Revision Without Revision Sequences: Self-Referential Truth

Journal of Philosophical Logic 48 (3):523-551 (2019)
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The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen’s supervaluation scheme which is simply based on ω-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of “grounded” true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes.

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Edoardo Rivello
Università di Torino

Citations of this work

Revision Without Revision Sequences: Self-Referential Truth.Edoardo Rivello - 2019 - Journal of Philosophical Logic 48 (3):523-551.
Designing Paradoxes: A Revision-theoretic Approach.Ming Hsiung - 2022 - Journal of Philosophical Logic 51 (4):739-789.
Paradoxes and contemporary logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
Revision Without Revision Sequences: Circular Definitions.Edoardo Rivello - 2019 - Journal of Philosophical Logic 48 (1):57-85.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Truth and paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.

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