Classical Determinate Truth I

Journal of Symbolic Logic 89 (1):218-261 (2024)
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We introduce and analyze a new axiomatic theory $\mathsf {CD}$ of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that $\mathsf {CD}$ is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are restricted to determinate sentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of $\mathsf {CD}$ are analyzed.



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Author Profiles

Volker Halbach
Oxford University
Kentaro Fujimoto
University of Bristol

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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.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
Can the Classical Logician Avoid the Revenge Paradoxes?Andrew Bacon - 2015 - Philosophical Review 124 (3):299-352.
What Truth Depends on.Hannes Leitgeb - 2005 - Journal of Philosophical Logic 34 (2):155-192.

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