Deflationism about truth, what is often simply called“deflationism”, is really not so much a theoryoftruth in the traditional sense, as it is a different, newer sortof approach to the topic. Traditional theories of truth are part of aphilosophical debate about the nature of a supposed property of truth.Philosophers offering such theories often make suggestions like thefollowing: truth consists in correspondence to the facts; truthconsists in coherence with a set of beliefs or propositions; truth iswhat is acceptable in the ideal limit of inquiry. According todeflationists, such suggestions are mistaken, and, moreover, they allshare a common mistake. The common mistake is to assume that truthhas a nature of the kind that philosophers might find outabout and develop theories of. The main idea of the deflationaryapproach is (a) that all that can be significantly said about truth isexhausted by an account of the role of the expression‘true’ or of the concept of truth in our talk and thought,and (b) that, by contrast with what traditional views assume, thisrole is neither metaphysically substantive nor explanatory. Forexample, according to deflationary accounts, to say that ‘snowis white’ is true, or that it is true that snow is white, is insome sense strongly equivalent to saying simply that snow is white,and this, according to the deflationary approach, is all that can besaid significantly about the truth of ‘snow is white’.Philosophers looking for some underlying nature of some truth propertythat is attributed with the use of the expression ‘true’are bound to be frustrated, the deflationist says, because they arelooking for something that isn’t there.

Deflationism comprises a variety of different versions, each of whichhave gone by different names, including at least the following:disquotationalism, minimalism, prosententialism, the redundancytheory, the disappearance theory, the no-truth theory. There has notalways been terminological consensus in the literature about how touse these labels: sometimes they have been used interchangeably;sometimes they have been used to mark distinctions between differentdevelopments of the same general approach. The actual variety ofdeflationary views has not always been clear in discussions of thisapproach, especially in the earlier literature, where importantdifferences are occasionally missed. To help clear this up, we willuse ‘deflationism’ to denote the general approach we wantto discuss and reserve other names for specific versions of thatapproach.

• 1. Central Themes in Deflationism
  • 1.1 The Equivalence Schema
  • 1.2 The Property of Truth
  • 1.3 The Utility of the Concept of Truth
• 2. History of Deflationism
• 3. The Varieties of Contemporary Deflationism
  • 3.1 Minimalism
  • 3.2 Disquotationalism
  • 3.3 Prosententialism
• 4. Objections to Deflationism
  • 4.1 The Explanatory Role of Truth
  • 4.2 Propositions Versus Sentences
  • 4.3 Correspondence
  • 4.4 Truth-Value Gaps
  • 4.5 The Generalization Problem
  • 4.6 Conservativeness
  • 4.7 Normativity
  • 4.8 Inflationist Deflationism?
  • 4.9 Truth and Meaning
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Central Themes in Deflationism

1.1 The Equivalence Schema

While deflationism can be developed in different ways, it is possibleto isolate some central themes emphasized by most philosophers whothink of themselves as deflationists. These shared themes pertain toendorsing a kind of metaphysical parsimony and positing a“deflated” role for what we can call thealethiclocutions (most centrally, the expressions ‘true’ and‘false’) in the instances of what is often calledtruth-talk. In this section, we will isolate three of thesethemes. The first, and perhaps most overarching, one has already beenmentioned: According to deflationists, there is some strongequivalence between a statement like ‘snow is white’ and astatement like “‘snow is white’ is true,” andthis is all that can significantly be said about that application ofthe notion of truth.

We may capture this idea more generally with the help of a schema,what is sometimes calledthe equivalence schema:

(ES)

\(\langle p\rangle\) is true if, and only if, \(p\).

In this schema, the angle brackets indicate an appropriatename-forming or nominalizing device, e.g., quotation marks or‘the proposition that …’, and the occurrences of‘\(p\)’ are replaced with matching declarative sentencesto yield instances of the schema.

The equivalence schema is often associated with the formal work ofAlfred Tarski (1935 [1956], 1944), which introduced the schema,

(T)

\(X\) is true if, and only if, \(p\).

In the instances of schema (T) (sometimes called “Convention(T)”), the ‘\(X\)’ gets filled in with a name of thesentence that goes in for the ‘\(p\)’, making (T) aversion of (ES). Tarski considered (T) to provide a criterion ofadequacy for any theory of truth, thereby allowing that there could bemore to say about truth than what the instances of the schema cover.Given that, together with the fact that he took the instances of (T)to be contingent, his theory does not qualify as deflationary.

By contrast with the Tarskian perspective on (T)/(ES), we canformulate the central theme of deflationism under consideration as theview, roughly, that the instances of (some version of) this schema docapture everything significant that can be said about applications ofthe notion of truth; in a slogan, the instances of the schemaexhaust the notion of truth. Approaches which depart fromdeflationism don’t disagree that (ES) tells us something abouttruth; what they (with Tarski) deny is that it is exhaustive, that ittells us the whole truth about truth. Since such approaches addsubstantive explanations of why the instances of the equivalenceschema hold, they are now often calledinflationaryapproaches to truth. Inflationism is the general approach shared bysuch traditional views as thecorrespondence theory of truth,coherence theory of truth,pragmatic theory of truth,identity theory of truth, and primitivist theory of truth, These theories all sharea collection of connected assumptions about the alethic locutions, theconcept of truth, and the property of truth. Inflationary theories allassume that the expression ‘is true’ is a descriptivepredicate, expressing an explanatory concept of truth, whichdetermines a substantive property of truth. From that shared set ofpresuppositions, the various traditional inflationary theories thendiverge from one another by providing different accounts of theassumed truth property. On inflationary views, the nature of the truthproperty explains why the instances of (ES) hold. Deflationary views,by contrast, reject some if not all of the standard assumptions thatlead to inflationary theories, resisting at least their move topositing any substantive truth property. Instead, deflationists offera different understanding of both the concept of truth and thefunctioning of the alethic locutions. A deflationist will take theinstances of (ES) to be “conceptually basic and explanatorilyfundamental” (Horwich 1998a, 21, n. 4; 50), or to be directconsequences of how the expression ‘true’ operates (cf.Quine 1970 [1986], Brandom 1988, and Field 1994a).

It is important to notice that even among deflationists theequivalence schema may be interpreted in different ways, and this isone way to distinguish different versions of deflationism from oneanother. One question about (ES) concerns the issue of what instancesof the schema are assumed to be about (equivalently: to what the namesin instances of (ES) are assumed to refer). According to one view, theinstances of this schema are about sentences, where a name for asentence can be formulated simply by putting quotation marks aroundit. In other words, for those who hold what might be called asententialist version of deflationism, the equivalence schemahas instances like (1):

(1)

‘Brutus killed Caesar’ is true if, and only if, Brutuskilled Caesar.

To make this explicit, we might say that, according to sententialistdeflationism, the equivalence schema is:

(ES-sent)

The sentence ‘\(p\)’ is true if, and only if,\(p\).

Notice that in this schema, the angle-brackets of (ES) have beenreplaced by quotation marks.

According to those who hold what might be called apropositionalist version of deflationism, by contrast,instances of the equivalence schema are about propositions, wherenames of propositions are, or can be taken to be, expressions of theform ‘the proposition that \(p\)’, where‘\(p\)’ is filled in with a declarative sentence. For thepropositionalist, in other words, instances of the equivalence schemaare properly interpreted not as being about sentences but instead asbeing about propositions, i.e., as biconditionals like (2) rather than(1):

(2)

The proposition that Brutus killed Caesar is true if, and only if,Brutus killed Caesar.

To make this explicit, we might say that, according topropositionalist deflationism, the equivalence schema is:

(ES-prop)

The proposition that \(p\) is true if, and only if, \(p\).

Interpreting the equivalence schema as (ES-sent) rather than as(ES-prop), or vice versa, thus yields different versions ofdeflationism, sententialist and propositionalist versions,respectively.

Another aspect that different readings of (ES) can vary acrossconcerns the nature of the equivalence that its instances assert. Onone view, the right-hand side and the left-hand side of such instancesare synonymous or analytically equivalent. Thus, for sententialistswho endorse this level of equivalence, (1) asserts that,“‘Brutus killed Caesar’ is true” means justwhat ‘Brutus killed Caesar’ means; while forpropositionalists who endorse analytic equivalence, (2) asserts that‘the proposition that Brutus killed Caesar is true’ meansthe same as ‘Brutus killed Caesar’. A second view is thatthe right-hand and left-hand sides of claims such as (1) and (2) arenot synonymous but are nonetheless necessarily equivalent; this viewmaintains that the two sides of each equivalence stand or falltogether in every possible world, despite having different meanings.And a third possible view is that claims such as (1) and (2) assertonly a material equivalence; this view interprets the ‘if andonly if’ in both (1) and (2) as simply the biconditional ofclassical logic.

This tripartite distinction between analytic, necessary, and materialequivalence, when combined with the distinction between sententialismand propositionalism, yields six different possible (although notexhaustive) readings of the instances of (ES):

While different versions of deflationism can be correlated to someextent with different positions in this chart, some chart positionshave also been occupied by more than one version of deflationism. Thelabels ‘redundancy theory’, ‘disappearancetheory’ and ‘no-truth theory’ have been used toapply to analytic versions of deflationism: positions \(\mathbf{A}\)or \(\mathbf{B}\). But there is a sense in which position\(\mathbf{A}\) is also occupied by versions of what is called“disquotationalism” (although the most prominentdisquotationalists tend to be leary of the notions of analyticity orsynonymy), and what is called “prosententialism” alsoposits an equivalence of what is said with the left- and right-handsides of the instances of (ES). The latter version of deflationism,however, does this without making the left-hand sides about sentencesnamed via quotation or about propositions understood as abstractentities. No deflationist has offered an account occupying position\(\mathbf{C}\), \(\mathbf{E}\), or \(\mathbf{F}\) (although theexplicit inspiration some disquotationalists have found inTarski’s work and his deployment of material equivalence mightmisleadingly suggest position \(\mathbf{E})\). Paul Horwich (1998a)uses the label ‘minimalism’ for a version ofpropositionalist deflationism that takes the instances of (ES-prop) toinvolve a necessary equivalence, thereby occupying position\(\mathbf{D}\). To a large extent, philosophers prefer one or another(or none) of the positions in the chart on the basis of their viewsfrom other parts of philosophy, typically their views about thephilosophy of language and metaphysics.

1.2 The Property of Truth

The second theme we will discuss focuses on the fact that when we say,for example, that the proposition that Brutus killed Caesar is true,we seem to be attributing a property to that proposition, namely, theproperty of being true. Deflationists are typically wary of thatclaim, insisting either that there is no property of being true atall, or, if there is one, it is of a certain kind, often called“thin” or “insubstantial”.

The suggestion that there is no truth property at all is advanced bysome philosophers in the deflationary camp; we will look at someexamples below. What makes this position difficult to sustain is that‘is true’ is grammatically speaking a predicate much like‘is metal’. If one assumes that grammatical predicatessuch as ‘is metal’ express properties, then,primafacie, the same would seem to go for ‘is true.’ Thispoint is not decisive, however. For one thing, it might be possible todistinguish the grammatical form of claims containing ‘istrue’ from their logical form; at the level of logical form, itmight be, as prosententialists maintain, that ‘is true’ isnot a predicate. For another, nominalists about propertieshave developed ways of thinking about grammatical predicates accordingto which these expressions don’t express properties at all. Adeflationist might appeal, perhaps selectively, to such proposals, inorder to say that ‘is true’, while a predicate, does notexpress a property.

Whatever the ultimate fate of these attempts to say that there is noproperty of truth may be, a suggestion among certain deflationists hasbeen to concede that there is a truth property but to deny it is aproperty of a certain kind; in particular to deny that it is (as wewill say) asubstantive property.

To illustrate the general idea, consider (3) and (4):

(3)

Caracas is the capital of Venezuela.

(4)

The earth revolves around the sun.

Do the propositions that these sentences express share a property ofbeing true? Well, in one intuitive sense they do: Since they both aretrue, we might infer that they both have the property of being true.From this point of view, there is a truth property: It is simply theproperty that all true propositions have.

On the other hand, when we say that two things share a property ofFness, we often mean more than simply that they are both\(F\). We often mean that two things that are \(F\) have someunderlying nature in common, for example, that there is a commonexplanation as to why they are both \(F\). It is in this second claimthat deflationists have in mind when they say that truth is not asubstantive property. Thus, in the case of our example, what, ifanything, explains the truth of (3) is that Caracas is the capital ofVenezuela, and what explains this is the political history ofVenezuela. On the other hand, what, if anything, explains the truth of(4) is that the earth revolves around the sun, and what explains thisis the physical nature of the solar system. The physical nature of thesolar system, however, has nothing to do with the political history ofVenezuela (or if it does, the connections are completely accidental!)and to that extent there is no shared explanation as to why (3) and(4) are both true. Therefore, in this substantive sense, they have noproperty in common.

It will help to bring out the contrast being invoked here if weconsider two properties distinct from a supposed property of beingtrue: the property of being a game and the property of being a mammal.Consider the games of chess and catch. Do both of these have theproperty of being a game? Well, in one sense, they do: they are bothgames that people can play. On the other hand, however, there is nocommon explanation as to why each counts as a game (cf. Wittgenstein1953, §66). We might then say that being a game is not asubstantive property and mean just this. But now compare the propertyof being a mammal. If two things are mammals, they have the propertyof being a mammal, but in addition there is some common explanation asto why they are both mammals – both are descended from the samefamily of creatures, say. According to one development ofdeflationism, the property of being true is more like the property ofbeing a game than it is like the property of being a mammal.

The comparisons between being true, being a game, and being a mammalare suggestive, but they still do not nail down exactly what it meansto say that truth is not a substantive property. The contemporaryliterature on deflationism contains several different approaches tothe idea. One such approach, which we will consider in detail inSection 4.1, involves denying that truth plays an explanatory role.Another approach, pursuing an analogy between being true and existing,describes truth as a “logical property” (for example,Field 1992, 322; Horwich 1998a, 37; Künne 2003, 91). A furtherapproach appeals toDavid Lewis’s (1983, 1986) view that, while every set of entities underwrites aproperty, there is a distinction betweensparse, ornatural, properties and more motley or disjointedabundant properties. On this approach, a deflationist mightsay that there is an abundant property of being true rather than asparse one (cf. Edwards 2013, Asay 2014, Kukla and Winsberg 2015, andArmour-Garb forthcoming). A different metaphysical idea may be toappeal to the contemporary discussion of grounding and the distinctionbetween groundable and ungroundable properties. In this context, agroundable property is one that is capable of being grounded in someother property, whether or not it is in fact grounded; an ungroundableproperty is a property that is not groundable (see Dasgupta 2015, 2016and Rabin 2020). From this point of view, a deflationist might saythat being true is an ungroundable property. Hence it is unlikeordinary, sparse/natural properties, such as being iron, which areboth capable of being grounded and are grounded, and it is also unlikefundamental physical properties, such as being a lepton, which arecapable of being grounded (in some other possible world) but are not(actually) grounded. We will not try to decide here which of thesedifferent views of properties is correct but simply note thatdeflationists who want to claim that there is a truth property, justnot a substantive one, have options for explaining what thismeans.

1.3 The Utility of the Concept of Truth

In light of the two central ideas discussed so far – the ideathat the equivalence schema is exhaustive of the notion of truth andthe idea that there is no substantive truth property – you mightwonder why we have a concept of truth in the first place. After all,contrast this question with the explanation of why we have the conceptof mammals. A natural suggestion is that it allows us to think andtalk about mammals and to develop theories of them. For deflationism,however, as we have just seen, being true is completely different frombeing a mammal; why then do we have a concept of truth? (An analogousquestion might be asked about the word ‘true’, i.e., whywe have the word ‘true’ and related words in our languageat all. In the following discussion we will not discriminate betweenquestions about the concept of truth and questions about the word‘true’ and will move back and forth between them.)

The question of why we have the concept of truth allows us tointroduce a third central theme in deflationism, which is an emphasisnot merely on the property of truth but on the concept of truth, or,equivalently for present purposes, on the word ‘true’ (cf.Leeds 1978). Far from supposing that there is no point having theconcept of truth, deflationists are usually at pains to point out thatanyone who has the concept of truth is in possession of a very usefulconcept indeed; in particular, anyone who has this concept is in aposition to express generalizations that would otherwise requirenon-standard logical devices, such as sentential variables andquantifiers for them.

Suppose, for example, that Jones for whatever reason decides thatSmith is an infallible guide to the nature of reality. We might thensay that Jones believes everything that Smith says. To say this much,however, is not to capture the content of Jones’s belief. Inorder to do that we need some way of generalizing on the embeddedsentence positions in a claim like:

(5)

If Smith says that birds are dinosaurs, then birds aredinosaurs.

To generalize on the relationship indicated in (5), beyond just whatSmith says about birds to anything she might say, what we want to dois generalize on the embedded occurrences of ‘birds aredinosaurs’. So, we need a (declarative) sentential variable,‘\(p\)’, and a universal quantifier governing it. What wewant is a way of capturing something along the lines of

(6)

For all \(p\), if Smith says that \(p\), then \(p.\)

The problem is that we cannot formulate this in English with our mostfamiliar way of generalizing because the ‘\(p\)’ in theconsequent is in a sentence-in-use position, rather than mentioned ornominalized context (as it is in the antecedent), meaning that thisformal variable cannot be replaced with a familiar Englishobject-variable expression, e.g., ‘it’.

This is where the concept of truth comes in. What we do in order togeneralize in the way under consideration is employ the truthpredicate with an object variable to produce the sentence,

(7)

For all \(x\), if what Smith said \(= x\), then \(x\) istrue.

Re-rendering the quasi-formal (7) into natural language yields,

(8)

Everything is such that, if it is what Smith said, then it istrue.

Or, to put the same thing more colloquially:

(9)

Everything Smith says is true.

The equivalence schema (ES-prop) allows us to use (7) (and therefore(9)) to express what it would otherwise require the unstatable (6) toexpress. For, on the basis of the schema, there is always anequivalence between whatever goes in for a sentence-in-use occurrenceof the variable ‘\(p\)’ and a context in which thatfilling of the sentential variable is nominalized. This reveals howthe truth predicate can be used to provide a surrogate for sententialvariables, simulating this non-standard logical device while stilldeploying the standard object variables already available in ordinarylanguage (‘it’) and the usual object quantifiers(‘everything’) that govern them.

This is how the use of the truth predicate in (9) gives us the contentof Jones’s belief. And the important point for deflationists isthat we could not have stated the content of this belief unless we hadthe concept of truth (the expression ‘true’). In fact, formost deflationists, it is this feature of the concept of truth –its role in the formation of these sorts of generalizations –that explains why we have a concept of truth at all. This is, as it isoften put, theraison d’être of the concept oftruth (cf. Field 1994a and Horwich 1998a).

2. History of Deflationism

According to Michael Dummett (1959 [1978]), deflationism originateswithGottlob Frege, as expressed in this famous quote by the latter:

It is … worthy of notice that the sentence ‘I smell thescent of violets’ has just the same content as the sentence‘It is true that I smell the scent of violets’. So itseems, then, that nothing is added to the thought by my ascribing toit the property of truth. (Frege 1918, 6)

This passage suggests that Frege embraces a deflationary view inposition \(\mathbf{B}\) (in the chart above), namely, an analyticpropositionalist version of deflationism. But this interpretation ofhis view is not so clear. As Scott Soames (1999, 21ff) points out,Frege (ibid.) distinguishes what we will call “opaque”truth ascriptions, like ‘My conjecture is true’, fromtransparent truth-ascriptions, like the one mentioned in the quotefrom Frege. Unlike with transparent cases, in opaque instances, onecannot simply strip ‘is true’ away and obtain anequivalent sentence, since the result is not even a sentence atall.

Frank Ramsey is the first philosopher to have suggested a position like\(\mathbf{B}\) (although he does not really accept propositions asabstract entities (see Ramsey 1927 (34–5) and 1929 (7)), despitesometimes talking in terms of propositions):

Truth and falsity are ascribed primarily to propositions. Theproposition to which they are ascribed may be either explicitly givenor described. Suppose first that it is explicitly given; then it isevident that ‘It is true that Caesar was murdered’ meansno more than that Caesar was murdered, and ‘It is false thatCaesar was murdered’ means no more than Caesar was not murdered.…. In the second case in which the proposition is described andnot given explicitly we have perhaps more of a problem, for we getstatements from which we cannot in ordinary language eliminate thewords ‘true’ or ‘false’. Thus if I say‘He is always right’, I mean that the propositions heasserts are always true, and there does not seem to be any way ofexpressing this without using the word ‘true’. But supposewe put it thus ‘For all \(p\), if he asserts \(p\), \(p\) istrue’, then we see that the propositional function \(p\) is trueis simply the same as \(p\), as e.g. its value ‘Caesar wasmurdered is true’ is the same as ‘Caesar wasmurdered’. (Ramsey 1927, 38–9)

On Ramsey’s redundancy theory (as it is often called), the truthoperator, ‘it is true that’ adds no content when prefixedto a sentence, meaning that in the instances of what we can think ofas the truth-operator version of (ES),

(ES-op)

It is true that \(p\) iff \(p\),

the left- and right-hand sides are meaning-equivalent. But Ramseyextends his redundancy theory beyond just the transparent instances oftruth-talk, maintaining that the truth predicate is, in principle,eliminable even in opaque ascriptions of the form ‘\(B\) istrue’ (which he (1929, 15, n. 7) explains in terms of sententialvariablesvia a formula along the lines of ‘\(\existsp\) (\(p \amp B\) is a belief that \(p\))’) and in explicitlyquantificational instances, like ‘Everything Einstein said istrue’ (explained as above). As the above quote illustrates,Ramsey recognizes that in truth ascriptions like these the truthpredicate fills a grammatical need, which keeps us from eliminating italtogether, but he held that even in these cases it contributes nocontent to anything said using it.

A.J. Ayer endorses a view similar to Ramsey’s. The following quote showsthat he embraces a meaning equivalence between the two sides of theinstances of both the sentential (position \(\mathbf{A})\) andsomething like (since, despite his use of the expression‘proposition’ to meansentence, he also considersinstances of truth-talk involving the prefix ‘it is truethat’, which could be read as employing‘that’-clauses) the propositional (position\(\mathbf{B})\) version of (ES).

[I]t is evident that a sentence of the form “\(p\) istrue” or “it is true that \(p\)” the reference totruth never adds anything to the sense. If I say that it is true thatShakespeare wroteHamlet, or that the proposition“Shakespeare wroteHamlet” is true, I am sayingno more than that Shakespeare wroteHamlet. Similarly, if Isay that it is false that Shakespeare wrote theIliad, I amsaying no more than that Shakespeare did not write theIliad.And this shows that the words ‘true’ and‘false’ are not used to stand for anything, but functionin the sentence merely as assertion and negation signs. That is tosay, truth and falsehood are not genuine concepts. Consequently, therecan be no logical problem concerning the nature of truth. (Ayer 1935,28. Cf. Ayer 1936 [1952, 89])

Ludwig Wittgenstein, under Ramsey’s influence, makes claims with strong affinitiesto deflationism in his later work. We can see a suggestion of anendorsement of deflationary positions \(\mathbf{A}\) or \(\mathbf{B}\)in his (1953, §136) statement that “\(p\) is true \(=p\)” and “\(p\) is false = not-\(p\)”, indicatingthat ascribing truth (or falsity) to a statement just amounts toasserting that very proposition (or its negation). Wittgenstein alsoexpresses this kind of view in manuscripts from the 1930s, where heclaims, “What he says is true = Things are as he says” and“[t]he word ‘true’ is used in contexts such as‘What he says is true’, but that says the same thing as‘He says \(\ldquo p\rdquo,\) and \(p\) is thecase’”. (Wittgenstein 1934 [1974, 123]) and 1937 [2005,61]), respectively)

Peter Strawson’s views on truth emerge most fully in his 1950 debate withJ.L. Austin. In keeping with deflationary position \(\mathbf{B}\), Strawson (1950,145–7) maintains that an utterance of ‘It is true that\(p\)’ just makes the same statement as an utterance of‘\(p\)’. However, in Strawson 1949 and 1950, he furtherendorses aperformative view, according to which an utteranceof a sentence like ‘That is true’ mainly functions to dosomethingbeyond mere re-assertion. This represents a shiftto an account of what the expression ‘true’does,from traditional accounts of what truth is, or even accounts of what‘true’ means.

Another figure briefly mentioned above who looms large in thedevelopment of deflationism isAlfred Tarski, with his (1935 [1956] and 1944) identification of a precise criterionof adequacy for any formal definition of truth: its implying all ofthe instances of what is sometimes called “Convention (T)”or “the (T)-schema”,

(T)

\(X\) is true if, and only if, \(p\).

To explain this schema a bit more precisely, in its instances the‘\(X\)’ gets replaced by a name of a sentence from theobject-languagefor which the truth predicate is beingdefined, and the ‘\(p\)’ gets replaced by a sentence thatis a translation of that sentence into the meta-language in which thetruth predicate is being defined. For Tarski, the ‘if and onlyif’ deployed in any instance of (T) expresses just a materialequivalence, putting his view at position \(\mathbf{E}\) in the chartfrom Section 1.1. Although this means that Tarski is not adeflationist himself (cf. Field 1994a, Ketland 1999, and Patterson2012), there is no denying the influence that his work and itspromotion of the (T)-schema have had on deflationism. Indeed, someearly deflationists, such asW.V.O. Quine and Stephen Leeds, are quite explicit about taking inspiration fromTarski’s work in developing their “disquotational”views, as is Horwich in his initial discussion of deflationism. Evencritics of deflationism have linked it with Tarski: Hilary Putnam(1983b, 1985) identifies deflationists as theorists who “referto the work of Alfred Tarski and to the semantical conception oftruth” and who take Tarski’s work “as a solution tothe philosophical problem of truth”.

The first fully developed deflationary view is the one that Quine(1970 [1986, 10–2]) presents. Given his skepticism about theexistence of propositions, Quine takes sentences to be the primaryentities to which ‘is true’ may be applied, making theinstances of (ES-sent) the equivalences that he accepts. He defines acategory of sentence that he dubs “eternal”, viz.,sentence types that have all their indexical/contextual factorsspecified, the tokens of which always have the same truth-values. Itis for these sentences that Quine offers his disquotational view. Ashe (ibid., 12) puts it,

This cancellatory force of the truth predicate is explicit inTarski’s paradigm:

‘Snow is white’ is true if and only if snow is white.

Quotation marks make all the difference between talking about wordsand talking about snow. The quotation is a name of a sentence thatcontains the name, namely ‘snow’, of snow. By calling thesentence true, we call snow white. The truth predicate is a device ofdisquotation.

As this quote suggests, Quine sees Tarski’s formal work ondefining truth predicates for formalized languages and his criterionof adequacy for doing so as underwriting a disquotational analysis ofthe truth predicate. This makes Quine’s view a different kind ofposition-\(\mathbf{A}\) account, since he takes the left-hand side ofeach instance of (ES-sent) to be, as we will put it (since Quinerejects the whole idea of meaning and meaning equivalence), somethinglike a mere syntactic variant of the right-hand side. This also meansthat Quine’s version of deflationism departs from inflationismby rejecting the latter’s presupposition that truth predicatesfunction todescribe the entities they get applied to, theway that other predicates, such as ‘is metal’, do.

Quine also emphasizes the importance of the truth predicate’srole as a means for expressing the kinds of otherwise inexpressiblegeneralizations discussed in Section 1.3. As he (1992, 80–1)explains it,

The truth predicate proves invaluable when we want to generalize alonga dimension that cannot be swept out by a general term … Theharder sort of generalization is illustrated by generalization on theclause ‘time flies’ in ‘If time flies then timeflies’…. We could not generalize as in ‘All men aremortal’ because ‘time flies’ is not, like‘Socrates’, a name of one of a range of objects (men) overwhich to generalize. We cleared this obstacle bysemanticascent: by ascending to a level where there were indeed objectsover which to generalize, namely linguistic objects, sentences.

So, if we want to generalize on embedded sentence-positions withinsome sentences, “we ascend to talk of truth and sentences”(Quine 1970 [1986, 11]). This maneuver allows us to “affirm someinfinite lot of sentences that we can demarcate only by talking aboutthe sentences” (ibid., 12).

Leeds (1978) (following Quine) makes it clear how the truth predicateis crucial for extending the expressive power of a language, despitethe triviality that disquotationalism suggests for the transparentinstances of truth-talk. He (ibid., 121) emphasizes the logical roleof the truth predicate in the expression of certain kinds ofgeneralizations that would otherwise be inexpressible in naturallanguage. Leeds, like Quine, notes that a central utility of the truthpredicate, in virtue of its yielding every instance of (ES-sent), isthe simulation of quantification into sentence-positions. But, unlikeQuine, Leeds glosses this logical role in terms of expressingpotentially infinite conjunctions (for universal generalization) orpotentially infinite disjunctions (for existential generalization).The truth predicate allows us to use the ordinary devices offirst-order logic in ways that provide surrogates for the non-standardlogical devices this would otherwise require. Leeds is also clearabout accepting the consequences of deflationism, that is, of takingthe logically expressive role of the truth predicate to exhaust itsfunction. In particular, he points out that there is no need to thinkthat truth plays any sort ofexplanatory role. We will returnto this point in Section 4.1.

Dorothy Grover, Joseph Camp, and Nuel Belnap (1975) develop adifferent variety of deflationism that they call a“prosentential theory”. This theory descends principallyfrom Ramsey’s views. In fact, Ramsey (1929, 10) made what isprobably the earliest use of the term ‘pro-sentence’ inhis account of the purpose of truth-talk. Prosentences are explainedas the sentence-level analog of pronouns. As in the case of pronouns,prosentences inherit their content anaphorically from other linguisticitems, in this case from some sentence typically called theprosentence’s “anaphoric antecedent” (although itneed not actually occur before the prosentence). As Grover,etal. develop this idea, this content inheritance can happen in twoways. The most basic one is called “lazy” anaphora. Herethe prosentence could simply be replaced with a repetition of itsantecedent, as in the sort of case that Strawson emphasized, where onesays “That is true” after someone else has made anassertion. According to Grover,et al., this instance oftruth-talk is a prosentence that inherits its content anaphoricallyfrom the other speaker’s utterance, so that the two speakersassert the same thing. As a result, Grover,et al. would takethe instances of (ES) to express meaning equivalences, but since they(ibid., 113–5) do not take the instances of truth-talk on theleft-hand sides of these equivalences to say anythingaboutany named entities, they would not read (ES) as either (ES-sent) or(ES-prop) on their standard interpretations. So, while theirprosententialism is similar to views in position \(\mathbf{A}\) or inposition \(\mathbf{B}\) in the chart above, it is also somewhatdifferent from both.

Grover,et al.’s project is to develop the theory“that ‘true’ can be thought of always as part of aprosentence” (ibid., 83). They explain that ‘it istrue’ and ‘that is true’ are generally availableprosentences that can go into any sentence-position. They considerthese expressions to be “atomic” in the sense of not beingsusceptible to a subject-predicate analysis giving the‘that’ or ‘it’ separate references (ibid.,91). Both of these prosentences can function in the “lazy”way, and Grover,et al. claim (ibid., 91–2, 114) that‘it is true’ can also operate as a quantificationalprosentence (i.e., a sentential variable), for example, in are-rendering of a sentence like,

(9)

Everything Smith says is true.

in terms of a “long-form” equivalent claim, such as

(8′)

Everything is such that, if Smith says that it is true, then it istrue.

One immediate concern that this version of prosententialism facespertains to what one might call the “paraphrasticgymnastics” that it requires. For example, a sentence like‘It is true that humans are causing climate change’ issaid to have for its underlying logical form the same form as‘Humans are causing climate change. That is true’ (ibid.,94). As a result, when one utters an instance of truth-talk of theform ‘It is true that \(p\)’, one states the content ofthe sentence that goes in for ‘\(p\)’twice. Incases of quotation, like “‘Birds are dinosaurs’ istrue”, Grover,et al. offer the following rendering,‘Consider: Birds are dinosaurs. That is true’ (ibid.,103). But taking this as the underlying form of quotational instanceof truth-talk requires rejecting the standard view that puttingquotation marks around linguistic items forms names of those items.These issues raise concerns regarding the adequacy of this version ofprosententialism.

3. The Varieties of Contemporary Deflationism

In this section, we explain the details of three prominent,contemporary accounts and indicate some concerns peculiar to each.

3.1 Minimalism

Minimalism is the version of deflationism that diverges the least frominflationism because it accepts many of the standard inflationarypresuppositions, including that ‘is true’ is a predicateused to describe entities as having (or lacking) a truth property.What makes minimalism a version of deflationism is its denial ofinflationism’s final assumption, namely, that the propertyexpressed by the truth predicate has a substantive nature. Drawinginspiration from Leeds (1978), Horwich (1982, 182) actually coins theterm ‘deflationism’ while describing “thedeflationary redundancy theory which denies the existence of surplusmeaning and contends that Tarski’s schema [”\(p\)“is true iff \(p\)] is quite sufficient to capture the concept.”Minimalism, Horwich’s mature deflationary position (1998a [FirstEdition, 1990]), adds to this earlier view. In particular, Horwich(ibid., 37, 125, 142) comes to embrace the idea that ‘istrue’ does express a property, but it is merely a “logicalproperty” (cf. Field 1992), rather than any substantive ornaturalistic property of truth with an analyzable underlying nature(Horwich 1998a, 2, 38, 120–1).

On the basis of natural language considerations, Horwich (ibid.,2–3, 39–40) holds that propositions are what the alethiclocutions describe directly. Any other entities that we can properlycall true are so only derivatively, on the basis of having somerelation to true propositions (ibid., 100–1 and Horwich 1998b,82–5). This seems to position Horwich well with respect toexplaining the instances of truth-talk that cause problems for Quineand Leeds, e.g., those about beliefs and theories. Regarding truthapplied directly to propositions, however, Horwich (1998a, 2–3)still explicitly endorses the thesis that Leeds emphasizes about theutility of the truth predicate (and, Horwich adds, the concept itexpresses), namely, that it “exists solely for the sake of acertain logical need”. While Horwich (ibid., 138–9) goesso far as to claim that the concept of truth has a“non-descriptive” function, he does not follow Quine andLeeds all the way to their rejection of the assumption that thealethic predicates function to describe truth-bearers. Rather, his(ibid., 31–3, 37) point of agreement with them is that themain function of the truth predicate is its role in providinga means for generalizing on embedded sentence positions, rather thansome role in the indication of specifically truth-involving states ofaffairs. Even so, Horwich (ibid., 38–40) still contends that theinstances of truth-talk do describe propositions, in the sense thatthey make statementsabout them, and they do so byattributing a property to those propositions.

The version of (ES) that Horwich (1998a, 6) makes the basis of histheory is what he also calls “the equivalence schema”,

(E)

It is true that \(p\) if and only if \(p\).

Since he takes truth-talk to involve describing propositions with apredicate, Horwich considers ‘it is true that \(p\)’ to bejust a trivial variant of ‘The proposition that \(p\) istrue’, meaning that his (E) is a version of (ES-prop) ratherthan of Ramsey’s (ES-op). He also employs the notation‘\(\langle p\rangle\)’ as shorthand specifically for‘the proposition that \(p\)’, generating a furtherrendering of his equivalence schema (ibid., 10) that we can clearlyrecognize as a version of (ES-prop), namely

(E)

\(\langle p\rangle\) is true iff \(p\).

Horwich considers the instances of (E) to constitute the axioms ofboth an account of the property of truth and an account of the conceptof truth, i.e., what is meant by the word ‘true’ (ibid.,136). According to minimalism, the instances of (E) are explanatorilyfundamental, which Horwich suggests is a reason for taking them to benecessary (ibid., 21, n. 4). This, combined with his view that theequivalence schema applies to propositions, places his minimalism inposition \(\mathbf{D}\) in the chart given in Section 1.1. Theinstances of (ES-prop) are thus explanatory of the functioning of thetruth predicate (of its role as a de-nominalizer of‘that’-clauses (ibid., 5)), rather than being explained bythat functioning (as the analogous equivalences are for bothdisquotationalism and prosententialism). Moreover, Horwich (ibid., 50,138) claims that they are also conceptually basic andapriori. He (ibid., 27–30, 33, 112) denies that truth admitsof any sort of explicit definition or reductive analysis in terms ofother concepts, such as reference or predicate-satisfaction. In fact,Horwich (ibid., 10–1, 111–2, 115–6) holds that theseother semantic notions should both be given their own, infinitelyaxiomatized, minimalist accounts, which would then clarify thenon-reductive nature of the intuitive connections between them and thenotion of truth.

Horwich (ibid., 27–30) maintains that the infinite axiomaticnature of minimalism is unavoidable. He (ibid., 25) rejects thepossibility of a finite formulation of minimalismvia the useofsubstitutional quantification. On the usual understanding of this non-standard type ofquantification, the quantifiers govern variables that serve to markplaces in linguistic strings, indicating that either all or some ofthe elements of an associated substitution class of linguistic itemsof a particular category can be substituted in for the variables.Since it is possible for the variables so governed to take sentencesas their substitution items, this allows for a type of quantificationgoverning sentence positions in complex sentences. Using this sort ofsentential substitutional quantification, the thought is, one canformulate a finite general principle that expresses Horwich’saccount of truth as follows:

(GT)

\(\forall x\, (x\) is true iff \(\Sigma p (x = \langle p\rangle\amp p)),\)

where ‘\(\Sigma\)’ is the existential substitutionalquantifier. (GT) is formally equivalent to the formulation that MarianDavid (1994, 100) presents as disquotationalism’s definition of‘true sentence’, here formulated for propositions instead.Horwich’s main reason for rejecting the proposed finiteformulation of minimalism, (GT), is that an account of substitutionalquantifiers seems (contra David 1994, 98–9) to require an appealto truth (since the quantifiers are explained as expressing that atleast one or that every item in the associated substitution classyields atrue sentence when substituted in for the governedvariables), generating circularity concerns (Horwich 1998a,25–6).

Moreover, on Horwich’s (ibid., 4, n. 1; Cf. 25, 32–3)understanding, the point of the truth predicate is to provide asurrogate for substitutional quantification and sentence-variables innatural language, so as “to achieve the effect of generalizingsubstitutionally over sentences … but by means of ordinary[quantifiers and] variables (i.e., pronouns), which range overobjects” (italics original). Horwich maintains that theinfinite “list-like” nature of minimalism poses no problemfor the view’s adequacy with respect to explaining all of ouruses of the truth predicate, and the bulk of Horwich 1998a attempts toestablish just that. However, Anil Gupta (1993a, 365) has pointed outthat minimalism’s infinite axiomatization in terms of theinstances of (E) for every (non-paradox-inducing) proposition makes itmaximally ideologically complex, in virtue of involving every otherconcept. (Moreover, the overtly “fragmented” nature of thetheory also makes it particularly vulnerable to the GeneralizationProblem that Gupta has raised, which we discuss in Section 4.5,below.)

Christopher Hill (2002) attempts to deal with some of the problemsthat Horwich’s view faces, by presenting a view that he takes tobe a newer version of minimalism, replacing Horwich’sequivalence schema with a universally quantified formula, employing akind of substitutional quantification to provide a finite definitionof ‘true thought (proposition)’. Hill’s (ibid., 22)formulation of his account,

(S)

For any object \(x\), \(x\) is true if and only if \((\Sigma p)((x=\) the thought that \(p)\) and \(p)\),

is formally similar to the formulation of minimalism in terms of (GT)that Horwich rejects, but to avoid the circularity concerns drivingthat rejection, Hill’s (ibid., 18–22) idea is to offerintroduction and elimination rules in the style of Gerhard Gentzen(1935 [1969]) as a means for defining the substitutional quantifiers.Horwich (1998a, 26) rejects even this inference-rule sort of approach,but he directs his critique against defininglinguisticsubstitutional quantification this way. Hill takes his substitutionalquantifiers to apply to thoughts (propositions) instead of sentences.But serious concerns have been raised regarding the coherence of thisnon-linguistic notion of substitutional quantification (cf. David2006, Gupta 2006b, Simmons 2006). As a result, it is unclear thatHill’s account is an improvement on Horwich’s version ofminimalism.

3.2 Disquotationalism

Like minimalism, disquotationalism agrees with inflationary accountsof truth that the alethic locutions function as predicates, at leastlogically speaking. However, as we explained in discussingQuine’s view in Section 2, disquotationalism diverges frominflationary views (and minimalism) at their shared assumption thatthese (alethic) predicates serve todescribe the entitiespicked out by the expressions with which they are combined,specifically as having or lacking a certain property.

Although Quine’s disquotationalism is inspired by Tarski’srecursive method for defining a truth predicate, that method is notwhat Quine’s view emphasizes. Field’s contemporarydisquotationism further departs from that aspect of Tarski’swork by looking directly to the instances of the (T)-schema that therecursive method must generate in order to satisfy Tarski’scriterion of material adequacy. Tarski himself (1944, 344–5)suggests at one point that each instance of (T) could be considered a“partial definition” of truth and considers (butultimately rejects; see Section 4.5) the thesis that a logicalconjunction of all of these partial definitions amounts to a generaldefinition of truth (for the language that the sentences belonged to).Generalizing slightly from Tarski, we can call this alternativeapproach “(T)-schema disquotationalism”, in contrast withthe Tarski-inspired approach that David (1994, 110–1) calls“recursive disquotationalism”. Field (1987, 1994a)develops a version of (T)-schema disquotationalism that he calls“pure disquotational truth”, focusing specifically on theinstances of his preferred version of (ES), the “disquotationalschema” (Field 1994a, 258),

(T[/ES-sent])

“\(p\)” is true if and only if \(p\).

Similar to the “single principle” formulation, (GT),rejected by Horwich (but endorsed by Hill), Field (ibid., 267) allowsthat one could take a “generalized” version of(T/ES-sent), prefixed with a universal substitutional quantifier,‘\(\Pi\)’, as having axiomatic status, or one couldincorporate schematic sentence variables directly into one’stheorizing language and reason directly with (T/ES-sent) as a schema(cf. ibid., 259). Either way, in setting out his version ofdeflationism, Field (ibid., 250), in contrast with Horwich, does nottake the instances of his version of (ES) as fundamental but insteadas following from the functioning of the truth predicate. OnField’s reading of (T/ES-sent), the use of the truth predicateon the left-hand side of an instance does not add any cognitivecontent beyond that which the mentioned utterance has (for thespeaker) on its own when used (as on the right-hand-side of(T/ES-sent)). As a result, each instance of (T/ES-sent) “holdsof conceptual necessity, that is, by virtue of the cognitiveequivalence of the left and right hand sides” (ibid., 258). Thisplaces Field’s deflationism also in position \(\mathbf{A}\) inthe chart from Section 1.1.

Following Leeds and Quine, Field (1999, 533–4) sees the centralutility of a purely disquotational truth predicate to be providing forthe expression of certain “fertile generalizations” thatcannot be made without using the truth predicate but which do notreally involve the notion of truth. Field (1994a, 264) notes that thetruth predicate plays “an important logical role: it allows usto formulate certain infinite conjunctions and disjunctions thatcan’t be formulated otherwise [n. 17: at least in a languagethat does not containsubstitutional quantifiers]”.

Field’s disquotationalism addresses some of the worries thatarose for earlier versions of this variety of deflationism, due totheir connections with Tarski’s method of defining truthpredicates. It also explains how to apply a disquotational truthpredicate to ambiguous and indexical utterances, thereby going beyondQuine’s (1970 [1986]) insistence on taking eternal sentences asthe subjects of the instances of (ES-sent) (cf. Field 1994a,278–81). So, Field’s view addresses some of the concernsthat David (1994, 130–66) raises for disquotationalism. However,an abiding concern about this variety of deflationism is that it is anaccount of truth as applied specifically to sentences. This opens thedoor to a version of the complaint that Strawson (1950) makes againstAustin’s account of truth, that it is not one’s act ofstating [here: the sentence one utters] but what thereby gets statedthat is the target of a truth ascription. William Alston (1996, 14)makes a similar point. While disquotationalists do not worry muchabout this, this scope restriction might strike others as problematicbecause it raises questions about how we are to understand truthapplied to beliefs or judgments, something that Hill (2002) worriesabout. Field (1978) treats beliefs as mental states relating thinkersto sentences (of a language of thought). But David (1994, 172–7)raises worries for applying disquotationalism to beliefs, even in thecontext of an account like Field’s. The view that we believesentences remains highly controversial, but it is one that, it seems,a Field-style disquotationalist must endorse. Similarly, suchdisquotationalists must take scientific theories to consist of sets ofsentences, in order for truth to be applicable to them. This too runsup against Strawson’s complaint because it suggests that onecould not state the same theory in a different language. These sortsof concerns continue to press for disquotationalists.

3.3 Prosententialism

As emerges from the discussion of Grover,et al. (1975) inSection 2, prosententialism is the form of deflationism that contraststhe most with inflationism, rejecting even the latter’s initialassumption that the alethic locutions function as predicates. Partlyin response to the difficulties confronting Grover,etal.’s prosentential account, Robert Brandom (1988 and 1994)has developed a variation on their view with an importantmodification. In place of taking the underlying logic of‘true’ as having this expression occur only as anon-separable component of the semantically atomic prosententialexpressions, ‘that is true’ and ‘it is true’,Brandom treats ‘is true’ as a separableprosentence-formingoperator. “It applies to aterm that is a sentence nominalization or that refers to or picks outa sentence tokening. It yields a prosentence that has that tokening asits anaphoric antecedent” (Brandom 1994, 305). In this way,Brandom’s account avoids most of the paraphrase concerns thatGrover,et al.’s prosententialism faces, while stillmaintaining prosententialism’s rejection of the contention thatthe alethic locutions function predicatively. As a consequence of hisoperator approach, Brandom gives quantificational uses of prosentencesa slightly different analysis. He (re)expands instances of truth-talklike the following,

(9)

Everything Smith says is true.

(10)

Something Jones said is true.

“back” into longer forms, such as

(8*)

For anything one can say, if Smith says it, then it is true.

(11)

For something one can say, Jones said it, and it is true.

and explains only the second ‘it’ as involved in aprosentence. The first ‘it’ in (8*) and (11) stillfunctions as a pronoun, anaphorically linked to a set of nounphrases (sentence nominalizations) supplying objects (sentencetokenings) as a domain being quantified over with standard (as opposedto sentential or “propositional”) quantifiers (ibid.,302).

Brandom presents a highly flexible view that takes ‘istrue’ as a general “denominalizing” device thatapplies to singular terms formed from the nominalization of sentencesbroadly, not just to pronouns that indicate them. A sentence like‘It is true that humans are causing climate change’,consideredvia a re-rendering as ‘That humans arecausing climate change is true’, isalready aprosentence on his view, as is a quote-name case like“‘Birds are dinosaurs’ is true”, and an opaqueinstance of truth-talk like ‘Goldbach’s Conjecture istrue’. In this way, Brandom offers a univocal and broaderprosentential account, according to which, “[i]n each use, aprosentence will have an anaphoric antecedent that determines a classof admissible substituends for the prosentence (in the lazy case, asingleton). This class of substituends determines the significance ofthe prosentence associated with it” (ibid.). As a result,Brandom can accept both (ES-sent) and (ES-prop) – the latterunderstood as involving no commitment to propositions as entities– on readings closer to their standard interpretations, takingthe instances of both to express meaning equivalences. Brandom’saccount thus seems to be located in both position \(\mathbf{A}\) andposition \(\mathbf{B}\) in the chart from Section 1.1, although, aswith any prosententialist view, it still denies that the instances of(ES) say anythingabout either sentences or propositions.

Despite its greater flexibility, however, Brandom’s accountstill faces the central worry confronting prosentential views, namelythat truth-talk really does seem predicative, and not just in itssurface grammatical form but in our inferential practices with it aswell. In arguing for the superiority of his view over that of Grover,et al., Brandom states that “[t]he account of truthtalk should bear the weight of … divergence of logical fromgrammatical form only if no similarly adequate account can beconstructed that lacks this feature” (ibid., 304). One mightfind it plausible to extend this principle beyond grammatical form, tobehavior in inferences as well. This is an abiding concern forattempts to resist inflationism by rejecting its initial assumption,namely, that the alethic locutions function as predicates.

4. Objections to Deflationism

In the remainder of this article, we consider a number of objectionsto deflationism. These are by no means the only objections that havebeen advanced against the approach, but they seem to be particularlyobvious and important ones.

4.1 The Explanatory Role of Truth

The first objection starts from the observation that (a) in certaincontexts an appeal to the notion of truth appears to have anexplanatory role and (b) deflationism seems to be inconsistent withthat appearance. Some of the contexts in which truth seems to have anexplanatory role involve philosophical projects, such as thetheory of meaning (which we will consider below) or explaining the nature ofknowledge. In these cases, the notion of explanation at issue is not so muchcausal as it isconceptual (see Armour-Garb and Woodbridgeforthcoming, for more on this). But the notion of truth seems alsosometimes to play acausal explanatory role, especially withregard to explaining various kinds of success – mainly thesuccess of scientific theories/method (cf. Putnam 1978 and Boyd 1983)and of people’s behavior (cf. Putnam 1978 and Field 1987), butalso the kind of success involved in learning from others (Field1972). The causal-explanatory role that the notion of truth appears toplay in accounts of these various kinds of success has seemed to manyphilosophers to constitute a major problem for deflationism. Forexample, Putnam (1978, 20–1, 38) claims, “the notions of‘truth’ and ‘reference’ have acausal-explanatory role in … anexplanation of thebehavior of scientists and the success of science”, and“the notion of truth can be used in causal explanations –the success of a man’s behavior may, after all, depend on thefact that certain of his beliefs aretrue – and theformal logic of ‘true’ [the feature emphasized bydeflationism] is not all there is to the notion oftruth”.

While a few early arguments against deflationism focus on the role oftruth in explanations of the success of science (see Williams 1986 andFine 1984a, 1984b for deflationary responses to Putnam and Boyd onthis), according to Field (1994a, 271), “the most serious worryabout deflationism is that it can’t make sense of theexplanatory role of truth conditions: e.g., their role in explainingbehavior, or their role in explaining the extent to which behavior issuccessful”. While few theorists endorse the thesis thatexplanations of behavior in general need to appeal to the notion oftruth (even a pre-deflationary Field (1987, 84–5) rejects this,but see Devitt 1997, 325–330, for an opposing position),explanations of the latter, i.e., of behavioralsuccess,still typically proceed in terms of an appeal to truth. This poses aprima facie challenge to deflationary views. To illustratethe problem, consider the role of the truth-value of anindividual’s belief in whether that person succeeds insatisfying her desires. Let us suppose that Mary wants to get to aparty, and she believes that it is being held at 1001 NorthsideAvenue. If her belief is true, then, other things being equal, she islikely to get to the party and get what she wants. But suppose thather belief is false, and the party is in fact being held at 1001Southside Avenue. Then it would be more likely, other things beingequal, that she won’t get what she wants. In an example of thissort, the truth of her belief seems to be playing a particular role inexplaining why she gets what she wants.

Assuming that Mary’s belief is true, and she gets to the party,it might seem natural to say that the latter success occursbecause her belief is true, which might seem to pose aproblem for deflationists. However, truth-involving explanations ofparticular instances of success like this don’t really pose agenuine problem. This is because if we are told the specific contentof the relevant belief, it is possible to replace the apparentlyexplanatory claim that the belief is true with an equivalent claimthat does not appeal to truth. In Mary’s particular case, wecould replace i) the claim that she believes that the party is beingheld at 1001 Northside Avenue, and her belief is true, with ii) theclaim that she believes that the party is being held at 1001 NorthsideAvenue, and the party \(is\) being held at 1001 Northside Avenue. Adeflationist can claim that the appeal to truth in the explanation ofMary’s success just provides an expressive convenience(including, perhaps, the convenience of expressing what wouldotherwise require an infinite disjunction (of conjunctions like ii)),by saying just that what Mary believed was true, if one did not knowexactly which belief Mary acted on) (cf. Horwich 1998a, 22–3,44–6).

While deflationists seem to be able to account for appeals to truth inexplanations of particular instances of success, the explanatory-rolechallenge to deflationism also cites the explanatory role that anappeal to truth appears to play in explaining the phenomenon ofbehavioral success more generally. An explanation of this sort mighttake the following form:

[1]

People act (in general) in such a way that their goals will beobtained (as well as possible in the given situation), or in such away that their expectations will not be frustrated, …if their beliefs are true.

[2]

Many beliefs [people have about how to attain their goals]are true.

[3]

So, as a consequence of [1] and [2], people have a tendency toattain certain kinds of goals. (Putnam 1978, 101)

The generality of [1] in this explanation seems to cover more casesthan any definite list of actual beliefs that someone has couldinclude. Moreover, the fact that [1] supports counterfactuals byapplying to whatever one might possibly believe (about attaininggoals) suggests that it is a law-like generalization. If the truthpredicate played a fundamental role in the expression of anexplanatorylaw, then deflationism would seem to beunsustainable.

A standard deflationary response to this line of reasoning involvesrejecting the thesis that [1] is a law, seeing it (and truth-involvingclaims like it) instead as functioning similarly to how the claim‘What Mary believes is true’ functions in an explanationof her particular instance of behavioral success, just expressing aneven more indefinite, and thus potentially infinite claim. The latteris what makes a claim like [1] seem like an explanatory law, but evenconsidering this indefiniteness, the standard deflationary account of[1] claims that the function of the appeal to the notion of truththere is still just to express a kind of generalization. One way tobring out this response is to note that, similar to the deflationary“infinite disjunction” account of the claim ‘WhatMary believes is true’, generalizations of the kind offered in[1] entail infiniteconjunctions of their instances, whichare claims that can be formulated without appeal to truth. Forexample, in the case of explaining someone, \(A\), accomplishing theirgoal of getting to a party, deflationsts typically claim that the roleof citing possession of a true belief is really just to express aninfinite conjunction with something like the following form:

If \(A\) believes that the party is 1001 Northside Avenue, and theparty is at 1001 Northside Avenue, then \(A\) will get what they want;and if \(A\) believes that the party is at 1001 Southside Avenue, andthe party is at 1001 Southside Ave, then \(A\) will get what theywant; and if \(A\) believes that party is at 17 Elm St, and the partyis at 17 Elm St, then \(A\) will get what they want; … and soon.

The equivalence schema (ES) allows one to capture this infiniteconjunction (of conditionals) in a finite way. For, on the basis ofthe schema, one can reformulate the infinite conjunction as:

If \(A\) believes that the party is 1001 Northside Avenue, and thatthe party is 1001 Northside Avenue is true, then \(A\) will get whatthey want; and if \(A\) believes that the party is at 1001 SouthsideAvenue, and that the party is at 1001 Southside Avenue is true, then\(A\) will get what they want, and if \(A\) believes that the party isat 17 Elm Street, and that the party is at 17 Elm Street is true, then\(A\) will get what they want; … and so on.

In turn, this (ES)-reformulated infinite conjunction can be expressedas a finite statement with a universal quantifier ranging overpropositions:

For every proposition \(x\), if what \(A\) believes \(= x\), and \(x\)is true, then \(A\) will get what they want, other things being equal.

The important point for a deflationist is that one could not expressthe infinite conjunction regarding the agent’s beliefs andbehavioral success unless one had the concept of truth. Butdeflationists also claim that this is all that the notion of truth isdoing here and in similar explanations (cf. Leeds 1978, 1995; Williams1986, Horwich 1998a).

How successful is this standard deflationary response? There areseveral critiques in the literature. Some (e.g., Damnjanovic 2005)argue that there is no distinction in the first place betweenappearing in a causal-explanatory generalization and being acausal-explanatory property. After all, suppose it is a truegeneralization that metal objects conduct electricity. That wouldnormally be taken as sufficient to show that being metal is acausal-explanatory property that one can cite in explaining whysomething conducts electricity. But isn’t this a counter, then,to deflationism’s thesis that, assuming there is a property oftruth at all, it is at most an insubstantial one? If a property is acausal or explanatory property, after all, it is hard to view it asinsubstantial.

The reasoning at issue here may be presented conveniently by expandingon the general argument considered above and proceeding from anapparently true causal generalization to the falsity of deflationism(ibid.):

P1.

If a person \(A\) has true beliefs, they will get what they want,other things being equal.

C1.

Therefore, if \(A\) has beliefs with the property of being true,\(A\) will get what they want other things being equal.

C2.

Therefore, the property of being true appears in acausal-explanatory generalization.

C3.

Therefore, the property of being true is a causal-explanatoryproperty.

C4.

Therefore, deflationism is false.

Can a deflationist apply the standard deflationary response to thisargument? Doing so would seem to involve rejecting the inference fromC2 to C3. After all, the standard reply would say that the role thatthe appeal to truth plays in P1, the apparent causal generalization,is simply its generalizing role of expressing a potentially infinite,disjointed conjunction of unrelated causal connections (cf. Leeds1995). So, applying this deflationary response basically hinges on theplausibility of rejecting the initial assumption that there is nodistinction between appearing in a causal-explanatory generalizationand being a causal-explanatory property.

It is worth noting two other responses beyond the standard one that adeflationist might make to the reasoning just set out. The firstoption is to deny the step from P1 to C1. This inference involves theexplicit introduction of the property of being true, and, as we haveseen, some deflationists deny that there is a truth property at all(cf. Quine 1970 [1986], Grover,et al. 1975, Leeds 1978,Brandom 1994). But, as we noted above, the idea that there is no truthproperty may be difficult to sustain given the apparent fact that‘is true’ functions grammatically as a predicate.

The second option is to deny the final step from C3 to C4 and concedethat there is a sense in which truth is a causal-explanatory propertyand yet say that it is still not a substantive property (cf.Damnjanovic 2005). For example, some philosophers (e.g., Friedman1974, van Fraassen 1980, Kitcher 1989, Jackson and Pettit 1990) haveoffered different understandings ofscientific explanation and causal explanation, according to which being a causal andexplanatory property might not conflict with being insubstantial(perhaps by being an abundant or ungroundable property). This might beenough to sustain a deflationary position.

The standard deflationary response to the explanatory-role challengehas also met with criticisms focused on providing explanations ofcertain “higher-level” phenomena. Philip Kitcher (2002,355–60) concludes that Horwich’s (1998a, 22–3)application of the standard response, in his account of how the notionof truth functions in explanations of behavioral success, misses themore systematic role that truth plays in explainingpatternsof successful behavior, such as when mean-ends beliefs flow from arepresentational device, like a map. Chase Wrenn (2011) agrees withKitcher that deflationists need to explain systematic as opposed tojust singular success, but against Kitcher he argues thatdeflationists are actually better off than inflationists on thisfront. Will Gamester (2018, 1252–5) raises a different“higher-level factor” challenge, one based on the putativeinability of the standard deflationary account of the role of truth inexplanations of behavioral success to distinguish between coincidentaland non-coincidental success. Gamester (ibid., 1256–7) claimsthat an inflationist could mark and account for the difference betweenthe two kinds of success with an explanation that appeals to thenotion of truth. But it is not clear that a deflationist cannot alsoavail herself of a version of this truth-involving explanation, takingit just as the way of expressing in natural language what one mightformally express with sentential variables and quantifiers (cf. Ramsey1927, 1929; Prior 1971, Wrenn 2021, and Armour-Garb and Woodbridgeforthcoming).

4.2 Propositions Versus Sentences

We noted earlier that deflationism can be presented in either asententialist version or a propositionalist version. Some philosophershave suggested, however, that the choice between these two versionsconstitutes a dilemma for deflationism (Jackson, Oppy, and Smith1994). The objection is that if deflationism is construed inaccordance with propositionalism, then it is trivial, but if it isconstrued in accordance with sententialism, it is false. To illustratethe dilemma, consider the following claim:

(12)

Snow is white is true if and only if snow is white.

Now, does ‘snow is white’ in (12) refer to asentence or a proposition? If, on the one hand, we take (12) to beabout a sentence, then, assuming (12) can be interpreted as making anecessary claim, it is false. On the face of it, after all, it takes alot more than snow’s being white for it to be the case that‘snow is white’ is true. In order for ‘snow iswhite’ to be true, it must be the case not only that snow iswhite, it must, in addition, be the case that ‘snow iswhite’means that snow is white. But this is a factabout language that (12) ignores. On the other hand, suppose we take‘snow is white’ in (12) to denote the propositionthat snow is white. Then the approach looks to be trivial, since theproposition that snow is white is defined as being the one that istrue just in case snow is white. Thus, deflationism faces the dilemmaof being false or trivial.

One response for the deflationist is to remain with thepropositionalist version of their doctrine and accept its triviality.A trivial doctrine, after all, at least has the advantage of beingtrue.

A second response is to resist the suggestion that propositionistdeflationism is trivial. For one thing, the triviality here does nothave its source in the concept of truth, but rather in the concept ofa proposition. Moreover, even if we agree that the proposition thatsnow is white is defined as the one that is true if and only if snowis white, this still leaves open whether truth is a substantiveproperty of that proposition; as such it leaves open whetherdeflationism or inflationism is correct.

A third response to this dilemma is to accept that deflationismappliesinter alia to sentences, but to argue (followingField 1994a) that the sentences to which it applies must beinterpreted sentences, i.e., sentences which already havemeaning attached to them. While it takes more than snow being white tomake the sentence ‘snow is white’ true, when we think ofit as divorced from its meaning, that is not so clear when we treat itas having the meaning it in fact has.

4.3 Correspondence

It is often said to be a platitude that true statements correspond tothe facts. The so-called “correspondence theory of truth”is built around this intuition and tries to explain the notion oftruth by appealing to the notions of correspondence and fact. But evenif one does notbuild one’s approach to truth aroundthis intuition, many philosophers regard it as a condition of adequacyon any approach that it accommodate this correspondence intuition.

It is often claimed, however, that deflationism has trouble meetingthis adequacy condition. One way to bring out the problem here is byfocusing on a particular articulation of the correspondence intuition,one favored by deflationists themselves (e.g., Horwich 1998a).According to this way of spelling it out, the intuition that a certainsentence or proposition “corresponds to the facts” is theintuition that the sentence or proposition is truebecause ofhow the world is; that is, the truth of the proposition isexplained by some fact, which is usually external to theproposition itself. We might express this by saying that someone whoendorses the correspondence intuition so understood would endorse:

(6)

The proposition that snow is white is truebecause snowis white.

The problem with (6) is that, when we combine it with deflationism– or at least with a necessary version of that approach –we can derive something that is plainly false. Anyone who assumes thatthe instances of the equivalence schema are necessary would clearly becommitted to the necessary truth of:

(7)

The proposition that snow is white is true iff snow is white.

And, since (7) is a necessary truth, under that assumption, it is veryplausible to suppose that (6) and (7) together entail:

(8)

Snow is white because snow is white.

But (8) is clearly false. The reason is that the ‘because’in (6) and (8) is a causal or explanatory relation, and plausibly suchrelations must obtain between distinct relata. But the relata in (8)are (obviously) not distinct. Hence, (8) is false, and this means thatthe conjunction of (6) and (7) must be false, and that deflationism isinconsistent with the correspondence intuition. To borrow a phrase ofMark Johnston’s (1989) – who mounts a similar argument ina different context – we might say that if deflationism is true,then what seems to be a perfectly good explanation in (6)goesmissing; if deflationism is true, after all, then (6) isequivalent to (8), and (8) is not an explanation of anything.

One way a deflationist might attempt to respond to this objection isby providing a different articulation of the correspondence intuition.For example, one might point out that the connection between theproposition that snow is white being true and snow’s being whiteis not a contingent connection and suggest that this rules out (6) asa successful articulation of the correspondence intuition. Thatintuition (one might continue) is more plausibly given voice by

(6*)

‘Snow is white’ is true because snow is white.

However, when (6*) is conjoined with (7), one cannot derive theproblematic (8), and thus, one might think, the objection fromcorrespondence might be avoided. Now, certainly this is a possiblesuggestion; the problem with it, however, is that a deflationist whothinks that (6*) is true is most plausibly construed as holding asententialist, rather than a propositionalist, version ofdeflationism. A sententialist version of deflationism will supply aversion of (7), viz.:

(7*)

‘Snow is white’ is true iff snow is white.

which, at least if it is interpreted as a necessary (or analytic)truth, will conspire with (6*) to yield (8). And we are back where westarted.

Another response would be to object that ‘because’ createsanopaque context – that is, the kind of context withinwhich one cannot substitute co-referring expressions and preservetruth. However, for this to work, ‘because’ must create anopaque context of the right kind. In general, we can distinguish twokinds of opaque context:intensional contexts, which allowthe substitution of necessarily co-referring expressions but notcontingently co-referring expressions; andhyperintensional contexts, which do not even allow the substitution of necessarilyco-referring expressions. If the inference from (6) and (7) to (8) isto be successfully blocked, it is necessary that ‘because’creates a hyperintensional context. A proponent of the correspondenceobjection might try to argue that while ‘because’ createsan intensional context, it does not create a hyperintensional context.But since a hyperintensional reading of ‘because’ hasbecome standard fare, this approach remains open to a deflationist andis not anad hoc fix.

A final, and most radical, response would be to reject thecorrespondence intuition outright. This response is not as drastic asit sounds. In particular, deflationists do not have to say thatsomeone who says ‘the proposition that snow is white correspondsto the facts’ is speaking falsely. Deflationists might do betterby saying that such a person is simply using a picturesque or ornateway of saying that the proposition is true, where truth is understoodin accordance with deflationism. Indeed, a deflationist can even agreethat, for certain rhetorical or conversational purposes, it might bemore effective to use talk of “correspondence to thefacts”. Nevertheless, it is important to see that this responsedoes involve a burden, since it involves rejecting a condition ofadequacy that many regard as binding.

4.4 Truth-Value Gaps

According to some metaethicists (moral non-cognitivists or expressivists), moral claims – such as the injunction thatone ought to return people’s phone calls – are neithertrue nor false. The same situation holds, according to somephilosophers of language, for claims that presuppose the existence ofsomething which does not in fact exist, such as the claim that thepresent King of France is bald; for sentences that are vague, such as‘These grains of sand constitute a heap’; and forsentences that are paradoxical, such as those that arise in connectionwith theLiar Paradox. Let us call this thesisthe gap, since it finds a gap in theclass of sentences between those that are true and those that arefalse.

The deflationary approach to truth has seemed to be inconsistent withthe gap, and this has been thought by some (e.g., Dummett 1959 [1978,4] and Holton 2000) to be an objection. The reason for the apparentinconsistency flows from a natural way to extend the deflationaryapproach from truth to falsity. The most natural thing for adeflationist to do is to introduce a falsity schema like:

(F-sent)

‘\(p\)’ is false iff \({\sim}p.\)

Following Holton (1993, 2000), we consider (F-sent) to be the relevantschema for falsity, rather than some propositional schema, since thestandard understanding of a gappy sentence is as one that does notexpress a proposition (cf. Jackson,et al. 1994).

With a schema like (F-sent) in hand, deflationists could say thingsabout falsity similar to what they say about truth: (F-sent) exhauststhe notion of falsity, there is no substantive property of falsity,the utility of the concept of falsity is just a matter of facilitatingthe expression of certain generalizations, etc.

However, there is a seeming incompatibility between (F-sent) and thegap. Suppose, forreductio, that ‘S’ is asentence that is neither true nor false. In that case, it is not thecase that ‘S’ is true, and it is not the case that‘S’ is false. But then, by (ES-sent) and (F-sent), we caninfer that it is not the case that S, and it is not the case thatnot-S; in short: \({\sim}\)S and \({\sim}{\sim}\)S, which is aclassical contradiction. Clearly, then, we must give up one of thesethings. But which one can we give up consistently withdeflationism?

In the context of ethical non-cognitivism, one possible response tothe apparent dilemma is to distinguish between a deflationary accountof truth and a deflationary account of truth-aptitude (cf.Jackson,et al. 1994). By accepting an inflationary accountof the latter, one can claim that ethical statements fail the robustcriteria of “truth-aptitude” (reidentified in terms ofexpression of belief), even if a deflationary view of truth stillallows the application of the truth predicate to them,viainstances of (ES). In the case ofvagueness, one might adopt epistemicism about it and claim that vague sentencesactually have truth-values, we just can’t know them (cf.Williamson 1994. For an alternative, see Field 1994b).

With respect to the Liar Paradox, the apparent conflict betweendeflationism and the gap has led some (e.g., Simmons 1999) to concludethat deflationism is hobbled with respect to dealing with the problem,since most prominent approaches to doing so, stemming from the work ofSaul Kripke (1975), involve an appeal to truth-value gaps. Onealternative strategy a deflationist might pursue in attempting toresolve the Liar is to offer a non-classical logic. Field 2008 adoptsthis approach and restricts the law of the excluded middle. JC Beall(2002) combines truth-value gaps with Kleene logic (see the entry onmany-valued Logic) and makes use of both weak and strongnegation. Armour-Garb and Beall (2001, 2003) argue that deflationists can andshould bedialetheists and accept that some truthbearers are both true and not true (seealso, Woodbridge 2005, 152–3, on adopting aparaconsistent logic that remains “quasi-classical”). By contrast, Armour-Garband Woodbridge (2013, 2015) develop a version of the“meaningless strategy” with respect to the Liar (based onGrover 1977), which they claim a deflationist can use to dissolve thatparadox and semantic pathology more generally, without acceptinggenuine truth-value gaps or giving up classical logic.

4.5 The Generalization Problem

Since deflationists place such heavy emphasis on the role of theconcept of truth in expressing generalizations, it seems somewhatironic that certain versions of deflationism have been criticized forbeing incapable of accounting for generalizations involvingtruth (Gupta 1993a, 1993b; Field 1994a, 2008; Horwich 1998a(137–8), 2001; Halbach 1999 and 2011 (57–9); Soames 1999,Armour-Garb 2004, 2010, 2011). The “GeneralizationProblem” (henceforth, \(GP)\) captures the worry that adeflationary account of truth is inadequate for explaining ourcommitments to general facts we express with certain uses of‘true’. This raises the question of whether and, if so,how, deflationary accounts earn the right to endorse suchgeneralizations.

Although Tarski (1935 [1956]) places great importance on the instancesof his (T)-schema, he comes to recognize that those instances do notprovide a fully adequate way of characterizing truth. Moreover, evenwhen the instances of (T) are taken as theorems, Tarski (ibid.) pointsout that taken all together they are insufficient for proving a‘true’-involving generalization like

(A)

All sentences of the form ‘If \(p\), then \(p\)’ aretrue.

since the collection of the instances of (T) is \(\omega\)-incomplete(where a theory, \(\theta\), is\(\omega\)-incomplete if\(\theta\) can prove every instance of an open formula‘\(Fx\)’ but cannot prove the universal generalization,‘\(\forall xFx\)’).

We arrive at a related problem when we combine a reliance on theinstances of some version of (ES) with Quine’s view about thefunctioning and utility of the truth predicate. He (1992, 81)considers the purpose of (A) to be to express a generalization oversentences like the following:

(B)

If it is raining, then it is raining.

(C)

If snow is white, then snow is white.

Quine points out that we want to be able to generalize on the embeddedsentences in those conditionals, by semantically ascending,abstracting logical form, and deriving (A). But, as Tarski (ibid.)notes, this feat cannot be achieved, given only a commitment to (theinstances of) (T). From (T) and (A), we can prove (B) and (C) but,given the finitude of deduction, when equipped only with the instancesof (T), we cannot prove (A). As a consequence of the CompactnessTheorem of first-order logic, anything provable from the totality ofthe instances of (T) is provable from just finitely many of them, soany theory that takes the totality of the instances of (T) tocharacterize truth will be unable to prove any generalization like(A).

To address the question of why we need to be able to prove thesetruth-involving generalizations, suppose that we accept a propositionlike \(\langle\)Every proposition of the form \(\langle\)if \(p\),then \(p\rangle\) is true\(\rangle\). Call this proposition“\(\beta\)”. Now take ‘\(\Gamma\)’ to standfor the collection of propositions that are the instances of\(\beta\). Horwich (2001) maintains that an account of the meaning of‘true’ will be adequate only if it aids in explaining whywe accept the members of \(\Gamma\), where such explanations amount toproofs of those propositions by, among other things, employing anexplanatory premise that does not explicitly concern the truthpredicate. So, one reason it is important to be able to prove a‘true’-involving generalization is because this is acondition of adequacy for an account of the meaning of that term. Onemight argue that anyone who grasps the concept of truth, and that ofthe relevant conditional, should be said to know \(\beta\). But if agiven account of truth, together with an account of the conditional(along, perhaps, with an account of other logical notions), does notentail \(\beta\), then it does not provide an acceptable account oftruth.

Here is another reason for thinking that generalizations like\(\beta\) must be proved. A theory of the meaning of‘true’ should explain our acceptance of propositions like\(\beta\), which, as Gupta (1993a) and Hill (2002) emphasize, shouldbe knowablea priori by anyone who possesses the concept oftruth (and who grasps the relevant logical concepts). But if such aproposition can be knowna priori on the basis of a grasp ofthe concept of truth (and of the relevant logical concepts), then atheory that purports to specify the meaning of ‘true’should be able to explain our acceptance of that proposition. But ifan account of the meaning of ‘true’ is going to do this,it must be possible to derive the proposition from one or more of theclauses that constitute our grasp of the concept of truth.

This creates a problem for a Horwichian minimalist. Let us supposethat \(\beta\) is one of the general propositions that must beprovable. Restricted to the resources available throughHorwich’s minimalism, we can show that \(\beta\) cannot bederived.

If a Horwichian minimalist could derive \(\beta\), it would have to bederived from the instances of

(E)

\(\langle p\rangle\) is true iff \(p.\)

But there cannot be a valid derivation of a universal generalizationfrom a set of particular propositions unless that set is inconsistent.Since, according to Horwich (1998a), every instance of (E) that ispart of his theory of truth is consistent, it follows that therecannot be a derivation of \(\beta\) from the instances of (E). This isa purely logical point. As such, considerations of pure logic dictatethat our acceptance of \(\beta\) cannot be explained byHorwich’s account of truth. Since Horwich takes all instances ofthe propositional version of (T) (i.e., (ES-prop)) as axioms, he canprove each of those instances. But, as we have seen, restricted to theinstances of the equivalence schema, he cannot prove thegeneralization, \(\beta\), i.e., \(\langle\)Every proposition of theform \(\langle\)if \(p\) then \(p\rangle\) is true\(\rangle\).

Some deflationists respond to the GP by using a version of (GT) toformulate their approach:

(GT)

\(\forall x\) \((x\) is true iff \(\Sigma p(x = \langle p\rangle\amp p)).\)

In this context, there are two things to notice about (GT). First, itis not a schema but a universally quantified formula. For this reason,it is possible to derive a generalization like \(\beta\) from it.Second, the existential quantifier, ‘\(\Sigma\)’, in (GT)must be a higher-order quantifier (see the entry onsecond-order and higher-order logic) that quantifies into sentential positions. We mentioned above anapproach that takes this quantifier as a substitutional one, where thesubstitution class consists of sentences. We also mentionedHill’s (2002) alternative version that takes the substitutionclass to be the set of all propositions. Künne (2003) suggests adifferent approach that takes ‘\(\Sigma\)’ to be anobjectual (domain and values) quantifier ranging over propositions.However, parallel to Horwich’s rejection of (GT) discussed inSection 3.1, all of these approaches have drawn criticism on thegrounds that the use of higher-order quantifiers to define truth iscircular (cf. Platts 1980, McGrath 2000), and may get the extension ofthe concept of truth wrong (cf. Sosa 1993).

An alternative deflationist approach to the GP attempts to show that,despite appearances, certain deflationary theories do have theresources to derive the relevant generalizations. Field (1994a,2001a), for example, suggests that we allow reasoning with schemasdirectly and proposes rules that would allow the derivation ofgeneralizations. Horwich (1998a, 2001) suggests a more informalapproach according to which we are justified in deriving \(\beta\)since an informal inspection of a derivation of some instance of\(\beta\) shows us that we could derive any instance of it. Forreplies to Horwich, see Armour-Garb 2004, 2010, 2011; Gupta 1993a,1993b; and Soames 1999. For responses to Armour-Garb’s attack onHorwich 2001, see Oms 2019 and Cieśliński 2018.

4.6 Conservativeness

An ideal theory of truth will be both consistent (e.g., avoid the LiarParadox) and adequate (e.g., allow us to derive all the essential lawsof truth, such as those at issue in the Generalization Problem). Yetit has recently been argued that even if deflationists can provide aconsistent theory of truth and avoid the GP, they still cannot providean adequate theory.

This argument turns on the notion of a conservative extension of atheory. Informally, a conservative extension of a theory is one thatdoes not allow us to prove anything that could not be proved from theoriginal, unextended theory. More formally, and applied to theories oftruth, a truth theory, \(Tr\) is conservative over some theory \(T\)formulated in language \(L\) if and only if for every sentence\(\phi\) of \(L\) in which the truth predicate does not occur, if \(Tr\cup L \vdash \phi\), then \(L \vdash \phi\) (where‘\(\vdash\)’ representsprovability). Certaintruth theories are conservative over arithmetic – e.g., theoriesthat implicitly define truth using only the instances of some versionof (ES) – and certain truth theories are not – e.g.,Tarski’s (1935 [1956], 1944) compositional theory. Specifically,the addition of certain truth theories allows us to prove thatarithmetic is consistent, something that we cannot do if we areconfined to arithmetic itself.

It has been argued (a) that conservative truth theories are inadequateand (b) that deflationists are committed to conservative truththeories. (See Shapiro 1998 and Ketland 1999; Horsten 1995 provides anearlier version of this argument.) We will explain the arguments for(a) below but to get a flavor of the arguments for (b), considerShapiro’s rhetorical question: “How thin can the notion ofarithmetic truth be, if by invoking it we can learn more about thenatural numbers?” Shapiro is surely right to press deflationistson their frequent claims that truth is “thin” or“insubstantial”. It might also be a worry fordeflationists if any adequate truth theory allowed us to derivenon-logical truths, if they endorse the thesis that truth is merely a“logical property”. On the other hand, deflationiststhemselves insist that truth is an expressively useful device, and sothey cannot be faulted for promoting a theory of truth that allows usto say more about matters not involving truth.

To see an argument for (a), consider a Gödel sentence, \(G\),formulated within the language of Peano Arithmetic (henceforth,\(PA)\). \(G\) is not a theorem of PA if PA is consistent (cf. theentry onGödel’s incompleteness theorems). But \(G\) becomes a theorem when PA is expanded by adding certainplausible principles that appear to govern a truth predicate. Thus,the resultant theory of arithmetical truth is strong enough to prove Gand appears therefore to be non-conservative over arithmetic. If, ashas been argued by a number of theorists, any adequate account oftruth will be non-conservative over a base theory, then deflationistsappear to be in trouble.

Understood in this way, the “Conservativeness Argument”(henceforth, \(CA)\) is a variant of the objection considered inSection 4.1, claiming that truth plays an explanatory role thatdeflationism cannot accommodate. There are several deflationaryresponses to the CA. Field (1999) argues that the worries that arisefrom the claim that deflationists are in violation of explanatoryconservativeness is unfounded. He (ibid., 537) appeals to theexpressive role of the truth predicate and maintains thatdeflationists are committed to a form of “explanatoryconservativeness” only insofar as there are no explanations inwhich the truth predicate is not playing its generalizing role. As aresult, he (ibid.) notes that “any use of ‘true’ inexplanations which derives solely from its role as a device ofgeneralization should be perfectly acceptable”. For responses toField, see Horsten 2011 (61) and Halbach 2011 (315–6).

Responding to the CA, Daniel Waxman (2017) identifies two readings of‘conservativeness’, one semantic and the other syntactic,which correspond to two conceptions of arithmetic. On the firstconception, arithmetic is understoodcategorically as givenby the standard model. On the second conception, arithmetic isunderstoodaxiomatically and is captured by the acceptance ofsome first-order theory, such as PA. Waxman argues that deflationismcan be conservative given either conception, so that the CA does notgo through.

Julien Murzi and Lorenzo Rossi (2018) argue that Waxman’sattempt at marrying deflationism with conservativeness – his“conservative deflationism” – is unsuccessful. They(ibid.) reject the adoption of this view on the assumption thatone’s conception of arithmetic is axiomatic, claiming, ineffect, that a deflationist’s commitment to a conservativeconception of truth is misguided (cf. Halbach 2011, Horsten 2011,Cieśliński 2015, and Galinon 2015).

Jody Azzouni (1999) defends the “first-orderdeflationist”, viz., a deflationist who endorses what Waxman(ibid.) calls “the axiomatic conception of arithmetic” andwhose subsequent understanding cannot rule out the eligibility ofnon-standard models. Azzouni accepts the need to prove certain‘true’-involving generalizations, but he maintains thatthere are some generalizations that areabout truths that afirst-order deflationist need not prove. He further contends that ifone does extend her theory of truth in a way that allows her toestablish these generalizations, she should not expect her theory tobe conservative, nor should she continue describing it as adeflationary view of truth. For a response to Azzouni(ibid.), see Waxman (2017, 453).

In line with Field’s response to the CA, Lavinia Picollo andThomas Schindler (2020) argue that the conservativeness constraintimposed by Horsten 1995, Shapiro 1998, Ketland 1999, and others is nota reasonable requirement to impose on deflationary accounts. Theycontend that the insistence on conservativeness arises from making toomuch of the metaphor of “insubstantiality” and that itfails to see what the function of the truth predicate really amountsto. Their leading idea is that, from a deflationist’sperspective, the logico-linguistic function of the truth predicate isto simulate sentential and predicate quantification in a first-ordersetting (cf. Horwich 1998a, 4, n. 1). They maintain that, for adeflationist, in conjunction with first-order quantifiers, the truthpredicate has the same function as sentential and predicatequantifiers. So, we should not expect the deflationist’s truththeory to conservatively extend its base theory.

4.7 Normativity

It is commonly said that our beliefs and assertions aim at truth, orpresent things as being true, and that truth is therefore anorm of assertion and belief. This putative fact about truthand assertion in particular has been seen to suggest that deflationismmust be false (cf. Wright 1992 and Bar-On and Simmons 2007). However,the felt incompatibility between normativity and deflationism isdifficult to make precise.

The first thing to note is that there is certainly a sense in whichdeflationism is consistent with the idea that truth is a norm ofassertion. To illustrate this, notice (as we saw in examiningtruth’s putative explanatory role) that we can obtain anintuitive understanding of this idea without mentioning truth at all,so long as we focus on a particular case. Suppose that for whateverreason Mary sincerely believes that snow is green, has good evidencefor this belief, and on the basis of this belief and evidence assertsthat snow is green. We might say that there is a norm of assertionthat implies that Mary is still open to criticism in this case. Afterall, since snow is not green, there must be somethingincorrect ordefective about Mary’s assertion(and similarly for her belief). It is this incorrectness ordefectiveness that the idea that truth is a norm of assertion (andbelief) is trying to capture.

To arrive at a general statement of the norm that lies behind thisparticular case, consider that here, what we recognize is

(13)

If someone asserts that snow is green when snow is not green, thenthat assertion is open to criticism.

To generalize on this, what we want to do is generalize on thepositions occupied by ‘snow is green’ and expresssomething along the lines of

(14)

For all \(p\), if someone asserts that \(p\) when \({\sim}p\),then that assertion is open to criticism.

The problem of providing a general statement like (14) is the sameissue first raised in Section 1.3, and the solution by now should befamiliar. To state the norm in general we would need to be able to dosomething we seem unable to do in ordinary language, namely, employsentential variables and quantifiers for them. But this is where thenotion of truth comes in. Because (ES) gives us itscontraposition,

(ES-con)

\({\sim}p\) iff \(\langle p\rangle\) is not true.

Reading ‘\(\langle p\rangle\)’ as ‘that\(p\)’, we can reformulate (14) as

(15)

For all \(p\), if someone asserts that \(p\) when that \(p\) isnot true, then that assertion is open to criticism.

But since the variable ‘\(p\)’ occurs only in nominalizedcontexts in (15), we can replace it with an object variable,‘\(x\)’, and bind this with an ordinary objectualquantifier, to get

(16)

For all \(x\), if someone asserts \(x\), and \(x\) is not true,then that assertion is open to criticism.

Or, to put it as some philosophers might:

(N)

Truth is a norm of assertion.

In short, then, deflationists need not deny that we appeal to thenotion of truth toexpress a norm of assertion; on thecontrary, the concept of truth seems required to state that verygeneralization.

If deflationists can account for the fact that we must apply thenotion of truth to express a norm of assertion, then does normativitypose any problem for deflationism? Crispin Wright (1992, 15–23)argues that it does, claiming that deflationism is inherently unstablebecause there is a distinctive norm for assertoric practice that goesbeyond the norms for warranted assertibility – that the norms oftruth and warranted assertibility are potentially extensionallydivergent. This separate norm of truth, he claims, is already implicitjust in acceptance of the instances of (ES). He points out that nothaving warrant to assert some sentence does not yield having warrantto assert its negation. However, because (ES) gives us (ES-con), wehave, in each instance, an inference (going from right to left) fromthe sentence mentioned not being true to the negation of the sentence.But the instance of (ES) for the negation of any sentence,

(ES-neg)

\(\langle{\sim} p \rangle\) is true iff \({\sim}p,\)

takes us (again, going from right to left) from the negated sentenceto an ascription of truth to that negated sentence. Thus, somesentence not being truedoes yield that the negation of thesentence is true, in contrast with warranted assertibility. Thisdifference, Wright (ibid., 18) claims, reveals that, bydeflationism’s own lights, the truth predicate expresses adistinct norm governing assertion, which is incompatible with thedeflationary contention “that ‘true’ is onlygrammatically a predicate whose role is not to attribute a substantialcharacteristic”.

Rejecting Wright’s argument for the instability of deflationism,Ian Rumfitt (1995, 103) notes that if we add the ideas of denyingsomething and of having warrant for doing so(“anti-warrant”) to Wright’s characterization ofdeflationism, this would make ‘is not true’ simply adevice of rejection governed by the norm that “[t]he predicate‘is not true’ may be applied to any sentence for which onehas an anti-warrant”. But then truth-talk’s behavior withnegation would not have to be seen as indicating that it marks adistinct norm beyond justified assertibilityand justifiabledeniability, which would be perfectly compatible withdeflationism.

Field (1994a, 264–5) offers a deflationary response toWright’s challenge (as well as to a similar objection regardingnormativity from Putnam (1983a, 279–80)), pointing again to thegeneralizing role of the truth predicate in such normative desires asone to utter only true sentences or one to have only true beliefs.Field agrees with Wright that truth-talk expresses a norm beyondwarranted assertibility, but he (1994a, 265) also maintains that“there is no difficulty in desiring that all one’s beliefsbe disquotationally true; and not only can each of us desire suchthings, there can be a general practice of badgering other to intohaving such desires”. Horwich (1996, 879–80) argues thatWright’s rejection of deflationism does not follow from showingthat one can use the truth predicate to express a norm beyondwarranted assertibility. Like Field, Horwich claims that Wright missedthe point that, in the expression of such a norm, the truth predicateis just playing its generalizing role. For other objections todeflationism based on truth’s normative role, see Price 1998,2003 and McGrath 2003.

4.8 Inflationist Deflationism?

Another objection to deflationism begins by drawing attention to alittle-known doctrine about truth that G.E. Moore held at thebeginning of the 20th Century. Richard Cartwright (1987, 73) describesthe view as follows: “a true proposition is one that has acertain simple unanalyzable property, and a false proposition is onethat lacks the property”. This doctrine about truth is to beunderstood as the analogue for the doctrine that Moore held aboutgoodness, namely that goodness is a simple, unanalyzable quality.

The potential problem that this Moorean view about truth presents fordeflationism might best be expressed in the form of a question: Whatis the difference between the Moorean view and deflationism? One mightreply that, according to deflationary theories, the concept of truthhas an important logical role, i.e., expressing certaingeneralizations, whereas the concept of goodness does not. However,this doesn’t really answer our question. For one thing, itisn’t clear that Moore’s notion of truth does not alsocapture generalizations, since it too will yield all of the instancesof (ES). For another, the idea that the concept of truth plays animportant logical role doesn’t distinguish the metaphysics ofdeflationary conceptions from the metaphysics of the Moorean view, andit is the metaphysics of the matter that the present objection reallybrings into focus. Alternatively, one might suggest that thedistinction between truth according to Moore’s view anddeflationary conceptions of truth is the distinction between having asimple unanalyzable nature, and not having any underlying nature atall. But what is that distinction? It is certainly not obvious thatthere is any distinction between having a nature about which nothingcan be said and having no nature at all.

How might a deflationist respond to this alleged problem? The key movewill be to focus on the property of being true. For the Moorean, thisproperty is a simple unanalyzable one. But deflationists need not becommitted to this. As we have seen, some deflationists think thatthere is no truth property at all. And even among deflationists whoaccept that there is some insubstantial truth property, it is notclear that this is the sort of property that the Moorean has in mind.To say that a property is unanalyzable suggests that the property is afundamental property. One might understand this in something like thesense that Lewis proposes, i.e., as a property that is sparse andperfectly natural. Or one might understand a fundamental property asone that is groundable but not grounded in anything. But deflationistsneed not understand a purported property of being true in either ofthese ways. As noted in Section 1.2, they may think of it as anabundant property rather than a sparse one, or as one that isungroundable. In this way, there are options available fordeflationists who want to distinguish themselves from the Moorean viewof truth.

4.9 Truth and Meaning

The final objection that we will consider concerns the relationbetween deflationism and theories of meaning, i.e., theories about howsentences get their meanings.

The orthodox approach to this last question appeals to the notion oftruth, suggesting, roughly, that a sentence \(S\) means that \(p\)just in case \(S\) is true if and only if \(p\). This approach tomeaning, known widely as “truth-conditional semantics”, ishistorically associated withDonald Davidson’s (1967) thesis that the “(T)-sentences” (i.e., theinstances of the (T)-schema) generated by a Tarski-truth-definitionfor a language give the meanings of the sentences they mention, byspecifying their truth conditions. In contemporary linguistics, aprominent approach to sentence meaning explains it in terms ofpropositions, understood (following Lewis 1970 and Stalnaker 1970) assets of possible worlds, which amount to encapsulations of truthconditions (Elbourne 2011, 50–51).

This has led a number of philosophers to argue that, on pain ofcircularity, deflationism cannot be combined with theories of meaningthat make use of the notion of truth to explain meaning – inother words, that deflationism is incompatible with truth-conditionaltheories of meaning. This assessment of deflationism stems fromDummett’s (1959 [1978, 7]) claim that the (T)-sentences (or theinstances of any other version of (ES)) cannot both tell us what thesentences they nominalize mean and give us an account of‘true’. As Horwich (1998a, 68) puts it, “we would befaced with something like a single equation and two unknowns”(cf. Davidson 1990, 1996; Horwich 1998b, Kalderon 1999, Collins2002).

The first thing to say regarding this objection is that, even ifdeflationism were inconsistent with truth-conditional theories ofmeaning, this would notautomatically constitute an objectionto deflationism. After all, there are alternative theories of meaningavailable, and most deflationists reject truth-conditional semanticsin favor of some “truth-free” alternative. The mainalternatives available include Brandom’s (1994) inferentialism,developed followingWilfrid Sellars (1974, 1979); Horwich’s (1998b) use-theory of meaning, inspiredby Wittgenstein 1953; and Field’s (1994a, 2001b)computational-role + indication-relations account. There is, however,a lot of work to be done before any of these theories can be regardedas adequate. Devitt 2001 makes this point in rejecting all of thesealternative approaches to meaning, claiming that the only viableapproach is (referential/)truth-conditional semantics.

While the orthodoxy of truth-conditional accounts of meaning addsweight to this challenge to deflationism, it is still, contra Devitt,an open question whether any non-truth-conditional account of meaningwill turn out to be adequate. Moreover, even if there is no viable“truth-free” account, several philosophers (e.g., Bar-on,et al. 2005) have argued that deflationism has no moreproblem with a truth-conditional theory of meaning than any otherapproach to truth does. Others have gone further, arguing positivelythat there is no incompatibility between deflationism andtruth-conditional theories. Alexis Burgess (2011, 407–410)argues that at least some versions of deflationism are compatible withmainstream model-theoretic semantics in linguistics (understood asproviding explanations of truth conditions) and the recognition of“the manifest power and progress of truth-conditionalsemantics”. Claire Horisk (2008) argues that“circularity” arguments for incompatibility (or, as sheprefers, “immiscibility”) fail. The only circularityinvolved here, she claims, is a harmless kind, so long as one is (likesome proponents of truth-conditional semantics) offering a reciprocal,rather than a reductive, analysis of meaning. Mark Lance (1997,186–7) claims that any version of deflationism based on ananaphoric reading of ‘is true’ (as in Brandom 1988, 1994)is independent of, and thus compatible with, any underlying account ofmeaning, including a truth-conditional one. Williams 1999 likewiseclaims that the role of truth in meaning theories for particularlanguages is just the expressive role that deflationists claimexhausts the notion of truth’s function. Of course, all of theseclaims have been contested, but they seem to show that the thesis thatdeflationism is inconsistent with a truth-conditional theory ofmeaning is neither a forgone conclusion nor necessarily an objectionto deflationism, even if the thesis is correct. (For furtherdiscussion of this issue, see Gupta 1993b, Field 2005, Gupta andMartinez-Fernandez 2005, Patterson 2005, and Horisk 2007.) That said,one outstanding question that remains regarding the viability of anydeflationary approach to truth is whether that approach can be squaredwith an adequate account of meaning.

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Acknowledgments

Bradley Armour-Garb and James Woodbridge joined Daniel Stoljar asco-authors of this (2021) version of this entry. Nicolas Damnjanovicwas a co-author with Daniel Stoljar on the previous (2010) version.Daniel Stoljar would like to thank Damnjanovic for his contributionsto the 2010 version, as well as Stewart Candlish, James Chase, JakobHohwy and Huw Price for help with the original (1997) version of theentry.