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MODAL DEFINABILITY IN KRIPKE’S THEORY OF TRUTH

Part of: Philosophical aspects of logic and foundations General logic

Published online by Cambridge University Press:  20 February 2026

JAMES WALSH
JAMES WALSH*
Affiliation:
NEW YORK UNIVERSITY USA
*
E-mail: jmw534@nyu.edu
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Abstract

In Outline of a Theory of Truth, Kripke introduces many of the central concepts of the logical study of truth and paradox. He informally defines some of these—such as groundedness and paradoxicality—using modal locutions. We introduce a modal language for regimenting these informal definitions. Though groundedness and paradoxicality are expressible in the modal language, we prove that intrinsicality—which Kripke emphasizes but does not define modally—is not. This follows from a characterization of the modally definable sets and relations and an attendant axiomatization of the modal semantics.

Keywords

theories of truthmodal logic

MSC classification

Primary: 03A05: Philosophical and critical 03B45: Modal logic (including the logic of norms) 03B50: Many-valued logic

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 19 , Issue 2 , June 2026 , pp. 269 - 290
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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