The correspondence theory of truth states that the "truth or "falsity of a "statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.
Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory attempts to posit a relationship between thoughts or statements on one hand, and things or facts on the other.
It is a traditional model which goes back at least to some of the "classical Greek philosophers such as "Socrates, "Plato, and "Aristotle. 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. As Aristotle claims in his Metaphysics: "To say that that which is, is not, and that which is not, is, is a falsehood; therefore, to say that which is, is, and that which is not, is not, is true".
Bertrand Russell theorized that a statement, to be true, must have a structural isomorphism with the state of affairs in the world that makes it true. For example, "A cat is on a mat" is true if, and only if, there is in the world a cat and a mat and the cat is related to the mat by virtue of being on it. If any of the three pieces (the cat, the mat, and the relation between them which correspond respectively to the subject, object, and verb of the statement) is missing, the statement is false.
Some sentences pose difficulties for this model, however. As just one example, adjectives such as "counterfeit", "alleged", or "false" do not have the usual simple meaning of restricting the meaning of the noun they modify: a "tall lawyer" is a kind of lawyer, but an "alleged lawyer" may not be.
J. L. Austin theorized that there need not be any structural parallelism between a true statement and the state of affairs that makes it true. It is only necessary that the semantics of the "language in which the statement is expressed are such as to correlate whole-for-whole the statement with the state of affairs. A false statement, for Austin, is one that is correlated by the language to a state of affairs that does not exist.
Historically, most advocates of correspondence theories have been "ontological "realists; that is, they believe that there is a world external to the minds of all humans. This is in contrast to "metaphysical idealists who hold that everything that exists is, in the end, just an idea in some mind. However, it is not strictly necessary that a correspondence theory be married to ontological realism. It is possible to hold, for example, that the facts of the world determine which statements are true and to also hold that the world (and its facts) is but a collection of ideas in the mind of some supreme being.
One attack on the theory claims that the correspondence theory succeeds in its appeal to the real world only in so far as the real world is reachable by us.
The direct "realist believes that we directly know objects as they are. Such a person can wholeheartedly adopt a correspondence theory of truth.
The rigorous "idealist believes that there are no real objects. The correspondence theory appeals to imaginary undefined entities, so it is incoherent.
The "skeptic believes that we have no knowledge. The correspondence theory is simply false.
Other positions hold that we have some type of awareness, perception, etc. of real-world objects which in some way falls short of direct knowledge of them. But such an indirect awareness or perception is itself an idea in one's mind, so that the correspondence theory of truth reduces to a correspondence between ideas about truth and ideas of the world, whereupon it becomes a coherence theory of truth.
Either the defender of the correspondence theory of truth offers some accompanying theory of the world, or he or she does not.
If no theory of the world is offered, the argument is so vague as to be useless or even unintelligible: truth would then be supposed to be correspondence to some undefined, unknown or ineffable world. It is difficult to see how a candidate truth could be more certain than the world we are to judge its degree of correspondence against.
On the other hand, as soon as the defender of the correspondence theory of truth offers a theory of the world, he or she is operating in some specific ontological or scientific theory, which stands in need of justification. But the only way to support the truth of this theory of the world that is allowed by the correspondence theory of truth is correspondence to the real world. Hence the argument is circular.
The assessment of truth and falsity is made possible by the existence of semantically mediated correlations between the members of some class of linguistic entities possessing assertoric force (in some versions of the Correspondence Theory propositions, in others sentences, or bodies of sentences), and the members of some class of extralinguistic entities: “states of affairs,” or “facts,” or bodies of truth-conditions, or of assertion-warranting circumstances.