Truth is one of the central subjects in philosophy. It is also one ofthe largest. Truth has been a topic of discussion in its own right forthousands of years. Moreover, a huge variety of issues in philosophyrelate to truth, either by relying on theses about truth, or implyingtheses about truth.

It would be impossible to survey all there is to say about truth inany coherent way. Instead, this essay will concentrate on the mainthemes in the study of truth in the contemporary philosophicalliterature. It will attempt to survey the key problems and theories ofcurrent interest, and show how they relate to one-another. A number ofother entries investigate many of these topics in greater depth.Generally, discussion of the principal arguments is left to them. Thegoal of this essay is only to provide an overview of the currentTheories. Many of the papers mentioned in this essay can be found inthe anthologies edited by Blackburn and Simmons (1999), Lynch (2001b),and Lynch et al. (2021). There are a number of book-length surveys ofthe topics discussed here, including Beall & Middleton 2024,Blackburn 2018, Burgess & Burgess 2011, Kirkham 1992, andKünne 2003. Also, a number of the topics discussed here, and manyfurther ones, are surveyed at more length in papers in Glanzberg2018.

The problem of truth is in a way easy to state: what truths are, andwhat (if anything) makes them true. But this simple statement masks agreat deal of controversy. Whether there is a metaphysical problem oftruth at all, and if there is, what kind of theory might address it,are all standing issues in the theory of truth. We will see a numberof distinct ways of answering these questions.

• 1. The neo-classical theories of truth
  • 1.1 The correspondence theory
  • 1.1.1 The origins of the correspondence theory
  • 1.1.2 The neo-classical correspondence theory
  • 1.2 The coherence theory
  • 1.3 Pragmatist theories
• 2. Tarski’s theory of truth
  • 2.1 Sentences as truth-bearers
  • 2.2 Convention T
  • 2.3 Recursive definition of truth
  • 2.4 Reference and satisfaction
• 3. Correspondence revisited
  • 3.1 Correspondence without facts
  • 3.2 Representation and Correspondence
  • 3.3 Facts again
  • 3.4 Truthmakers
• 4. Realism and anti-realism
  • 4.1 Realism and truth
  • 4.2 Anti-realism and truth
  • 4.3 Anti-realism and pragmatism
  • 4.4 Truth pluralism
• 5. Deflationism
  • 5.1 The redundancy theory
  • 5.2 Minimalist theories
  • 5.3 Disquotationalism
  • 5.4 The logical status of the Tarski biconditionals
  • 5.5 Critical response
• 6. Truth and language
  • 6.1 Truth-bearers
  • 6.2 Truth and truth conditions
  • 6.3 Truth conditions and deflationism
  • 6.4 Truth and the theory of meaning
  • 6.5 The coherence theory and meaning
  • 6.6 Truth and assertion
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. The neo-classical theories of truth

Much of the contemporary literature on truth takes as its startingpoint some ideas which were prominent in the early part of the 20thcentury. There were a number of views of truth under discussion atthat time, the most significant for the contemporary literature beingthe correspondence, coherence, and pragmatist theories of truth.

These theories all attempt to directly answer thenaturequestion: what is the nature of truth? They take this question atface value: there are truths, and the question to be answered concernstheir nature. In answering this question, each theory makes the notionof truth part of a more thoroughgoing metaphysics or epistemology.Explaining the nature of truth becomes an application of somemetaphysical system, and truth inherits significant metaphysicalpresuppositions along the way.

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

1.1 The correspondence theory

Perhaps the most important of the neo-classical theories for thecontemporary literature is the correspondence theory. Ideas that soundstrikingly like a correspondence theory are no doubt very old. Theymight well be found in Aristotle or Aquinas. When we turn to the late19th and early 20th centuries where we pick up the story of theneo-classical theories of truth, it is clear that ideas aboutcorrespondence were central to the discussions of the time. In spiteof their importance, however, it is strikingly difficult to find anaccurate citation in the early 20th century for the receivedneo-classical view. Furthermore, the way the correspondence theoryactually emerged will provide some valuable reference points for thecontemporary debate. For these reasons, we dwell on the origins of thecorrespondence theory in the late 19th and early 20th centuries atgreater length than those of the other neo-classical views, beforeturning to its contemporary neo-classical form. For an overview of thecorrespondence theory, see David 2018.

1.1.1 The origins of the correspondence theory

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

Let us pick up the thread of this story in the years between 1898 andabout 1910. These years are marked by Moore and Russell’srejection of idealism. Yet at this point, they do not hold acorrespondence theory of truth. Indeed Moore (1899) sees thecorrespondence theory as a source of idealism, and rejects it. Russellfollows Moore in this regard. (For discussion of Moore’s earlycritique of idealism, where he rejects the correspondence theory oftruth, see Baldwin 1991. Hylton [1990] provides an extensivediscussion of Russell in the context of British idealism. An overviewof these issues is given in Baldwin 2018.)

In this period, Moore and Russell hold a version of theidentitytheory of truth. They say comparatively little about it, but itis stated briefly in Moore (1899; 1902) and Russell (1904). Accordingto the identity theory, a true proposition isidentical to afact. Specifically, in Moore and Russell’s hands, the theorybegins with propositions, understood as the objects of beliefs andother propositional attitudes. Propositions are what are believed, andgive the contents of beliefs. They are also, according to this theory,the primary bearers of truth. When a proposition is true, it isidentical to a fact, and a belief in that proposition is correct.(Related ideas about the identity theory and idealism are discussed byMcDowell [1994] and further developed by Hornsby [2001].)

The identity theory Moore and Russell espoused takes truth to be aproperty of propositions. Furthermore, taking up an idea familiar toreaders of Moore, the property of truth is a simple unanalyzableproperty. Facts are understood as simply those propositions which aretrue. There are true propositions and false ones, and facts just aretrue propositions. There is thus no “difference between truthand 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, Candlish and Damnjanovic 2018,Cartwright 1987, Dodd 2000, Johnston 2018, and the entry on theidentity theory of truth.)

Moore and Russell came to reject the identity theory of truth in favorof a correspondence theory, sometime around 1910 (as we see in Moore1953, which reports lectures he gave in 1910–1911, and Russell1910b). They do so because they came to reject the existence ofpropositions. Why? Among reasons, they came to doubt that there couldbe any such things as false propositions, and then concluded thatthere are no such things as propositions at all.

Why did Moore and Russell find false propositions problematic? A fullanswer to this question is a point of scholarship that would take ustoo far afield. (Moore himself lamented that he could not “putthe objection in a clear and convincing way” [1953, p. 263], butsee Cartwright 1987 and David 2001 for careful and clear explorationof the arguments.) But very roughly, the identification of facts withtrue propositions left them unable to see what a false propositioncould 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 propositionscount as true. Hence, they cannot exist, and so there are no falsepropositions. As Russell (1956, p. 223) later says, propositions seemto be at best “curious shadowy things” in addition tofacts.

As Cartwright (1987) reminds us, it is useful to think of thisargument in the context of Russell’s slightly earlier viewsabout propositions. As we see clearly in Russell (1903), for instance,he takes propositions to have constituents. But they are not merecollections of constituents, but a ‘unity’ which bringsthe constituents together. (We thus confront the ‘problem of theunity 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 theproperty of singing? If that is what the unity consists in, then weseem to have nothing other than the fact that Ramey sings. But then wecould not have genuine false propositions without having falsefacts.

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

A belief is true if and only if itcorresponds to a fact.

Views like this are held by Moore (1953) and Russell (1910b; 1912). Ofcourse, to understand such a theory, we need to understand the crucialrelation of correspondence, as well as the notion of a fact to which abelief corresponds. We now turn to these questions. In doing so, wewill leave the history, and present a somewhat more modernreconstruction of a correspondence theory. (For more on facts andproposition in this period, see Sullivan and Johnston 2018.)

1.1.2 The neo-classical correspondence theory

The correspondence theory of truth is at its core an ontologicalthesis: a belief is true if thereexists an appropriateentity – a fact – to which it corresponds. If there is nosuch entity, the belief is false.

Facts, for the neo-classical correspondence theory, are entities intheir own right. Facts are generally taken to be composed ofparticulars and properties and relations or universals, at least. Theneo-classical correspondence theory thus only makes sense within thesetting of a metaphysics that includes such facts. Hence, it is noaccident that as Moore and Russell turn away from the identity theoryof truth, the metaphysics of facts takes on a much more significantrole in their views. This perhaps becomes most vivid in the laterRussell (1956, p. 182), where the existence of facts is the“first truism.” (The influence of Wittgenstein’sideas to appear in theTractatus (1922) on Russell in thisperiod was strong, and indeed, theTractatus remains one ofthe important sources for the neo-classical correspondence theory. Formore recent extensive discussions of facts, see Armstrong 1997 andNeale 2001.)

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

What is the relation of correspondence? One of the standing objectionsto the classical correspondence theory is that a fully adequateexplanation of correspondence proves elusive. But for a simple belief,like that Ramey sings, we can observe that the structure of the fact\(\langle\)Ramey,Singing\(\rangle\) matches thesubject-predicate form of thethat-clause which reports thebelief, and may well match the structure of the belief itself.

So far, we have very much the kind of view that Moore and Russellwould have found congenial. But the modern form of the correspondencetheory seeks to round out the explanation of correspondence by appealtopropositions. Indeed, it is common to base acorrespondence theory of truth upon the notion of astructuredproposition. Propositions are again cast as the contents ofbeliefs and assertions, and propositions have structure which at leastroughly corresponds to the structure of sentences. At least, forsimple beliefs like that Ramey sings, the proposition has the samesubject predicate structure as the sentence. (Proponents of structuredpropositions, such as Kaplan 1989, often look to Russell 1903 forinspiration, and find unconvincing Russell’s reasons forrejecting them.)

With facts and structured propositions in hand, an attempt may be madeto explain the relation of correspondence. Correspondence holdsbetween a proposition and a fact when the proposition and fact havethe same structure, and the same constituents at each structuralposition. When they correspond, the proposition and fact thus mirroreach-other. In our simple example, we might have:

Propositions, though structured like facts, can be true or false. In afalse case, like the proposition that Ramey dances, we would find nofact at the bottom of the corresponding diagram. Beliefs are true orfalse depending on whether the propositions which are believedare.

We have sketched this view for simple propositions like theproposition that Ramey sings. How to extend it to more complex cases,like general propositions or negative propositions, is an issue wewill not delve into here. It requires deciding whether there arecomplex facts, such as general facts or negative facts, or whetherthere is a more complex relation of correspondence between complexpropositions and simple facts. (The issue of whether there are suchcomplex 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 keyto truth is a relation between propositions and the world, whichobtains when the world contains a fact that is structurally similar tothe 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-classicalcorrespondence theory. This theory offers us a paradigm example of acorrespondence theory of truth.

The leading idea of the correspondence theory is familiar. It is aform of the older idea that true beliefs show the right kind ofresemblance to what is believed. In contrast to earlierempiricist theories, the thesis is not that one’s ideasperse resemble what they are about. Rather, the propositions whichgive the contents of one’s true beliefs mirror reality, invirtue of entering into correspondence relations to the right piecesof it.

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

For more on the correspondence theory, see David 1994, 2018, and theentry on thecorrespondence theory of truth.

1.2 The coherence theory

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

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

Many idealists at that time did indeed hold coherence theories. Let ustake 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 isthe character of a significant whole (p. 76).

We will not attempt a full exposition of Joachim’s view, whichwould take us well beyond the discussion of truth into the details ofBritish idealism. But a few remarks about his theory will help to givesubstance to the quoted passage.

Perhaps most importantly, Joachim talks of ‘truth’ in thesingular. This is not merely a turn of phrase, but a reflection of hismonistic idealism. Joachim insists that what is true is the“whole complete truth” (p. 90). Individual judgments orbeliefs are certainly not the whole complete truth. Such judgmentsare, according to Joachim, only true to a degree. One aspect of thisdoctrine is a kind of holism about content, which holds that anyindividual belief or judgment gets its content only in virtue of beingpart of a system of judgments. But even these systems are only true toa degree, measuring the extent to which they express the content ofthe single ‘whole complete truth’. Any real judgment wemight make will only be partially true.

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

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

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

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 beliefin the system, or entailed by a belief in the system. We may assume,with Joachim, that the condition of coherence will be stronger thanconsistency. With the idealists generally, we might suppose thatfeatures of the believing subject will come into play.

This theory is offered as an analysis of the nature of truth, and notsimply a test or criterion for truth. Put as such, it is clearly notJoachim’s theory (it lacks his monism, and he rejectspropositions), but it is a standard take on coherence in thecontemporary literature. (It is the way the coherence theory is givenin Walker 1989, for instance. See also Young 2001 for a recent defenseof a coherence theory.) Let us take this as our neo-classical versionof the coherence theory. The contrast with the correspondence theoryof truth is clear. Far from being a matter of whether the worldprovides a suitable object to mirror a proposition, truth is a matterof how beliefs are related to each-other.

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

The steps in this argument may be questioned by a number ofcontemporary epistemological views. But the coherence theory also goeshand-in-hand with its own metaphysics as well. The coherence theory istypically associated with idealism. As we have already discussed,forms of it were held by British idealists such as Joachim, and laterby Blanshard (in America). An idealist should see the last step in thejustification argument as quite natural. More generally, an idealistwill see little (if any) room between a system of beliefs and theworld it is about, leaving the coherence theory of truth as anextremely 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 theidentity theory of truth. See Baldwin 1991 for some discussion.)However, it is hard to see much of a way to hold the coherence theoryof truth without maintaining some form of idealism. If there isnothing to truth beyond what is to be found in an appropriate systemof beliefs, then it would seem one’s beliefs constitute theworld in a way that amounts to idealism. (Walker [1989] argues thatevery coherence theorist must be an idealist, but not vice-versa.)

The neo-classical correspondence theory seeks to capture the intuitionthat truth is a content-to-world relation. It captures this in themost straightforward way, by asking for an object in the world to pairup with a true proposition. The neo-classical coherence theory, incontrast, insists that truth is not a content-to-world relation atall; rather, it is a content-to-content, or belief-to-belief,relation. The coherence theory requires some metaphysics which canmake the world somehow reflect this, and idealism appears to be it. (Adistant descendant of the neo-classical coherence theory that does notrequire idealism will be discussed in section 6.5 below.)

For more on the coherence theory, see Walker 2018 and the entry on thecoherence theory of truth.

1.3 Pragmatist theories

A different perspective on truth was offered by the Americanpragmatists. As with the neo-classical correspondence and coherencetheories, the pragmatist theories go with some typical slogans. Forexample, 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 whatpractical value truth has. True beliefs are guaranteed not to conflictwith subsequent experience. Likewise, Peirce’s slogan tells usthat true beliefs will remain settled at the end of prolonged inquiry.Peirce’s slogan is perhaps most typically associated withpragmatist views of truth, so we might take it to be our canonicalneo-classical theory. However, the contemporary literature does notseem 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 roomfor the idea that truth involves a kind of correspondence, insofar asthe scientific method of inquiry is answerable to some independentworld. Peirce, for instance, does not reject a correspondence theoryoutright; rather, he complains that it provides merely a‘nominal’ or ‘transcendental’ definition oftruth (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 extendeddiscussion.)

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

For more on pragmatist theories of truth, see Misak 2018 and the entryon thepragmatic theory of truth. James’ views are discussed further in the entry onWilliam James. Peirce’s views are discussed further in the entry onCharles Sanders Peirce.

2. Tarski’s theory of truth

Modern forms of the classical theories survive. Many of these moderntheories, notably correspondence theories, draw on ideas developed byTarski.

In this regard, it is important to bear in mind that his seminal workon truth (1935) is very much of a piece with other works inmathematical logic, such as his paper of 1931, and as much as anythingthis 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 usefultools that may be employed in a wide range of philosophical projects.(See Patterson 2012 for more on Tarski’s work in its historicalcontext.)

Tarski’s work has a number of components, which we will considerin turn.

2.1 Sentences as truth-bearers

In the classical debate on truth at the beginning of the 20th centurywe considered in section 1, the issue of truth-bearers was of greatsignificance. For instance, Moore and Russell’s turn to thecorrespondence theory was driven by their views on whether there arepropositions to be the bearers of truth. Many theories we reviewedtookbeliefs to be the bearers of truth.

In contrast, Tarski and much of the subsequent work on truth takessentences to be the primary bearers of truth. This is not anentirely novel development: Russell (1956) also takes truth to applyto sentence (which he calls ‘propositions’ in that text).But whereas much of the classical debate takes the issue of theprimary bearers of truth to be a substantial and importantmetaphysical one, Tarski is quite casual about it. His primary reasonfor taking sentences as truth-bearers is convenience, and heexplicitly distances himself from any commitment about thephilosophically contentious issues surrounding other candidatetruth-bearers (e.g., Tarski 1944). (Russell [1956] makes a similarsuggestion that sentences are the appropriate truth-bearers “forthe purposes of logic” (p. 184), though he still takes theclassical metaphysical issues to be important.)

We will return to the issue of the primary bearers of truth in section6.1. For the moment, it will be useful to simply follow Tarski’slead. But it should be stressed that for this discussion, sentencesarefully interpreted sentences, having meanings. We willalso assume that the sentences in question do not change their contentacross occasions of use, i.e., that they display nocontext-dependence. We are taking sentences to be what Quine (1960)calls ‘eternal sentences’.

In some places (e.g., 1944), Tarski refers to his view as the‘semantic conception of truth’. It is not entirely clearjust what Tarski had in mind by this, but it is clear enough thatTarski’s theory defines truth for sentences in terms of conceptslike reference and satisfaction, which are intimately related to thebasic semantic functions of names and predicates (according to manyapproaches to semantics). For more discussion, see Woleński 2001,2019.

2.2 Convention T

Let us suppose we have a fixed language \(\mathbf{L}\) whose sentencesare fully interpreted. The basic question Tarski poses is what anadequatetheory of truth for \(\mathbf{L}\) would be.Tarski’s answer is embodied in what he callsConventionT:

An adequate theory of truth for \(\mathbf{L}\) must imply, for eachsentence \(\ulcorner \phi \urcorner\) of \(\mathbf{L}\):

\(\ulcorner \phi \urcorner\) is true if and only if \(\phi\).

(We have simplified Tarski’s presentation somewhat. It isimportant that this is a schema, capturing all the instances forwell-formed sentences of \(\mathbf{L}\). We are hence using thetechnical device of quasi-quotation, as in ‘\(\ulcorner \phi\urcorner\)’, that allows us to see through a schematic letterto its instances. For a more thorough explanation of quasi-quotation,see Quine 1940, but it simply gives us quotation that gets the rightresults for schematic letters.) This is an adequacy condition fortheories, not a theory itself. Given the assumption that\(\mathbf{L}\) is fully interpreted, we may assume that each sentence\(\ulcorner \phi \urcorner\) in fact has a truth value. In light ofthis, Convention T guarantees that the truth predicate given by thetheory will beextensionally correct, i.e., have as itsextension all and only the true sentences of \(\mathbf{L}\).

Convention T draws our attention to the biconditionals of theform:

\(\ulcorner \ulcorner \phi \urcorner\) is true if and only if \(\phi\urcorner\),

which are usually called theTarski biconditionals for alanguage \(\mathbf{L}\).

2.3 Recursive definition of truth

Tarski does not merely propose a condition of adequacy for theories oftruth, he also shows how to meet it. One of his insights is that ifthe language \(\mathbf{L}\) displays the right structure, then truthfor \(\mathbf{L}\) can be defined recursively. For instance, let ussuppose that \(\mathbf{L}\) is a simple formal language, containingtwo atomic sentences ‘snow is white’ and ‘grass isgreen’, and the sentential connectives \(\ulcorner \vee\urcorner\) and \(\ulcorner \neg \urcorner\).

In spite of its simplicity, \(\mathbf{L}\) contains infinitely manydistinct sentences. But truth can be defined for all of them byrecursion.

1. Base clauses:
   1. ‘Snow is white’ is true if and only if snow iswhite.
   2. ‘Grass is green’ is true if and only if grass isgreen.
2. Recursion clauses. For any sentences \(\phi\) and \(\psi\) of\(\mathbf{L}\):
   1. \(\ulcorner \phi \vee \psi \urcorner\) is true if and only if\(\ulcorner \phi \urcorner\) is true or \(\ulcorner \psi \urcorner\)is true.
   2. \(\ulcorner \neg \phi \urcorner\) is true if and only if it is notthe case that \(\ulcorner \phi \urcorner\) is true.

This theory satisfies Convention T.

2.4 Reference and satisfaction

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

Tarski’s techniques go further, however. They do not stop withatomic sentences. Tarski notes that truth for each atomic sentence canbe defined in terms of two closely related notions:referenceandsatisfaction. Let us consider a language \(\mathbf{L}'\),just like \(\mathbf{L}\) except that instead of simply having twoatomic sentences, \(\mathbf{L}'\) breaks atomic sentences into termsand predicates. \(\mathbf{L}'\) contains terms ‘snow’ and‘grass’ (let us engage in the idealization that these aresimply singular terms), and predicates ‘is white’ and‘is green’. So \(\mathbf{L}'\) is like \(\mathbf{L}\), butalso contains the sentences ‘Snow is green’ and‘Grass is white’.)

We can define truth for atomic sentences of \(\mathbf{L}'\) in thefollowing way.

1. Base clauses:
   1. ‘Snow’ refers to snow.
   2. ‘Grass’ refers to grass.
   3. a satisfies ‘is white’ if and only ifa is white.
   4. a satisfies ‘is green’ if and only ifa is green.
2. For any atomic sentence \(\ulcorner t\) is \(P \urcorner\):\(\ulcorner t\) is \(P \urcorner\) is true if and only if the referentof \(\ulcorner t \urcorner\) satisfies \(\ulcorner P\urcorner\).

One of Tarski’s key insights is that the apparatus ofsatisfaction allows for a recursive definition of truth for sentenceswithquantifiers, though we will not examine that here. Wecould repeat the recursion clauses for \(\mathbf{L}\) to produce afull theory of truth for \(\mathbf{L}'\).

Let us say that a Tarskian theory of truth is a recursive theory,built up in ways similar to the theory of truth for \(\mathbf{L}'\).Tarski goes on to demonstrate some key applications of such a theoryof truth. A Tarskian theory of truth for a language \(\mathbf{L}\) canbe used to show that theories in \(\mathbf{L}\) are consistent. Thiswas especially important to Tarski, who was concerned the Liar paradoxwould make theories in languages containing a truth predicateinconsistent.

For more, see Ray 2018 and the entries onaxiomatic theories of truth, theLiar paradox, andTarski’s truth definitions.

3. Correspondence revisited

The correspondence theory of truth expresses the very natural ideathat truth is a content-to-world or word-to-world relation: what wesay or think is true or false in virtue of the way the world turns outto be. We suggested that, against a background like the metaphysics offacts, it does so in a straightforward way. But the idea ofcorrespondence is certainly not specific to this framework. Indeed, itis controversial whether a correspondence theory should rely on anyparticular metaphysics at all. The basic idea of correspondence, asTarski (1944) and others have suggested, is captured in the sloganfrom Aristotle’sMetaphysics Γ 7.27, “tosay of what is that it is, or of what is not that it is not, istrue” (Ross 1928). ‘What is’, it is natural enoughto say, is a fact, but this natural turn of phrase may well notrequire a full-blown metaphysics of facts. (For a discussion ofAristotle’s views in a historical context, see Szaif 2018.)

Yet without the metaphysics of facts, the notion of correspondence asdiscussed in section 1.1 loses substance. This has led to two distinctstrands in contemporary thinking about the correspondence theory. Onestrand seeks to recast the correspondence theory in a way that doesnot rely on any particular ontology. Another seeks to find anappropriate ontology for correspondence, either in terms of facts orother entities. We will consider each in turn.

3.1 Correspondence without facts

Tarski himself sometimes suggested that his theory was a kind ofcorrespondence theory of truth. Whether his own theory is acorrespondence theory, and even whether it provides any substantialphilosophical 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 accountto fail.”) But a number of philosophers (e.g., Davidson [1969]and Field [1972]) have seen Tarski’s theory as providing atleast the core of a correspondence theory of truth which dispenseswith the metaphysics of facts.

Tarski’s theory shows how truth for a sentence isdetermined by certain properties of its constituents; inparticular, by properties of reference and satisfaction (as well as bythe logical constants). As it is normally understood, reference is thepreeminent word-to-world relation. Satisfaction is naturallyunderstood as a word-to-world relation as well, which relates apredicate to the things in the world that bear it. The Tarskianrecursive definition shows how truth is determined by reference andsatisfaction, and so is in effect determined by the things in theworld we refer to and the properties they bear. This, one mightpropose, is all the correspondence we need. It is not correspondenceof sentences or propositions to facts; rather, it is correspondence ofour expressions to objects and the properties they bear, and then waysof working out the truth of claims in terms of this.

This is certainly not the neo-classical idea of correspondence. In notpositing facts, it does not posit any single object to which a trueproposition or sentence might correspond. Rather, it shows how truthmight be worked out from basic word-to-world relations. However, anumber of authors have noted that Tarski’s theory cannot byitself provide us with such an account of truth. As we will discussmore fully in section 4.2, Tarski’s apparatus is in factcompatible with theories of truth that are certainly notcorrespondence theories.

Field (1972), in an influential discussion and diagnosis of what islacking in Tarski’s account, in effect points out that whetherwe really have something worthy of the name‘correspondence’ depends on our having notions ofreference and satisfaction which genuinely establish word-to-worldrelations. (Field does not use the term ‘correspondence’,but does talk about, e.g., the “connection between words andthings” (p. 373).) By itself, Field notes, Tarski’s theorydoes not offer an account of reference and satisfaction at all.Rather, it offers a number ofdisquotation clauses, suchas:

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

These clauses have an air of triviality (though whether they are to beunderstood as trivial principles or statements of non-trivial semanticfacts has been a matter of some debate). With Field, we might proposeto supplement clauses like these with an account of reference andsatisfaction. Such a theory should tell us what makes it the case thatthe word ‘snow’ refer to snow. (In his paper of 1972,Field was envisaging a physicalist account, along the lines of thecausal theory of reference.) This shouldinter alia guaranteethat truth is really determined by word-to-world relations, so inconjunction with the Tarskian recursive definition, it could provide acorrespondence 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 standon the nature of particulars, or of the properties or universals thatunderwrite facts about satisfaction. However, it may not be entirelydevoid of metaphysical implications, as we will discuss further insection 4.1.

For more discussion, see Sher 1999.

3.2 Representation and Correspondence

Much of the subsequent discussion of Field-style approaches tocorrespondence has focused on the role of representation in theseviews. Field’s own (1972) discussion relies on a causal relationbetween terms and their referents, and a similar relation forsatisfaction. These are instances of representation relations.According to representational views, meaningful items, like perhapsthoughts or sentences or their constituents, have their contents invirtue of standing in the right relation to thethings theyrepresent. On many views, including Field’s, a name stands insuch a relation to its bearer, and the relation is a causal one.

The project of developing a naturalist account of the representationrelation has been an important one in the philosophy of mind andlanguage. (See the entry onmental representation.) But, it has implications for the theory of truth. Representationalviews of content lead naturally to correspondence theories of truth.To make this vivid, suppose you hold that sentences or beliefs standin a representation relation to some objects. It is natural to supposethat for true beliefs or sentences, those objects would be facts. Wethen have a correspondence theory, with the correspondence relationexplicated as a representation relation: a truth bearer is true if itrepresents a fact.

As we have discussed, many contemporary views reject facts, but onecan hold a representational view of content without them. Oneinterpretation of Field’s theory is just that. The relations ofreference and satisfaction are representation relations, and truth forsentences is determined compositionally in terms of thoserepresentation relations, and the nature of the objects theyrepresent. If we have such relations, we have the building blocks fora correspondence theory without facts. Field (1972) anticipated anaturalist reduction of the representation via a causal theory, butany view that accepts representation relations for truth bearers ortheir constituents can provide a similar theory of truth. (See Jackson2006 and Lynch 2009 for further discussion.)

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

3.3 Facts again

There have been a number of correspondence theories that do make useof facts. Some are notably different from the neo-classical theorysketched in section 1.1. For instance, Austin (1950) proposes a viewin which each statement (understood roughly as an utterance event)corresponds to both a fact or situation, and a type of situation. Itis true if the former is of the latter type. This theory, which hasbeen developed bysituation theory (e.g., Barwise and Perry1986), rejects the idea that correspondence is a kind of mirroringbetween a fact and a proposition. Rather, correspondence relations toAustin are entirely conventional. (See Vision 2004 for an extendeddefense of an Austinian correspondence theory.) As an ordinarylanguage philosopher, Austin grounds his notion of fact more inlinguistic usage than in an articulated metaphysics, but he defendshis use of fact-talk in Austin (1961b).

In a somewhat more Tarskian spirit, formal theories of facts or statesof affairs have also been developed. For instance, Taylor (1976)provides a recursive definition of a collection of ‘states ofaffairs’ for a given language. Taylor’s states of affairsseem to reflect the notion of fact at work in the neo-classicaltheory, though as an exercise in logic, they are officiallyn-tuples of objects andintensions.

There are more metaphysically robust notions of fact in the currentliterature. For instance, Armstrong (1997) defends a metaphysics inwhich facts (under the name ‘states of affairs’) aremetaphysically fundamental. The view has much in common with theneo-classical one. Like the neo-classical view, Armstrong endorses aversion of the correspondence theory. States of affairs aretruthmakers for propositions, though Armstrong argues thatthere may be many such truthmakers for a given proposition, and viceversa. (Armstrong also envisages a naturalistic account ofpropositions as classes of equivalent belief-tokens.)

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

In contrast to the approach to correspondence discussed in section3.1, which offered correspondence with minimal ontologicalimplications, this view returns to the ontological basis ofcorrespondence that was characteristic of the neo-classicaltheory.

For more on facts, see the entry onfacts.

3.4 Truthmakers

The truthmaker principle is often put as the schema:

If \(\phi\), then there is anx such that necessarily, ifx exists, then \(\phi\).

(Fox [1987] proposed putting the principle this way, rather thanexplicitly in terms of truth.)

The truthmaker principle expresses theontological aspect ofthe neo-classical correspondence theory. Not merely must truth obtainin virtue of word-to-world relations, but there must be a thing thatmakes each truth true. (For one view on this, see Merricks 2007.)Indeed, sometimes the truthmaker principle is simply put that‘truth supervenes on being’, i.e. that any possible worldsalike in what things exist and what properties they exemplify arealike in what is true in them (again following Merricks 2007.) Formore discussion, see for instance Bigelow 1988 (Part III), Lewis 2001,and Sider 2001 (Chapter 2).

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

As we saw in discussing the neo-classical correspondence theory,truthmaker theories, and fact-like theories in particular, raise anumber of issues. One which has been discussed at length, forinstance, is whether there arenegative facts. Negative factswould be the truthmakers for negated sentences. Russell (1956)notoriously expresses ambivalence about whether there are negativefacts. Armstrong (1997) rejects them, while Beall (2000), Cameron(2008), and Jago (2018) defend them.

Truthmaker theory has been the subject of a great deal of recentdiscussion. See, for instance, the overview in Asay 2023, Cameron2018, the papers in Beebee and Dodd 2005, and the entry ontruthmakers.

Another recent focus of attention has been on truthmaker semantics.This area explores how fact-like truthmakers (and falsitymakers) canprovide a framework for hyperintensional semantics. This hasapplications in logic, as perhaps first noted by van Fraassen (1969)and extensively developed by Fine (e.g., 2017) and Yablo (2014). Foran overview of applications to linguistics, see Champollion 2024.Views here can be quite subtle. For instance, in a great deal of work(reviewed in Fine 2017), Fine has expressed skepticism abouttruthmaking as a guide to metaphysics. His focus, along withcollaborators (e.g., Fine & Jago 2019), is on the semantics ofhyperintensionality, and the logics that go with it.

4. Realism and anti-realism

The neo-classical theories we surveyed in section 1 made the theory oftruth an application of their background metaphysics (and in somecases epistemology). In section 2 and especially in section 3, wereturned to the issue of what sorts of ontological commitments mightgo with the theory of truth. There we saw a range of options, fromrelatively ontologically non-committal theories, to theories requiringhighly specific ontologies.

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

4.1 Realism and truth

In discussing the approach to correspondence of section 3.1, we notedthat it has few ontological requirements. It relies on there beingobjects of reference, and something about the world which makes fordeterminate satisfaction relations; but beyond that, it isontologically neutral. But as we mentioned there, this is not to saythat it has no metaphysical implications. A correspondence theory oftruth, of any kind, is often taken to embody a form ofrealism.

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

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

(Wright [1992] offers a nice statement of this way of thinking aboutrealism.) These theses imply that our claims are objectively true orfalse, depending on how the world they are about is. The world that werepresent in our thoughts or language is an objective world. (Realismmay be restricted to some subject-matter, or range of discourse, butfor simplicity, we will talk about only its global form.)

It is often argued that these theses require some form of thecorrespondence theory of truth. (Putnam [1978, p. 18] notes,“Whatever else realists say, they typically say that theybelieve in a ‘correspondence theory of truth’.”) Atleast, they are supported by the kind of correspondence theory withoutfacts discussed in section 3.1, such as Field’s proposal. Such atheory will provide an account of objective relations of reference andsatisfaction, and show how these determine the truth or falsehood ofwhat we say about the world. Field’s own approach (1972) to thisproblem seeks a physicalist explanation of reference. But realism is amore general idea than physicalism. Any theory that provides objectiverelations of reference and satisfaction, and builds up a theory oftruth from them, would give a form of realism. (Making the objectivityof 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 theproperty ofbivalence. As Dummett has stressed (e.g., 1959,1976, 1983, 1991), a realist should see there being a fact of thematter one way or the other about whether any given claim is correct.Hence, one important mark of realism is that it goes together with theprinciple ofbivalence: every truth-bearer (sentence orproposition) is true or false. In much of his work, Dummett has madethis the characteristic mark of realism, and often identifies realismabout some subject-matter with accepting bivalence for discourse aboutthat subject-matter. At the very least, it captures a great deal ofwhat is more loosely put in the statement of realism above.

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

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

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

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

4.2 Anti-realism and truth

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

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

So understood, verificationism is a theory of truth. The claim is notthat verification is the most important epistemic notion, but thattruthjust is verifiability. As with the kind of realism weconsidered in section 4.1, this view expresses its metaphysicalcommitments in its explanation of the nature of truth. Truth is not,to this view, a fully objective matter, independent of us or ourthoughts. Instead, truth is constrained by our abilities to verify,and is thus constrained by our epistemic situation. Truth is to asignificant degree an epistemic matter, which is typical of manyanti-realist positions.

As Dummett says, the verificationist notion of truth does not appearto support bivalence. Any statement that reaches beyond what we can inprinciple verify or refute (verify its negation) will be acounter-example to bivalence. Take, for instance, the claim that thereis some substance, say uranium, present in some region of the universetoo distant to be inspected by us within the expected lifespan of theuniverse. Insofar as this really would be in principle unverifiable,we have no reason to maintain it is true or false according to theverificationist 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 warrantedassertibility. Assertibility, as well as verifiability, has beenimportant 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 thecoherence theory of truthper se. But in some ways, asDummett himself has noted, it might be construed as a descendant– perhaps very distant – of idealism. If idealism is themost drastic form of rejection of the independence of mind and world,Dummettian anti-realism is a more modest form, which sees epistemologyimprinted in the world, rather than the wholesale embedding of worldinto mind. At the same time, the idea of truth as warrantedassertibility or verifiability reiterates a theme from the pragmatistviews of truth we surveyed in section 1.3.

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

For more on anti-realism and truth, see Shieh 2018, the papers inGreenough and Lynch 2006, and the entry onrealism.

4.3 Anti-realism and pragmatism

Many commentators see a close connection between Dummett’santi-realism and the pragmatists’ views of truth, in that bothput great weight on ideas of verifiability or assertibility. Dummetthimself stressed parallels between anti-realism and intuitionism inthe philosophy of mathematics.

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

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

Davidson’s views on truth have also been associated withpragmatism, notably by Rorty (1986). Davidson has distanced himselffrom this interpretation (e.g., 1990), but he does highlightconnections between truth and belief and meaning. Insofar as these arehuman attitudes or relate to human actions, Davidson grants there issome 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 andanti-realism, and has become increasingly important in the currentliterature, is that of pluralism about truth. This view, developed inwork 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 discoursewhat we say is true in virtue of a correspondence-like relation, whilein others it is its true in virtue of a kind of assertibility relationthat is closer in spirit to the anti-realist views we have justdiscussed.

Such a proposal might suggest there are multiple concepts of truth, orthat the term ‘true’ is itself ambiguous. However, whetheror not a pluralist view is committed to such claims has been disputed.In particular, Lynch (2001b, 2009) develops a version of pluralismwhich takes truth to be a functional role concept. The functional roleof truth is characterized by a range of principles that articulatesuch features of truth as its objectivity, its role in inquiry, andrelated ideas we have encountered in considering various theories oftruth. (A related point about platitudes governing the concept oftruth is made by Wright [1992].) But according to Lynch, these displaythe functional role of truth. Furthermore, Lynch claims that onanalogy with analytic functionalism, these principles can be seen asderiving from our pre-theoretic or ‘folk’ ideas abouttruth.

Like all functional role concepts, truth must be realized, andaccording to Lynch it may be realized in different ways in differentsettings. Such multiple realizability has been one of the hallmarks offunctional role concepts discussed in the philosophy of mind. Forinstance, Lynch suggests that for ordinary claims about materialobjects, truth might be realized by a correspondence property (whichhe links to representational views), while for moral claims truthmight be manifest by an assertibility property along more anti-realistlines.

For more on pluralism about truth, see Pedersen and Lynch 2018,Pedersen & Wright 2013, and the entry onpluralist theories of truth.

5. Deflationism

We began in section 1 with the neo-classical theories, which explainedthe nature of truth within wider metaphysical systems. We thenconsidered some alternatives in sections 2 and 3, some of which hadmore modest ontological implications. But we still saw in section 4that substantial theories of truth tend to imply metaphysical theses,or evenembody metaphysical positions.

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

5.1 The redundancy theory

Deflationist ideas appear quite early on, including a well-knownargument against correspondence in Frege 1918–19. However, manydeflationists take their cue from an idea of Ramsey (1927), oftencalled theequivalence thesis:

\(\ulcorner \ulcorner \phi \urcorner\) is true \(\urcorner\) has thesame meaning as \(\ulcorner \phi \urcorner\).

(Ramsey himself takes truth-bearers to be propositions rather thansentences. Glanzberg 2003b questions whether Ramsey’s account ofpropositions really makes him a deflationist.)

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

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

To assert that \(\ulcorner \phi \urcorner\) is true is just to assertthat \(\phi\).

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

In either its speech act or meaning form, the redundancy theory arguesthere is no property of truth. It is commonly noted that theequivalence thesis itself is not enough to sustain the redundancytheory. It merely holds that when truth occurs in the outermostposition in a sentence, and the full sentence to which truth ispredicated is quoted, then truth is eliminable. What happens in otherenvironments is left to be seen. Modern developments of the redundancytheory include Grover et al. 1975.

5.2 Minimalist theories

The equivalence principle looks familiar: it has something like theform of theTarski biconditionals discussed in section 2.2.However, it is a stronger principle, which identifies the two sides ofthe biconditional – either their meanings or the speech actsperformed with them. The Tarski biconditionals themselves are simplymaterial biconditionals.

A number of deflationary theories look to the Tarski biconditionalsrather than the full equivalence principle. Their key idea is thateven if we do not insist on redundancy, we may still hold thefollowing theses:

1. For a given language \(\mathbf{L}\) and every \(\phi\) in\(\mathbf{L}\), the biconditionals \(\ulcorner \ulcorner \phi\urcorner\) is true if and only if \(\phi \urcorner\) hold bydefinition (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 asminimalist.Officially, this is the name of the view of Horwich (1990), but wewill apply it somewhat more widely. (Horwich’s view differs insome specific respects from what is presented here, such aspredicating truth of propositions, but we believe it is close enoughto what is sketched here to justify the name.)

The second thesis, that the Tarski biconditionals are all there is tosay about truth, captures something similar to the redundancytheory’s view. It comes near to saying that truth is not aproperty at all; to the extent that truth is a property, there is nomore to it than the disquotational pattern of the Tarskibiconditionals. As Horwich puts it, there is no substantial underlyingmetaphysics to truth. And as Soames (1984) stresses, certainly nothingthat could ground as far-reaching a view as realism oranti-realism.

5.3 Disquotationalism

Another variety of deflationism, that has become particularlyimportant in recent discussions, goes under the labeldisquotationalism, initially developed by Leeds (1978) andQuine (1970), and more recently defended by such authors as Beall(e.g., 2005) and Field (e.g., 1994). Disquotationalism focuses on twomain points. One is to stake out a very strong and ‘pure’form of the equivalence thesis, that holds that \(\ulcorner \ulcorner\phi \urcorner\ \textrm{is true} \urcorner\) and \(\ulcorner \phi\urcorner\) are equivalent in the strongest sense. According to Field(1994), they are cognitively equivalent for a speaker. Field notesclearly, as we will discuss more in section 6 below, that for thisclaim to be substantial, our notion of content or cognitivesignificance must not itself be understood in truth-conditional terms.(Field prefers a conceptual role account of content.)

Disquotationalism makes vivid an issue that all deflationistsencounter. If there is no substantial property of truth, or a strongform of the equivalence thesis holds, what role does our term‘true’ play? The answer is found in the name‘disquotationalism’. Disquotationalism takes its name froma feature that most all deflationists recognize: the Tarskibiconditionals or the equivalence thesis allows us to move from aquoted sentence as an argument of the truth predicate to an unquotedsentence. Thus, truth is described as a device ofdisquotation. Such a device allows us to make some usefulclaims which we could not formulate otherwise, such as theblindascription ‘The next thing that Bill says will betrue’. (Such uses were noted by Strawson [1950]. For more onblind ascriptions and their relation to deflationism, see Azzouni2001.)

Disquotationalists such as Beall (2005) and Field (1994) focus on animportant logical property of the truth predicate. A truth predicateallows us to express what would otherwise be (potentially) infiniteconjunctions or disjunctions. A good example is the notoriousstatement of Papal infallibility, which roughly says ‘Everythinga Pope says is true’. This would otherwise have to be put as thepotentially infinite conjunction of all things all popes will eversay.

Thus, according to disquotationalists, truth is really a purelylogical device, which extends our resources for expressingconjunctions. With Beall (2005), we could even imagine that such adevice was introduced into our languages via the stipulation of somerules. The Tarski biconditionals are examples of such rules. Beallhimself prefers a ‘rule form’ of the Tarski biconditionalsthat makes \(\ulcorner \ulcorner \phi \urcorner\ \textrm{is true}\urcorner\) and \(\ulcorner \phi \urcorner\) intersubstitible in allnon-opaque contexts. One could also construe the clauses of arecursive Tarskian theory as stipulated. (There are some significantlogical differences between these options. See Halbach 1999, Ketland1999, and Shapiro 1998 for discussion.)

5.4 The logical status of the Tarski biconditionals

Looking at the disquotationalist claim that truth is somehow a logicaldevice, and other deflationist views that hold that the Tarskibiconditionals are somehow vacuous or constitute a definition, wemight ask if the Tarski biconditionals are simply logical truths. Thetruth predicate would then be a kind of vacuous logical operator,rendering the biconditionals themselves logical truths. For instance,Priest (2007) suggests that the Tarski biconditionals are logicaltruths. To pursue this idea, we might take inspiration from the manycombinatory logics that include an identity combinator, or thehorizontal stroke in Frege’s logic. (See the entries on oncombinatory logic andFrege’s logic.)

An especially well-developed version of this idea comes from Zalta(2014), who argues that the Tarski biconditionals are not only logicaltruths, but they are even tautologies. It takes some set-up to makethis claim. In brief, one role of truth is to allow sentences to alsofunction as terms, which can be arguments of predicates. In ordinarylanguage, we see this with the operator ‘that’, whichturns the sentence \(\ulcorner \phi \urcorner\) into the term\(\ulcorner \textrm{that-}\phi \urcorner \), which then combines withthe truth predicate to make a sentence that is equivalent to\(\ulcorner \phi \urcorner\). If we assume our logic includeslambda-binders (\(\lambda\)), we can see these functions as beingcarried out by a zero-place \(\lambda\)-binder, which in effect allowssentences to simultaneously function as terms. But conversely, theseterms are themselves zero-place, and so can function as sentences. Theresult, according to Zalta, is that we can reformulate the Tarskibiconditionals as having the form \(\ulcorner [\lambda \: \phi] \iff\phi \urcorner\). Here, the truth predicate is replaces by a logicaloperator \(\lambda\). Zalta then argues in detail that the resultingbiconditionals are not only logical truths in familiar higher-orderlogics including \(\lambda\)-abstraction, but that they aretautologies according to the standards of higher order logic.

Amongst those broadly sympathetic to deflationism, there issubstantial debate over the logical status of the Tarskibiconditionals. (Those sympathetic to varieties of the correspondencetheory will generally not see the biconditionals as logical truths.)As we have noted, Priest (2007) and Zalta (2014) argue in differentways that they are logical truths. In contrast, Cook (2012) arguesthat instances of the Tarski biconditionals cannot all be logicaltruths, based on some widely accepted ideas about what counts as alogical truth. Though Cook’s argument does not depend on theLiar paradox, some theories surrounding the paradox have to acceptthat there are false instances of the Tarski biconditionals. (SeeMcGee 1992, and for more background, the entry on theLiar paradox.) Beall (2021) takes a very nuanced view, describing truth as an‘emergent logical property’. There are a great many issuesabout logic at play here, including how the Tarski biconditionals areto be formulated, and what the standards for logicality are. For acareful discussion of these matters, see Wyatt 2016.

For more on deflationism, see Azzouni 2018 and the entry on thedeflationary theory of truth.

5.5 Critical response

The critical discussion of deflationism is vast. We refer readers tothe entry on thedeflationary theory of truth and the overview in Azzouni 2018. A seminal contribution is Gupta1993. Other noteworthy contributions among many include Halbach 1999,Heck 2004, Ketland 1999, and Shapiro 1998.

6. Truth and language

One of the important themes in the literature on truth is itsconnection to meaning, or more generally, to language. This has provedan important application of ideas about truth, and an important issuein the study of truth itself. This section will consider a number ofissues relating truth and language.

6.1 Truth-bearers

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

In spite of the number of options under discussion, and thesignificance that has sometimes been placed on the choice, there is animportant similarity between candidate truth-bearers. Consider therole of truth-bearers in the correspondence theory, for instance. Wehave seen versions of it which take beliefs, propositions, orinterpreted sentences to be the primary bearers of truth. But all ofthem rely upon the idea that their truth-bearers aremeaningful, and are thereby able to say something about whatthe world is like. (We might say that they are able to represent theworld, but that is to use ‘represent’ in a wider sensethan we saw in section 3.2. No assumptions about just what stands inrelations to what objects are required to see truth-bearers asmeaningful.) It is in virtue of being meaningful that truth-bearersare able to enter into correspondence relations. Truth-bearers arethings which meaningfully make claims about what the world is like,and are true or false depending on whether the facts in the world areas described.

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

Though Tarski works with sentences, the same can be said of histheory. The sentences to which Tarski’s theory applies are fullyinterpreted, and so also are meaningful. They characterize the worldas being some way or another, and this in turn determines whether theyare true or false. Indeed, Tarski needs there to be a fact of thematter about whether each sentence is true or false (abstracting awayfrom context dependence), to ensure that the Tarski biconditionals dotheir job of fixing the extension of ‘is true’. (But notethat just what this fact of the matter consists in is left open by theTarskian apparatus.)

We thus find the usual candidate truth-bearers linked in a tightcircle: interpreted sentences, the propositions they express, thebelief speakers might hold towards them, and the acts of assertionthey might perform with them are all connected by providing somethingmeaningful. This makes them reasonable bearers of truth. For thisreason, it seems, contemporary debates on truth have been much lessconcerned with the issue of truth-bearers than were the classicalones. Some issues remain, of course. Different metaphysicalassumptions may place primary weight on some particular node in thecircle, and some metaphysical views still challenge the existence ofsome of the nodes. Perhaps more importantly, different views on thenature of meaning itself might cast doubt on the coherence of some ofthe nodes. Notoriously for instance, Quineans (e.g., Quine 1960) denythe existence of intensional entities, including propositions. Evenso, it increasingly appears doubtful that attention to truthperse will bias us towards one particular primary bearer oftruth.

For more on these issues, see King 2018.

6.2 Truth and truth conditions

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

The neo-classical theories of truth start with truth-bearers which arealready understood to be meaningful, and explain how they get theirtruth values. But along the way, they often do something more. Takethe neo-classical correspondence theory, for instance. This theory, ineffect, starts with a view of how propositions are meaningful. Theyare so in virtue of having constituents in the world, which arebrought together in the right way. There are many complications aboutthe nature of meaning, but at a minimum, this tells us what the truthconditions associated with a proposition are. The theory then explainshow such truth conditions can lead to the truth valuetrue,by the right factexisting.

Many theories of truth are like the neo-classical correspondencetheory in being as much theories of how truth-bearers are meaningfulas of how their truth values are fixed. Again, abstracting from somecomplications about meaning, this makes them theories both of truthconditions and truthvalues. (This idea perhapsfirst appears in mature form in Ramsey 1927. Ramsey of course isheavily influenced by Wittgenstein 1922.) The Tarskian theory of truthcan be construed this way too. This can be seen both in the way theTarski biconditionals are understood, and how a recursive theory oftruth is understood. As we explained Convention T in section 2.2, theprimary role of a Tarski biconditional of the form \(\ulcorner\ulcorner \phi \urcorner\) is true if and only if \(\phi \urcorner\)is to fix whether \(\ulcorner \phi \urcorner\) is in the extension of‘is true’ or not. But it can also be seen as stating thetruth conditions of \(\ulcorner \phi \urcorner\). Both relyon the fact that the unquoted occurrence of \(\ulcorner \phi\urcorner\) is an occurrence of an interpreted sentence, which has atruth value, but also provides its truth conditions upon occasions ofuse.

Likewise, the base clauses of the recursive definition of truth, thosefor reference and satisfaction, are taken to state the relevantsemantic properties of constituents of an interpreted sentence. Indiscussing Tarski’s theory of truth in section 2, we focused onhow these determine the truth value of a sentence. But they also showus the truth conditions of a sentence are determined by these semanticproperties. For instance, for a simple sentence like ‘Snow iswhite’, the theory tells us that the sentence is true if thereferent of ‘Snow’ satisfies ‘white’. This canbe understood as telling us that the truthconditions of‘Snow is white’ are those conditions in which the referentof ‘Snow’ satisfies the predicate ‘iswhite’.

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

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

6.3 Truth conditions and deflationism

Any theory that provides a substantial account of truth conditions canoffer a simple account of truth values: a truth-bearer provides truthconditions, and it is true if and only if the actual way things are isamong them. Because of this, any such theory will imply a strong, butvery particular, biconditional, close in form to the Tarskibiconditionals. It can be made most vivid if we think of propositionsas sets of truth conditions. Letp be a proposition, i.e., aset of truth conditions, and leta be the ‘actualworld’, the condition that actually obtains. Then we can almosttrivially see:

p is true if and only if \(a \in p\).

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

Though this may look like a principle that deflationists shouldapplaud, it is not. Rather, it shows that deflationists cannot reallyhold a truth-conditional view of content at all. If they do, then theyinter alia have a non-deflationary theory of truth, simply bylinking truth value to truth conditions through the abovebiconditional. It is typical of thoroughgoing deflationist theories topresent a non-truth-conditional theory of the contents of sentences: anon-truth-conditional account of what makes truth-bearers meaningful.We take it this is what is offered, for instance, by theusetheory of propositions in Horwich (1990). It is certainly one of theleading ideas of Field (1986, 1994), which explore how a conceptualrole account of content would ground a deflationist view of truth.Once one has a non-truth-conditional account of content, it is thenpossible to add a deflationist truth predicate, and use this to givepurely deflationist statements of truth conditions. But the startingpoint must be a non-truth-conditional view of what makes truth-bearersmeaningful.

Both deflationists and anti-realists start with something other thancorrespondence truth conditions. But whereas an anti-realist willpropose a different theory of truth conditions, a deflationists willstart with an account of content which is not a theory of truthconditions at all. The deflationist will then propose that the truthpredicate, given by the Tarski biconditionals, is an additionaldevice, not for understanding content, but for disquotation. It is auseful device, as we discussed in section 5.3, but it has nothing todo with content. To a deflationist, the meaningfulness oftruth-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 ofmeaning. At least, as we have seen, a Tarskian theory can be seen asshowing how the truth conditions of a sentence are determined by thesemantic properties of its parts. More generally, as we see in much ofthe work of Davidson and of Dummett (e.g., 1959, 1976, 1983, 1991),giving a theory of truth conditions can be understood as a crucialpart of giving a theory of meaning. Thus, any theory of truth thatfalls into the broad category of those which are theories of truthconditions can be seen as part of a theory of meaning. (For morediscussion of these issues, see Higginbotham 1986, 1989, and theexchange between Higginbotham [1992] and Soames [1992].)

A number of commentators on Tarski (e.g., Etchemendy [1988] and Soames[1984]) have observed that the Tarskian apparatus needs to beunderstood in a particular way to make it suitable for giving a theoryof meaning. Tarski’s work is often taken to show how todefine a truth predicate. If it is so used, then whether ornot a sentence is true becomes, in essence, a truth of mathematics.Presumably what truth conditions sentences of a natural language haveis a contingent matter, so a truth predicate defined in this waycannot be used to give a theory of meaning for them. But the Tarskianapparatus need not be used just to explicitly define truth. Therecursive characterization of truth can be used to state the semanticproperties of sentences and their constituents, as a theory of meaningshould. In such an application, truth is not taken to be explicitlydefined, but rather the truth conditions of sentences are taken to bedescribed. (See Heck 1997 for more discussion.)

6.5 The coherence theory and meaning

Inspired by Quine (e.g., 1960), Davidson himself is well known fortaking a different approach to using a theory of truth as a theory ofmeaning than is implicit in Field 1972. Whereas a Field-inspiredrepresentational approach is based on a causal account of reference,Davidson (e.g., 1973) proposes a process ofradicalinterpretation in which an interpreter builds a Tarskian theoryto 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 aretrue – a conclusion that squares well with the coherence theoryof truth. This is a weaker claim than the neo-classical coherencetheory would make. It does not insist that all the members of anycoherent set of beliefs are true, or that truth simply consists inbeing a member of such a coherent set. But all the same, theconclusion that most of our beliefs are true, because their contentsare to be understood through a process of radical interpretation whichwill make them a coherent and rational system, has a clear affinitywith the neo-classical coherence theory.

Davidson (1986) thought his view of truth had enough affinity with theneo-classical coherence theory to warrant being called a coherencetheory of truth, while at the same time he saw the role of Tarskianapparatus as warranting the claim that his view was also compatiblewith 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 anyunderstanding of the role of Tarski’s theory in radicalinterpretation that involves the kind of representational apparatusrelied on by Field (1972), as we discussed in sections 3.1 and 3.2. Inthe “Afterthoughts” to Davidson 1986, he also concludedthat his view departs too far from the neo-classical coherence theoryto be named one. What is important is rather the role of radicalinterpretation in the theory of content, and its leading to the ideathat belief is veridical. These are indeed points connected tocoherence, but not to the coherence theory of truth per se. They alsocomprise a strong form of anti-representationalism. Thus, though hedoes not advance a coherence theory of truth, he does advance a theorythat stands in opposition to the representational variants of thecorrespondence theory we discussed in section 3.2.

For more on Davidson, see Glanzberg 2013 and the entry onDonald Davidson.

6.6 Truth and assertion

The relation between truth and meaning is not the only place wheretruth and language relate closely. Another is the idea, alsomuch-stressed in the writings of Dummett (e.g., 1959), of the relationbetween 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 saysomething 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 liesdoes not. Any speaker whose aim is to flatter, or to deceive, aims atsomething other than truth.

The motivation for the truth-assertion platitude is rather different.It looks at assertion as a practice, in which certain rules areconstitutive. As is often noted, the natural parallel here iswith games, like chess or baseball, which are defined by certainrules. The platitude holds that it is constitutive of the practice ofmaking assertions that assertions aim at truth. An assertion by itsnature presents what it is saying as true, and any assertion whichfails to be true isipso facto liable to criticism, whetheror not the person making the assertion themself wished to have saidsomething true or to have lied.

Dummett’s original discussion of this idea was partially acriticism of deflationism (in particular, of views in Strawson 1950).The idea that we fully explain the concept of truth by way of theTarski biconditionals is challenged by the claim that thetruth-assertion platitude is fundamental to truth. As Dummett thereput it, what is left out by the Tarski biconditionals, and captured bythe truth-assertion platitude, is thepoint of the concept oftruth, or what the concept is used for. (For further discussion, seeGlanzberg 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 oftruth in the constitutive rules is itself controversial. The leadingalternative, defended by Williamson (1996), is that knowledge, nottruth, is fundamental to the constitutive rules of assertion.Williamson defends an account of assertion based on the rule that onemust assert only what one knows.

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

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Acknowledgments

Thanks to Josh Parsons for advice on metaphysics, and to Jc Beall,Justin Khoo, Jason Stanley, Paul Teller, and anonymous referees forvery helpful comments on earlier drafts.