The concept of truth is central to Western philosophical thought, especially to such branches of philosophy as metaphysics, epistemology, and the philosophy of language. In particular, the correspondence theory of truth has long been associated with a realist metaphysics, according to which objects exist independently of cognition by the human mind. Alternatives to the correspondence theory have, by contrast, been associated with antirealist metaphysics.
The Correspondence Theory: Ancient and Modern
The correspondence theory of truth holds that a belief or proposition is true when it corresponds to the way the world is. The theory originated with Plato (c. 428–348 or 347 B.C.E.) and held the stage in Western theories of truth through the eighteenth century. At Theaetetus 188c–189b, Plato considered what is sometimes called the "existence" theory of truth: true opinion is thinking what is, while false opinion is thinking what is not (pp. 893–895). Plato dismissed this view of false opinion on the ground that to think what is not is to think nothing, and this is no more possible than to see nothing. At Sophist 240d–241a and 260c–263d, Plato proposed an alternative theory of truth designed to circumvent this difficulty: a thought resembles a sentence in consisting of a noun and a verb, and one's thought can be about something even though it is false because the noun refers to an object while the verb misdescribes this object (pp. 984, 1007–1011). This is a correspondence theory in the sense that truth requires that the truth bearer concatenate a noun and verb just as the object to which the noun refers has the property expressed by the verb.
At De Interpretatione 16a10–19, Aristotle (384–322 B.C.E.) endorsed Plato's Sophist point against the existence theory when he proposed that truth and falsity require names and verbs in combination or separation (p. 25). His definition of truth at Metaphysics 7, 1011b26ff is committed to complex truth bearers: "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true …" (pp. 1597–1598).
The Stoics also offered a correspondence theory: "They [the Stoics] say that a true proposition [ axioma ] is that which is and is contradictory to something" (Sextus Empiricus, p. 203). However, the Stoics parted with Aristotle in defending the principle of bivalence, that there are only two truth values, true and false. St. Thomas Aquinas (c. 1224–1274) said that "truth is primarily in intellect; and secondarily in things, by virtue of a relation to intellect as to their origin" (p. 63).
Philosophers of the seventeenth and eighteenth centuries also accepted the correspondence definition of truth, but they differed from their ancient and medieval predecessors in emphasizing that the definition has no utility as a criterion of truth, that is, as a means to judge whether given propositions are true. René Descartes (1596–1650) conceded that "the word truth, in the strict sense, denotes the conformity of thought with its object" (p. 65). But he denied that this definition is useful for clarifying or explaining the concept: "it seems a notion so transcendentally clear that nobody can be ignorant of it" (p. 65); a definition can only cause confusion. He offered clear and distinct perception as a criterion of truth.
Baruch Spinoza (1632–1677) expressly applied true to ideas in Ethics: "A true idea must agree with its object" (p. 410). The axiom is used to show that reason regards things as necessary.
John Locke (1632–1704) endorsed the Platonic-Aristotelian view that true applies strictly to truth bearers of subject-predicate form—to propositions, in particular. He did not, however, formulate a correspondence definition of true proposition. Instead, he offered an account of the conditions in Page 2381 | Top of Article which truth is ascribed to ideas. Though ideas do not have a subject-predicate form and are thus not strictly true, one nevertheless ascribes truth to them in a manner that derives from one's "tacit supposition of their conformity to" their object (p. 514). When I ascribe truth to an idea belonging to another individual, I say that the idea is true when I suppose it conforms to my idea; and when I ascribe truth to my own idea, I suppose it is "conformable to some real existence" (Locke, p. 515). David Hume (1711–1776) loosely follows Locke in his account of the kinds of truth in the Treatise: "Truth is of two kinds, consisting either in the discovery of the proportions of ideas, consider'd as such, or in the conformity of our ideas of objects to their real existence" (p. 448). The second kind of truth, concerning matters of fact, echoes Locke's account of the ascription of truth to my own ideas and defines truth for matters of fact as conformity to the real existence of objects. Note that Hume endorses a correspondence theory only for matters of fact, not for matters of reason (or the discovery of proportions of ideas).
In the Critique of Pure Reason, Immanuel Kant (1724–1804) defined truth as correspondence: "The nominal definition of truth, namely that it is the agreement of cognition with its object, is here granted and presupposed; but one demands to know what is the general and certain criterion of the truth of any cognition" (p. 197). However, Kant denied that there is a universal material criterion of truth and observed that a universal formal criterion of truth, being nothing but logic, is sufficient only for consistency, not truth. Georg Wilhelm Friedrich Hegel (1770–1831) too accepted a correspondence definition of truth in his Science of Logic: "Objective truth is no doubt the Idea itself as the reality that corresponds to the Notion" (p. 784). But he did not see this as helping us with subjective truth.
Pragmatist and Coherence Theories
In Logic, Kant noted that to judge whether a cognition is true, one must compare it with its object, and this requires another cognition of the object, which may be fallible—hence the judgment of truth is not sufficient for truth. Kant took this to show that the correspondence definition is useless as a criterion of truth. By contrast, followers of Kant took it to show that correspondence truth is unknowable or even unthinkable, since it requires comparing a cognition with its uncognized object, which is uncognizable. One can compare a cognition only with other cognitions. Moreover, a cognition cannot copy or resemble an object. This difficulty led many philosophers in the nineteenth century to seek an alternative to the correspondence definition, and they naturally sought to define truth in terms of the criterion of truth.
In "How to Make Our Ideas Clear," the American pragmatist Charles Sanders Peirce (1839–1914) proposed a method of clarifying our everyday conceptions: a conception is to be identified with the conception of the practical effects of its object. For example, "To say that a body is heavy means simply that, in the absence of opposing force, it will fall" (1992b, p. 48). Applying this to truth, to say that a belief is true is to say that it would permanently survive sustained inquiry conducted in a proper way. This is an epistemic definition of truth, since it defines truth in terms of proper inquiry. An epistemic definition runs into circularity if proper inquiry is in turn defined in terms of the aim of true belief. In "The Fixation of Belief," Peirce answered this threat of circularity by characterizing proper inquiry without employing the notion of truth—as inquiry that fixes belief by eliminating doubt.
Like Peirce, William James (1842–1910) applied a pragmatist theory of meaning to true and identified the notion of true belief with that of the consequences for experience of the belief's being true—"truth's cash-value in experiential terms" (p. 200). James differed from Peirce in characterizing a true belief as one that is eventually verifiable, rather than one that would be permanently fixed in sustained inquiry. This allows the possibility that a true belief will be permanently retracted after its eventual verification in sustained inquiry. James was more pragmatist than Peirce in attempting to use his pragmatist theory of true belief to explain the practical, and not merely cognitive, utility of true belief. A true belief is one that would fit my experience in a counterfactual circumstance. Because my true belief that the cowpath leads to a house would fit my experience were I to go down the path, it enables me to select the more useful course of action—going down the path that leads to food, as opposed to one that does not. Moreover, James, unlike Peirce, was guided in his choice of a definition of truth by the aim of finding a definition that explains the practical utility of true belief.
British idealists developed coherence theories of truth in the late nineteenth century. One motivation for these theories was epistemological: knowledge of whether a given judgment is true cannot result from comparing the target judgment with its object, as the correspondence theory requires; it must result from comparing judgments with other judgments. The available criterion here is coherence of the judgments with one another. This motivation for the coherence theory received its most extensive expression in the twentieth century in the American idealist Brand Blanshard (1892–1987) (pp. 225–237, 268). An alternative metaphysical motivation, to be found in the work of Francis Herbert Bradley (1846–1924) and Harold H. Joachim (1868–1938), appeals to the doctrine of internal relations. According to this doctrine, every relation is grounded in the natures of the relata. This is said by Bertrand Russell (1872–1970) to be equivalent to the monistic theory of truth, that judgments are not true one by one, but only abstracted from a concrete known whole (1906–1907, p. 37). From monism, it is supposed to follow that the truth of a judgment consists in its coherence with the whole, rather than in correspondence. Russell objects to the coherence theory on the ground that it does not rule out contrary propositions both being true: "coherence as the definition of truth fails because there is no proof that there can be only one coherent system" (1912, p. 122).
The Correspondence Theory: Twentieth Century
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.
Deflationary theories treat the truth predicate as having only a logical or grammatical function, rather than as ascribing a property or relation to a truth bearer, as on correspondence, pragmatist, and coherence theories. Frank Plumpton Ramsey (1903–1930) proposed, contrary to Moore, that true generally makes no substantive contribution to what is asserted in a Page 2383 | Top of Article statement: "'it is true that Caesar was murdered' means no more than that Caesar was murdered" (p. 157). "Whatever he says is true" comes out "For all p, if he says that p, then p." This is called the redundancy theory of truth. It is deflationary in denying that true expresses a property of truth bearers or a relation of correspondence between truth bearers and the way the world is.
In Philosophical Investigations (1958), Ludwig Wittgenstein (1889–1951) rejected his idea presented in the Tractatus (1961, originally published in 1922) that "This is how things are" expresses the general form of a proposition. This form of words does express a proposition, but "To say that this proposition agrees or does not agree with reality would be obvious nonsense." Rather, it is a propositional variable the value of which is fixed by an earlier statement, in the way the referent of a pronoun is fixed by an earlier use of a name. This proposal, known as the "prosentential" theory of truth because it treats "That is true" as a "prosentence," was subsequently developed by Dorothy Grover, Joseph L. Camp, Jr., and Nuel D. Belnap, Jr. (1975).
Willard Van Orman Quine (1908–2000) proposed that the truth predicate is used for semantic ascent, which in certain cases is indispensable for expressive purposes: "If we want to affirm some infinite lot of sentences that we can demarcate only by talking about sentences, then the truth predicate has its use" (p. 11). If we wish to say only that Tom is mortal, we can say "'Tom is mortal' is true," but we need not do so. But if we wish to affirm each of the sentences of Euclidean geometry, we have no option but to say "All the sentences of Euclidean geometry are true." We are saying no more than we would say by uttering each of the sentences, but since there are infinitely many of them, we cannot utter them all. For this reason, the truth predicate is practically indispensable. This suggests a disquotational theory of truth on which the content of true for a language is given by all the equivalences: "p" is true just in case p (for all sentences "p" of the language). Presumably, occurrences of true in contexts like "What he said is true" or "That is true" would be either spelled out in the manner of Ramsey or implicitly defined by the T-equivalences in virtue of the fact that the subject of the sentence refers to a particular sentence. Paul Horwich developed a related minimalist theory of truth by taking as the axioms of the theory all the equivalences: the proposition that p is true if and only if p (1990). These deflationary theories have, in common with Moore's and Russell's correspondence theories, the disadvantage of entailing the principle of bivalence, which prohibits "truth-value gaps," as in borderline vague sentences or sentences with presuppositions that fail. A correspondence theory such as Field's can be formulated in a way that avoids bivalence (1972). Deflationary theories also differ from correspondence theories in making it impossible to ascribe truth to sentences in a language we can't understand. Field argued in a 1986 article that a deflationary notion of truth cannot be employed to account for how our tendency to believe truths explains our practical success in action.
Some have denied that truth is definable. Gottlob Frege (1848–1925) argued that if truth is definable as a property, then any judgment of whether an idea is true would involve judging whether the idea has the property, and the question would then arise whether it is true that the idea has the property, generating a circle (1956). The early Moore (1953, p. 262) and Donald Davidson (1917–2003) also denied that truth is definable. Since 1980, philosophers (e.g., Huw Price) have shown an interest in functionalist accounts of truth, which characterize truth in terms of its cognitive or social function, rather than define the concept in other terms.
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