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ULTIMATE TRUTH VIS-À-VIS STABLE TRUTH

  • P. D. WELCH (a1)
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 ‘revenge-immune’ solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a ‘determinately true’ operator can be introduced in other settings.

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*SCHOOL OF MATHEMATICS, UNIVERSITY OF BRISTOL, BRISTOL BS8 1TW, UK. E-mail: p.welch@bristol.ac.uk
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K Barwise . (1975). Admissible Sets and Structures, Perspectives in Mathematical Logic. Berlin: Springer Verlag.

J Burgess . (1986). The truth is never simple. Journal for Symbolic Logic, 51(3), 663681.

K Devlin . (1984). Constructibility, Perspectives in Mathematical Logic. Berlin, Heidelberg: Springer Verlag.

H Field . (2003). A revenge-immune solution to the semantic paradoxes. Journal of Philosophical Logic, 32(3), 139177.

J. D. Hamkins , & A Lewis . (2000). Infinite time Turing machines. Journal of Symbolic Logic, 65(2), 567604.

H Herzberger . (1982a). Naive semantics and the Liar paradox. Journal of Philosophy, 79, 479497.

H Herzberger . (1982b). Notes on naive semantics. Journal of Philosophical Logic, 11, 61102.

S Kripke . (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690716.

S Simpson . (1999). Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic. Berlin: Springer.

P. D Welch . (2000). Eventually infinite time Turing degrees: Infinite time decidable reals. Journal for Symbolic Logic, 65(3), 11931203.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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