Abstract
It has been proposed that the law of non-contradiction be revised to permit the simultaneous truth and falsity of the key sentences of the logical paradoxes, e.g., “This sentence is false”. In an attempt to show to what extent this bizarre suggestion of inconsistent models or truth-value “gluts” is a coherent suggestion it is proved that a first-order language for number theory can be semantically closed by having its own global truth predicate under some non-standard interpretation and thus that it actually can contain the Liar sentence. It is proved that in this interpretation the Liar sentence is both true and false, although not every sentence is.
Similar content being viewed by others
Bibliography
Davis, L., ‘An Alternative Formulation of Kripke's Theory of Truth’, Journal of Philosophical Logic 8 (1979), 289–296.
Hazen, A., ‘Davis's Formulation of Kripke's Theory of Truth: A Correction’, Journal of Philosophical Logic 10 (1981), 309–311.
Kripke, S., ‘Outline of a Theory of Truth’, The Journal of Philosophy 72 (1975), 690–716.
Priest, G., ‘The Logic of Paradox’, Journal of Philosophical Logic 8 (1979), 219–241.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dowden, B.H. Accepting inconsistencies from the paradoxes. J Philos Logic 13, 125–130 (1984). https://doi.org/10.1007/BF00453017
Issue Date:
DOI: https://doi.org/10.1007/BF00453017