Ultimate truth vis- à- vis stable truth

Review of Symbolic Logic 1 (1):126-142 (2008)
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Abstract

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings.

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Citations of this work

Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
Revision Revisited.Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch - 2012 - Review of Symbolic Logic 5 (4):642-664.

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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.
The Revision Theory of Truth.Vann Mcgee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
Notes on Naive Semantics.Hans Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
The Truth is Never Simple.John P. Burgess - 1986 - Journal of Symbolic Logic 51 (3):663-681.
A Revenge-Immune Solution to the Semantic Paradoxes.Hartry Field - 2003 - Journal of Philosophical Logic 32 (2):139-177.

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