theory turns out to be quite simple. Moreover, the new construction can be used to model various conceptions of what a conditional connective is, in ways that are precluded to both Kripke’s and Field’s theories.
Keywords Naïve truth  Kripke’s theory of truth  Field’s theories of truth  Conditional connective  Łukasiewicz logics  Partial semantics
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DOI 10.1007/s10992-015-9384-4
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
The Revision Theory of Truth.Vann McGee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
Axiomatizing Kripke's Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
Truth.Michael Dummett - 1959 - Proceedings of the Aristotelian Society 59:141-162.

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Citations of this work BETA

HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
Model-Theoretic Semantics and Revenge Paradoxes.Lorenzo Rossi - 2019 - Philosophical Studies 176 (4):1035-1054.
A Unified Theory of Truth and Paradox.Lorenzo Rossi - 2019 - Review of Symbolic Logic 12 (2):209-254.

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