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Correspondence theory is a traditional model which goes back at least to some of the ancient Greek philosophers such as Plato and Aristotle. [2] [3] This class of theories holds that the truth or the falsity of a representation is determined solely by how it relates to a reality; that is, by whether it accurately describes that reality.
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The correspondence theory of truth states that truth consists in correspondence with reality. [7] Or in the words of Thomas Aquinas: "A judgment is said to be true when it conforms to the external reality". [14] Truthmaker theory is closely related to correspondence theory; some authors see it as a modern version of correspondence theory. [15]
1:1 correspondence, an older name for a bijection; Multivalued function; Correspondence (algebraic geometry), between two algebraic varieties; Corresponding sides and corresponding angles, between two polygons; Correspondence (category theory), the opposite of a profunctor; Correspondence (von Neumann algebra) or bimodule, a type of Hilbert space
The doctrine of analogy and correspondence, present in all esoteric schools of thinking, upholds that the Whole is One and that its different levels (realms, worlds) are equivalent systems, whose parts are in strict correspondence. So much so that a part in a realm symbolically reflects and interacts with the corresponding part in another realm.
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox.
An undecidable problem in correspondence theory. Journal of Symbolic Logic 56:1261–1272. Marcus Kracht, 1993. How completeness and correspondence theory got married. In de Rijke, editor, Diamonds and Defaults, pages 175–214. Kluwer. Henrik Sahlqvist, 1975. Correspondence and completeness in the first- and second-order semantics for modal logic.
A proof of the correspondence theorem can be found here. Similar results hold for rings , modules , vector spaces , and algebras . More generally an analogous result that concerns congruence relations instead of normal subgroups holds for any algebraic structure .