Essay History Language Philosophical Truth

1. History of the Correspondence Theory

The correspondence theory is often traced back to Aristotle’s well-known definition of truth (Metaphysics 1011b25): “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”—but virtually identical formulations can be found in Plato (Cratylus 385b2, Sophist 263b). It is noteworthy that this definition does not highlight the basic correspondence intuition. Although it does allude to a relation (saying something of something) to reality (what is), the relation is not made very explicit, and there is no specification of what on the part of reality is responsible for the truth of a saying. As such, the definition offers a muted, relatively minimal version of a correspondence theory. (For this reason it has also been claimed as a precursor of deflationary theories of truth.) Aristotle sounds much more like a genuine correspondence theorist in the Categories (12b11, 14b14), where he talks of underlying things that make statements true and implies that these things (pragmata) are logically structured situations or facts (viz., his sitting and his not sitting are said to underlie the statements “He is sitting” and “He is not sitting”, respectively). Most influential is Aristotle’s claim in De Interpretatione (16a3) that thoughts are “likenessess” (homoiomata) of things. Although he nowhere defines truth in terms of a thought’s likeness to a thing or fact, it is clear that such a definition would fit well into his overall philosophy of mind. (Cf. Crivelli 2004; Szaif 2006.)

1.1 Metaphysical and Semantic Versions

In medieval authors we find a division between “metaphysical” and “semantic” versions of the correspondence theory. The former are indebted to the truth-as-likeness theme suggested by Aristotle’s overall views, the latter are modeled on Aristotle’s more austere definition from Metaphysics 1011b25.

The metaphysical version presented by Thomas Aquinas is the best known: “Veritas est adaequatio rei et intellectus” (Truth is the equation of thing and intellect), which he restates as: “A judgment is said to be true when it conforms to the external reality”. He tends to use “conformitas” and “adaequatio”, but also uses “correspondentia”, giving the latter a more generic sense (De Veritate, Q.1, A.1-3; cf. Summa Theologiae, Q.16). Aquinas credits the Neoplatonist Isaac Israeli with this definition, but there is no such definition in Isaac. Correspondence formulations can be traced back to the Academic skeptic Carneades, 2nd century B.C., whom Sextus Empiricus (Adversos Mathematicos, vii, 168) reports as having taught that a presentation “is true when it is in accord (symphonos) with the object presented, and false when it is in discord with it”. Similar accounts can be found in various early commentators on Plato and Aristotle (cf. Künne 2003, chap. 3.1), including some Neoplatonists: Proklos (In Tim., II 287, 1) speaks of truth as the agreement or adjustment (epharmoge) between knower and the known. Philoponus (In Cat., 81, 25-34) emphasizes that truth is neither in the things or states of affairs (pragmata) themselves, nor in the statement itself, but lies in the agreement between the two. He gives the simile of the fitting shoe, the fit consisting in a relation between shoe and foot, not to be found in either one by itself. Note that his emphasis on the relation as opposed to its relata is laudable but potentially misleading, because x’s truth (its being true) is not to be identified with a relation, R, between x and y, but with a general relational property of x, taking the form (∃y)(xRy & Fy). Further early correspondence formulations can be found in Avicenna (Metaphysica, 1.8-9) and Averroes (Tahafut, 103, 302). They were introduced to the scholastics by William of Auxerre, who may have been the intended recipient of Aquinas’ mistaken attribution (cf. Boehner 1958; Wolenski 1994).

Aquinas’ balanced formula “equation of thing and intellect” is intended to leave room for the idea that “true” can be applied not only to thoughts and judgments but also to things or persons (e.g. a true friend). Aquinas explains that a thought is said to be true because it conforms to reality, whereas a thing or person is said to be true because it conforms to a thought (a friend is true insofar as, and because, she conforms to our, or God’s, conception of what a friend ought to be). Medieval theologians regarded both, judgment-truth as well as thing/person-truth, as somehow flowing from, or grounded in, the deepest truth which, according to the Bible, is God: “I am the way and the truth and the life” (John 14, 6). Their attempts to integrate this Biblical passage with more ordinary thinking involving truth gave rise to deep metaphysico-theological reflections. The notion of thing/person-truth, which thus played a very important role in medieval thinking, is disregarded by modern and contemporary analytic philosophers but survives to some extent in existentialist and continental philosophy.

Medieval authors who prefer a semantic version of the correspondence theory often use a peculiarly truncated formula to render Aristotle’s definition: A (mental) sentence is true if and only if, as it signifies, so it is (sicut significat, ita est). This emphasizes the semantic relation of signification while remaining maximally elusive about what the “it” is that is signified by a true sentence and de-emphasizing the correspondence relation (putting it into the little words “as” and “so”). Foreshadowing a favorite approach of the 20th century, medieval semanticists like Ockham (Summa Logicae, II) and Buridan (Sophismata, II) give exhaustive lists of different truth-conditional clauses for sentences of different grammatical categories. They refrain from associating true sentences in general with items from a single ontological category. (Cf. Moody 1953; Adams McCord 1987; Perler 2006.)

Authors of the modern period generally convey the impression that the correspondence theory of truth is far too obvious to merit much, or any, discussion. Brief statements of some version or other can be found in almost all major writers; see e.g.: Descartes 1639, ATII 597; Spinoza, Ethics, axiom vi; Locke, Essay, 4.5.1; Leibniz, New Essays, 4.5.2; Hume, Treatise, 3.1.1; and Kant 1787, B82. Berkeley, who does not seem to offer any account of truth, is a potentially significant exception. Due to the influence of Thomism, metaphysical versions of the theory are much more popular with the moderns than semantic versions. But since the moderns generally subscribe to a representational theory of the mind (the theory of ideas), they would seem to be ultimately committed to spelling out relations like correspondence or conformity in terms of a psycho-semantic representation relation holding between ideas, or sentential sequences of ideas (Locke’s “mental propositions”), and appropriate portions of reality, thereby effecting a merger between metaphysical and semantic versions of the correspondence theory.

1.2 Object-Based and Fact-Based Versions

It is helpful to distinguish between “object-based” and “fact-based” versions of correspondence theories, depending on whether the corresponding portion of reality is said to be an object or a fact (cf. Künne 2003, chap. 3).

Traditional versions of object-based theories assumed that the truth-bearing items (usually taken to be judgments) have subject-predicate structure. An object-based definition of truth might look like this:

A judgment is true if and only if its predicate corresponds to its object (i.e., to the object referred to by the subject term of the judgment).

Note that this actually involves two relations to an object: (i) a reference relation, holding between the subject term of the judgment and the object the judgment is about (its object); and (ii) a correspondence relation, holding between the predicate term of the judgment and a property of the object. Owing to its reliance on the subject-predicate structure of truth-bearing items, the account suffers from an inherent limitation: it does not cover truthbearers that lack subject-predicate structure (e.g. conditionals, disjunctions), and it is not clear how the account might be extended to cover them. The problem is obvious and serious; it was nevertheless simply ignored in most writings. Object-based correspondence was the norm until relatively recently.

Object-based correspondence became the norm through Plato’s pivotal engagement with the problem of falsehood, which was apparently notorious at its time. In a number of dialogues, Plato comes up against an argument, advanced by various Sophists, to the effect that false judgment is impossible—roughly: To judge falsely is to judge what is not. But one cannot judge what is not, for it is not there to be judged. To judge something that is not is to judge nothing, hence, not to judge at all. Therefore, false judgment is impossible. (Cf. Euthydemus 283e-288a; Cratylus 429c-e; Republic 478a-c; Theaetetus 188d-190e.) Plato has no good answer to this patent absurdity until the Sophist (236d-264b), where he finally confronts the issue at length. The key step in his solution is the analysis of truthbearers as structured complexes. A simple sentence, such as “Theaetetus sits.”, though simple as a sentence, is still a complex whole consisting of words of different kinds—a name (onoma) and a verb (rhema)—having different functions. By weaving together verbs with names the speaker does not just name a number of things, but accomplishes something: meaningful speech (logos) expressive of the interweaving of ideas (eidon symploken). The simple sentence is true when Theaetetus, the person named by the name, is in the state of sitting, ascribed to him through the verb, and false, when Theaetetus is not in that state but in another one (cf. 261c-263d; see Denyer 1991; Szaif 1998). Only things that are show up in this account: in the case of falsehood, the ascribed state still is, but it is a state different from the one Theaetetus is in. The account is extended from speech to thought and belief via Plato’s well known thesis that “thought is speech that occurs without voice, inside the soul in conversation with itself” (263e)—the historical origin of the language-of-thought hypothesis. The account does not take into consideration sentences that contain a name of something that is not (“Pegasus flies”), thus bequeathing to posterity a residual problem that would become more notorious than the problem of falsehood.

Aristotle, in De Interpretatione, adopts Plato’s account without much ado—indeed, the beginning of De Interpretatione reads like a direct continuation of the passages from the Sophist mentioned above. He emphasizes that truth and falsehood have to do with combination and separation (cf. De Int. 16a10; in De Anima 430a25, he says: “where the alternative of true and false applies, there we always find a sort of combining of objects of thought in a quasi-unity”). Unlike Plato, Aristotle feels the need to characterize simple affirmative and negative statements (predications) separately—translating rather more literally than is usual: “An affirmation is a predication of something toward something, a negation is a predication of something away from something” (De Int. 17a25). This characterization reappears early in the Prior Analytics (24a). It thus seems fair to say that the subject-predicate analysis of simple declarative sentences—the most basic feature of Aristotelian term logic which was to reign supreme for many centuries—had its origin in Plato’s response to a sophistical argument against the possibility of falsehood. One may note that Aristotle’s famous definition of truth (see Section 1) actually begins with the definition of falsehood.

Fact-based correspondence theories became prominent only in the 20th century, though one can find remarks in Aristotle that fit this approach (see Section 1)—somewhat surprisingly in light of his repeated emphasis on subject-predicate structure wherever truth and falsehood are concerned. Fact-based theories do not presuppose that the truth-bearing items have subject-predicate structure; indeed, they can be stated without any explicit reference to the structure of truth-bearing items. The approach thus embodies an alternative response to the problem of falsehood, a response that may claim to extricate the theory of truth from the limitations imposed on it through the presupposition of subject-predicate structure inherited from the response to the problem of falsehood favored by Plato, Aristotle, and the medieval and modern tradition.

The now classical formulation of a fact-based correspondence theory was foreshadowed by Hume (Treatise, 3.1.1) and Mill (Logic, 1.5.1). It appears in its canonical form early in the 20th century in Moore (1910-11, chap. 15) and Russell: “Thus a belief is true when there is a corresponding fact, and is false when there is no corresponding fact” (1912, p. 129; cf. also his 1905, 1906, 1910, and 1913). The self-conscious emphasis on facts as the corresponding portions of reality—and a more serious concern with problems raised by falsehood—distinguishes this version from its foreshadowings. Russell and Moore’s forceful advocacy of truth as correspondence to a fact was, at the time, an integral part of their defense of metaphysical realism. Somewhat ironically, their formulations are indebted to their idealist opponents, F. H. Bradley (1883, chaps. 1&2), and H. H. Joachim (1906), the latter was an early advocate of the competing coherence theory, who had set up a correspondence-to-fact account of truth as the main target of his attack on realism. Later, Wittgenstein (1921) and Russell (1918) developed “logical atomism”, which introduces an important modification of the fact-based correspondence approach (see below, Section 7.1). Further modifications of the correspondence theory, bringing a return to more overtly semantic and broadly object-based versions, were influenced by Tarski’s (1935) technical work on truth (cf. Field 1972, Popper 1972).

2. Truthbearers, Truthmakers, Truth

2.1 Truthbearers

Correspondence theories of truth have been given for beliefs, thoughts, ideas, judgments, statements, assertions, utterances, sentences, and propositions. It has become customary to talk of truthbearers whenever one wants to stay neutral between these choices. Five points should be kept in mind:

  1. The term “truthbearer” is somewhat misleading. It is intended to refer to bearers of truth or falsehood (truth-value-bearers), or alternatively, to things of which it makes sense to ask whether they are true or false, thus allowing for the possibility that some of them might be neither.
  2. One distinguishes between secondary and primary truthbearers. Secondary truthbearers are those whose truth-values (truth or falsehood) are derived from the truth-values of primary truthbearers, whose truth-values are not derived from any other truthbearers. Consequently, the term “true” is usually regarded as ambiguous, taking its primary meaning when applied to primary truthbearers and various secondary meanings when applied to other truthbearers. This is, however, not a brute ambiguity, since the secondary meanings are supposed to be derived, i.e. definable from, the primary meaning together with additional relations. For example, one might hold that propositions are true or false in the primary sense, whereas sentences are true or false in a secondary sense, insofar as they express propositions that are true or false (in the primary sense). The meanings of “true”, when applied to truthbearers of different kinds, are thus connected in a manner familiar from what Aristotelians called “analogical” uses of a term—nowadays one would call this “focal meaning”; e.g., “healthy” in “healthy organism” and “healthy food”, the latter being defined as healthy in the secondary sense of contributing to the healthiness (primary sense) of an organism.
  3. It is often unproblematic to advocate one theory of truth for bearers of one kind and another theory for bearers of a different kind (e.g., a deflationary theory of truth, or an identity theory, applied to propositions, could be a component of some form of correspondence theory of truth for sentences). Different theories of truth applied to bearers of different kinds do not automatically compete. The standard segregation of truth theories into competing camps (found in textbooks, handbooks, and dictionaries) proceeds under the assumption—really a pretense—that they are intended for primary truthbearers of the same kind.
  4. Confusingly, there is little agreement as to which entities are properly taken to be primary truthbearers. Nowadays, the main contenders are public language sentences, sentences of the language of thought (sentential mental representations), and propositions. Popular earlier contenders—beliefs, judgments, statements, and assertions—have fallen out of favor, mainly for two reasons:
    1. The problem of logically complex truthbearers. A subject, S, may hold a disjunctive belief (the baby will be a boy or the baby will be a girl), while believing only one, or neither, of the disjuncts. Also, S may hold a conditional belief (if whales are fish, then some fish are mammals) without believing the antecedent or the consequent. Also, S will usually hold a negative belief (not everyone is lucky) without believing what is negated. In such cases, the truth-values of S’s complex beliefs depend on the truth-values of their constituents, although the constituents may not be believed by S or by anyone. This means that a view according to which beliefs are primary truthbearers seems unable to account for how the truth-values of complex beliefs are connected to the truth-values of their simpler constituents—to do this one needs to be able to apply truth and falsehood to belief-constituents even when they are not believed. This point, which is equally fundamental for a proper understanding of logic, was made by all early advocates of propositions (cf. Bolzano 1837, I.§§22, 34; Frege 1879, §§2-5; Husserl 1900, I.§11; Meinong 1902, §6). The problem arises in much the same form for views that would take judgments, statements, or assertions as primary truthbearers. The problem is not easily evaded. Talk of unbelieved beliefs (unjudged judgments, unstated statements, unasserted assertions) is either absurd or simply amounts to talk of unbelieved (unjudged, unstated, unasserted) propositions or sentences. It is noteworthy, incidentally, that quite a few philosophical proposals (concerning truth as well as other matters) run afoul of the simple observation that there are unasserted and unbelieved truthbearers (cf. Geach 1960 & 1965).
    2. The duality of state/content a.k.a. act/object. The noun “belief” can refer to the state of believing or to its content, i.e., to what is believed. If the former, the state of believing, can be said to be true or false at all, which is highly questionable, then only insofar as the latter, what is believed, is true or false. Similarly for nouns referring to mental acts or their objects (contents), such as “judgment”, “statement”, and “assertion”.
  5. Mental sentences were the preferred primary truthbearers throughout the medieval period. They were neglected in the first half of the 20th century, but made a comeback in the second half through the revival of the representational theory of the mind (especially in the form of the language-of-thought hypothesis, cf. Fodor 1975). Somewhat confusingly (to us now), for many centuries the term “proposition” (propositio) was reserved exclusively for sentences, written, spoken or mental. This use was made official by Boethius in the 6th century, and is still found in Locke’s Essay in 1705 and in Mill’s Logic in 1843. Some time after that, e.g., in Moore’s 1901-01, “proposition” switched sides, the term now being used for what is said by uttering a sentence, for what is believed, judged, stated, assumed (etc.)—with occasional reversions to medieval usage, e.g. in Russell (1918, 1919).

2.2 Truthmakers

Talk of truthmakers serves a function similar, but correlative, to talk of truthbearers. A truthmaker is anything that makes some truthbearer true. Different versions of the correspondence theory will have different, and often competing, views about what sort of items true truthbearers correspond to (facts, states of affairs, events, things, tropes, properties). It is convenient to talk of truthmakers whenever one wants to stay neutral between these choices. Four points should be kept in mind:

  1. The notion of a truthmaker is tightly connected with, and dependent on, the relational notion of truthmaking: a truthmaker is whatever stands in the truthmaking relation to some truthbearer. Despite the causal overtones of “maker” and “making”, this relation is usually not supposed to be a causal relation.
  2. The terms “truthmaking” and “truthmaker” are ambiguous. For illustration, consider a classical correspondence theory on which x is true if and only if x corresponds to some fact. One can say (a) that x is made true by a fact, namely the fact (or a fact) that x corresponds to. One can also say (b) that x is made true by x’s correspondence to a fact. Both uses of “is made true by” are correct and both occur in discussions of truth. But they are importantly different and must be distinguished. The (a)-use is usually the intended one; it expresses a relation peculiar to truth and leads to a use of “truthmaker” that actually picks out the items that would normally be intended by those using the term. The (b)-use does not express a relation peculiar to truth; it is just an instance (for “F” = “true”) of the generic formula “what makes an F-thing an F” that can be employed to elicit the definiens of a proposed definition of F. Compare: what makes an even number even is its divisibility by 2; what makes a right action right is its having better consequences than available alternative actions. Note that anyone proposing a definition or account of truth can avail themselves of the notion of truthmaking in the (b)-sense; e.g., a coherence theorist, advocating that a belief is true if and only if it coheres with other beliefs, can say: what makes a true belief true is its coherence with other beliefs. So, on the (b)-use, “truthmaking” and “truthmaker” do not signal any affinity with the basic idea underlying the correspondence theory of truth, whereas on the (a)-use these terms do signal such an affinity.
  3. Talk of truthmaking and truthmakers goes well with the basic idea underlying the correspondence theory; hence, it might seem natural to describe a traditional fact-based correspondence theory as maintaining that the truthmakers are facts and that the correspondence relation is the truthmaking relation. However, the assumption that the correspondence relation can be regarded as (a species of) the truthmaking relation is dubious. Correspondence appears to be a symmetric relation (if x corresponds to y, then y corresponds to x), whereas it is usually taken for granted that truthmaking is an asymmetric relation, or at least not a symmetric one. It is hard to see how a symmetric relation could be (a species of) an asymmetric or non-symmetric relation (cf. David 2009.)
  4. Talk of truthmaking and truthmakers is frequently employed during informal discussions involving truth but tends to be dropped when a more formal or official formulation of a theory of truth is produced (one reason being that it seems circular to define or explain truth in terms of truthmakers or truthmaking). However, in recent years, the informal talk has been turned into an official doctrine: “truthmaker theory”. This theory should be distinguished from informal truthmaker talk: not everyone employing the latter would subscribe to the former. Moreover, truthmaker theory should not simply be assumed to be a version of the correspondence theory; indeed, some advocates present it as a competitor to the correspondence theory (see below, Section 8.5).

2.3 Truth

The abstract noun “truth” has various uses. (a) It can be used to refer to the general relational property otherwise referred to as being true; though the latter label would be more perspicuous, it is rarely used, even in philosophical discussions. (b) The noun “truth” can be used to refer to the concept that “picks out” the property and is expressed in English by the adjective “true”. Some authors do not distinguish between concept and property; others do, or should: an account of the concept might differ significantly from an account of the property. To mention just one example, one might maintain, with some plausibility, that an account of the concept ought to succumb to the liar paradox (see the entry on the liar paradox), otherwise it wouldn’t be an adequate account of our concept of truth; this idea is considerably less plausible in the case of the property. Any proposed “definition of truth” might be intend as a definition of the property or of the concept or both; its author may or may not be alive to the difference. (c) The noun “truth” can be used, finally, to refer to some set of true truthbarers (possibly unknown), as in: “The truth is out there”, and: “The truth about this matter will never be known”.

3. Simple Versions of the Correspondence Theory

The traditional centerpiece of any correspondence theory is a definition of truth. Nowadays, a correspondence definition is most likely intended as a “real definition”, i.e., as a definition of the property, which does not commit its advocate to the claim that the definition provides a synonym for the term “true”. Most correspondence theorists would consider it implausible and unnecessarily bold to maintain that “true” means the same as “corresponds with a fact”. Some simple forms of correspondence definitions of truth should be distinguished (“iff” means “if and only if”; the variable, “x”, ranges over whatever truthbearers are taken as primary; the notion of correspondence might be replaced by various related notions):

(1)x is true iff x corresponds to some fact;
x is false iff x does not correspond to any fact.
(2)x is true iff x corresponds to some state of affairs that obtains;
x is false iff x corresponds to some state of affairs that does not obtain.

Both forms invoke portions of reality—facts/states of affairs—that are typically denoted by that-clauses or by sentential gerundives, viz. the fact/state of affairs that snow is white, or the fact/state of affairs of snow’s being white. (2)’s definition of falsehood is committed to there being (existing) entities of this sort that nevertheless fail to obtain, such as snow’s being green. (1)’s definition of falsehood is not so committed: to say that a fact does not obtain means, at best, that there is no such fact, that no such fact exists. It should be noted that this terminology is not standardized: some authors use “state of affairs” much like “fact” is used here (e.g. Armstrong 1997). The question whether non-obtaining beings of the relevant sort are to be accepted is the substantive issue behind such terminological variations. The difference between (2) and (1) is akin to the difference between Platonism about properties (embraces uninstantiated properties) and Aristotelianism about properties (rejects uninstantiated properties).

Advocates of (2) hold that facts are states of affairs that obtain, i.e., they hold that their account of truth is in effect an analysis of (1)’s account of truth. So disagreement turns largely on the treatment of falsehood, which (1) simply identifies with the absence of truth.

The following points might be made for preferring (2) over (1): (a) Form (2) does not imply that things outside the category of truthbearers (tables, dogs) are false just because they don’t correspond to any facts. One might think this “flaw” of (1) is easily repaired: just put an explicit specification of the desired category of truthbearers into both sides of (1). However, some worry that truthbearer categories, e.g. declarative sentences or propositions, cannot be defined without invoking truth and falsehood, which would make the resultant definition implicitly circular. (b) Form (2) allows for items within the category of truthbearers that are neither true nor false, i.e., it allows for the failure of bivalence. Some, though not all, will regard this as a significant advantage. (c) If the primary truthbearers are sentences or mental states, then states of affairs could be their meanings or contents, and the correspondence relation in (2) could be understood accordingly, as the relation of representation, signification, meaning, or having-as-content. Facts, on the other hand, cannot be identified with the meanings or contents of sentences or mental states, on pain of the absurd consequence that false sentences and beliefs have no meaning or content. (d) Take a truth of the form ‘p or q’, where ‘p’ is true and ‘q’ false. What are the constituents of the corresponding fact? Since ‘q’ is false, they cannot both be facts (cf. Russell 1906-07, p. 47f.). Form (2) allows that the fact corresponding to ‘p or q’ is an obtaining disjunctive state of affairs composed of a state of affairs that obtains and a state of affairs that does not obtain.

The main point in favor of (1) over (2) is that (1) is not committed to counting non-obtaining states of affairs, like the state of affairs that snow is green, as constituents of reality.

(One might observe that, strictly speaking, (1) and (2), being biconditionals, are not ontologically committed to anything. Their respective commitments to facts and states of affairs arise only when they are combined with claims to the effect that there is something that is true and something that is false. The discussion assumes some such claims as given.)

Both forms, (1) and (2), should be distinguished from:

(3)x is true iff x corresponds to some fact that exists;
x is false iff x corresponds to some fact that does not exist,

which is a confused version of (1), or a confused version of (2), or, if unconfused, signals commitment to Meinongianism, i.e., the thesis that there are things/facts that do not exist. The lure of (3) stems from the desire to offer more than a purely negative correspondence account of falsehood while avoiding commitment to non-obtaining states of affairs. Moore at times succumbs to (3)’s temptations (1910-11, pp. 267 & 269, but see p. 277). It can also be found in the 1961 translation of Wittgenstein (1921, 4.25), who uses “state of affairs” (Sachverhalt) to refer to (atomic) facts. The translation has Wittgenstein saying that an elementary proposition is false, when the corresponding state of affairs (atomic fact) does not exist—but the German original of the same passage looks rather like a version of (2). Somewhat ironically, a definition of form (3) reintroduces Plato’s problem of falsehood into a fact-based correspondence theory, i.e., into a theory of the sort that was supposed to provide an alternative solution to that very problem (see Section 1.2).

A fourth simple form of correspondence definition was popular for a time (cf. Russell 1918, secs. 1 & 3; Broad 1933, IV.2.23; Austin 1950, fn. 23), but seems to have fallen out of favor:

(4)x is true iff x corresponds (agrees) with some fact;
x is false iff x mis-corresponds (disagrees) with some fact.

This formulation attempts to avoid (2)’s commitment to non-obtaining states of affairs and (3)’s commitment to non-existent facts by invoking the relation of mis-correspondence, or disagreement, to account for falsehood. It differs from (1) in that it attempts to keep items outside the intended category of x’s from being false: supposedly, tables and dogs cannot mis-correspond with a fact. Main worries about (4) are: (a) its invocation of an additional, potentially mysterious, relation, which (b) seems difficult to tame: Which fact is the one that mis-corresponds with a given falsehood? and: What keeps a truth, which by definition corresponds with some fact, from also mis-corresponding with some other fact, i.e., from being a falsehood as well?

In the following, I will treat definitions (1) and (2) as paradigmatic; moreover, since advocates of (2) agree that obtaining states of affairs are facts, it is often convenient to condense the correspondence theory into the simpler formula provided by (1), “truth is correspondence to a fact”, at least as long as one is not particularly concerned with issues raised by falsehood.

4. Arguments for the Correspondence Theory

The main positive argument given by advocates of the correspondence theory of truth is its obviousness. Descartes: “I have never had any doubts about truth, because it seems a notion so transcendentally clear that nobody can be ignorant of it...the word ‘truth’, in the strict sense, denotes the conformity of thought with its object” (1639, AT II 597). Even philosophers whose overall views may well lead one to expect otherwise tend to agree. Kant: “The nominal definition of truth, that it is the agreement of [a cognition] with its object, is assumed as granted” (1787, B82). William James: “Truth, as any dictionary will tell you, is a property of certain of our ideas. It means their ‘agreement’, as falsity means their disagreement, with ‘reality’” (1907, p. 96). Indeed, The Oxford English Dictionary tells us: “Truth, n. Conformity with fact; agreement with reality”.

In view of its claimed obviousness, it would seem interesting to learn how popular the correspondence theory actually is. There are some empirical data. The PhilPapers Survey (conducted in 2009; cf. Bourget and Chalmers 2014), more specifically, the part of the survey targeting all regular faculty members in 99 leading departments of philosophy, reports the following responses to the question: “Truth: correspondence, deflationary, or epistemic?” Accept or lean toward: correspondence 50.8%; deflationary 24.8%; other 17.5%; epistemic 6.9%. The data suggest that correspondence-type theories may enjoy a weak majority among professional philosophers and that the opposition is divided. This fits with the observation that typically, discussions of the nature of truth take some version of the correspondence theory as the default view, the view to be criticized or to be defended against criticism.

Historically, the correspondence theory, usually in an object-based version, was taken for granted, so much so that it did not acquire this name until comparatively recently, and explicit arguments for the view are very hard to find. Since the (comparatively recent) arrival of apparently competing approaches, correspondence theorists have developed negative arguments, defending their view against objections and attacking (sometimes ridiculing) competing views.

5. Objections to the Correspondence Theory

Objection 1: Definitions like (1) or (2) are too narrow. Although they apply to truths from some domains of discourse, e.g., the domain of science, they fail for others, e.g. the domain of morality: there are no moral facts.

The objection recognizes moral truths, but rejects the idea that reality contains moral facts for moral truths to correspond to. Logic provides another example of a domain that has been “flagged” in this way. The logical positivists recognized logical truths but rejected logical facts. Their intellectual ancestor, Hume, had already given two definitions of “true”, one for logical truths, broadly conceived, the other for non-logical truths: “Truth or falsehood consists in an agreement or disagreement either to the real relations of ideas, or to real existence and matter of fact” (Hume, Treatise, 3.1.1, cf. 2.3.10; see also Locke, Essay, 4.5.6, for a similarly two-pronged account but in terms of object-based correspondence).

There are four possible responses to objections of this sort: (a) Noncognitivism, which says that, despite appearances to the contrary, claims from the flagged domain are not truth-evaluable to begin with, e.g., moral claims are commands or expressions of emotions disguised as truthbearers; (b) Error theory, which says that all claims from the flagged domain are false; (c) Reductionism, which says that truths from the flagged domain correspond to facts of a different domain regarded as unproblematic, e.g., moral truths correspond to social-behavioral facts, logical truths correspond to facts about linguistic conventions; and (d) Standing firm, i.e., embracing facts of the flagged domain.

The objection in effect maintains that there are different brands of truth (of the property being true, not just different brands of truths) for different domains. On the face of it, this conflicts with the observation that there are many obviously valid arguments combining premises from flagged and unflagged domains. The observation is widely regarded as refuting non-cognitivism, once the most popular (concessive) response to the objection.

In connection with this objection, one should take note of the recently developed “multiple realizability” view of truth, according to which truth is not to be identified with correspondence to fact but can be realized by correspondence to fact for truthbearers of some domains of discourse and by other properties for truthbearers of other domains of discourse, including “flagged” domains. Though it retains important elements of the correspondence theory, this view does not, strictly speaking, offer a response to the objection on behalf of the correspondence theory and should be regarded as one of its competitors (see below, Section 8.2).

Objection 2: Correspondence theories are too obvious. They are trivial, vacuous, trading in mere platitudes. Locutions from the “corresponds to the facts”-family are used regularly in everyday language as idiomatic substitutes for “true”. Such common turns of phrase should not be taken to indicate commitment to a correspondence theory in any serious sense. Definitions like (1) or (2) merely condense some trivial idioms into handy formulas; they don’t deserve the grand label “theory”: there is no theoretical weight behind them (cf. Woozley 1949, chap. 6; Davidson 1969; Blackburn 1984, chap. 7.1).

In response, one could point out: (a) Definitions like (1) or (2) are “mini-theories”—mini-theories are quite common in philosophy—and it is not at all obvious that they are vacuous merely because they are modeled on common usage. (b) There are correspondence theories that go beyond these definitions. (c) The complaint implies that definitions like (1) and/or (2) are generally accepted and are, moreover, so shallow that they are compatible with any deeper theory of truth. This makes it rather difficult to explain why some thinkers emphatically reject all correspondence formulations. (d) The objection implies that the correspondence of S’s belief with a fact could be said to consist in, e.g., the belief’s coherence with S’s overall belief system. This is wildly implausible, even on the most shallow understanding of “correspondence” and “fact”.

Objection 3: Correspondence theories are too obscure.

Objections of this sort, which are the most common, protest that the central notions of a correspondence theory carry unacceptable commitments and/or cannot be accounted for in any respectable manner. The objections can be divided into objections primarily aimed at the correspondence relation and its relatives (3.C1, 3.C2), and objections primarily aimed at the notions of fact or state of affairs (3.F1, 3.F2):

3.C1: The correspondence relation must be some sort of resemblance relation. But truthbearers do not resemble anything in the world except other truthbearers—echoing Berkeley’s “an idea can be like nothing but an idea”.

3.C2: The correspondence relation is very mysterious: it seems to reach into the most distant regions of space (faster than light?) and time (past and future). How could such a relation possibly be accounted for within a naturalistic framework? What physical relation could it possibly be?

3.F1: Given the great variety of complex truthbearers, a correspondence theory will be committed to all sorts of complex “funny facts” that are ontologically disreputable. Negative, disjunctive, conditional, universal, probabilistic, subjunctive, and counterfactual facts have all given cause for complaint on this score.

3.F2: All facts, even the most simple ones, are disreputable. Fact-talk, being wedded to that-clauses, is entirely parasitic on truth-talk. Facts are too much like truthbearers. Facts are fictions, spurious sentence-like slices of reality, “projected from true sentences for the sake of correspondence” (Quine 1987, p. 213; cf. Strawson 1950).

6. Correspondence as Isomorphism

Some correspondence theories of truth are two-liner mini-theories, consisting of little more than a specific version of (1) or (2). Normally, one would expect a bit more, even from a philosophical theory (though mini-theories are quite common in philosophy). One would expect a correspondence theory to go beyond a mere definition like (1) or (2) and discharge a triple task: it should tell us about the workings of the correspondence relation, about the nature of facts, and about the conditions that determine which truthbearers correspond to which facts.

One can approach this by considering some general principles a correspondence theory might want to add to its central principle to flesh out her theory. The first such principle says that the correspondence relation must not collapse into identity—“It takes two to make a truth” (Austin 1950, p. 118):

No truth is identical with a fact correspondence to which is sufficient for its being a truth.

It would be much simpler to say that no truth is identical with a fact. However, some authors, e.g. Wittgenstein 1921, hold that a proposition (Satz, his truthbearer) is itself a fact, though not the same fact as the one that makes the proposition true (see also King 2007). Nonidentity is usually taken for granted by correspondence theorists as constitutive of the very idea of a correspondence theory—authors who advance contrary arguments to the effect that correspondence must collapse into identity regard their arguments as objections to any form of correspondence theory (cf. Moore 1901/02, Frege 1918-19, p. 60).

Concerning the correspondence relation, two aspects can be distinguished: correspondence as correlation and correspondence as isomorphism (cf. Pitcher 1964; Kirkham 1992, chap. 4). Pertaining to the first aspect, familiar from mathematical contexts, a correspondence theorist is likely to adopt claim (a), and some may in addition adopt claim (b), of:

(a) Every truth corresponds to exactly one fact;
(b) Different truths correspond to different facts.

Together, (a) and (b) say that correspondence is a one-one relation. This seems needlessly strong, and it is not easy to find real-life correspondence theorists who explicitly embrace part (b): Why shouldn’t different truths correspond to the same fact, as long as they are not too different? Explicit commitment to (a) is also quite rare. However, correspondence theorists tend to move comfortably from talk about a given truth to talk about the fact it corresponds to—a move that signals commitment to (a).

Correlation does not imply anything about the inner nature of the corresponding items. Contrast this with correspondence as isomorphism, which requires the corresponding items to have the same, or sufficiently similar, constituent structure. This aspect of correspondence, which is more prominent (and more notorious) than the previous one, is also much more difficult to make precise. Let us say, roughly, that a correspondence theorist may want to add a claim to her theory committing her to something like the following:

If an item of kind K corresponds to a certain fact, then they have the same or sufficiently similar structure: the overall correspondence between a true K and a fact is a matter of part-wise correspondences, i.e. of their having corresponding constituents in corresponding places in the same structure, or in sufficiently similar structures.

The basic idea is that truthbearers and facts are both complex structured entities: truthbearers are composed of (other truthbearers and ultimately of) words, or concepts; facts are composed of (other facts or states of affairs and ultimately of) things, properties, and relations. The aim is to show how the correspondence relation is generated from underlying relations between the ultimate constituents of truthbearers, on the one hand, and the ultimate constituents of their corresponding facts, on the other. One part of the project will be concerned with these correspondence-generating relations: it will lead into a theory that addresses the question how simple words, or concepts, can be about things, properties, and relations; i.e., it will merge with semantics or psycho-semantics (depending on what the truthbearers are taken to be). The other part of the project, the specifically ontological part, will have to provide identity criteria for facts and explain how their simple constituents combine into complex wholes. Putting all this together should yield an account of the conditions determining which truthbearers correspond to which facts.

Correlation and Structure reflect distinct aspects of correspondence. One might want to endorse the former without the latter, though it is hard to see how one could endorse the latter without embracing at least part (a) of the former.

The isomorphism approach offers an answer to objection 3.C1. Although the truth that the cat is on the mat does not resemble the cat or the mat (the truth doesn’t meow or smell, etc.), it does resemble the fact that the cat is on the mat. This is not a qualitative resemblance; it is a more abstract, structural resemblance.

The approach also puts objection 3.C2 in some perspective. The correspondence relation is supposed to reduce to underlying relations between words, or concepts, and reality. Consequently, a correspondence theory is little more than a spin-off from semantics and/or psycho-semantics, i.e. the theory of intentionality construed as incorporating a representational theory of the mind (cf. Fodor 1989). This reminds us that, as a relation, correspondence is no more—but also no less—mysterious than semantic relations in general. Such relations have some curious features, and they raise a host of puzzles and difficult questions—most notoriously: Can they be explained in terms of natural (causal) relations, or do they have to be regarded as irreducibly non-natural aspects of reality? Some philosophers have claimed that semantic relations are too mysterious to be taken seriously, usually on the grounds that they are not explainable in naturalistic terms. But one should bear in mind that this is a very general and extremely radical attack on semantics as a whole, on the very idea that words and concepts can be about things. The common practice to aim this attack specifically at the correspondence theory seems misleading. As far as the intelligibility of the correspondence relation is concerned, the correspondence theory will stand, or fall, with the general theory of reference and intentionality.

It should be noted, though, that these points concerning objections 3.C1 and 3.C2 are not independent of one’s views about the nature of the primary truthbearers. If truthbearers are taken to be sentences of an ordinary language (or an idealized version thereof), or if they are taken to be mental representations (sentences of the language of thought), the above points hold without qualification: correspondence will be a semantic or psycho-semantic relation. If, on the other hand, the primary truthbearers are taken to be propositions, there is a complication:

  1. On a broadly Fregean view of propositions, propositions are constituted by concepts of objects and properties (in the logical, not the psychological, sense of “concept”). On this view, the above points still hold, since the relation between concepts, on the one hand, and the objects and properties they are concepts of, on the other, appears to be a semantic relation, a concept-semantic relation.
  2. On the so-called Russellian view of propositions (which the early Russell inherited mostly from early Moore), propositions are constituted, not of concepts of objects and properties, but of the objects and properties themselves (cf. Russell 1903). On this view, the points above will most likely fail, since the correspondence relation would appear to collapse into the identity relation when applied to true Russellian propositions. It is hard to see how a true Russellian proposition could be anything but a fact: What would a fact be, if not this sort of thing? So the principle of Nonidentity is rejected, and with it goes the correspondence theory of truth: “Once it is definitely recognized that the proposition is to denote, not a belief or form of words, but an object of belief, it seems plain that a truth differs in no respect from the reality with which it was supposed merely to correspond” (Moore 1901-02, p. 717). A simple, fact-based correspondence theory, applied to propositions understood in the Russellian way, thus reduces to an identity theory of truth, on which a proposition is true iff it is a fact, and false, iff it is not a fact. See below, Section 8.3; and the entries on propositions, singular propositions, and structured propositions in this encyclopedia.

But Russellians don’t usually renounce the correspondence theory entirely. Though they have no room for (1) from Section 3, when applied to propositions as truthbearers, correspondence will enter into their account of truth for sentences, public or mental. The account will take the form of Section 3’s (2), applied to categories of truthbearers other than propositions, where Russellian propositions show up on the right-hand side in the guise of states of affairs that obtain or fail to obtain. Commitment to states of affairs in addition to propositions is sometimes regarded with scorn, as a gratuitous ontological duplication. But Russellians are not committed to states of affairs in addition to propositions, for propositions, on their view, must already be states of affairs. This conclusion is well nigh inevitable, once true propositions have been identified with facts. If a true proposition is a fact, then a false proposition that might have been true would have been a fact, if it had been true. So, a (contingent) false proposition must be the same kind of being as a fact, only not a fact—an unfact; but that just is a non-obtaining state of affairs under a different name. Russellian propositions are states of affairs: the false ones are states of affairs that do not obtain, and the true ones are states of affairs that do obtain.

The Russellian view of propositions is popular nowadays. Somewhat curiously, contemporary Russellians hardly ever refer to propositions as facts or states of affairs. This is because they are much concerned with understanding belief, belief attributions, and the semantics of sentences. In such contexts, it is more natural to talk proposition-language than state-of-affairs-language. It feels odd (wrong) to say that someone believes a state of affairs, or that states of affairs are true or false. For that matter, it also feels odd (wrong) to say that some propositions are facts, that facts are true, and that propositions obtain or fail to obtain. Nevertheless, all of this must be the literal truth, according to the Russellians. They have to claim that “proposition” and “state of affairs”, much like “evening star” and “morning star”, are different names for the same things—they come with different associations and are at home in somewhat different linguistic environments, which accounts for the felt oddness when one name is transported to the other’s environment.

Returning to the isomorphism approach in general, on a strict or naïve implementation of this approach, correspondence will be a one-one relation between truths and corresponding facts, which leaves the approach vulnerable to objections against funny facts (3.F1): each true truthbearer, no matter how complex, will be assigned a matching fact. Moreover, since a strict implementation of isomorphism assigns corresponding entities to all (relevant) constituents of truthbearers, complex facts will contain objects corresponding to the logical constants (“not”, “or”, “if-then”, etc.), and these “logical objects” will have to be regarded as constituents of the world. Many philosophers have found it hard to believe in the existence of all these funny facts and funny quasi-logical objects.

The isomorphism approach has never been advocated in a fully naïve form, assigning corresponding objects to each and every wrinkle of our verbal or mental utterings. Instead, proponents try to isolate the “relevant” constituents of truthbearers through meaning analysis, aiming to uncover the logical form, or deep structure, behind ordinary language and thought. This deep structure might then be expressed in an ideal-language (typically, the language of predicate logic), whose syntactic structure is designed to mirror perfectly the ontological structure of reality. The resulting view—correspondence as isomorphism between properly analyzed truthbearers and facts—avoids assigning strange objects to such phrases as “the average husband”, “the sake of”, and “the present king of France”; but the view remains committed to logically complex facts and to logical objects corresponding to the logical constants.

Austin (1950) rejects the isomorphism approach on the grounds that it projects the structure of our language onto the world. On his version of the correspondence theory (a more elaborated variant of (4) applied to statements), a statement as a whole is correlated to a state of affairs by arbitrary linguistic conventions without mirroring the inner structure of its correlate (cf. also Vision 2004). This approach appears vulnerable to the objection that it avoids funny facts at the price of neglecting systematicity. Language does not provide separate linguistic conventions for each statement: that would require too vast a number of conventions. Rather, it seems that the truth-values of statements are systematically determined, via a relatively small set of conventions, by the semantic values (relations to reality) of their simpler constituents. Recognition of this systematicity is built right into the isomorphism approach.

Critics frequently echo Austin’s “projection”-complaint, 3.F2, that a traditional correspondence theory commits “the error of reading back into the world the features of language” (Austin 1950, p. 155; cf. also, e.g., Rorty 1981). At bottom, this is a pessimistic stance: if there is a prima facie structural resemblance between a mode of speech or thought and some ontological category, it is inferred, pessimistically, that the ontological category is an illusion, a matter of us projecting the structure of our language or thought into the world. Advocates of traditional correspondence theories can be seen as taking the opposite stance: unless there are specific reasons to the contrary, they are prepared to assume, optimistically, that the structure of our language and/or thought reflects genuine ontological categories, that the structure of our language and/or thought is, at least to a significant extent, the way it is because of the structure of the world.

7. Modified Versions of the Correspondence Theory

7.1 Logical Atomism

Wittgenstein (1921) and Russell (1918) propose modified fact-based correspondence accounts of truth as part of their program of logical atomism. Such accounts proceed in two stages. At the first stage, the basic truth-definition, say (1) from Section 3, is restricted to a special subclass of truthbearers, the so-called elementary or atomic truthbearers, whose truth is said to consist in their correspondence to (atomic) facts: if x is elementary, then x is true iff x corresponds to some (atomic) fact. This restricted definition serves as the base-clause for truth-conditional recursion-clauses given at the second stage, at which the truth-values of non-elementary, or molecular, truthbearers are explained recursively in terms of their logical structure and the truth-values of their simpler constituents. For example: a sentence of the form ‘not-p’ is true iff ‘p’ is false; a sentence of the form ‘p and q’ is true iff ‘p’ is true and ‘q’ is true; a sentence of the form ‘p or q’ is true iff ‘p’ is true or ‘q’ is true, etc. These recursive clauses (called “truth conditions”) can be reapplied until the truth of a non-elementary, molecular sentence of arbitrary complexity is reduced to the truth or falsehood of its elementary, atomic constituents.

Logical atomism exploits the familiar rules, enshrined in the truth-tables, for evaluating complex formulas on the basis of their simpler constituents. These rules can be understood in two different ways: (a) as tracing the ontological relations between complex facts and constituent simpler facts, or (b) as tracing logico-semantic relations, exhibiting how the truth-values of complex sentences can be explained in terms of their logical relations to simpler constituent sentences together with the correspondence and non-correspondence of simple, elementary sentences to atomic facts. Logical atomism takes option (b).

Logical atomism is designed to go with the ontological view that the world is the totality of atomic facts (cf. Wittgenstein 1921, 2.04); thus accommodating objection 3.F2 by doing without funny facts: atomic facts are all the facts there are—although real-life atomists tend to allow conjunctive facts, regarding them as mere aggregates of atomic facts. An elementary truth is true because it corresponds to an atomic fact: correspondence is still isomorphism, but it holds exclusively between elementary truths and atomic facts. There is no match between truths and facts at the level of non-elementary, molecular truths; e.g., ‘p’, ‘p or q’, and ‘p or r’ might all be true merely because ‘p’ corresponds to a fact). The trick for avoiding logically complex facts lies in not assigning any entities to the logical constants. Logical complexity, so the idea goes, belongs to the structure of language and/or thought; it is not a feature of the world. This is expressed by Wittgenstein in an often quoted passage (1921, 4.0312): “My fundamental idea is that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts”; and also by Russell (1918, p. 209f.): “You must not look about the real world for an object which you can call ‘or’, and say ‘Now look at this. This is ‘or’’”.

Though accounts of this sort are naturally classified as versions of the correspondence theory, it should be noted that they are strictly speaking in conflict with the basic forms presented in Section 3. According to logical atomism, it is not the case that for every truth there is a corresponding fact. It is, however, still the case that the being true of every truth is explained in terms of correspondence to a fact (or non-correspondence to any fact) together with (in the case of molecular truths) logical notions detailing the logical structure of complex truthbearers. Logical atomism attempts to avoid commitment to logically complex, funny facts via structural analysis of truthbearers. It should not be confused with a superficially similar account maintaining that molecular facts are ultimately constituted by atomic facts. The latter account would admit complex facts, offering an ontological analysis of their structure, and would thus be compatible with the basic forms presented in Section 3, because it would be compatible with the claim that for every truth there is a corresponding fact. (For more on classical logical atomism, see Wisdom 1931-1933, Urmson 1953, and the entries on Russell's logical atomism and Wittgenstein's logical atomism in this encyclopedia.)

While Wittgenstein and Russell seem to have held that the constituents of atomic facts are to be determined on the basis of a priori considerations, Armstrong (1997, 2004) advocates an a posteriori form of logical atomism. On his view, atomic facts are composed of particulars and simple universals (properties and relations). The latter are objective features of the world that ground the objective resemblances between particulars and explain their causal powers. Accordingly, what particulars and universals there are will have to be determined on the basis of total science.

Problems: Logical atomism is not easy to sustain and has rarely been held in a pure form. Among its difficulties are the following: (a) What, exactly, are the elementary truthbearers? How are they determined? (b) There are molecular truthbearers, such as subjunctives and counterfactuals, that tend to provoke the funny-fact objection but cannot be handled by simple truth-conditional clauses, because their truth-values do not seem to be determined by the truth-values of their elementary constituents. (c) Are there universal facts corresponding to true universal generalizations? Wittgenstein (1921) disapproves of universal facts; apparently, he wants to re-analyze universal generalizations as infinite conjunctions of their instances. Russell (1918) and Armstrong (1997, 2004) reject this analysis; they admit universal facts. (d) Negative truths are the most notorious problem case, because they clash with an appealing principle, the “truthmaker principle” (cf. Section 8.5), which says that for every truth there must be something in the world that makes it true, i.e., every true truthbearer must have a truthmaker. Suppose ‘p’ is elementary. On the account given above, ‘not-p’ is true iff ‘p’ is false iff ‘p’ does not correspond to any fact; hence, ‘not-p’, if true, is not made true by any fact: it does not seem to have a truthmaker. Russell finds himself driven to admit negative facts, regarded by many as paradigmatically disreputable portions of reality. Wittgenstein sometimes talks of atomic facts that do not exist and calls their very nonexistence a negative fact (cf. 1921, 2.06)—but this is hardly an atomic fact itself. Armstrong (1997, chap. 8.7; 2004, chaps. 5-6) holds that negative truths are made true by a second-order “totality fact” which says of all the (positive) first-order facts that they are all the first-order facts.

Atomism and the Russellian view of propositions (see Section 6). By the time Russell advocated logical atomism (around 1918), he had given up on what is now referred to as the Russellian conception of propositions (which he and G. E. Moore held around 1903). But Russellian propositons are popular nowadays. Note that logical atomism is not for the friends of Russellian propositions. The argument is straightforward. We have logically complex beliefs some of which are true. According to the friends of Russellian propositions, the contents of our beliefs are Russellian propositions, and the contents of our true beliefs are true Russellian propositions. Since true Russellian propositions are facts, there must be at least as many complex facts as there are true beliefs with complex contents (and at least as many complex states of affairs as there are true or false beliefs with complex contents). Atomism may work for sentences, public or mental, and for Fregean propositions; but not for Russellian propositions.

Logical atomism is designed to address objections to funny facts (3.F1). It is not designed to address objections to facts in general (3.F2). Here logical atomists will respond by defending (atomic) facts. According to one defense, facts are needed because mere objects are not sufficiently articulated to serve as truthmakers. If a were the sole truthmaker of ‘a is F’, then the latter should imply ‘a is G’, for any ‘G’. So the truthmaker for ‘a is F’ needs at least to involve a and Fness. But since Fness is a universal, it could be instantiated in another object, b, hence the mere existence of a and Fness is not sufficient for making true the claim ‘a is F’: a and Fness need to be tied together in the fact of a’s being F. Armstrong (1997) and Olson (1987) also maintain that facts are needed to make sense of the tie that binds particular objects to universals.

In this context it is usually emphasized that facts do not supervene on, hence, are not reducible to, their constituents. Facts are entities over and above the particulars and universals of which they are composed: a’s loving b and b’s loving a are not the same fact even though they have the very same constituents.

Another defense of facts, surprisingly rare, would point out that many facts are observable: one can see that the cat is on the mat; and this is different from seeing the cat, or the mat, or both. The objection that many facts are not observable would invite the rejoinder that many objects are not observable either. (See Austin 1961, Vendler 1967, chap. 5, and Vision 2004, chap. 3, for more discussion of anti-fact arguments; see also the entry facts in this encyclopedia.)

Some atomists propose an atomistic version of definition (1), but without facts, because they regard facts as slices of reality too suspiciously sentence-like to be taken with full ontological seriousness. Instead, they propose events and/or objects-plus-tropes (a.k.a. modes, particularized qualities, moments) as the corresponding portions of reality. It is claimed that these items are more “thingy” than facts but still sufficiently articulated—and sufficiently abundant—to serve as adequate truthmakers (cf. Mulligan, Simons, and Smith 1984).

7.2 Logical “Subatomism”

Logical atomism aims at getting by without logically complex truthmakers by restricting definitions like (1) or (2) from Section 3 to elementary truthbearers and accounting for the truth-values of molecular truthbearers recursively in terms of their logical structure and atomic truthmakers (atomic facts, events, objects-plus-tropes). More radical modifications of the correspondence theory push the recursive strategy even further, entirely discarding definitions like (1) or (2), and hence the need for atomic truthmakers, by going, as it were, “subatomic”.

Such accounts analyze truthbearers, e.g., sentences, into their subsentential constituents and dissolve the relation of correspondence into appropriate semantic subrelations: names refer to, or denote, objects; predicates (open sentences) apply to, or are satisfied by objects. Satisfaction of complex predicates can be handled recursively in terms of logical structure and satisfaction of simpler constituent predicates: an object o satisfies ‘x is not F’ iff o does not satisfy ‘x is F’; o satisfies ‘x is F or x is G’ iff o satisfies ‘x is F’ or o satisfies ‘x is G’; and so on. These recursions are anchored in a base-clause addressing the satisfaction of primitive predicates: an object o satisfies ‘x is F’ iff o instantiates the property expressed by ‘F’. Some would prefer a more nominalistic base-clause for satisfaction, hoping to get by without seriously invoking properties. Truth for singular sentences, consisting of a name and an arbitrarily complex predicate, is defined thus: A singular sentence is true iff the object denoted by the name satisfies the predicate. Logical machinery provided by Tarski (1935) can be used to turn this simplified sketch into a more general definition of truth—a definition that handles sentences containing relational predicates and quantifiers and covers molecular sentences as well. Whether Tarski’s own definition of truth can be regarded as a correspondence definition, even in this modified sense, is under debate (cf. Popper 1972; Field 1972, 1986; Kirkham 1992, chaps. 5-6; Soames 1999; Künne 2003, chap. 4; Patterson 2008.)

Subatomism constitutes a return to (broadly) object-based correspondence. Since it promises to avoid facts and all similarly articulated, sentence-like slices of reality, correspondence theorists who take seriously objection 3.F2 favor this approach: not even elementary truthbearers are assigned any matching truthmakers. The correspondence relation itself has given way to two semantic relations between constituents of truthbearers and objects: reference (or denotation) and satisfaction—relations central to any semantic theory. Some advocates envision causal accounts of reference and satisfaction (cf. Field 1972; Devitt 1982, 1984; Schmitt 1995; Kirkham 1992, chaps. 5-6). It turns out that relational predicates require talk of satisfaction by ordered sequences of objects. Davidson (1969, 1977) maintains that satisfaction by sequences is all that remains of the traditional idea of correspondence to facts; he regards reference and satisfaction as “theoretical constructs” not in need of causal, or any, explanation.

Problems: (a) The subatomistic approach accounts for the truth-values of molecular truthbearers in the same way as the atomistic approach; consequently, molecular truthbearers that are not truth-functional still pose the same problems as in atomism. (b) Belief attributions and modal claims pose special problems; e.g., it seems that “believes” is a relational predicate, so that “John believes that snow is white” is true iff “believes” is satisfied by John and the object denoted by “that snow is white”; but the latter appears to be a proposition or state of affairs, which threatens to let in through the back-door the very sentence-like slices of reality the subatomic approach was supposed to avoid, thus undermining the motivation for going subatomic. (c) The phenomenon of referential indeterminacy threatens to undermine the idea that the truth-values of elementary truthbearers are always determined by the denotation and/or satisfaction of their constituents; e.g., pre-relativistic uses of the term “mass” are plausibly taken to lack determinate reference (referring determinately neither to relativistic mass nor to rest mass); yet a claim like “The mass of the earth is greater than the mass of the moon” seems to be determinately true even when made by Newton (cf. Field 1973).

Problems for both versions of modified correspondence theories: (a) It is not known whether an entirely general recursive definition of truth, one that covers all truthbearers, can be made available. This depends on unresolved issues concerning the extent to which truthbearers are amenable to the kind of structural analyses that are presupposed by the recursive clauses. The more an account of truth wants to exploit the internal structure of truthbearers, the more it will be hostage to the (limited) availability of appropriate structural analyses of the relevant truthbearers. (b) Any account of truth employing a recursive framework may be virtually committed to taking sentences (maybe sentences of the language of thought) as primary truthbearers. After all, the recursive clauses rely heavily on what appears to be the logico-syntactic structure of truthbearers, and it is unclear whether anything but sentences can plausibly be said to possess that kind of structure. But the thesis that sentences of any sort are to be regarded as the primary truthbearers is contentious. Whether propositions can meaningfully be said to have an analogous (albeit non-linguistic) structure is under debate (cf. Russell 1913, King 2007). (c) If clauses like “‘p or q’ is true iff ‘p’ is true or ‘q’ is true” are to be used in a recursive account of our notion of truth, as opposed to some other notion, it has to be presupposed that ‘or’ expresses disjunction: one cannot define “or” and “true” at the same time. To avoid circularity, a modified correspondence theory (be it atomic or subatomic) must hold that the logical connectives can be understood without reference to correspondence truth.

7.3 Relocating Correspondence

Definitions like (1) and (2) from Section 3 assume, naturally, that truthbearers are true because they, the truthbearers themselves, correspond to facts. There are however views that reject this natural assumption. They propose to account for the truth of truthbearers of certain kinds, propositions, not by way of their correspondence to facts, but by way of the correspondence to facts of other items, the ones that have propositions as their contents. Consider the state of believing that p (or the activity of judging that p). The state (the activity) is not, strictly speaking, true or false; rather, what is true or false is its content, the proposition that p. Nevertheless, on the present view, it is the state of believing that p that corresponds or fails to correspond to a fact. So truth/falsehood for propositions can be defined in the following manner: x is a true/false proposition iff there is a belief state B such that x is the content of B and B corresponds/fails to correspond to a fact.

Such a modification of fact-based correspondence can be found in Moore (1927, p. 83) and Armstrong (1973, 4.iv & 9). It can be adapted to atomistic (Armstrong) and subatomistic views, and to views on which sentences (of the language of thought) are the primary bearers of truth and falsehood. However, by taking the content-carrying states as the primary corresponders, it entails that there are no truths/falsehoods that are not believed by someone. Most advocates of propositions as primary bearers of truth and falsehood will regard this as a serious weakness, holding that there are very many true and false propositions that are not believed, or even entertained, by anyone. Armstrong (1973) combines the view with an instrumentalist attitude towards propositions, on which propositions are mere abstractions from mental states and should not be taken seriously, ontologically speaking.

8. The Correspondence Theory and Its Competitors

8.1 Traditional Competitors

Against the traditional competitors—coherentist, pragmatist, and verificationist and other epistemic theories of truth—correspondence theorists raise two main sorts of objections. First, such accounts tend to lead into relativism. Take, e.g., a coherentist account of truth. Since it is possible that ‘p’ coheres with the belief system of S while ‘not-p’ coheres with the belief system of S*, the coherentist account seems to imply, absurdly, that contradictories, ‘p’ and ‘not-p’, could both be true. To avoid embracing contradictions, coherentists often commit themselves (if only covertly) to the objectionable relativistic view that ‘p’ is true-for-S and ‘not-p’ is true-for-S*. Second, the accounts tend to lead into some form of idealism or anti-realism, e.g., it is possible for the belief that p to cohere with someone’s belief system, even though it is not a fact that p; also, it is possible for it to be a fact that p, even if no one believes that p at all or if the belief does not cohere with anyone’s belief system. Cases of this sort are frequently cited as counterexamples to coherentist accounts of truth. Dedicated coherentists tend to reject such counterexamples, insisting that they are not possible after all. Since it is hard to see why they would not be possible, unless its being a fact that p were determined by the belief’s coherence with other beliefs, this reaction commits them to the anti-realist view that the facts are (largely) determined by what we believe.

This offers a bare outline of the overall shape the debates tend to take. For more on the correspondence theory vs. its traditional competitors see, e.g., Vision 1988; Kirkham 1992, chaps. 3, 7-8; Schmitt 1995; Künne 2003, chap. 7; and essays in Lynch 2001. Walker 1989 is a book-lenght discussion of coherence theories of truth. See also the entries on pragmatism, relativism, the coherence theory of truth, in this encyclopedia.

8.2 Pluralism

The correspondence theory is sometimes accused of overreaching itself: it does apply, so the objection goes, to truths from some domains of discourse, e.g., scientific discourse and/or discourse about everyday midsized physical things, but not to truths from various other domains of discourse, e.g., ethical and/or aesthetic discourse (see the first objection in Section 5 above). Alethic pluralism grows out of this objection, maintaining that truth is constituted by different properties for true propositions from different domains of discourse: by correspondence to fact for true propositions from the domain of scientific or everyday discourse about physical things; by some epistemic property, such as coherence or superassertibility, for true propositions from the domain of ethical and aesthetic discourse, and maybe by still other properties for other domains of discourse. This suggests a position on which the term “true” is multiply ambiguous, expressing different properties when applied to propositions from different domains. However, contemporary pluralists reject this problematic idea, maintaining instead that truth is “multiply realizable”. That is, the term “true” is univocal, it expresses one concept or property, truth (being true), but one that can be realized by or manifested in different properties (correspondence to fact, coherence or superassertibility, and maybe others) for true propositions from different domains of discourse. Truth itself is not to be identified with any of its realizing properties. Instead, it is characterized, quasi axiomatically, by a set of alleged “platitudes”, including, according to Crispin Wright’s (1999) version, “transparency” (to assert is to present as true), “contrast” (a proposition may be true without being justified, and v.v.), “timelesness” (if a proposition is ever true, then it always is), “absoluteness” (there is no such thing as a proposition being more or less true), and others.

Though it contains the correspondence theory as one ingredient, alethic pluralism is nevertheless a genuine competitor, for it rejects the thesis that truth is correspondence to reality. Moreover, it equally contains competitors of the correspondence theory as further ingredients.

Alethic pluralism in its contemporary form is a relatively young position. It was inaugurated by Crispin Wright (1992; see also 1999) and was later developed into a somewhat different form by Lynch (2009). Critical discussion is still at a relatively nascent stage (but see Vision 2004, chap. 4, for extended discussion of Wright). It will likely focus on two main problem areas.

First, it seems difficult to sort propositions into distinct kinds according to the subject matter they are about. Take, e.g., the proposition that killing is morally wrong, or the proposition that immoral acts happen in space-time. What are they about? Intuitively, their subject matter is mixed, belonging to the physical domain, the biological domain, and the domain of ethical discourse. It is hard to see how pluralism can account for the truth of such mixed propositions, belonging to more than one domain of discourse: What will be the realizing property?

Second, pluralists are expected to explain how the platitudes can be “converted” into an account of truth itself. Lynch (2009) proposes to construe truth as a functional property, defined in terms of a complex functional role which is given by the conjunction of the platitudes (somewhat analogous to the way in which functionalists in the philosophy of mind construe mental states as functional states, specified in terms of their functional roles—though in their case the relevant functional roles are causal roles, which is not a feasible option when it comes to the truth-role). Here the main issue will be to determine (a) whether such an account really works, when the technical details are laid out, and (b) whether it is plausible to claim that properties as different as correspondence to a fact, on the one hand, and coherence or superassertibilty, on the other, can be said to play one and the same role—a claim that seems required by the thesis that these different properties all realize the same property, being true.

For more on pluralism, see e.g. the essays in Monnoyer (2007) and in Pedersen & Wright (2013); and the entry on pluralist theories of truth in this encyclopedia.

8.3 The Identity Theory of Truth

According to the identity theory of truth, true propositions do not correspond to facts, they are facts: the true proposition that snow is white = the fact that snow is white. This non-traditional competitor of the correspondence theory threatens to collapse the correspondence relation into identity. (See Moore 1901-02; and Dodd 2000 for a book-length defense of this theory and discussion contrasting it with the correspondence theory; and see the entry the identity theory of truth: in this encyclopedia.)

In response, a correspondence theorist will point out: (a) The identity theory is defensible only for propositions as truthbearers, and only for propositions construed in a certain way, namely as having objects and properties as constituents rather than ideas or concepts of objects and properties; that is, for Russellian propositions. Hence, there will be ample room (and need) for correspondence accounts of truth for other types of truthbearers, including propositions, if they are construed as constituted, partly or wholly, of concepts of objects and properties. (b) The identity theory is committed to the unacceptable consequence that facts are true. (c) The identity theory rests on the assumption that that-clauses always denote propositions, so that the that-clause in “the fact that snow is white” denotes the proposition that snow is white. The assumption can be questioned. That-clauses can be understood as ambiguous names, sometimes denoting propositions and sometimes denoting facts. The descriptive phrases “the proposition…” and “the fact…” can be regarded as serving to disambiguate the succeeding ambiguous that-clauses—much like the descriptive phrases in “the philosopher Socrates” and “the soccer-player Socrates” serve to disambiguate the ambiguous name “Socrates” (cf. David 2002).

8.4 Deflationism About Truth

At present the most noticeable competitors to correspondence theories are deflationary accounts of truth (or ‘true’). Deflationists maintain that correspondence theories need to be deflated; that their central notions, correspondence and fact (and their relatives), play no legitimate role in an adequate account of truth and can be excised without loss. A correspondence-type formulation like

(5) “Snow is white” is true iff it corresponds to the fact that snow is white,

is to be deflated to

(6) “Snow is white” is true iff snow is white,

which, according to deflationists, says all there is to be said about the truth of “Snow is white”, without superfluous embellishments (cf. Quine 1987, p. 213).

Correspondence theorists protest that (6) cannot lead to anything deserving to be regarded as an account of truth. It is concerned with only one particular sentence (“Snow is white”), and it resists generalization. (6) is a substitution instance of the schema

(7) “p” is true iff p,

which does not actually say anything itself (it is not truth-evaluable) and cannot be turned into a genuine generalization about truth, because of its essential reliance on the schematic letter “p”, a mere placeholder. The attempt to turn (7) into a generalization produces nonsense along the lines of “For every x, “x” is true iff x”, or requires invocation of truth: “Every substitution instance of the schema ““p” is true iff p” is true”. Moreover, no genuine generalizations about truth can be accounted for on the basis of (7). Correspondence definitions, on the other hand, do yield genuine generalizations about truth. Note that definitions like (1) and (2) in Section 3 employ ordinary objectual variables (not mere schematic placeholders); the definitions are easily turned into genuine generalizations by prefixing the quantifier phrase “For every x

1. The neo-classical theories of truth

Much of the contemporary literature on truth takes as its starting point some ideas which were prominent in the early part of the 20th century. There were a number of views of truth under discussion at that time, the most significant for the contemporary literature being the correspondence, coherence, and pragmatist theories of truth.

These theories all attempt to directly answer the nature question: what is the nature of truth? They take this question at face value: there are truths, and the question to be answered concerns their nature. In answering this question, each theory makes the notion of truth part of a more thoroughgoing metaphysics or epistemology. Explaining the nature of truth becomes an application of some metaphysical system, and truth inherits significant metaphysical presuppositions along the way.

The goal of this section is to characterize the ideas of the correspondence, coherence and pragmatist theories which animate the contemporary debate. In some cases, the received forms of these theories depart from the views that were actually defended in the early 20th century. We thus dub them the ‘neo-classical theories’. Where appropriate, we pause to indicate how the neo-classical theories emerge from their ‘classical’ roots in the early 20th century.

1.1 The correspondence theory

Perhaps the most important of the neo-classical theories for the contemporary literature is the correspondence theory. Ideas that sound strikingly like a correspondence theory are no doubt very old. They might well be found in Aristotle or Aquinas. When we turn to the late 19th and early 20th centuries where we pick up the story of the neo-classical theories of truth, it is clear that ideas about correspondence were central to the discussions of the time. In spite of their importance, however, it is strikingly difficult to find an accurate citation in the early 20th century for the received neo-classical view. Furthermore, the way the correspondence theory actually emerged will provide some valuable reference points for the contemporary debate. For these reasons, we dwell on the origins of the correspondence theory in the late 19th and early 20th centuries at greater length than those of the other neo-classical views, before turning to its contemporary neo-classical form.

1.1.1 The origins of the correspondence theory

The basic idea of the correspondence theory is that what we believe or say is true if it corresponds to the way things actually are – to the facts. This idea can be seen in various forms throughout the history of philosophy. Its modern history starts with the beginnings of analytic philosophy at the turn of the 20th century, particularly in the work of G. E. Moore and Bertrand Russell.

Let us pick up the thread of this story in the years between 1898 and about 1910. These years are marked by Moore and Russell's rejection of idealism. Yet at this point, they do not hold a correspondence theory of truth. Indeed Moore (1899) sees the correspondence theory as a source of idealism, and rejects it. Russell follows Moore in this regard. (For discussion of Moore's early critique of idealism, where he rejects the correspondence theory of truth, see Baldwin (1991). Hylton (1990) provides an extensive discussion of Russell in the context of British idealism.)

In this period, Moore and Russell hold a version of the identity theory of truth. They say comparatively little about it, but it is stated briefly in Moore (1899; 1902) and Russell (1904). According to the identity theory, a true proposition is identical to a fact. Specifically, in Moore and Russell's hands, the theory begins with propositions, understood as the objects of beliefs and other propositional attitudes. Propositions are what are believed, and give the contents of beliefs. They are also, according to this theory, the primary bearers of truth. When a proposition is true, it is identical to a fact, and a belief in that proposition is correct. (Related ideas about the identity theory and idealism are discussed by McDowell (1994) and further developed by Hornsby (2001).)

The identity theory Moore and Russell espoused takes truth to be a property of propositions. Furthermore, taking up an idea familiar to readers of Moore, the property of truth is a simple unanalyzable property. Facts are understood as simply those propositions which are true. There are true propositions and false ones, and facts just are true propositions. There is thus no “difference between truth and the reality to which it is supposed to correspond” (Moore, 1902, p. 21). (For further discussion of the identity theory of truth, see Baldwin (1991), Candlish (1999), Cartwright (1987), Dodd (2000), and the entry on the identity theory of truth.)

Moore and Russell came to reject the identity theory of truth in favor of a correspondence theory, sometime around 1910 (as we see in Moore, 1953, which reports lectures he gave in 1910–1911, and Russell, 1910b). They do so because they came to reject the existence of propositions. Why? Among reasons, they came to doubt that there could be any such things as false propositions, and then concluded that there are no such things as propositions at all.

Why did Moore and Russell find false propositions problematic? A full answer to this question is a point of scholarship that would take us too far afield. (Moore himself lamented that he could not “put the objection in a clear and convincing way” (1953, p. 263), but see Cartwright (1987) and David (2001) for careful and clear exploration of the arguments.) But very roughly, the identification of facts with true propositions left them unable to see what a false proposition could be other than something which is just like a fact, though false. If such things existed, we would have fact-like things in the world, which Moore and Russell now see as enough to make false propositions count as true. Hence, they cannot exist, and so there are no false propositions. As Russell (1956, p. 223) later says, propositions seem to be at best “curious shadowy things” in addition to facts.

As Cartwright (1987) reminds us, it is useful to think of this argument in the context of Russell's slightly earlier views about propositions. As we see clearly in Russell (1903), for instance, he takes propositions to have constituents. But they are not mere collections of constituents, but a ‘unity’ which brings the constituents together. (We thus confront the ‘problem of the unity of the proposition’.) But what, we might ask, would be the ‘unity’ of a proposition that Samuel Ramey sings – with constituents Ramey and singing – except Ramey bearing the property of singing? If that is what the unity consists in, then we seem to have nothing other than the fact that Ramey sings. But then we could not have genuine false propositions without having false facts.

As Cartwright also reminds us, there is some reason to doubt the cogency of this sort of argument. But let us put the assessment of the arguments aside, and continue the story. From the rejection of propositions a correspondence theory emerges. The primary bearers of truth are no longer propositions, but beliefs themselves. In a slogan:

A belief is true if and only if it corresponds to a fact.

Views like this are held by Moore (1953) and Russell (1910b; 1912). Of course, to understand such a theory, we need to understand the crucial relation of correspondence, as well as the notion of a fact to which a belief corresponds. We now turn to these questions. In doing so, we will leave the history, and present a somewhat more modern reconstruction of a correspondence theory.

1.1.2 The neo-classical correspondence theory

The correspondence theory of truth is at its core an ontological thesis: a belief is true if there exists an appropriate entity – a fact – to which it corresponds. If there is no such entity, the belief is false.

Facts, for the neo-classical correspondence theory, are entities in their own right. Facts are generally taken to be composed of particulars and properties and relations or universals, at least. The neo-classical correspondence theory thus only makes sense within the setting of a metaphysics that includes such facts. Hence, it is no accident that as Moore and Russell turn away from the identity theory of truth, the metaphysics of facts takes on a much more significant role in their views. This perhaps becomes most vivid in the later Russell (1956, p. 182), where the existence of facts is the “first truism.” (The influence of Wittgenstein's ideas to appear in the Tractatus (1922) on Russell in this period was strong, and indeed, the Tractatus remains one of the important sources for the neo-classical correspondence theory. For more recent extensive discussions of facts, see Armstrong (1997) and Neale (2001).)

Consider, for example, the belief that Ramey sings. Let us grant that this belief is true. In what does its truth consist, according to the correspondence theory? It consists in there being a fact in the world, built from the individual Ramey, and the property of singing. Let us denote this <Ramey, Singing>. This fact exists. In contrast, the world (we presume) contains no fact <Ramey, Dancing>. The belief that Ramey sings stands in the relation of correspondence to the fact <Ramey, Singing>, and so the belief is true.

What is the relation of correspondence? One of the standing objections to the classical correspondence theory is that a fully adequate explanation of correspondence proves elusive. But for a simple belief, like that Ramey sings, we can observe that the structure of the fact <Ramey, Singing> matches the subject-predicate form of the that-clause which reports the belief, and may well match the structure of the belief itself.

So far, we have very much the kind of view that Moore and Russell would have found congenial. But the modern form of the correspondence theory seeks to round out the explanation of correspondence by appeal to propositions. Indeed, it is common to base a correspondence theory of truth upon the notion of a structured proposition. Propositions are again cast as the contents of beliefs and assertions, and propositions have structure which at least roughly corresponds to the structure of sentences. At least, for simple beliefs like that Ramey sings, the proposition has the same subject predicate structure as the sentence. (Proponents of structured propositions, such as Kaplan (1989), often look to Russell (1903) for inspiration, and find unconvincing Russell's reasons for rejecting them.)

With facts and structured propositions in hand, an attempt may be made to explain the relation of correspondence. Correspondence holds between a proposition and a fact when the proposition and fact have the same structure, and the same constituents at each structural position. When they correspond, the proposition and fact thus mirror each-other. In our simple example, we might have:

proposition thatRameysings

Propositions, though structured like facts, can be true or false. In a false case, like the proposition that Ramey dances, we would find no fact at the bottom of the corresponding diagram. Beliefs are true or false depending on whether the propositions which are believed are.

We have sketched this view for simple propositions like the proposition that Ramey sings. How to extend it to more complex cases, like general propositions or negative propositions, is an issue we will not delve into here. It requires deciding whether there are complex facts, such as general facts or negative facts, or whether there is a more complex relation of correspondence between complex propositions and simple facts. (The issue of whether there are such complex facts marks a break between Russell (1956) and Wittgenstein (1922) and the earlier views which Moore (1953) and Russell (1912) sketch.)

According to the correspondence theory as sketched here, what is key to truth is a relation between propositions and the world, which obtains when the world contains a fact that is structurally similar to the proposition. Though this is not the theory Moore and Russell held, it weaves together ideas of theirs with a more modern take on (structured) propositions. We will thus dub it the neo-classical correspondence theory. This theory offers us a paradigm example of a correspondence theory of truth.

The leading idea of the correspondence theory is familiar. It is a form of the older idea that true beliefs show the right kind of resemblance to what is believed. In contrast to earlier empiricist theories, the thesis is not that one's ideas per se resemble what they are about. Rather, the propositions which give the contents of one's true beliefs mirror reality, in virtue of entering into correspondence relations to the right pieces of it.

In this theory, it is the way the world provides us with appropriately structured entities that explains truth. Our metaphysics thus explains the nature of truth, by providing the entities needed to enter into correspondence relations.

For more on the correspondence theory, see David (1994) and the entry on the correspondance theory of truth.

1.2 The coherence theory

Though initially the correspondence theory was seen by its developers as a competitor to the identity theory of truth, it was also understood as opposed to the coherence theory of truth.

We will be much briefer with the historical origins of the coherence theory than we were with the correspondence theory. Like the correspondence theory, versions of the coherence theory can be seen throughout the history of philosophy. (See, for instance, Walker (1989) for a discussion of its early modern lineage.) Like the correspondence theory, it was important in the early 20th century British origins of analytic philosophy. Particularly, the coherence theory of truth is associated with the British idealists to whom Moore and Russell were reacting.

Many idealists at that time did indeed hold coherence theories. Let us take as an example Joachim (1906). (This is the theory that Russell (1910a) attacks.) Joachim says that:

Truth in its essential nature is that systematic coherence which is the character of a significant whole (p. 76).

We will not attempt a full exposition of Joachim's view, which would take us well beyond the discussion of truth into the details of British idealism. But a few remarks about his theory will help to give substance to the quoted passage.

Perhaps most importantly, Joachim talks of ‘truth’ in the singular. This is not merely a turn of phrase, but a reflection of his monistic idealism. Joachim insists that what is true is the “whole complete truth” (p. 90). Individual judgments or beliefs are certainly not the whole complete truth. Such judgments are, according to Joachim, only true to a degree. One aspect of this doctrine is a kind of holism about content, which holds that any individual belief or judgment gets its content only in virtue of being part of a system of judgments. But even these systems are only true to a degree, measuring the extent to which they express the content of the single ‘whole complete truth’. Any real judgment we might make will only be partially true.

To flesh out Joachim's theory, we would have to explain what a significant whole is. We will not attempt that, as it leads us to some of the more formidable aspects of his view, e.g., that it is a “process of self-fulfillment” (p. 77). But it is clear that Joachim takes ‘systematic coherence’ to be stronger than consistency. In keeping with his holism about content, he rejects the idea that coherence is a relation between independently identified contents, and so finds it necessary to appeal to ‘significant wholes’.

As with the correspondence theory, it will be useful to recast the coherence theory in a more modern form, which will abstract away from some of the difficult features of British idealism. As with the correspondence theory, it can be put in a slogan:

A belief is true if and only if it is part of a coherent system of beliefs.

To further the contrast with the neo-classical correspondence theory, we may add that a proposition is true if it is the content of a belief in the system, or entailed by a belief in the system. We may assume, with Joachim, that the condition of coherence will be stronger than consistency. With the idealists generally, we might suppose that features of the believing subject will come into play.

This theory is offered as an analysis of the nature of truth, and not simply a test or criterion for truth. Put as such, it is clearly not Joachim's theory (it lacks his monism, and he rejects propositions), but it is a standard take on coherence in the contemporary literature. (It is the way the coherence theory is given in Walker (1989), for instance. See also Young (2001) for a recent defense of a coherence theory.) Let us take this as our neo-classical version of the coherence theory. The contrast with the correspondence theory of truth is clear. Far from being a matter of whether the world provides a suitable object to mirror a proposition, truth is a matter of how beliefs are related to each-other.

The coherence theory of truth enjoys two sorts of motivations. One is primarily epistemological. Most coherence theorists also hold a coherence theory of knowledge; more specifically, a coherence theory of justification. According to this theory, to be justified is to be part of a coherent system of beliefs. An argument for this is often based on the claim that only another belief could stand in a justification relation to a belief, allowing nothing but properties of systems of belief, including coherence, to be conditions for justification. Combining this with the thesis that a fully justified belief is true forms an argument for the coherence theory of truth. (An argument along these lines is found in Blanshard (1939), who holds a form of the coherence theory closely related to Joachim's.)

The steps in this argument may be questioned by a number of contemporary epistemological views. But the coherence theory also goes hand-in-hand with its own metaphysics as well. The coherence theory is typically associated with idealism. As we have already discussed, forms of it were held by British idealists such as Joachim, and later by Blanshard (in America). An idealist should see the last step in the justification argument as quite natural. More generally, an idealist will see little (if any) room between a system of beliefs and the world it is about, leaving the coherence theory of truth as an extremely natural option.

It is possible to be an idealist without adopting a coherence theory. (For instance, many scholars read Bradley as holding a version of the identity theory of truth. See Baldwin (1991) for some discussion.) However, it is hard to see much of a way to hold the coherence theory of truth without maintaining some form of idealism. If there is nothing to truth beyond what is to be found in an appropriate system of beliefs, then it would seem one's beliefs constitute the world in a way that amounts to idealism. (Walker (1989) argues that every coherence theorist must be an idealist, but not vice-versa.)

The neo-classical correspondence theory seeks to capture the intuition that truth is a content-to-world relation. It captures this in the most straightforward way, by asking for an object in the world to pair up with a true proposition. The neo-classical coherence theory, in contrast, insists that truth is not a content-to-world relation at all; rather, it is a content-to-content, or belief-to-belief, relation. The coherence theory requires some metaphysics which can make the world somehow reflect this, and idealism appears to be it. (A distant descendant of the neo-classical coherence theory that does not require idealism will be discussed in section 6.5 below.)

For more on the coherence theory, see the entry on the coherence theory of truth.

1.3 Pragmatist theories

A different perspective on truth was offered by the American pragmatists. As with the neo-classical correspondence and coherence theories, the pragmatist theories go with some typical slogans. For example, Peirce is usually understood as holding the view that:

Truth is the end of inquiry.

(See, for instance Hartshorne et al., 1931–58, §3.432.) Both Peirce and James are associated with the slogan that:

Truth is satisfactory to believe.

James (e.g., 1907) understands this principle as telling us what practical value truth has. True beliefs are guaranteed not to conflict with subsequent experience. Likewise, Peirce's slogan tells us that true beliefs will remain settled at the end of prolonged inquiry. Peirce's slogan is perhaps most typically associated with pragmatist views of truth, so we might take it to be our canonical neo-classical theory. However, the contemporary literature does not seem to have firmly settled upon a received ‘neo-classical’ pragmatist theory.

In her reconstruction (upon which we have relied heavily), Haack (1976) notes that the pragmatists' views on truth also make room for the idea that truth involves a kind of correspondence, insofar as the scientific method of inquiry is answerable to some independent world. Peirce, for instance, does not reject a correspondence theory outright; rather, he complains that it provides merely a ‘nominal’ or ‘transcendental’ definition of truth (e.g Hartshorne et al., 1931–58, §5.553, §5.572), which is cut off from practical matters of experience, belief, and doubt (§5.416). (See Misak (2004) for an extended discussion.)

This marks an important difference between the pragmatist theories and the coherence theory we just considered. Even so, pragmatist theories also have an affinity with coherence theories, insofar as we expect the end of inquiry to be a coherent system of beliefs. As Haack also notes, James maintains an important verificationist idea: truth is what is verifiable. We will see this idea re-appear in section 4.

James' views are discussed further in the entry on William James. Peirce's views are discussed further in the entry on Charles Sanders Peirce.

2. Tarski's theory of truth

Modern forms of the classical theories survive. Many of these modern theories, notably correspondence theories, draw on ideas developed by Tarski.

In this regard, it is important to bear in mind that his seminal work on truth (1935) is very much of a piece with other works in mathematical logic, such as his (1931), and as much as anything this work lays the ground-work for the modern subject of model theory – a branch of mathematical logic, not the metaphysics of truth. In this respect, Tarski's work provides a set of highly useful tools that may be employed in a wide range of philosophical projects. (See Patterson (2012) for more on Tarski's work in its historical context.)

Tarski's work has a number of components, which we will consider in turn.

2.1 Sentences as truth-bearers

In the classical debate on truth at the beginning of the 20th century we considered in section 1, the issue of truth-bearers was of great significance. For instance, Moore and Russell's turn to the correspondence theory was driven by their views on whether there are propositions to be the bearers of truth. Many theories we reviewed took beliefs to be the bearers of truth.

In contrast, Tarski and much of the subsequent work on truth takes sentences to be the primary bearers of truth. This is not an entirely novel development: Russell (1956) also takes truth to apply to sentence (which he calls ‘propositions’ in that text). But whereas much of the classical debate takes the issue of the primary bearers of truth to be a substantial and important metaphysical one, Tarski is quite casual about it. His primary reason for taking sentences as truth-bearers is convenience, and he explicitly distances himself from any commitment about the philosophically contentious issues surrounding other candidate truth-bearers (e.g., Tarski, 1944). (Russell (1956) makes a similar suggestion that sentences are the appropriate truth-bearers “for the purposes of logic” (p. 184), though he still takes the classical metaphysical issues to be important.)

We will return to the issue of the primary bearers of truth in section 6.1. For the moment, it will be useful to simply follow Tarski's lead. But it should be stressed that for this discussion, sentences are fully interpreted sentences, having meanings. We will also assume that the sentences in question do not change their content across occasions of use, i.e., that they display no context-dependence. We are taking sentences to be what Quine (1960) calls ‘eternal sentences’.

In some places (e.g., Tarski, 1944), Tarski refers to his view as the ‘semantic conception of truth’. It is not entirely clear just what Tarski had in mind by this, but it is clear enough that Tarski's theory defines truth for sentences in terms of concepts like reference and satisfaction, which are intimately related to the basic semantic functions of names and predicates (according to many approaches to semantics).

2.2 Convention T

Let us suppose we have a fixed language L whose sentences are fully interpreted. The basic question Tarski poses is what an adequate theory of truth forL would be. Tarski's answer is embodied in what he calls Convention T:

An adequate theory of truth for L must imply, for each sentence φ of L
φ  is true if and only if φ .

(We have simplified Tarski's presentation somewhat.) This is an adequacy condition for theories, not a theory itself. Given the assumption that L is fully interpreted, we may assume that each sentence φ in fact has a truth value. In light of this, Convention T guarantees that the truth predicate given by the theory will be extensionally correct, i.e., have as its extension all and only the true sentences of L .

Convention T draws our attention to the biconditionals of the form

  φ is true if and only if φ ,

which are usually called the Tarski biconditionals for a language L .

2.3 Recursive definition of truth

Tarski does not merely propose a condition of adequacy for theories of truth, he also shows how to meet it. One of his insights is that if the language L displays the right structure, then truth for L can be defined recursively. For instance, let us suppose that L is a simple formal language, containing two atomic sentences ‘snow is white’ and ‘grass is green’, and the sentential connectives ∨ and ¬.

In spite of its simplicity, L contains infinitely many distinct sentences. But truth can be defined for all of them by recursion.

  1. Base clauses:
    1. ‘Snow is white’ is true if and only if snow is white.
    2. ‘Grass is green’ is true if and only if grass is green.
  2. Recursion clauses. For any sentences φ and ψ of L:
    1. φ ∨ ψ is true if and only if φ is true or ψ is true.
    2. ¬φ is true if and only if it is not the case that φ is true.

This theory satisfies Convention T.

2.4 Reference and satisfaction

This may look trivial, but in defining an extensionally correct truth predicate for an infinite language with four clauses, we have made a modest application of a very powerful technique.

Tarski's techniques go further, however. They do not stop with atomic sentences. Tarski notes that truth for each atomic sentence can be defined in terms of two closely related notions: reference and satisfaction. Let us consider a language L′ , just like L except that instead of simply having two atomic sentences, L′ breaks atomic sentences into terms and predicates. L′ contains terms ‘snow’ and ‘grass’ (let us engage in the idealization that these are simply singular terms), and predicates ‘is white’ and ‘is green’. So L′ is like L , but also contains the sentences ‘Snow is green’ and ‘Grass is white’.)

We can define truth for atomic sentences of L′ in the following way.

  1. Base clauses:
    1. ‘Snow’ refers to snow.
    2. ‘Grass’ refers to grass.
    3. a satisfies ‘is white’ if and only if a is white.
    4. a satisfies ‘is green’ if and only if a is green.
  2. For any atomic sentence t is P : t is P is true if and only if the referent of t satisfies P.

One of Tarski's key insights is that the apparatus of satisfaction allows for a recursive definition of truth for sentences with quantifiers, though we will not examine that here. We could repeat the recursion clauses for L to produce a full theory of truth for L′.

Let us say that a Tarskian theory of truth is a recursive theory, built up in ways similar to the theory of truth for L′. Tarski goes on to demonstrate some key applications of such a theory of truth. A Tarskian theory of truth for a language L can be used to show that theories in L are consistent. This was especially important to Tarski, who was concerned the Liar paradox would make theories in languages containing a truth predicate inconsistent.

For more, see the entries on axiomatic theories of truth, the Liar paradox, and Tarski's truth definitions.

3. Correspondence revisited

The correspondence theory of truth expresses the very natural idea that truth is a content-to-world or word-to-world relation: what we say or think is true or false in virtue of the way the world turns out to be. We suggested that, against a background like the metaphysics of facts, it does so in a straightforward way. But the idea of correspondence is certainly not specific to this framework. Indeed, it is controversial whether a correspondence theory should rely on any particular metaphysics at all. The basic idea of correspondence, as Tarski (1944) and others have suggested, is captured in the slogan from Aristotle's Metaphysics Γ 7.27, “to say of what is that it is, or of what is not that it is not, is true” (Ross, 1928). ‘What is’, it is natural enough to say, is a fact, but this natural turn of phrase may well not require a full-blown metaphysics of facts.

Yet without the metaphysics of facts, the notion of correspondence as discussed in section 1.1 loses substance. This has led to two distinct strands in contemporary thinking about the correspondence theory. One strand seeks to recast the correspondence theory in a way that does not rely on any particular ontology. Another seeks to find an appropriate ontology for correspondence, either in terms of facts or other entities. We will consider each in turn.

3.1 Correspondence without facts

Tarski himself sometimes suggested that his theory was a kind of correspondence theory of truth. Whether his own theory is a correspondence theory, and even whether it provides any substantial philosophical account of truth at all, is a matter of controversy. (One rather drastic negative assessment from Putnam (1985–86, p. 333) is that “As a philosophical account of truth, Tarski's theory fails as badly as it is possible for an account to fail.”) But a number of philosophers (e.g., Davidson, 1969; Field, 1972) have seen Tarski's theory as providing at least the core of a correspondence theory of truth which dispenses with the metaphysics of facts.

Tarski's theory shows how truth for a sentence is determined by certain properties of its constituents; in particular, by properties of reference and satisfaction (as well as by the logical constants). As it is normally understood, reference is the preeminent word-to-world relation. Satisfaction is naturally understood as a word-to-world relation as well, which relates a predicate to the things in the world that bear it. The Tarskian recursive definition shows how truth is determined by reference and satisfaction, and so is in effect determined by the things in the world we refer to and the properties they bear. This, one might propose, is all the correspondence we need. It is not correspondence of sentences or propositions to facts; rather, it is correspondence of our expressions to objects and the properties they bear, and then ways of working out the truth of claims in terms of this.

This is certainly not the neo-classical idea of correspondence. In not positing facts, it does not posit any single object to which a true proposition or sentence might correspond. Rather, it shows how truth might be worked out from basic word-to-world relations. However, a number of authors have noted that Tarski's theory cannot by itself provide us with such an account of truth. As we will discuss more fully in section 4.2, Tarski's apparatus is in fact compatible with theories of truth that are certainly not correspondence theories.

Field (1972), in an influential discussion and diagnosis of what is lacking in Tarski's account, in effect points out that whether we really have something worthy of the name ‘correspondence’ depends on our having notions of reference and satisfaction which genuinely establish word-to-world relations. (Field does not use the term ‘correspondence’, but does talk about e.g., the “connection between words and things” (p. 373).) By itself, Field notes, Tarski's theory does not offer an account of reference and satisfaction at all. Rather, it offers a number of disquotation clauses, such as:

  1. ‘Snow’ refers to snow.
  2. a satisfies ‘is white’ if and only if a is white.

These clauses have an air of triviality (though whether they are to be understood as trivial principles or statements of non-trivial semantic facts has been a matter of some debate). With Field, we might propose to supplement clauses like these with an account of reference and satisfaction. Such a theory should tell us what makes it the case that the word ‘snow’ refer to snow. (In 1972, Field was envisaging a physicalist account, along the lines of the causal theory of reference.) This should inter alia guarantee that truth is really determined by word-to-world relations, so in conjunction with the Tarskian recursive definition, it could provide a correspondence theory of truth.

Such a theory clearly does not rely on a metaphysics of facts. Indeed, it is in many ways metaphysically neutral, as it does not take a stand on the nature of particulars, or of the properties or universals that underwrite facts about satisfaction. However, it may not be entirely devoid of metaphysical implications, as we will discuss further in section 4.1.

3.2 Representation and Correspondence

Much of the subsequent discussion of Field-style approaches to correspondence has focused on the role of representation in these views. Field's own (1972) discussion relies on a causal relation between terms and their referents, and a similar relation for satisfaction. These are instances of representation relations. According to representational views, meaningful items, like perhaps thoughts or sentences or their constituents, have their contents in virtue of standing in the right relation to the things they represent. On many views, including Field's, a name stands in such a relation to its bearer, and the relation is a causal one.

The project of developing a naturalist account of the representation relation has been an important one in the philosophy of mind and language. (See the entry on mental representation.) But, it has implications for the theory of truth. Representational views of content lead naturally to correspondence theories of truth. To make this vivid, suppose you hold that sentences or beliefs stand in a representation relation to some objects. It is natural to suppose that for true beliefs or sentences, those objects would be facts. We then have a correspondence theory, with the correspondence relation explicated as a representation relation: a truth bearer is true if it represents a fact.

As we have discussed, many contemporary views reject facts, but one can hold a representational view of content without them. One interpretation of Field's theory is just that. The relations of reference and satisfaction are representation relations, and truth for sentences is determined compositionally in terms of those representation relations, and the nature of the objects they represent. If we have such relations, we have the building blocks for a correspondence theory without facts. Field (1972) anticipated a naturalist reduction of the representation via a causal theory, but any view that accepts representation relations for truth bearers or their constituents can provide a similar theory of truth. (See Jackson (2006) and Lynch (2009) for further discussion.)

Representational views of content provide a natural way to approach the correspondence theory of truth, and likewise, anti-representational views provide a natural way to avoid the correspondence theory of truth. This is most clear in the work of Davidson, as we will discuss more in section 6.5.

3.3 Facts again

There have been a number of correspondence theories that do make use of facts. Some are notably different from the neo-classical theory sketched in section 1.1. For instance, Austin (1950) proposes a view in which each statement (understood roughly as an utterance event) corresponds to both a fact or situation, and a type of situation. It is true if the former is of the latter type. This theory, which has been developed by situation theory (e.g., Barwise and Perry, 1986), rejects the idea that correspondence is a kind of mirroring between a fact and a proposition. Rather, correspondence relations to Austin are entirely conventional. (See Vision (2004) for an extended defense of an Austinian correspondence theory.) As an ordinary language philosopher, Austin grounds his notion of fact more in linguistic usage than in an articulated metaphysics, but he defends his use of fact-talk in Austin (1961b).

In a somewhat more Tarskian spirit, formal theories of facts or states of affairs have also been developed. For instance, Taylor (1976) provides a recursive definition of a collection of ‘states of affairs’ for a given language. Taylor's states of affairs seem to reflect the notion of fact at work in the neo-classical theory, though as an exercise in logic, they are officially n-tuples of objects and intensions.

There are more metaphysically robust notions of fact in the current literature. For instance, Armstrong (1997) defends a metaphysics in which facts (under the name ‘states of affairs’) are metaphysically fundamental. The view has much in common with the neo-classical one. Like the neo-classical view, Armstrong endorses a version of the correspondence theory. States of affairs are truthmakers for propositions, though Armstrong argues that there may be many such truthmakers for a given proposition, and vice versa. (Armstrong also envisages a naturalistic account of propositions as classes of equivalent belief-tokens.)

Armstrong's primary argument is what he calls the ‘truthmaker argument’. It begins by advancing a truthmaker principle, which holds that for any given truth, there must be a truthmaker – a “something in the world which makes it the case, that serves as an ontological ground, for this truth” (p. 115). It is then argued that facts are the appropriate truthmakers.

In contrast to the approach to correspondence discussed in section 3.1, which offered correspondence with minimal ontological implications, this view returns to the ontological basis of correspondence that was characteristic of the neo-classical theory.

For more on facts, see the entry on facts.

3.4 Truthmakers

The truthmaker principle is often put as the schema:

If φ , then there is an x such that necessarily, if x exists, then φ .

(Fox (1987) proposed putting the principle this way, rather than explicitly in terms of truth.)

The truthmaker principle expresses the ontological aspect of the neo-classical correspondence theory. Not merely must truth obtain in virtue of word-to-world relations, but there must be a thing that makes each truth true.

The neo-classical correspondence theory, and Armstrong, cast facts as the appropriate truthmakers. However, it is a non-trivial step from the truthmaker principle to the existence of facts. There are a number of proposals in the literature for how other sorts of objects could be truthmakers; for instance, tropes (called ‘moments’, in Mulligan et al., 1984). Parsons (1999) argues that the truthmaker principle (presented in a somewhat different form) is compatible with there being only concrete particulars.

As we saw in discussing the neo-classical correspondence theory, truthmaker theories, and fact theories in particular, raise a number of issues. One which has been discussed at length, for instance, is whether there are negative facts. Negative facts would be the truthmakers for negated sentences. Russell (1956) notoriously expresses ambivalence about whether there are negative facts. Armstrong (1997) rejects them, while Beall (2000) defends them. (For more discussion of truthmakers, see the papers in Beebee and Dodd (2005).)

4. Realism and anti-realism

The neo-classical theories we surveyed in section 1 made the theory of truth an application of their background metaphysics (and in some cases epistemology). In section 2 and especially in section 3, we returned to the issue of what sorts of ontological commitments might go with the theory of truth. There we saw a range of options, from relatively ontologically non-committal theories, to theories requiring highly specific ontologies.

There is another way in which truth relates to metaphysics. Many ideas about realism and anti-realism are closely related to ideas about truth. Indeed, many approaches to questions about realism and anti-realism simply make them questions about truth.

4.1 Realism and truth

In discussing the approach to correspondence of section 3.1, we noted that it has few ontological requirements. It relies on there being objects of reference, and something about the world which makes for determinate satisfaction relations; but beyond that, it is ontologically neutral. But as we mentioned there, this is not to say that it has no metaphysical implications. A correspondence theory of truth, of any kind, is often taken to embody a form of realism.

The key features of realism, as we will take it, are that:

  1. The world exists objectively, independently of the ways we think about it or describe it.
  2. Our thoughts and claims are about that world.

(Wright (1992) offers a nice statement of this way of thinking about realism.) These theses imply that our claims are objectively true or false, depending on how the world they are about is. The world that we represent in our thoughts or language is an objective world. (Realism may be restricted to some subject-matter, or range of discourse, but for simplicity, we will talk about only its global form.)

It is often argued that these theses require some form of the correspondence theory of truth. (Putnam (1978, p. 18) notes, “Whatever else realists say, they typically say that they believe in a ‘correspondence theory of truth’.”) At least, they are supported by the kind of correspondence theory without facts discussed in section 3.1, such as Field's proposal. Such a theory will provide an account of objective relations of reference and satisfaction, and show how these determine the truth or falsehood of what we say about the world. Field's own approach (1972) to this problem seeks a physicalist explanation of reference. But realism is a more general idea than physicalism. Any theory that provides objective relations of reference and satisfaction, and builds up a theory of truth from them, would give a form of realism. (Making the objectivity of reference the key to realism is characteristic of work of Putnam, e.g., 1978.)

Another important mark of realism expressed in terms of truth is the property of bivalence. As Dummett has stressed (e.g., 1959; 1976; 1983; 1991), a realist should see there being a fact of the matter one way or the other about whether any given claim is correct. Hence, one important mark of realism is that it goes together with the principle of bivalence: every truth-bearer (sentence or proposition) is true or false. In much of his work, Dummett has made this the characteristic mark of realism, and often identifies realism about some subject-matter with accepting bivalence for discourse about that subject-matter. At the very least, it captures a great deal of what is more loosely put in the statement of realism above.

Both the approaches to realism, through reference and through bivalence, make truth the primary vehicle for an account of realism. A theory of truth which substantiates bivalence, or builds truth from a determinate reference relation, does most of the work of giving a realistic metaphysics. It might even simply be a realistic metaphysics.

We have thus turned on its head the relation of truth to metaphysics we saw in our discussion of the neo-classical correspondence theory in section 1.1. There, a correspondence theory of truth was built upon a substantial metaphysics. Here, we have seen how articulating a theory that captures the idea of correspondence can be crucial to providing a realist metaphysics. (For another perspective on realism and truth, see Alston (1996). Devitt (1984) offers an opposing view to the kind we have sketched here, which rejects any characterization of realism in terms of truth or other semantic concepts.)

In light of our discussion in section 1.1.1, we should pause to note that the connection between realism and the correspondence theory of truth is not absolute. When Moore and Russell held the identity theory of truth, they were most certainly realists. The right kind of metaphysics of propositions can support a realist view, as can a metaphysics of facts. The modern form of realism we have been discussing here seeks to avoid basing itself on such particular ontological commitments, and so prefers to rely on the kind of correspondence-without-facts approach discussed in section 3.1. This is not to say that realism will be devoid of ontological commitments, but the commitments will flow from whichever specific claims about some subject-matter are taken to be true.

For more on realism and truth, see Fumerton (2002) and the entry on realism.

4.2 Anti-realism and truth

It should come as no surprise that the relation between truth and metaphysics seen by modern realists can also be exploited by anti-realists. Many modern anti-realists see the theory of truth as the key to formulating and defending their views. With Dummett (e.g., 1959; 1976; 1991), we might expect the characteristic mark of anti-realism to be the rejection of bivalence.

Indeed, many contemporary forms of anti-realism may be formulated as theories of truth, and they do typically deny bivalence. Anti-realism comes in many forms, but let us take as an example a (somewhat crude) form of verificationism. Such a theory holds that a claim is correct just insofar as it is in principle verifiable, i.e., there is a verification procedure we could in principle carry out which would yield the answer that the claim in question was verified.

So understood, verificationism is a theory of truth. The claim is not that verification is the most important epistemic notion, but that truth just is verifiability. As with the kind of realism we considered in section 4.1, this view expresses its metaphysical commitments in its explanation of the nature of truth. Truth is not, to this view, a fully objective matter, independent of us or our thoughts. Instead, truth is constrained by our abilities to verify, and is thus constrained by our epistemic situation. Truth is to a significant degree an epistemic matter, which is typical of many anti-realist positions.

As Dummett says, the verificationist notion of truth does not appear to support bivalence. Any statement that reaches beyond what we can in principle verify or refute (verify its negation) will be a counter-example to bivalence. Take, for instance, the claim that there is some substance, say uranium, present in some region of the universe too distant to be inspected by us within the expected lifespan of the universe. Insofar as this really would be in principle unverifiable, we have no reason to maintain it is true or false according to the verificationist theory of truth.

Verificationism of this sort is one of a family of anti-realist views. Another example is the view that identifies truth with warranted assertibility. Assertibility, as well as verifiability, has been important in Dummett's work. (See also works of McDowell, e.g., 1976 and Wright, e.g., 1976; 1982; 1992.)

Anti-realism of the Dummettian sort is not a descendant of the coherence theory of truth per se. But in some ways, as Dummett himself has noted, it might be construed as a descendant – perhaps very distant – of idealism. If idealism is the most drastic form of rejection of the independence of mind and world, Dummettian anti-realism is a more modest form, which sees epistemology imprinted in the world, rather than the wholesale embedding of world into mind. At the same time, the idea of truth as warranted assertibility or verifiability reiterates a theme from the pragmatist views of truth we surveyed in section 1.3.

Anti-realist theories of truth, like the realist ones we discussed in section 4.1, can generally make use of the Tarskian apparatus. Convention T, in particular, does not discriminate between realist and anti-realist notions of truth. Likewise, the base clauses of a Tarskian recursive theory are given as disquotation principles, which are neutral between realist and anti-realist understandings of notions like reference. As we saw with the correspondence theory, giving a full account of the nature of truth will generally require more than the Tarskian apparatus itself. How an anti-realist is to explain the basic concepts that go into a Tarskian theory is a delicate matter. As Dummett and Wright have investigated in great detail, it appears that the background logic in which the theory is developed will have to be non-classical.

For more on anti-realism and truth, see the papers in Greenough and Lynch (2006) and the entry on realism.

4.3 Anti-realism and pragmatism

Many commentators see a close connection between Dummett's anti-realism and the pragmatists' views of truth, in that both put great weight on ideas of verifiability or assertibility. Dummett himself stressed parallels between anti-realism and intuitionism in the philosophy of mathematics.

Another view on truth which returns to pragmatist themes is the ‘internal realism’ of Putnam (1981). There Putnam glosses truth as what would be justified under ideal epistemic conditions. With the pragmatists, Putnam sees the ideal conditions as something which can be approximated, echoing the idea of truth as the end of inquiry.

Putnam is cautious about calling his view anti-realism, preferring the label ‘internal realism’. But he is clear that he sees his view as opposed to realism (‘metaphysical realism’, as he calls it).

Davidson's views on truth have also been associated with pragmatism, notably by Rorty (1986). Davidson has distanced himself from this interpretation (e.g., 1990), but he does highlight connections between truth and belief and meaning. Insofar as these are human attitudes or relate to human actions, Davidson grants there is some affinity between his views and those of some pragmatists (especially, he says, Dewey).

4.4 Truth pluralism

Another view that has grown out of the literature on realism and anti-realism, and has become increasingly important in the current literature, is that of pluralism about truth. This view, developed in work of Lynch (e.g. 2001b; 2009) and Wright (e.g. 1992; 1999), proposes that there are multiple ways for truth bearers to be true. Wright, in particular, suggests that in certain domains of discourse what we say is true in virtue of a correspondence-like relation, while in others it is its true in virtue of a kind of assertibility relation that is closer in spirit to the anti-realist views we have just discussed.

Such a proposal might suggest there are multiple concepts of truth, or that the term ‘true’ is itself ambiguous. However, whether or not a pluralist view is committed to such claims has been disputed. In particular, Lynch (2001b; 2009) develops a version of pluralism which takes truth to be a functional role concept. The functional role of truth is characterized by a range of principles that articulate such features of truth as its objectivity, its role in inquiry, and related ideas we have encountered in considering various theories of truth. (A related point about platitudes governing the concept of truth is made by Wright (1992).) But according to Lynch, these display the functional role of truth. Furthermore, Lynch claims that on analogy with analytic functionalism, these principles can be seen as deriving from our pre-theoretic or ‘folk’ ideas about truth.

Like all functional role concepts, truth must be realized, and according to Lynch it may be realized in different ways in different settings. Such multiple realizability has been one of the hallmarks of functional role concepts discussed in the philosophy of mind. For instance, Lynch suggests that for ordinary claims about material objects, truth might be realized by a correspondence property (which he links to representational views), while for moral claims truth might be manifest by an assertibility property along more anti-realist lines.

For more on pluralism about truth, see the entry on pluralist theories of truth.

5. Deflationism

We began in section 1 with the neo-classical theories, which explained the nature of truth within wider metaphysical systems. We then considered some alternatives in sections 2 and 3, some of which had more modest ontological implications. But we still saw in section 4 that substantial theories of truth tend to imply metaphysical theses, or even embody metaphysical positions.

One long-standing trend in the discussion of truth is to insist that truth really does not carry metaphysical significance at all. It does not, as it has no significance on its own. A number of different ideas have been advanced along these lines, under the general heading of deflationism.

5.1 The redundancy theory

Deflationist ideas appear quite early on, including a well-known argument against correspondence in Frege (1918–19). However, many deflationists take their cue from an idea of Ramsey (1927), often called the equivalence thesis:

  φ is true has the same meaning as φ.

(Ramsey himself takes truth-bearers to be propositions rather than sentences. Glanzberg (2003b) questions whether Ramsey's account of propositions really makes him a deflationist.)

This can be taken as the core of a theory of truth, often called the redundancy theory. The redundancy theory holds that there is no property of truth at all, and appearances of the expression ‘true’ in our sentences are redundant, having no effect on what we express.

The equivalence thesis can also be understood in terms of speech acts rather than meaning:

To assert that φ is true is just to assert that φ.

This view was advanced by Strawson (1949; 1950), though Strawson also argues that there are other important aspects of speech acts involving ‘true’ beyond what is asserted. For instance, they may be acts of confirming or granting what someone else said. (Strawson would also object to my making sentences the bearers of truth.)

In either its speech act or meaning form, the redundancy theory argues there is no property of truth. It is commonly noted that the equivalence thesis itself is not enough to sustain the redundancy theory. It merely holds that when truth occurs in the outermost position in a sentence, and the full sentence to which truth is predicated is quoted, then truth is eliminable. What happens in other environments is left to be seen. Modern developments of the redundancy theory include Grover et al. (1975).

5.2 Minimalist theories

The equivalence principle looks familiar: it has something like the form of the Tarski biconditionals discussed in section 2.2. However, it is a stronger principle, which identifies the two sides of the biconditional – either their meanings or the speech acts performed with them. The Tarski biconditionals themselves are simply material biconditionals.

A number of deflationary theories look to the Tarski biconditionals rather than the full equivalence principle. Their key idea is that even if we do not insist on redundancy, we may still hold the following theses:

  1. For a given language L and every φ in L, the biconditionals   φ is true if and only if φ hold by definition (or analytically, or trivially, or by stipulation …).
  2. This is all there is to say about the concept of truth.

We will refer to views which adopt these as minimalist. Officially, this is the name of the view of Horwich (1990), but we will apply it somewhat more widely. (Horwich's view differs in some specific respects from what is presented here, such as predicating truth of propositions, but we believe it is close enough to what is sketched here to justify the name.)

The second thesis, that the Tarski biconditionals are all there is to say about truth, captures something similar to the redundancy theory's view. It comes near to saying that truth is not a property at all; to the extent that truth is a property, there is no more to it than the disquotational pattern of the Tarski biconditionals. As Horwich puts it, there is no substantial underlying metaphysics to truth. And as Soames (1984) stresses, certainly nothing that could ground as far-reaching a view as realism or anti-realism.

5.3 Other aspects of deflationism

If there is no property of truth, or no substantial property of truth, what role does our term ‘true’ play? Deflationists typically note that the truth predicate provides us with a convenient device of disquotation. Such a device allows us to make some useful claims which we could not formulate otherwise, such as the blind ascription ‘The next thing that Bill says will be true’. (For more on blind ascriptions and their relation to deflationism, see Azzouni, 2001.) A predicate obeying the Tarski biconditionals can also be used to express what would otherwise be (potentially) infinite conjunctions or disjunctions, such as the notorious statement of Papal infallibility put ‘Everything the Pope says is true’. (Suggestions like this are found in Leeds, 1978 and Quine, 1970.)

Recognizing these uses for a truth predicate, we might simply think of it as introduced into a language by stipulation. The Tarski biconditionals themselves might be stipulated, as the minimalists envisage. One could also construe the clauses of a recursive Tarskian theory as stipulated. (There are some significant logical differences between these two options. See Halbach (1999) and Ketland (1999) for discussion.) Other deflationists, such as Beall (2005) or Field (1994), might prefer to focus here on rules of inference or rules of use, rather than the Tarski biconditionals themselves.

There are also important connections between deflationist ideas about truth and certain ideas about meaning. These are fundamental to the deflationism of Field (1986; 1994), which will be discussed in section 6.3. For an insightful critique of deflationism, see Gupta (1993).

For more on deflationism, see the entry on the deflationary theory of truth.

6. Truth and language

One of the important themes in the literature on truth is its connection to meaning, or more generally, to language. This has proved an important application of ideas about truth, and an important issue in the study of truth itself. This section will consider a number of issues relating truth and language.

6.1 Truth-bearers

There have been many debates in the literature over what the primary bearers of truth are. Candidates typically include beliefs, propositions, sentences, and utterances. We have already seen in section 1 that the classical debates on truth took this issue very seriously, and what sort of theory of truth was viable was often seen to depend on what the bearers of truth are.

In spite of the number of options under discussion, and the significance that has sometimes been placed on the choice, there is an important similarity between candidate truth-bearers. Consider the role of truth-bearers in the correspondence theory, for instance. We have seen versions of it which take beliefs, propositions, or interpreted sentences to be the primary bearers of truth. But all of them rely upon the idea that their truth-bearers are meaningful, and are thereby able to say something about what the world is like. (We might say that they are able to represent the world, but that is to use ‘represent’ in a wider sense than we saw in section 3.2. No assumptions about just what stands in relations to what objects are required to see truth-bearers as meaningful.) It is in virtue of being meaningful that truth-bearers are able to enter into correspondence relations. Truth-bearers are things which meaningfully make claims about what the world is like, and are true or false depending on whether the facts in the world are as described.

Exactly the same point can be made for the anti-realist theories of truth we saw in section 4.2, though with different accounts of how truth-bearers are meaningful, and what the world contributes. Though it is somewhat more delicate, something similar can be said for coherence theories, which usually take beliefs, or whole systems of beliefs, as the primary truth-bearers. Though a coherence theory will hardly talk of beliefs representing the facts, it is crucial to the coherence theory that beliefs are contentful beliefs of agents, and that they can enter into coherence relations. Noting the complications in interpreting the genuine classical coherence theories, it appears fair to note that this requires truth-bearers to be meaningful, however the background metaphysics (presumably idealism) understands meaning.

Though Tarski works with sentences, the same can be said of his theory. The sentences to which Tarski's theory applies are fully interpreted, and so also are meaningful. They characterize the world as being some way or another, and this in turn determines whether they are true or false. Indeed, Tarski needs there to be a fact of the matter about whether each sentence is true or false (abstracting away from context dependence), to ensure that the Tarski biconditionals do their job of fixing the extension of ‘is true’. (But note that just what this fact of the matter consists in is left open by the Tarskian apparatus.)

We thus find the usual candidate truth-bearers linked in a tight circle: interpreted sentences, the propositions they express, the belief speakers might hold towards them, and the acts of assertion they might perform with them are all connected by providing something meaningful. This makes them reasonable bearers of truth. For this reason, it seems, contemporary debates on truth have been much less concerned with the issue of truth-bearers than were the classical ones. Some issues remain, of course. Different metaphysical assumptions may place primary weight on some particular node in the circle, and some metaphysical views still challenge the existence of some of the nodes. Perhaps more importantly, different views on the nature of meaning itself might cast doubt on the coherence of some of the nodes. Notoriously for instance, Quineans (e.g., Quine, 1960) deny the existence of intensional entities, including propositions. Even so, it increasingly appears doubtful that attention to truth per se will bias us towards one particular primary bearer of truth.

6.2 Truth and truth conditions

There is a related, but somewhat different point, which is important to understanding the theories we have canvassed.

The neo-classical theories of truth start with truth-bearers which are already understood to be meaningful, and explain how they get their truth values. But along the way, they often do something more. Take the neo-classical correspondence theory, for instance. This theory, in effect, starts with a view of how propositions are meaningful. They are so in virtue of having constituents in the world, which are brought together in the right way. There are many complications about the nature of meaning, but at a minimum, this tells us what the truth conditions associated with a proposition are. The theory then explains how such truth conditions can lead to the truth value true, by the right fact existing.

Many theories of truth are like the neo-classical correspondence theory in being as much theories of how truth-bearers are meaningful as of how their truth values are fixed. Again, abstracting from some complications about meaning, this makes them theories both of truth conditions and truth values. The Tarskian theory of truth can be construed this way too. This can be seen both in the way the Tarski biconditionals are understood, and how a recursive theory of truth is understood. As we explained Convention T in section 2.2, the primary role of a Tarski biconditional of the form   φ is true if and only if φ is to fix whether φ is in the extension of ‘is true’ or not. But it can also be seen as stating the truth conditions of φ. Both rely on the fact that the unquoted occurrence of φ is an occurrence of an interpreted sentence, which has a truth value, but also provides its truth conditions upon occasions of use.

Likewise, the base clauses of the recursive definition of truth, those for reference and satisfaction, are taken to state the relevant semantic properties of constituents of an interpreted sentence. In discussing Tarski's theory of truth in section 2, we focused on how these determine the truth value of a sentence. But they also show us the truth conditions of a sentence are determined by these semantic properties. For instance, for a simple sentence like ‘Snow is white’, the theory tells us that the sentence is true if the referent of ‘Snow’ satisfies ‘white’. This can be understood as telling us that the truth conditions of ‘Snow is white’ are those conditions in which the referent of ‘Snow’ satisfies the predicate ‘is white’.

As we saw in sections 3 and 4, the Tarskian apparatus is often seen as needing some kind of supplementation to provide a full theory of truth. A full theory of truth conditions will likewise rest on how the Tarskian apparatus is put to use. In particular, just what kinds of conditions those in which the referent of ‘snow’ satisfies the predicate ‘is white’ are will depend on whether we opt for realist or anti-realist theories. The realist option will simply look for the conditions under which the stuff snow bears the property of whiteness; the anti-realist option will look to the conditions under which it can be verified, or asserted with warrant, that snow is white.

There is a broad family of theories of truth which are theories of truth conditions as well as truth values. This family includes the correspondence theory in all its forms – classical and modern. Yet this family is much wider than the correspondence theory, and wider than realist theories of truth more generally. Indeed, virtually all the theories of truth that make contributions to the realism/anti-realism debate are theories of truth conditions. In a slogan, for many approaches to truth, a theory of truth is a theory of truth conditions.

6.3 Truth conditions and deflationism

Any theory that provides a substantial account of truth conditions can offer a simple account of truth values: a truth-bearer provides truth conditions, and it is true if and only if the actual way things are is among them. Because of this, any such theory will imply a strong, but very particular, biconditional, close in form to the Tarski biconditionals. It can be made most vivid if we think of propositions as sets of truth conditions. Let p be a proposition, i.e., a set of truth conditions, and let a be the ‘actual world’, the condition that actually obtains. Then we can almost trivially see:

p is true if and only if ap.

This is presumably necessary. But it is important to observe that it is in one respect crucially different from the genuine Tarski biconditionals. It makes no use of a non-quoted sentence, or in fact any sentence at all. It does not have the disquotational character of the Tarski biconditionals.

Though this may look like a principle that deflationists should applaud, it is not. Rather, it shows that deflationists cannot really hold a truth-conditional view of content at all. If they do, then they inter alia have a non-deflationary theory of truth, simply by linking truth value to truth conditions through the above biconditional. It is typical of thoroughgoing deflationist theories to present a non-truth-conditional theory of the contents of sentences: a non-truth-conditional account of what makes truth-bearers meaningful. We take it this is what is offered, for instance, by the use theory of propositions in Horwich (1990). It is certainly one of the leading ideas of Field (1986; 1994), which explore how a conceptual role account of content would ground a deflationist view of truth. Once one has a non-truth-conditional account of content, it is then possible to add a deflationist truth predicate, and use this to give purely deflationist statements of truth conditions. But the starting point must be a non-truth-conditional view of what makes truth-bearers meaningful.

Both deflationists and anti-realists start with something other than correspondence truth conditions. But whereas an anti-realist will propose a different theory of truth conditions, a deflationists will start with an account of content which is not a theory of truth conditions at all. The deflationist will then propose that the truth predicate, given by the Tarski biconditionals, is an additional device, not for understanding content, but for disquotation. It is a useful device, as we discussed in section 5.3, but it has nothing to do with content. To a deflationist, the meaningfulness of truth-bearers has nothing to do with truth.

6.4 Truth and the theory of meaning

It has been an influential idea, since the seminal work of Davidson (e.g., 1967), to see a Tarskian theory of truth as a theory of meaning. At least, as we have seen, a Tarskian theory can be seen as showing how the truth conditions of a sentence are determined by the semantic properties of its parts. More generally, as we see in much of the work of Davidson and of Dummett (e.g., 1959; 1976; 1983; 1991), giving a theory of truth conditions can be understood as a crucial part of giving a theory of meaning. Thus, any theory of truth that falls into the broad category of those which are theories of truth conditions can be seen as part of a theory of meaning. (For more discussion of these issues, see Higginbotham (1986; 1989) and the exchange between Higginbotham (1992) and Soames (1992).)

A number of commentators on Tarski (e.g., Etchemendy, 1988; Soames, 1984) have observed that the Tarskian apparatus needs to be understood in a particular way to make it suitable for giving a theory of meaning. Tarski's work is often taken to show how to define a truth predicate. If it is so used, then whether or not a sentence is true becomes, in essence, a truth of mathematics. Presumably what truth conditions sentences of a natural language have is a contingent matter, so a truth predicate defined in this way cannot be used to give a theory of meaning for them. But the Tarskian apparatus need not be used just to explicitly define truth. The recursive characterization of truth can be used to state the semantic properties of sentences and their constituents, as a theory of meaning should. In such an application, truth is not taken to be explicitly defined, but rather the truth conditions of sentences are taken to be described. (See Heck, 1997 for more discussion.)

6.5 The coherence theory and meaning

Inspired by Quine (e.g., 1960), Davidson himself is well known for taking a different approach to using a theory of truth as a theory of meaning than is implicit in Field (1972). Whereas a Field-inspired representational approach is based on a causal account of reference, Davidson (e.g., 1973) proposes a process of radical interpretation in which an interpreter builds a Tarskian theory to interpret a speaker as holding beliefs which are consistent, coherent, and largely true.

This led Davidson (e.g. 1986) to argue that most of our beliefs are true – a conclusion that squares well with the coherence theory of truth. This is a weaker claim than the neo-classical coherence theory would make. It does not insist that all the members of any coherent set of beliefs are true, or that truth simply consists in being a member of such a coherent set. But all the same, the conclusion that most of our beliefs are true, because their contents are to be understood through a process of radical interpretation which will make them a coherent and rational system, has a clear affinity with the neo-classical coherence theory.

In Davidson (1986), he thought his view of truth had enough affinity with the neo-classical coherence theory to warrant being called a coherence theory of truth, while at the same time he saw the role of Tarskian apparatus as warranting the claim that his view was also compatible with a kind of correspondence theory of truth.

In later work, however, Davidson reconsidered this position. In fact, already in Davidson (1977) he had expressed doubt about any understanding of the role of Tarski's theory in radical interpretation that involves the kind of representational apparatus relied on by Field (1972), as we discussed in sections 3.1 and 3.2. In the “Afterthoughts” to Davidson (1986), he also concluded that his view departs too far from the neo-classical coherence theory to be named one. What is important is rather the role of radical interpretation in the theory of content, and its leading to the idea that belief is veridical. These are indeed points connected to coherence, but not to the coherence theory of truth per se. They also comprise a strong form of anti-representationalism. Thus, though he does not advance a coherence theory of truth, he does advance a theory that stands in opposition to the representational variants of the correspondence theory we discussed in section 3.2.

For more on Davidson, see Glanzberg (2013) and the entry on Donald Davidson.

6.6 Truth and assertion

The relation between truth and meaning is not the only place where truth and language relate closely. Another is the idea, also much-stressed in the writings of Dummett (e.g., 1959), of the relation between truth and assertion. Again, it fits into a platitude:

Truth is the aim of assertion.

A person making an assertion, the platitude holds, aims to say something true.

It is easy to cast this platitude in a way that appears false. Surely, many speakers do not aim to say something true. Any speaker who lies does not. Any speaker whose aim is to flatter, or to deceive, aims at something other than truth.

The motivation for the truth-assertion platitude is rather different. It looks at assertion as a practice, in which certain rules are constitutive. As is often noted, the natural parallel here is with games, like chess or baseball, which are defined by certain rules. The platitude holds that it is constitutive of the practice of making assertions that assertions aim at truth. An assertion by its nature presents what it is saying as true, and any assertion which fails to be true is ipso facto liable to criticism, whether or not the person making the assertion themself wished to have said something true or to have lied.

Dummett's original discussion of this idea was partially a criticism of deflationism (in particular, of views of Strawson, 1950). The idea that we fully explain the concept of truth by way of the Tarski biconditionals is challenged by the claim that the truth-assertion platitude is fundamental to truth. As Dummett there put it, what is left out by the Tarski biconditionals, and captured by the truth-assertion platitude, is the point of the concept of truth, or what the concept is used for. (For further discussion, see Glanzberg, 2003a and Wright, 1992.)

Whether or not assertion has such constitutive rules is, of course, controversial. But among those who accept that it does, the place of truth in the constitutive rules is itself controversial. The leading alternative, defended by Williamson (1996), is that knowledge, not truth, is fundamental to the constitutive rules of assertion. Williamson defends an account of assertion based on the rule that one must assert only what one knows.

For more on truth and assertion, see the papers in Brown and Cappelen (2011) and the entry on assertion.


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