Truth

The correspondence theory was revived at the beginning of the twentieth century by the founders of analytic philosophy, G. E. Moore (1873–1958) and Russell, in reaction to James, Bradley, and Joachim. The new correspondence theories addressed the worries of idealists and pragmatists about just what the correspondence relation is, if not the discredited copying relation, and what the terms of the relation are.

In lectures delivered in 1910 and 1911, Moore posed a problem like the one Plato urged against the existence theory of truth. On the one hand, if one believes that God exists, and this is true, one believes a fact (that God exists), and this fact is. On the other hand, one believes the same thing whether the belief is true or false; so there must be a fact even if one believes falsely that God exists; yet in this case there is no such fact (pp. 250–251). In "Beliefs and Propositions," Moore resolved this dilemma by denying that what one believes in a true or false belief is a fact. The clause "that p" in the description "the belief that p" does not name any fact or indeed anything at all. A belief, whether true or false, is not a relation between a believer and a fact, or even between a believer and a proposition. So one can believe the same thing in a false belief as in a true belief, even though for the false belief there is no fact. Moore nevertheless found it convenient to speak of beliefs as referring to facts: "To say that a belief is true is to say that the fact to which it refers is or has being; while to say that a belief is false is to say that the fact to which it refers is not—that there is no such fact" (p. 267). Moore was unable to analyze what is involved in referring (which amounts to correspondence when the fact referred to has being), but he was quite clear that, although "the belief that p is true" is equivalent to "p" on the assumption that the belief p exists, this is not a definition of truth precisely because "p" says nothing about the belief p or a correspondence relation.

Russell tried to say what correspondence is in his work between 1906 and 1912. Othello's belief that Desdemona loves Cassio is a four-term relation between Othello, Desdemona, the relation of loving, and Cassio, while the corresponding fact (if there is one) is a two-term relation of loving between Desdemona and Cassio. Correspondence is then a certain match between the terms in the belief relation and the fact (1912, pp. 124–130). Later, Russell abandoned the idea that a false proposition is one that does not correspond to a fact, in favor of the view that it is one that bears a different correspondence relation to a pertinent fact (1956, p. 187). The latter view avoids a commitment to the idea that the clause "that p" in the description of a false belief names a fact, but it is encumbered with the burden of defining the two correspondence relations so that they cannot both obtain, on pain of allowing a proposition to be both true and false.

The British ordinary language philosopher John Langshaw Austin (1911–1960) proposed a correspondence theory in his article "Truth" (1950). His theory takes statements as truth bearers and states of affairs as truth makers, and it defines correspondence as a correlation that relies on conventions of two kinds: "demonstrative" conventions relating token states of affairs to statements, and "descriptive" conventions relating types of states of affairs to sentence types expressing those statements. A statement is true when the state of affairs to which it is correlated by demonstrative conventions is of a type with which the sentence used in making the statement is correlated by descriptive conventions. The British philosopher P. F. Strawson (b.1919) attacked Austin's theory, and correspondence theories more generally, on the ground that there are no bearers of truth values, there are no entities in the world amounting to facts, and there is no relation of correspondence (1950). Strawson endorsed the opposing view that an assertion made by uttering "It is true that p" makes no assertion beyond one made by uttering "p," although it may be used to do things other than make this assertion (for example, confirm or grant the assertion that p).

The Polish-American logician Alfred Tarski (c. 1902–1983) offered a "semantic" conception of the truth of sentences in a given interpreted and unambiguous formalized language L. His account was intended to capture an Aristotelian notion of truth. Tarski set as a material adequacy condition on a theory of truth-in-L what is called Convention T: that the theory entails all sentences of the form "X is a true sentence if and only if p," where X is a name of some sentence of L, and p is the translation of this sentence into the metalanguage of the theory. Tarski then demonstrated that a recursive truth definition satisfies Convention T.

The basic idea of the truth definition is that a sentence such as "a is F" (for a name "a" and a predicate "F") is true just in case F applies to the object denoted by a, where application is defined case by case for each name in the language L. Now let us give a Tarski-like truth definition for a simple language L with two names, "a" and "b," and one predicate "F." We may begin by defining truth separately for each atomic sentence of L in semantic terms like "applies" and "denotes." (Tarski made central a notion of satisfaction related to application.) The basis clause is: "a is F" is true just in case "F" applies to the object denoted by "a"; and similarly for "b is F." We then define "denotes" for each name: "a" denotes x just in case x a; and similarly for "b." We define "applies": "F" applies to y just in case (y a and a is F) or (y b and b is F). This has been called a disquotational definition of the semantic terms. Finally, we define truth for nonatomic sentences by exploiting the truth-functional properties of logical connectives like "or" and "not." Treating truth as involving subject-predicate form is mandated by the need to satisfy Convention T.

Tarski's theory formulated in terms of "denotes" and "applies" is plausibly regarded as a correspondence theory. However, Hartry H. Field (b. 1946) charged that Tarski's definition of truth does not reduce truth to a physicalistically acceptable property, as Tarski desired (1972). For Tarski's disquotational definitions of semantic terms do not provide an explanatory reduction of those terms to any general physical properties. This is shown by the fact that if we augment L by adding a new name or predicate to form a language L, the definition of truth-in-L gives no hint of what truth-in-L amounts to. Field proposed that we remedy such difficulties by fitting Tarski's theory in terms of semantic concepts with a physicalistically acceptable causal theory of denotation and application, rather than a disquotational definition of these concepts.