The correspondence theory of truth is generally applied to any view explicitly embracing the idea that the truth of propositions consists in their relation to reality, i.e., that truth is a relational property been judgments and some portion of reality.
According to some commentators, one version of the correspondence theory is the theory of truth in object languages with respect to metalanguages due to Alfred Tarski. However, the bearing of this on a correspondence theory of truth is debated (SEP: The Correspondence Theory of Truth).
Herbert Keuth, Tarski’s definition of truth and the correspondence theory, Philosophy of Science Vol. 45, No. 3 (Sep., 1978), pp. 420-430
Gila Sher, What is Tarski’s theory of truth? (pdf)
Stanford Encyclopedia of Philosophy, The Correspondence Theory of Truth
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