## 1. Central Themes in Deflationism


### 1.1 The Equivalence Schema



While deflationism can be developed in different ways, it is possible
to isolate some central themes emphasized by most philosophers who
think of themselves as deflationists. These shared themes pertain to
endorsing a kind of metaphysical parsimony and positing a
"deflated" role for what we can call the *alethic
locutions* (most centrally, the expressions 'true' and
'false') in the instances of what is often called
*truth-talk*. In this section, we will isolate three of these
themes. The first, and perhaps most overarching, one has already been
mentioned: According to deflationists, there is some strong
equivalence between a statement like 'snow is white' and a
statement like "'snow is white' is true," and
this is all that can significantly be said about that application of
the notion of truth.



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



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


In this schema, the angle brackets indicate an appropriate
name-forming or nominalizing device, e.g., quotation marks or
'the proposition that ...', and the occurrences of
'\(p\)' are replaced with matching declarative sentences
to yield instances of the schema.



The equivalence schema is often associated with the formal work of
 Alfred 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 the
sentence that goes in for the '\(p\)', making (T) a
version of (ES). Tarski considered (T) to provide a criterion of
adequacy for any theory of truth, thereby allowing that there could be
more 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 can
formulate the central theme of deflationism under consideration as the
view, roughly, that the instances of (some version of) this schema do
capture everything significant that can be said about applications of
the notion of truth; in a slogan, the instances of the schema
*exhaust* the notion of truth. Approaches which depart from
deflationism don't disagree that (ES) tells us something about
truth; what they (with Tarski) deny is that it is exhaustive, that it
tells us the whole truth about truth. Since such approaches add
substantive explanations of why the instances of the equivalence
schema hold, they are now often called *inflationary*
approaches to truth. Inflationism is the general approach shared by
such traditional views as the
 correspondence theory of truth,
 coherence theory of truth,
 pragmatic theory of truth,
 identity theory of truth, and primitivist theory of truth, These theories all share
a collection of connected assumptions about the alethic locutions, the
concept of truth, and the property of truth. Inflationary theories all
assume that the expression 'is true' is a descriptive
predicate, expressing an explanatory concept of truth, which
determines a substantive property of truth. From that shared set of
presuppositions, the various traditional inflationary theories then
diverge from one another by providing different accounts of the
assumed truth property. On inflationary views, the nature of the truth
property explains why the instances of (ES) hold. Deflationary views,
by contrast, reject some if not all of the standard assumptions that
lead to inflationary theories, resisting at least their move to
positing any substantive truth property. Instead, deflationists offer
a different understanding of both the concept of truth and the
functioning of the alethic locutions. A deflationist will take the
instances of (ES) to be "conceptually basic and explanatorily
fundamental" (Horwich 1998a, 21, n. 4; 50), or to be direct
consequences of how the expression 'true' operates (cf.
Quine 1970 [1986], Brandom 1988, and Field 1994a).



It is important to notice that even among deflationists the
equivalence schema may be interpreted in different ways, and this is
one way to distinguish different versions of deflationism from one
another. One question about (ES) concerns the issue of what instances
of the schema are assumed to be about (equivalently: to what the names
in instances of (ES) are assumed to refer). According to one view, the
instances of this schema are about sentences, where a name for a
sentence can be formulated simply by putting quotation marks around
it. In other words, for those who hold what might be called a
*sententialist* version of deflationism, the equivalence schema
has instances like (1):



(1)
'Brutus killed Caesar' is true if, and only if, Brutus
killed Caesar.


To make this explicit, we might say that, according to sententialist
deflationism, 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 been
replaced by quotation marks.



According to those who hold what might be called a
*propositionalist* version of deflationism, by contrast,
instances of the equivalence schema are about propositions, where
names of propositions are, or can be taken to be, expressions of the
form 'the proposition that \(p\)', where
'\(p\)' is filled in with a declarative sentence. For the
propositionalist, in other words, instances of the equivalence schema
are properly interpreted not as being about sentences but instead as
being 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 to
propositionalist 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 of
deflationism, sententialist and propositionalist versions,
respectively.



Another aspect that different readings of (ES) can vary across
concerns the nature of the equivalence that its instances assert. On
one view, the right-hand side and the left-hand side of such instances
are synonymous or analytically equivalent. Thus, for sententialists
who endorse this level of equivalence, (1) asserts that,
"'Brutus killed Caesar' is true" means just
what 'Brutus killed Caesar' means; while for
propositionalists who endorse analytic equivalence, (2) asserts that
'the proposition that Brutus killed Caesar is true' means
the same as 'Brutus killed Caesar'. A second view is that
the right-hand and left-hand sides of claims such as (1) and (2) are
not synonymous but are nonetheless necessarily equivalent; this view
maintains that the two sides of each equivalence stand or fall
together in every possible world, despite having different meanings.
And a third possible view is that claims such as (1) and (2) assert
only a material equivalence; this view interprets the 'if and
only if' in both (1) and (2) as simply the biconditional of
classical logic.



This tripartite distinction between analytic, necessary, and material
equivalence, when combined with the distinction between sententialism
and propositionalism, yields six different possible (although not
exhaustive) readings of the instances of (ES):




|  | *Sentential* | *Propositional* |
| --- | --- | --- |
| *Analytic* | \(\mathbf{A}\) | \(\mathbf{B}\) |
| *Necessary* | \(\mathbf{C}\) | \(\mathbf{D}\) |
| *Material* | \(\mathbf{E}\) | \(\mathbf{F}\) |



While different versions of deflationism can be correlated to some
extent with different positions in this chart, some chart positions
have also been occupied by more than one version of deflationism. The
labels 'redundancy theory', 'disappearance
theory' and 'no-truth theory' have been used to
apply 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 prominent
disquotationalists tend to be leary of the notions of analyticity or
synonymy), and what is called "prosententialism" also
posits an equivalence of what is said with the left- and right-hand
sides of the instances of (ES). The latter version of deflationism,
however, does this without making the left-hand sides about sentences
named via quotation or about propositions understood as abstract
entities. No deflationist has offered an account occupying position
\(\mathbf{C}\), \(\mathbf{E}\), or \(\mathbf{F}\) (although the
explicit inspiration some disquotationalists have found in
Tarski's work and his deployment of material equivalence might
misleadingly suggest position \(\mathbf{E})\). Paul Horwich (1998a)
uses the label 'minimalism' for a version of
propositionalist deflationism that takes the instances of (ES-prop) to
involve 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 views
from other parts of philosophy, typically their views about the
philosophy 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, the
property of being true. Deflationists are typically wary of that
claim, insisting either that there is no property of being true at
all, 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 by
some philosophers in the deflationary camp; we will look at some
examples 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 predicates
such as 'is metal' express properties, then, *prima
facie*, the same would seem to go for 'is true.' This
point is not decisive, however. For one thing, it might be possible to
distinguish the grammatical form of claims containing 'is
true' from their logical form; at the level of logical form, it
might be, as prosententialists maintain, that 'is true' is
*not* a predicate. For another, nominalists about properties
have developed ways of thinking about grammatical predicates according
to which these expressions don't express properties at all. A
deflationist might appeal, perhaps selectively, to such proposals, in
order to say that 'is true', while a predicate, does not
express a property.



Whatever the ultimate fate of these attempts to say that there is no
property of truth may be, a suggestion among certain deflationists has
been to concede that there is a truth property but to deny it is a
property of a certain kind; in particular to deny that it is (as we
will say) a *substantive* 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 of
being true? Well, in one intuitive sense they do: Since they both are
true, 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 the
property that all true propositions have.



On the other hand, when we say that two things share a property of
*Fness*, we often mean more than simply that they are both
\(F\). We often mean that two things that are \(F\) have some
underlying nature in common, for example, that there is a common
explanation as to why they are both \(F\). It is in this second claim
that deflationists have in mind when they say that truth is not a
substantive property. Thus, in the case of our example, what, if
anything, explains the truth of (3) is that Caracas is the capital of
Venezuela, and what explains this is the political history of
Venezuela. On the other hand, what, if anything, explains the truth of
(4) is that the earth revolves around the sun, and what explains this
is the physical nature of the solar system. The physical nature of the
solar system, however, has nothing to do with the political history of
Venezuela (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 no
property in common.



It will help to bring out the contrast being invoked here if we
consider two properties distinct from a supposed property of being
true: 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 the
property of being a game? Well, in one sense, they do: they are both
games that people can play. On the other hand, however, there is no
common explanation as to why each counts as a game (cf. Wittgenstein
1953, SS66). We might then say that being a game is not a
substantive property and mean just this. But now compare the property
of being a mammal. If two things are mammals, they have the property
of being a mammal, but in addition there is some common explanation as
to why they are both mammals - both are descended from the same
family of creatures, say. According to one development of
deflationism, the property of being true is more like the property of
being a game than it is like the property of being a mammal.



The comparisons between being true, being a game, and being a mammal
are suggestive, but they still do not nail down exactly what it means
to say that truth is not a substantive property. The contemporary
literature on deflationism contains several different approaches to
the idea. One such approach, which we will consider in detail in
Section 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; Kunne 2003, 91). A further
approach appeals to
 David Lewis's
 (1983, 1986) view that, while every set of entities underwrites a
property, there is a distinction between *sparse*, or
*natural*, properties and more motley or disjointed
*abundant* properties. On this approach, a deflationist might
say that there is an abundant property of being true rather than a
sparse one (cf. Edwards 2013, Asay 2014, Kukla and Winsberg 2015, and
Armour-Garb forthcoming). A different metaphysical idea may be to
appeal to the contemporary discussion of grounding and the distinction
between groundable and ungroundable properties. In this context, a
groundable property is one that is capable of being grounded in some
other property, whether or not it is in fact grounded; an ungroundable
property is a property that is not groundable (see Dasgupta 2015, 2016
and Rabin 2020). From this point of view, a deflationist might say
that being true is an ungroundable property. Hence it is unlike
ordinary, sparse/natural properties, such as being iron, which are
both capable of being grounded and are grounded, and it is also unlike
fundamental physical properties, such as being a lepton, which are
capable of being grounded (in some other possible world) but are not
(actually) grounded. We will not try to decide here which of these
different views of properties is correct but simply note that
deflationists who want to claim that there is a truth property, just
not a substantive one, have options for explaining what this
means.


### 1.3 The Utility of the Concept of Truth



In light of the two central ideas discussed so far - the idea
that the equivalence schema is exhaustive of the notion of truth and
the idea that there is no substantive truth property - you might
wonder why we have a concept of truth in the first place. After all,
contrast this question with the explanation of why we have the concept
of mammals. A natural suggestion is that it allows us to think and
talk about mammals and to develop theories of them. For deflationism,
however, as we have just seen, being true is completely different from
being a mammal; why then do we have a concept of truth? (An analogous
question might be asked about the word 'true', i.e., why
we have the word 'true' and related words in our language
at all. In the following discussion we will not discriminate between
questions 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 to
introduce a third central theme in deflationism, which is an emphasis
not 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 the
concept of truth, deflationists are usually at pains to point out that
anyone who has the concept of truth is in possession of a very useful
concept indeed; in particular, anyone who has this concept is in a
position to express generalizations that would otherwise require
non-standard logical devices, such as sentential variables and
quantifiers for them.



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



(5)
If Smith says that birds are dinosaurs, then birds are
dinosaurs.


To generalize on the relationship indicated in (5), beyond just what
Smith says about birds to anything she might say, what we want to do
is generalize on the embedded occurrences of 'birds are
dinosaurs'. So, we need a (declarative) sentential variable,
'\(p\)', and a universal quantifier governing it. What we
want 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 most
familiar way of generalizing because the '\(p\)' in the
consequent is in a sentence-in-use position, rather than mentioned or
nominalized context (as it is in the antecedent), meaning that this
formal variable cannot be replaced with a familiar English
object-variable expression, e.g., 'it'.



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



(7)
For all \(x\), if what Smith said \(= x\), then \(x\) is
true.


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



(8)
Everything is such that, if it is what Smith said, then it is
true.


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) to
express. For, on the basis of the schema, there is always an
equivalence between whatever goes in for a sentence-in-use occurrence
of the variable '\(p\)' and a context in which that
filling of the sentential variable is nominalized. This reveals how
the truth predicate can be used to provide a surrogate for sentential
variables, simulating this non-standard logical device while still
deploying the standard object variables already available in ordinary
language ('it') and the usual object quantifiers
('everything') that govern them.



This is how the use of the truth predicate in (9) gives us the content
of Jones's belief. And the important point for deflationists is
that we could not have stated the content of this belief unless we had
the concept of truth (the expression 'true'). In fact, for
most 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 is
often put, the *raison d'etre* of the concept of
truth (cf. Field 1994a and Horwich 1998a).


## 2. History of Deflationism



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



> 
> It is ... worthy of notice that the sentence 'I smell the
> scent of violets' has just the same content as the sentence
> 'It is true that I smell the scent of violets'. So it
> seems, then, that nothing is added to the thought by my ascribing to
> it the property of truth. (Frege 1918, 6)
> 



This passage suggests that Frege embraces a deflationary view in
position \(\mathbf{B}\) (in the chart above), namely, an analytic
propositionalist version of deflationism. But this interpretation of
his 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', from
transparent truth-ascriptions, like the one mentioned in the quote
from Frege. Unlike with transparent cases, in opaque instances, one
cannot simply strip 'is true' away and obtain an
equivalent sentence, since the result is not even a sentence at
all.



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



> 
> Truth and falsity are ascribed primarily to propositions. The
> proposition to which they are ascribed may be either explicitly given
> or described. Suppose first that it is explicitly given; then it is
> evident that 'It is true that Caesar was murdered' means
> no more than that Caesar was murdered, and 'It is false that
> Caesar was murdered' means no more than Caesar was not murdered.
> .... In the second case in which the proposition is described and
> not given explicitly we have perhaps more of a problem, for we get
> statements from which we cannot in ordinary language eliminate the
> words 'true' or 'false'. Thus if I say
> 'He is always right', I mean that the propositions he
> asserts are always true, and there does not seem to be any way of
> expressing this without using the word 'true'. But suppose
> we put it thus 'For all \(p\), if he asserts \(p\), \(p\) is
> true', then we see that the propositional function \(p\) is true
> is simply the same as \(p\), as e.g. its value 'Caesar was
> murdered is true' is the same as 'Caesar was
> murdered'. (Ramsey 1927, 38-9)
> 



On Ramsey's redundancy theory (as it is often called), the truth
operator, 'it is true that' adds no content when prefixed
to a sentence, meaning that in the instances of what we can think of
as 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 Ramsey
extends his redundancy theory beyond just the transparent instances of
truth-talk, maintaining that the truth predicate is, in principle,
eliminable even in opaque ascriptions of the form '\(B\) is
true' (which he (1929, 15, n. 7) explains in terms of sentential
variables *via* a formula along the lines of '\(\exists
p\) (\(p \amp B\) is a belief that \(p\))') and in explicitly
quantificational instances, like 'Everything Einstein said is
true' (explained as above). As the above quote illustrates,
Ramsey recognizes that in truth ascriptions like these the truth
predicate fills a grammatical need, which keeps us from eliminating it
altogether, but he held that even in these cases it contributes no
content to anything said using it.



A.J. Ayer
 endorses a view similar to Ramsey's. The following quote shows
that he embraces a meaning equivalence between the two sides of the
instances of both the sentential (position \(\mathbf{A})\) and
something like (since, despite his use of the expression
'proposition' to mean *sentence*, he also considers
instances of truth-talk involving the prefix 'it is true
that', 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 "\(p\) is
> true" or "it is true that \(p\)" the reference to
> truth never adds anything to the sense. If I say that it is true that
> Shakespeare wrote *Hamlet*, or that the proposition
> "Shakespeare wrote *Hamlet*" is true, I am saying
> no more than that Shakespeare wrote *Hamlet*. Similarly, if I
> say that it is false that Shakespeare wrote the *Iliad*, I am
> saying no more than that Shakespeare did not write the *Iliad*.
> And this shows that the words 'true' and
> 'false' are not used to stand for anything, but function
> in the sentence merely as assertion and negation signs. That is to
> say, truth and falsehood are not genuine concepts. Consequently, there
> can 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 affinities
to deflationism in his later work. We can see a suggestion of an
endorsement of deflationary positions \(\mathbf{A}\) or \(\mathbf{B}\)
in his (1953, SS136) statement that "\(p\) is true \(=
p\)" and "\(p\) is false = not-\(p\)", indicating
that ascribing truth (or falsity) to a statement just amounts to
asserting that very proposition (or its negation). Wittgenstein also
expresses this kind of view in manuscripts from the 1930s, where he
claims, "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 the
case'". (Wittgenstein 1934 [1974, 123]) and 1937 [2005,
61]), respectively)



Peter Strawson's
 views on truth emerge most fully in his 1950 debate with
 J.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 further
endorses a *performative* view, according to which an utterance
of a sentence like 'That is true' mainly functions to do
something *beyond* mere re-assertion. This represents a shift
to 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 the
development of deflationism is
 Alfred Tarski,
 with his (1935 [1956] and 1944) identification of a precise criterion
of adequacy for any formal definition of truth: its implying all of
the 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 the
object-language *for* which the truth predicate is being
defined, and the '\(p\)' gets replaced by a sentence that
is a translation of that sentence into the meta-language in which the
truth predicate is being defined. For Tarski, the 'if and only
if' deployed in any instance of (T) expresses just a material
equivalence, putting his view at position \(\mathbf{E}\) in the chart
from Section 1.1. Although this means that Tarski is not a
deflationist himself (cf. Field 1994a, Ketland 1999, and Patterson
2012), there is no denying the influence that his work and its
promotion of the (T)-schema have had on deflationism. Indeed, some
early deflationists, such as
 W.V.O. Quine
 and Stephen Leeds, are quite explicit about taking inspiration from
Tarski's work in developing their "disquotational"
views, as is Horwich in his initial discussion of deflationism. Even
critics of deflationism have linked it with Tarski: Hilary Putnam
(1983b, 1985) identifies deflationists as theorists who "refer
to the work of Alfred Tarski and to the semantical conception of
truth" and who take Tarski's work "as a solution to
the philosophical problem of truth".



The first fully developed deflationary view is the one that Quine
(1970 [1986, 10-2]) presents. Given his skepticism about the
existence of propositions, Quine takes sentences to be the primary
entities to which 'is true' may be applied, making the
instances of (ES-sent) the equivalences that he accepts. He defines a
category of sentence that he dubs "eternal", viz.,
sentence types that have all their indexical/contextual factors
specified, the tokens of which always have the same truth-values. It
is for these sentences that Quine offers his disquotational view. As
he (ibid., 12) puts it,



> 
> 
> This cancellatory force of the truth predicate is explicit in
> Tarski's paradigm:
> 
> 
> 
> > 
> > 'Snow is white' is true if and only if snow is white.
> > 
> 
> 
> 
> Quotation marks make all the difference between talking about words
> and talking about snow. The quotation is a name of a sentence that
> contains the name, namely 'snow', of snow. By calling the
> sentence true, we call snow white. The truth predicate is a device of
> disquotation.
> 
> 
> 



As this quote suggests, Quine sees Tarski's formal work on
defining truth predicates for formalized languages and his criterion
of adequacy for doing so as underwriting a disquotational analysis of
the truth predicate. This makes Quine's view a different kind of
position-\(\mathbf{A}\) account, since he takes the left-hand side of
each instance of (ES-sent) to be, as we will put it (since Quine
rejects the whole idea of meaning and meaning equivalence), something
like a mere syntactic variant of the right-hand side. This also means
that Quine's version of deflationism departs from inflationism
by rejecting the latter's presupposition that truth predicates
function to *describe* the entities they get applied to, the
way that other predicates, such as 'is metal', do.



Quine also emphasizes the importance of the truth predicate's
role as a means for expressing the kinds of otherwise inexpressible
generalizations discussed in Section 1.3. As he (1992, 80-1)
explains it,



> 
> The truth predicate proves invaluable when we want to generalize along
> a dimension that cannot be swept out by a general term ... The
> harder sort of generalization is illustrated by generalization on the
> clause 'time flies' in 'If time flies then time
> flies'.... We could not generalize as in 'All men are
> mortal' because 'time flies' is not, like
> 'Socrates', a name of one of a range of objects (men) over
> which to generalize. We cleared this obstacle by *semantic
> ascent*: by ascending to a level where there were indeed objects
> over which to generalize, namely linguistic objects, sentences.
> 



So, if we want to generalize on embedded sentence-positions within
some sentences, "we ascend to talk of truth and sentences"
(Quine 1970 [1986, 11]). This maneuver allows us to "affirm some
infinite lot of sentences that we can demarcate only by talking about
the sentences" (ibid., 12).



Leeds (1978) (following Quine) makes it clear how the truth predicate
is crucial for extending the expressive power of a language, despite
the triviality that disquotationalism suggests for the transparent
instances of truth-talk. He (ibid., 121) emphasizes the logical role
of the truth predicate in the expression of certain kinds of
generalizations that would otherwise be inexpressible in natural
language. Leeds, like Quine, notes that a central utility of the truth
predicate, in virtue of its yielding every instance of (ES-sent), is
the simulation of quantification into sentence-positions. But, unlike
Quine, Leeds glosses this logical role in terms of expressing
potentially infinite conjunctions (for universal generalization) or
potentially infinite disjunctions (for existential generalization).
The truth predicate allows us to use the ordinary devices of
first-order logic in ways that provide surrogates for the non-standard
logical devices this would otherwise require. Leeds is also clear
about accepting the consequences of deflationism, that is, of taking
the logically expressive role of the truth predicate to exhaust its
function. In particular, he points out that there is no need to think
that truth plays any sort of *explanatory* role. We will return
to this point in Section 4.1.



Dorothy Grover, Joseph Camp, and Nuel Belnap (1975) develop a
different variety of deflationism that they call a
"prosentential theory". This theory descends principally
from Ramsey's views. In fact, Ramsey (1929, 10) made what is
probably the earliest use of the term 'pro-sentence' in
his account of the purpose of truth-talk. Prosentences are explained
as the sentence-level analog of pronouns. As in the case of pronouns,
prosentences inherit their content anaphorically from other linguistic
items, in this case from some sentence typically called the
prosentence's "anaphoric antecedent" (although it
need not actually occur before the prosentence). As Grover, *et
al*. develop this idea, this content inheritance can happen in two
ways. The most basic one is called "lazy" anaphora. Here
the prosentence could simply be replaced with a repetition of its
antecedent, as in the sort of case that Strawson emphasized, where one
says "That is true" after someone else has made an
assertion. According to Grover, *et al*., this instance of
truth-talk is a prosentence that inherits its content anaphorically
from the other speaker's utterance, so that the two speakers
assert the same thing. As a result, Grover, *et al.* would take
the instances of (ES) to express meaning equivalences, but since they
(ibid., 113-5) do not take the instances of truth-talk on the
left-hand sides of these equivalences to say anything *about*
any named entities, they would not read (ES) as either (ES-sent) or
(ES-prop) on their standard interpretations. So, while their
prosententialism is similar to views in position \(\mathbf{A}\) or in
position \(\mathbf{B}\) in the chart above, it is also somewhat
different from both.



Grover, *et al*.'s project is to develop the theory
"that 'true' can be thought of always as part of a
prosentence" (ibid., 83). They explain that 'it is
true' and 'that is true' are generally available
prosentences that can go into any sentence-position. They consider
these expressions to be "atomic" in the sense of not being
susceptible 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 quantificational
prosentence (i.e., a sentential variable), for example, in a
re-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 is
true.


One immediate concern that this version of prosententialism faces
pertains to what one might call the "paraphrastic
gymnastics" that it requires. For example, a sentence like
'It is true that humans are causing climate change' is
said 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 the
form 'It is true that \(p\)', one states the content of
the sentence that goes in for '\(p\)' *twice*. In
cases of quotation, like "'Birds are dinosaurs' is
true", 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 instance
of truth-talk requires rejecting the standard view that putting
quotation marks around linguistic items forms names of those items.
These issues raise concerns regarding the adequacy of this version of
prosententialism.


## 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 from
inflationism because it accepts many of the standard inflationary
presuppositions, including that 'is true' is a predicate
used to describe entities as having (or lacking) a truth property.
What makes minimalism a version of deflationism is its denial of
inflationism's final assumption, namely, that the property
expressed by the truth predicate has a substantive nature. Drawing
inspiration from Leeds (1978), Horwich (1982, 182) actually coins the
term 'deflationism' while describing "the
deflationary redundancy theory which denies the existence of surplus
meaning 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 [First
Edition, 1990]), adds to this earlier view. In particular, Horwich
(ibid., 37, 125, 142) comes to embrace the idea that 'is
true' does express a property, but it is merely a "logical
property" (cf. Field 1992), rather than any substantive or
naturalistic 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 alethic
locutions describe directly. Any other entities that we can properly
call true are so only derivatively, on the basis of having some
relation to true propositions (ibid., 100-1 and Horwich 1998b,
82-5). This seems to position Horwich well with respect to
explaining the instances of truth-talk that cause problems for Quine
and Leeds, e.g., those about beliefs and theories. Regarding truth
applied directly to propositions, however, Horwich (1998a, 2-3)
still explicitly endorses the thesis that Leeds emphasizes about the
utility of the truth predicate (and, Horwich adds, the concept it
expresses), namely, that it "exists solely for the sake of a
certain logical need". While Horwich (ibid., 138-9) goes
so far as to claim that the concept of truth has a
"non-descriptive" function, he does not follow Quine and
Leeds all the way to their rejection of the assumption that the
alethic predicates function to describe truth-bearers. Rather, his
(ibid., 31-3, 37) point of agreement with them is that the
*main* function of the truth predicate is its role in providing
a means for generalizing on embedded sentence positions, rather than
some role in the indication of specifically truth-involving states of
affairs. Even so, Horwich (ibid., 38-40) still contends that the
instances of truth-talk do describe propositions, in the sense that
they make statements *about* them, and they do so by
attributing a property to those propositions.



The version of (ES) that Horwich (1998a, 6) makes the basis of his
theory 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 a
predicate, Horwich considers 'it is true that \(p\)' to be
just a trivial variant of 'The proposition that \(p\) is
true', meaning that his (E) is a version of (ES-prop) rather
than of Ramsey's (ES-op). He also employs the notation
'\(\langle p\rangle\)' as shorthand specifically for
'the proposition that \(p\)', generating a further
rendering of his equivalence schema (ibid., 10) that we can clearly
recognize 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 of
both an account of the property of truth and an account of the concept
of truth, i.e., what is meant by the word 'true' (ibid.,
136). According to minimalism, the instances of (E) are explanatorily
fundamental, which Horwich suggests is a reason for taking them to be
necessary (ibid., 21, n. 4). This, combined with his view that the
equivalence schema applies to propositions, places his minimalism in
position \(\mathbf{D}\) in the chart given in Section 1.1. The
instances of (ES-prop) are thus explanatory of the functioning of the
truth predicate (of its role as a de-nominalizer of
'that'-clauses (ibid., 5)), rather than being explained by
that functioning (as the analogous equivalences are for both
disquotationalism and prosententialism). Moreover, Horwich (ibid., 50,
138) claims that they are also conceptually basic and *a
priori*. He (ibid., 27-30, 33, 112) denies that truth admits
of any sort of explicit definition or reductive analysis in terms of
other concepts, such as reference or predicate-satisfaction. In fact,
Horwich (ibid., 10-1, 111-2, 115-6) holds that these
other semantic notions should both be given their own, infinitely
axiomatized, minimalist accounts, which would then clarify the
non-reductive nature of the intuitive connections between them and the
notion of truth.



Horwich (ibid., 27-30) maintains that the infinite axiomatic
nature of minimalism is unavoidable. He (ibid., 25) rejects the
possibility of a finite formulation of minimalism *via* the use
of
 substitutional quantification.
 On the usual understanding of this non-standard type of
quantification, the quantifiers govern variables that serve to mark
places in linguistic strings, indicating that either all or some of
the elements of an associated substitution class of linguistic items
of a particular category can be substituted in for the variables.
Since it is possible for the variables so governed to take sentences
as their substitution items, this allows for a type of quantification
governing sentence positions in complex sentences. Using this sort of
sentential substitutional quantification, the thought is, one can
formulate a finite general principle that expresses Horwich's
account of truth as follows:



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


where '\(\Sigma\)' is the existential substitutional
quantifier. (GT) is formally equivalent to the formulation that Marian
David (1994, 100) presents as disquotationalism's definition of
'true sentence', here formulated for propositions instead.
Horwich's main reason for rejecting the proposed finite
formulation of minimalism, (GT), is that an account of substitutional
quantifiers seems (contra David 1994, 98-9) to require an appeal
to truth (since the quantifiers are explained as expressing that at
least one or that every item in the associated substitution class
yields a *true sentence* when substituted in for the governed
variables), 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 a
surrogate for substitutional quantification and sentence-variables in
natural language, so as "to achieve the effect of generalizing
substitutionally over sentences ... but by means of ordinary
[quantifiers and] variables (i.e., pronouns), which range over
*objects*" (italics original). Horwich maintains that the
infinite "list-like" nature of minimalism poses no problem
for the view's adequacy with respect to explaining all of our
uses of the truth predicate, and the bulk of Horwich 1998a attempts to
establish just that. However, Anil Gupta (1993a, 365) has pointed out
that minimalism's infinite axiomatization in terms of the
instances of (E) for every (non-paradox-inducing) proposition makes it
maximally ideologically complex, in virtue of involving every other
concept. (Moreover, the overtly "fragmented" nature of the
theory also makes it particularly vulnerable to the Generalization
Problem that Gupta has raised, which we discuss in Section 4.5,
below.)



Christopher Hill (2002) attempts to deal with some of the problems
that Horwich's view faces, by presenting a view that he takes to
be a newer version of minimalism, replacing Horwich's
equivalence schema with a universally quantified formula, employing a
kind of substitutional quantification to provide a finite definition
of '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 driving
that rejection, Hill's (ibid., 18-22) idea is to offer
introduction 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 defining *linguistic*
substitutional quantification this way. Hill takes his substitutional
quantifiers to apply to thoughts (propositions) instead of sentences.
But serious concerns have been raised regarding the coherence of this
non-linguistic notion of substitutional quantification (cf. David
2006, Gupta 2006b, Simmons 2006). As a result, it is unclear that
Hill's account is an improvement on Horwich's version of
minimalism.


### 3.2 Disquotationalism



Like minimalism, disquotationalism agrees with inflationary accounts
of truth that the alethic locutions function as predicates, at least
logically speaking. However, as we explained in discussing
Quine's view in Section 2, disquotationalism diverges from
inflationary views (and minimalism) at their shared assumption that
these (alethic) predicates serve to *describe* the entities
picked 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's
recursive method for defining a truth predicate, that method is not
what Quine's view emphasizes. Field's contemporary
disquotationism further departs from that aspect of Tarski's
work by looking directly to the instances of the (T)-schema that the
recursive method must generate in order to satisfy Tarski's
criterion 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 (but
ultimately rejects; see Section 4.5) the thesis that a logical
conjunction of all of these partial definitions amounts to a general
definition of truth (for the language that the sentences belonged to).
Generalizing slightly from Tarski, we can call this alternative
approach "(T)-schema disquotationalism", in contrast with
the 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 the
instances of his preferred version of (ES), the "disquotational
schema" (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) allows
that one could take a "generalized" version of
(T/ES-sent), prefixed with a universal substitutional quantifier,
'\(\Pi\)', as having axiomatic status, or one could
incorporate schematic sentence variables directly into one's
theorizing language and reason directly with (T/ES-sent) as a schema
(cf. ibid., 259). Either way, in setting out his version of
deflationism, Field (ibid., 250), in contrast with Horwich, does not
take the instances of his version of (ES) as fundamental but instead
as following from the functioning of the truth predicate. On
Field's reading of (T/ES-sent), the use of the truth predicate
on the left-hand side of an instance does not add any cognitive
content beyond that which the mentioned utterance has (for the
speaker) on its own when used (as on the right-hand-side of
(T/ES-sent)). As a result, each instance of (T/ES-sent) "holds
of conceptual necessity, that is, by virtue of the cognitive
equivalence of the left and right hand sides" (ibid., 258). This
places Field's deflationism also in position \(\mathbf{A}\) in
the chart from Section 1.1.



Following Leeds and Quine, Field (1999, 533-4) sees the central
utility of a purely disquotational truth predicate to be providing for
the expression of certain "fertile generalizations" that
cannot be made without using the truth predicate but which do not
really involve the notion of truth. Field (1994a, 264) notes that the
truth predicate plays "an important logical role: it allows us
to formulate certain infinite conjunctions and disjunctions that
can't be formulated otherwise [n. 17: at least in a language
that does not contain *substitutional quantifiers*]".



Field's disquotationalism addresses some of the worries that
arose for earlier versions of this variety of deflationism, due to
their connections with Tarski's method of defining truth
predicates. It also explains how to apply a disquotational truth
predicate to ambiguous and indexical utterances, thereby going beyond
Quine's (1970 [1986]) insistence on taking eternal sentences as
the subjects of the instances of (ES-sent) (cf. Field 1994a,
278-81). So, Field's view addresses some of the concerns
that David (1994, 130-66) raises for disquotationalism. However,
an abiding concern about this variety of deflationism is that it is an
account of truth as applied specifically to sentences. This opens the
door to a version of the complaint that Strawson (1950) makes against
Austin's account of truth, that it is not one's act of
stating [here: the sentence one utters] but what thereby gets stated
that is the target of a truth ascription. William Alston (1996, 14)
makes a similar point. While disquotationalists do not worry much
about this, this scope restriction might strike others as problematic
because it raises questions about how we are to understand truth
applied to beliefs or judgments, something that Hill (2002) worries
about. Field (1978) treats beliefs as mental states relating thinkers
to sentences (of a language of thought). But David (1994, 172-7)
raises worries for applying disquotationalism to beliefs, even in the
context of an account like Field's. The view that we believe
sentences remains highly controversial, but it is one that, it seems,
a Field-style disquotationalist must endorse. Similarly, such
disquotationalists must take scientific theories to consist of sets of
sentences, in order for truth to be applicable to them. This too runs
up against Strawson's complaint because it suggests that one
could not state the same theory in a different language. These sorts
of concerns continue to press for disquotationalists.


### 3.3 Prosententialism



As emerges from the discussion of Grover, *et al*. (1975) in
Section 2, prosententialism is the form of deflationism that contrasts
the most with inflationism, rejecting even the latter's initial
assumption that the alethic locutions function as predicates. Partly
in response to the difficulties confronting Grover, *et
al*.'s prosentential account, Robert Brandom (1988 and 1994)
has developed a variation on their view with an important
modification. In place of taking the underlying logic of
'true' as having this expression occur only as a
non-separable component of the semantically atomic prosentential
expressions, 'that is true' and 'it is true',
Brandom treats 'is true' as a separable
*prosentence-forming* *operator*. "It applies to a
term that is a sentence nominalization or that refers to or picks out
a sentence tokening. It yields a prosentence that has that tokening as
its anaphoric antecedent" (Brandom 1994, 305). In this way,
Brandom's account avoids most of the paraphrase concerns that
Grover, *et al*.'s prosententialism faces, while still
maintaining prosententialism's rejection of the contention that
the alethic locutions function predicatively. As a consequence of his
operator approach, Brandom gives quantificational uses of prosentences
a slightly different analysis. He (re)expands instances of truth-talk
like 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 a
prosentence. The first 'it' in (8\*) and (11) still
functions as a pro*noun*, anaphorically linked to a set of noun
phrases (sentence nominalizations) supplying objects (sentence
tokenings) as a domain being quantified over with standard (as opposed
to sentential or "propositional") quantifiers (ibid.,
302).



Brandom presents a highly flexible view that takes 'is
true' as a general "denominalizing" device that
applies to singular terms formed from the nominalization of sentences
broadly, not just to pronouns that indicate them. A sentence like
'It is true that humans are causing climate change',
considered *via* a re-rendering as 'That humans are
causing climate change is true', is *already* a
prosentence on his view, as is a quote-name case like
"'Birds are dinosaurs' is true", and an opaque
instance of truth-talk like 'Goldbach's Conjecture is
true'. In this way, Brandom offers a univocal and broader
prosentential account, according to which, "[i]n each use, a
prosentence will have an anaphoric antecedent that determines a class
of admissible substituends for the prosentence (in the lazy case, a
singleton). This class of substituends determines the significance of
the prosentence associated with it" (ibid.). As a result,
Brandom can accept both (ES-sent) and (ES-prop) - the latter
understood as involving no commitment to propositions as entities
- on readings closer to their standard interpretations, taking
the instances of both to express meaning equivalences. Brandom's
account thus seems to be located in both position \(\mathbf{A}\) and
position \(\mathbf{B}\) in the chart from Section 1.1, although, as
with any prosententialist view, it still denies that the instances of
(ES) say anything *about* either sentences or propositions.



Despite its greater flexibility, however, Brandom's account
still faces the central worry confronting prosentential views, namely
that truth-talk really does seem predicative, and not just in its
surface grammatical form but in our inferential practices with it as
well. In arguing for the superiority of his view over that of Grover,
*et al*., Brandom states that "[t]he account of truth
talk should bear the weight of ... divergence of logical from
grammatical form only if no similarly adequate account can be
constructed that lacks this feature" (ibid., 304). One might
find it plausible to extend this principle beyond grammatical form, to
behavior in inferences as well. This is an abiding concern for
attempts 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 objections
to deflationism. These are by no means the only objections that have
been advanced against the approach, but they seem to be particularly
obvious and important ones.


### 4.1 The Explanatory Role of Truth



The first objection starts from the observation that (a) in certain
contexts an appeal to the notion of truth appears to have an
explanatory role and (b) deflationism seems to be inconsistent with
that appearance. Some of the contexts in which truth seems to have an
explanatory role involve philosophical projects, such as the
 theory of meaning
 (which we will consider below) or explaining the nature of
 knowledge.
 In these cases, the notion of explanation at issue is not so much
causal as it is *conceptual* (see Armour-Garb and Woodbridge
forthcoming, for more on this). But the notion of truth seems also
sometimes to play a *causal* explanatory role, especially with
regard to explaining various kinds of success - mainly the
success of scientific theories/method (cf. Putnam 1978 and Boyd 1983)
and of people's behavior (cf. Putnam 1978 and Field 1987), but
also the kind of success involved in learning from others (Field
1972). The causal-explanatory role that the notion of truth appears to
play in accounts of these various kinds of success has seemed to many
philosophers to constitute a major problem for deflationism. For
example, Putnam (1978, 20-1, 38) claims, "the notions of
'truth' and 'reference' have a
causal-explanatory role in ... an *explanation* of the
behavior 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 the
fact that certain of his beliefs are *true* - and the
formal logic of 'true' [the feature emphasized by
deflationism] is not all there is to the notion of
*truth*".



While a few early arguments against deflationism focus on the role of
truth in explanations of the success of science (see Williams 1986 and
Fine 1984a, 1984b for deflationary responses to Putnam and Boyd on
this), according to Field (1994a, 271), "the most serious worry
about deflationism is that it can't make sense of the
explanatory role of truth conditions: e.g., their role in explaining
behavior, or their role in explaining the extent to which behavior is
successful". While few theorists endorse the thesis that
explanations of behavior in general need to appeal to the notion of
truth (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 behavioral *success*,
still typically proceed in terms of an appeal to truth. This poses a
*prima facie* challenge to deflationary views. To illustrate
the problem, consider the role of the truth-value of an
individual's belief in whether that person succeeds in
satisfying her desires. Let us suppose that Mary wants to get to a
party, and she believes that it is being held at 1001 Northside
Avenue. If her belief is true, then, other things being equal, she is
likely to get to the party and get what she wants. But suppose that
her belief is false, and the party is in fact being held at 1001
Southside Avenue. Then it would be more likely, other things being
equal, that she won't get what she wants. In an example of this
sort, the truth of her belief seems to be playing a particular role in
explaining 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 occurs
*because* her belief is true, which might seem to pose a
problem for deflationists. However, truth-involving explanations of
particular instances of success like this don't really pose a
genuine problem. This is because if we are told the specific content
of the relevant belief, it is possible to replace the apparently
explanatory claim that the belief is true with an equivalent claim
that does not appeal to truth. In Mary's particular case, we
could replace i) the claim that she believes that the party is being
held at 1001 Northside Avenue, and her belief is true, with ii) the
claim that she believes that the party is being held at 1001 Northside
Avenue, and the party \(is\) being held at 1001 Northside Avenue. A
deflationist can claim that the appeal to truth in the explanation of
Mary's success just provides an expressive convenience
(including, perhaps, the convenience of expressing what would
otherwise require an infinite disjunction (of conjunctions like ii)),
by saying just that what Mary believed was true, if one did not know
exactly which belief Mary acted on) (cf. Horwich 1998a, 22-3,
44-6).



While deflationists seem to be able to account for appeals to truth in
explanations of particular instances of success, the explanatory-role
challenge to deflationism also cites the explanatory role that an
appeal to truth appears to play in explaining the phenomenon of
behavioral success more generally. An explanation of this sort might
take the following form:



> 
> 
> [1]
> People act (in general) in such a way that their goals will be
> obtained (as well as possible in the given situation), or in such a
> way 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 to
> attain certain kinds of goals. (Putnam 1978, 101)
> 
> 



The generality of [1] in this explanation seems to cover more cases
than any definite list of actual beliefs that someone has could
include. Moreover, the fact that [1] supports counterfactuals by
applying to whatever one might possibly believe (about attaining
goals) suggests that it is a law-like generalization. If the truth
predicate played a fundamental role in the expression of an
explanatory *law*, then deflationism would seem to be
unsustainable.



A standard deflationary response to this line of reasoning involves
rejecting the thesis that [1] is a law, seeing it (and truth-involving
claims like it) instead as functioning similarly to how the claim
'What Mary believes is true' functions in an explanation
of her particular instance of behavioral success, just expressing an
even more indefinite, and thus potentially infinite claim. The latter
is what makes a claim like [1] seem like an explanatory law, but even
considering this indefiniteness, the standard deflationary account of
[1] claims that the function of the appeal to the notion of truth
there is still just to express a kind of generalization. One way to
bring out this response is to note that, similar to the deflationary
"infinite disjunction" account of the claim 'What
Mary believes is true', generalizations of the kind offered in
[1] entail infinite *conjunctions* of their instances, which
are claims that can be formulated without appeal to truth. For
example, in the case of explaining someone, \(A\), accomplishing their
goal of getting to a party, deflationsts typically claim that the role
of citing possession of a true belief is really just to express an
infinite conjunction with something like the following form:



> 
> If \(A\) believes that the party is 1001 Northside Avenue, and the
> party is at 1001 Northside Avenue, then \(A\) will get what they want;
> and if \(A\) believes that the party is at 1001 Southside Avenue, and
> the party is at 1001 Southside Ave, then \(A\) will get what they
> want; and if \(A\) believes that party is at 17 Elm St, and the party
> is at 17 Elm St, then \(A\) will get what they want; ... and so
> on.
> 



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



> 
> If \(A\) believes that the party is 1001 Northside Avenue, and that
> the party is 1001 Northside Avenue is true, then \(A\) will get what
> they want; and if \(A\) believes that the party is at 1001 Southside
> Avenue, 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 is
> at 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 expressed
as a finite statement with a universal quantifier ranging over
propositions:



> 
> 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 express
the infinite conjunction regarding the agent's beliefs and
behavioral success unless one had the concept of truth. But
deflationists also claim that this is all that the notion of truth is
doing here and in similar explanations (cf. Leeds 1978, 1995; Williams
1986, Horwich 1998a).



How successful is this standard deflationary response? There are
several critiques in the literature. Some (e.g., Damnjanovic 2005)
argue that there is no distinction in the first place between
appearing in a causal-explanatory generalization and being a
causal-explanatory property. After all, suppose it is a true
generalization that metal objects conduct electricity. That would
normally be taken as sufficient to show that being metal is a
causal-explanatory property that one can cite in explaining why
something conducts electricity. But isn't this a counter, then,
to deflationism's thesis that, assuming there is a property of
truth at all, it is at most an insubstantial one? If a property is a
causal or explanatory property, after all, it is hard to view it as
insubstantial.



The reasoning at issue here may be presented conveniently by expanding
on the general argument considered above and proceeding from an
apparently 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 a
> causal-explanatory generalization.
> C3.
> Therefore, the property of being true is a causal-explanatory
> property.
> C4.
> Therefore, deflationism is false.
> 
> 



Can a deflationist apply the standard deflationary response to this
argument? Doing so would seem to involve rejecting the inference from
C2 to C3. After all, the standard reply would say that the role that
the 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. Leeds
1995). So, applying this deflationary response basically hinges on the
plausibility of rejecting the initial assumption that there is no
distinction between appearing in a causal-explanatory generalization
and being a causal-explanatory property.



It is worth noting two other responses beyond the standard one that a
deflationist might make to the reasoning just set out. The first
option is to deny the step from P1 to C1. This inference involves the
explicit introduction of the property of being true, and, as we have
seen, 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 truth
property 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 concede
that there is a sense in which truth is a causal-explanatory property
and yet say that it is still not a substantive property (cf.
Damnjanovic 2005). For example, some philosophers (e.g., Friedman
1974, van Fraassen 1980, Kitcher 1989, Jackson and Pettit 1990) have
offered different understandings of
 scientific explanation
 and causal explanation, according to which being a causal and
explanatory property might not conflict with being insubstantial
(perhaps by being an abundant or ungroundable property). This might be
enough to sustain a deflationary position.



The standard deflationary response to the explanatory-role challenge
has also met with criticisms focused on providing explanations of
certain "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 notion
of truth functions in explanations of behavioral success, misses the
more systematic role that truth plays in explaining *patterns*
of successful behavior, such as when mean-ends beliefs flow from a
representational device, like a map. Chase Wrenn (2011) agrees with
Kitcher that deflationists need to explain systematic as opposed to
just singular success, but against Kitcher he argues that
deflationists are actually better off than inflationists on this
front. Will Gamester (2018, 1252-5) raises a different
"higher-level factor" challenge, one based on the putative
inability of the standard deflationary account of the role of truth in
explanations of behavioral success to distinguish between coincidental
and non-coincidental success. Gamester (ibid., 1256-7) claims
that an inflationist could mark and account for the difference between
the two kinds of success with an explanation that appeals to the
notion of truth. But it is not clear that a deflationist cannot also
avail herself of a version of this truth-involving explanation, taking
it just as the way of expressing in natural language what one might
formally express with sentential variables and quantifiers (cf. Ramsey
1927, 1929; Prior 1971, Wrenn 2021, and Armour-Garb and Woodbridge
forthcoming).


### 4.2 Propositions Versus Sentences



We noted earlier that deflationism can be presented in either a
sententialist version or a propositionalist version. Some philosophers
have suggested, however, that the choice between these two versions
constitutes a dilemma for deflationism (Jackson, Oppy, and Smith
1994). The objection is that if deflationism is construed in
accordance with propositionalism, then it is trivial, but if it is
construed in accordance with sententialism, it is false. To illustrate
the 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 a
sentence or a proposition? If, on the one hand, we take (12) to be
about a sentence, then, assuming (12) can be interpreted as making a
necessary claim, it is false. On the face of it, after all, it takes a
lot more than snow's being white for it to be the case that
'snow is white' is true. In order for 'snow is
white' to be true, it must be the case not only that snow is
white, it must, in addition, be the case that 'snow is
white' *means that* snow is white. But this is a fact
about language that (12) ignores. On the other hand, suppose we take
'*snow is white*' in (12) to denote the proposition
that snow is white. Then the approach looks to be trivial, since the
proposition that snow is white is defined as being the one that is
true just in case snow is white. Thus, deflationism faces the dilemma
of being false or trivial.



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



A second response is to resist the suggestion that propositionist
deflationism is trivial. For one thing, the triviality here does not
have its source in the concept of truth, but rather in the concept of
a proposition. Moreover, even if we agree that the proposition that
snow is white is defined as the one that is true if and only if snow
is white, this still leaves open whether truth is a substantive
property of that proposition; as such it leaves open whether
deflationism or inflationism is correct.



A third response to this dilemma is to accept that deflationism
applies *inter alia* to sentences, but to argue (following
Field 1994a) that the sentences to which it applies must be
*interpreted* sentences, i.e., sentences which already have
meaning attached to them. While it takes more than snow being white to
make the sentence 'snow is white' true, when we think of
it as divorced from its meaning, that is not so clear when we treat it
as having the meaning it in fact has.


### 4.3 Correspondence



It is often said to be a platitude that true statements correspond to
the facts. The so-called "correspondence theory of truth"
is built around this intuition and tries to explain the notion of
truth by appealing to the notions of correspondence and fact. But even
if one does not *build* one's approach to truth around
this intuition, many philosophers regard it as a condition of adequacy
on any approach that it accommodate this correspondence intuition.



It is often claimed, however, that deflationism has trouble meeting
this adequacy condition. One way to bring out the problem here is by
focusing 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 certain
sentence or proposition "corresponds to the facts" is the
intuition that the sentence or proposition is true *because* of
how the world is; that is, the truth of the proposition is
*explained* by some fact, which is usually external to the
proposition itself. We might express this by saying that someone who
endorses the correspondence intuition so understood would endorse:



(6)
The proposition that snow is white is true *because* snow
is 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 that
the instances of the equivalence schema are necessary would clearly be
committed 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 very
plausible 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 such
relations must obtain between distinct relata. But the relata in (8)
are (obviously) not distinct. Hence, (8) is false, and this means that
the conjunction of (6) and (7) must be false, and that deflationism is
inconsistent with the correspondence intuition. To borrow a phrase of
Mark Johnston's (1989) - who mounts a similar argument in
a different context - we might say that if deflationism is true,
then what seems to be a perfectly good explanation in (6) *goes
missing*; if deflationism is true, after all, then (6) is
equivalent to (8), and (8) is not an explanation of anything.



One way a deflationist might attempt to respond to this objection is
by providing a different articulation of the correspondence intuition.
For example, one might point out that the connection between the
proposition that snow is white being true and snow's being white
is not a contingent connection and suggest that this rules out (6) as
a successful articulation of the correspondence intuition. That
intuition (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 the
problematic (8), and thus, one might think, the objection from
correspondence might be avoided. Now, certainly this is a possible
suggestion; the problem with it, however, is that a deflationist who
thinks that (6\*) is true is most plausibly construed as holding a
sententialist, rather than a propositionalist, version of
deflationism. A sententialist version of deflationism will supply a
version 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 we
started.



Another response would be to object that 'because' creates
an *opaque context* - that is, the kind of context within
which one cannot substitute co-referring expressions and preserve
truth. However, for this to work, 'because' must create an
opaque context of the right kind. In general, we can distinguish two
kinds of opaque context: *intensional* contexts, which allow
the substitution of necessarily co-referring expressions but not
contingently co-referring expressions; and
 hyperintensional
 contexts, which do not even allow the substitution of necessarily
co-referring expressions. If the inference from (6) and (7) to (8) is
to be successfully blocked, it is necessary that 'because'
creates a hyperintensional context. A proponent of the correspondence
objection might try to argue that while 'because' creates
an intensional context, it does not create a hyperintensional context.
But since a hyperintensional reading of 'because' has
become standard fare, this approach remains open to a deflationist and
is not an *ad hoc* fix.



A final, and most radical, response would be to reject the
correspondence intuition outright. This response is not as drastic as
it sounds. In particular, deflationists do not have to say that
someone who says 'the proposition that snow is white corresponds
to the facts' is speaking falsely. Deflationists might do better
by saying that such a person is simply using a picturesque or ornate
way of saying that the proposition is true, where truth is understood
in accordance with deflationism. Indeed, a deflationist can even agree
that, for certain rhetorical or conversational purposes, it might be
more effective to use talk of "correspondence to the
facts". Nevertheless, it is important to see that this response
does involve a burden, since it involves rejecting a condition of
adequacy 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 that
one ought to return people's phone calls - are neither
true nor false. The same situation holds, according to some
philosophers of language, for claims that presuppose the existence of
something which does not in fact exist, such as the claim that the
present King of France is bald; for sentences that are vague, such as
'These grains of sand constitute a heap'; and for
sentences that are paradoxical, such as those that arise in connection
with the
 Liar Paradox.
 Let us call this thesis *the gap*, since it finds a gap in the
class of sentences between those that are true and those that are
false.



The deflationary approach to truth has seemed to be inconsistent with
the 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 apparent
inconsistency flows from a natural way to extend the deflationary
approach from truth to falsity. The most natural thing for a
deflationist 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 relevant
schema for falsity, rather than some propositional schema, since the
standard understanding of a gappy sentence is as one that does not
express a proposition (cf. Jackson, *et al.* 1994).



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



However, there is a seeming incompatibility between (F-sent) and the
gap. Suppose, for *reductio,* that 'S' is a
sentence that is neither true nor false. In that case, it is not the
case that 'S' is true, and it is not the case that
'S' is false. But then, by (ES-sent) and (F-sent), we can
infer that it is not the case that S, and it is not the case that
not-S; in short: \({\sim}\)S and \({\sim}{\sim}\)S, which is a
classical contradiction. Clearly, then, we must give up one of these
things. But which one can we give up consistently with
deflationism?



In the context of ethical non-cognitivism, one possible response to
the apparent dilemma is to distinguish between a deflationary account
of truth and a deflationary account of truth-*aptitude* (cf.
Jackson, *et al.* 1994). By accepting an inflationary account
of the latter, one can claim that ethical statements fail the robust
criteria of "truth-aptitude" (reidentified in terms of
expression of belief), even if a deflationary view of truth still
allows the application of the truth predicate to them, *via*
instances of (ES). In the case of
 vagueness,
 one might adopt epistemicism about it and claim that vague sentences
actually 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 between
deflationism and the gap has led some (e.g., Simmons 1999) to conclude
that deflationism is hobbled with respect to dealing with the problem,
since most prominent approaches to doing so, stemming from the work of
Saul Kripke (1975), involve an appeal to truth-value gaps. One
alternative strategy a deflationist might pursue in attempting to
resolve the Liar is to offer a non-classical logic. Field 2008 adopts
this approach and restricts the law of the excluded middle. JC Beall
(2002) combines truth-value gaps with Kleene logic (see the entry on
 many-valued Logic)
 and makes use of both weak and strong
 negation.
 Armour-Garb and Beall (2001, 2003) argue that deflationists can and
should be
 dialetheists
 and accept that some truthbearers are both true and not true (see
also, Woodbridge 2005, 152-3, on adopting a
 paraconsistent logic
 that remains "quasi-classical"). By contrast, Armour-Garb
and Woodbridge (2013, 2015) develop a version of the
"meaningless strategy" with respect to the Liar (based on
Grover 1977), which they claim a deflationist can use to dissolve that
paradox and semantic pathology more generally, without accepting
genuine truth-value gaps or giving up classical logic.


### 4.5 The Generalization Problem



Since deflationists place such heavy emphasis on the role of the
concept of truth in expressing generalizations, it seems somewhat
ironic that certain versions of deflationism have been criticized for
being incapable of accounting for generalizations involving
*truth* (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 "Generalization
Problem" (henceforth, \(GP)\) captures the worry that a
deflationary account of truth is inadequate for explaining our
commitments 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 such
generalizations.



Although Tarski (1935 [1956]) places great importance on the instances
of his (T)-schema, he comes to recognize that those instances do not
provide a fully adequate way of characterizing truth. Moreover, even
when the instances of (T) are taken as theorems, Tarski (ibid.) points
out that taken all together they are insufficient for proving a
'true'-involving generalization like



(A)
All sentences of the form 'If \(p\), then \(p\)' are
true.


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 the
instances of some version of (ES) with Quine's view about the
functioning and utility of the truth predicate. He (1992, 81)
considers the purpose of (A) to be to express a generalization over
sentences 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 embedded
sentences 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 (the
instances of) (T). From (T) and (A), we can prove (B) and (C) but,
given the finitude of deduction, when equipped only with the instances
of (T), we cannot prove (A). As a consequence of the Compactness
Theorem of first-order logic, anything provable from the totality of
the instances of (T) is provable from just finitely many of them, so
any theory that takes the totality of the instances of (T) to
characterize truth will be unable to prove any generalization like
(A).



To address the question of why we need to be able to prove these
truth-involving generalizations, suppose that we accept a proposition
like \(\langle\)Every proposition of the form \(\langle\)if \(p\),
then \(p\rangle\) is true\(\rangle\). Call this proposition
"\(\beta\)". Now take '\(\Gamma\)' to stand
for 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 why
we accept the members of \(\Gamma\), where such explanations amount to
proofs of those propositions by, among other things, employing an
explanatory premise that does not explicitly concern the truth
predicate. So, one reason it is important to be able to prove a
'true'-involving generalization is because this is a
condition of adequacy for an account of the meaning of that term. One
might argue that anyone who grasps the concept of truth, and that of
the relevant conditional, should be said to know \(\beta\). But if a
given account of truth, together with an account of the conditional
(along, perhaps, with an account of other logical notions), does not
entail \(\beta\), then it does not provide an acceptable account of
truth.



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, should
be knowable *a priori* by anyone who possesses the concept of
truth (and who grasps the relevant logical concepts). But if such a
proposition can be known *a priori* on the basis of a grasp of
the concept of truth (and of the relevant logical concepts), then a
theory that purports to specify the meaning of 'true'
should be able to explain our acceptance of that proposition. But if
an account of the meaning of 'true' is going to do this,
it must be possible to derive the proposition from one or more of the
clauses that constitute our grasp of the concept of truth.



This creates a problem for a Horwichian minimalist. Let us suppose
that \(\beta\) is one of the general propositions that must be
provable. Restricted to the resources available through
Horwich's minimalism, we can show that \(\beta\) cannot be
derived.



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



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


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



Some deflationists respond to the GP by using a version of (GT) to
formulate 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, it
is 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 on
 second-order and higher-order logic)
 that quantifies into sentential positions. We mentioned above an
approach that takes this quantifier as a substitutional one, where the
substitution class consists of sentences. We also mentioned
Hill's (2002) alternative version that takes the substitution
class to be the set of all propositions. Kunne (2003) suggests a
different approach that takes '\(\Sigma\)' to be an
objectual (domain and values) quantifier ranging over propositions.
However, parallel to Horwich's rejection of (GT) discussed in
Section 3.1, all of these approaches have drawn criticism on the
grounds that the use of higher-order quantifiers to define truth is
circular (cf. Platts 1980, McGrath 2000), and may get the extension of
the 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 the
resources to derive the relevant generalizations. Field (1994a,
2001a), for example, suggests that we allow reasoning with schemas
directly and proposes rules that would allow the derivation of
generalizations. Horwich (1998a, 2001) suggests a more informal
approach 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. For
replies to Horwich, see Armour-Garb 2004, 2010, 2011; Gupta 1993a,
1993b; and Soames 1999. For responses to Armour-Garb's attack on
Horwich 2001, see Oms 2019 and Cieslinski 2018.


### 4.6 Conservativeness



An ideal theory of truth will be both consistent (e.g., avoid the Liar
Paradox) and adequate (e.g., allow us to derive all the essential laws
of truth, such as those at issue in the Generalization Problem). Yet
it has recently been argued that even if deflationists can provide a
consistent theory of truth and avoid the GP, they still cannot provide
an adequate theory.



This argument turns on the notion of a conservative extension of a
theory. Informally, a conservative extension of a theory is one that
does not allow us to prove anything that could not be proved from the
original, unextended theory. More formally, and applied to theories of
truth, 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
'\(\vdash\)' represents *provability*). Certain
truth theories are conservative over arithmetic - e.g., theories
that implicitly define truth using only the instances of some version
of (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 that
arithmetic is consistent, something that we cannot do if we are
confined to arithmetic itself.



It has been argued (a) that conservative truth theories are inadequate
and (b) that deflationists are committed to conservative truth
theories. (See Shapiro 1998 and Ketland 1999; Horsten 1995 provides an
earlier version of this argument.) We will explain the arguments for
(a) below but to get a flavor of the arguments for (b), consider
Shapiro's rhetorical question: "How thin can the notion of
arithmetic truth be, if by invoking it we can learn more about the
natural numbers?" Shapiro is surely right to press deflationists
on their frequent claims that truth is "thin" or
"insubstantial". It might also be a worry for
deflationists if any adequate truth theory allowed us to derive
non-logical truths, if they endorse the thesis that truth is merely a
"logical property". On the other hand, deflationists
themselves insist that truth is an expressively useful device, and so
they cannot be faulted for promoting a theory of truth that allows us
to say more about matters not involving truth.



To see an argument for (a), consider a Godel sentence, \(G\),
formulated within the language of Peano Arithmetic (henceforth,
\(PA)\). \(G\) is not a theorem of PA if PA is consistent (cf. the
entry on
 Godel's incompleteness theorems).
 But \(G\) becomes a theorem when PA is expanded by adding certain
plausible principles that appear to govern a truth predicate. Thus,
the resultant theory of arithmetical truth is strong enough to prove G
and appears therefore to be non-conservative over arithmetic. If, as
has been argued by a number of theorists, any adequate account of
truth will be non-conservative over a base theory, then deflationists
appear to be in trouble.



Understood in this way, the "Conservativeness Argument"
(henceforth, \(CA)\) is a variant of the objection considered in
Section 4.1, claiming that truth plays an explanatory role that
deflationism cannot accommodate. There are several deflationary
responses to the CA. Field (1999) argues that the worries that arise
from the claim that deflationists are in violation of explanatory
conservativeness is unfounded. He (ibid., 537) appeals to the
expressive role of the truth predicate and maintains that
deflationists are committed to a form of "explanatory
conservativeness" only insofar as there are no explanations in
which the truth predicate is not playing its generalizing role. As a
result, he (ibid.) notes that "any use of 'true' in
explanations which derives solely from its role as a device of
generalization should be perfectly acceptable". For responses to
Field, 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 first
conception, arithmetic is understood *categorically* as given
by the standard model. On the second conception, arithmetic is
understood *axiomatically* and is captured by the acceptance of
some first-order theory, such as PA. Waxman argues that deflationism
can be conservative given either conception, so that the CA does not
go through.



Julien Murzi and Lorenzo Rossi (2018) argue that Waxman's
attempt at marrying deflationism with conservativeness - his
"conservative deflationism" - is unsuccessful. They
(ibid.) reject the adoption of this view on the assumption that
one's conception of arithmetic is axiomatic, claiming, in
effect, that a deflationist's commitment to a conservative
conception of truth is misguided (cf. Halbach 2011, Horsten 2011,
Cieslinski 2015, and Galinon 2015).



Jody Azzouni (1999) defends the "first-order
deflationist", viz., a deflationist who endorses what Waxman
(ibid.) calls "the axiomatic conception of arithmetic" and
whose subsequent understanding cannot rule out the eligibility of
non-standard models. Azzouni accepts the need to prove certain
'true'-involving generalizations, but he maintains that
there are some generalizations that are *about* truths that a
first-order deflationist need not prove. He further contends that if
one does extend her theory of truth in a way that allows her to
establish these generalizations, she should not expect her theory to
be conservative, nor should she continue describing it as a
*deflationary* view of truth. For a response to Azzouni
(ibid.), see Waxman (2017, 453).



In line with Field's response to the CA, Lavinia Picollo and
Thomas Schindler (2020) argue that the conservativeness constraint
imposed by Horsten 1995, Shapiro 1998, Ketland 1999, and others is not
a reasonable requirement to impose on deflationary accounts. They
contend that the insistence on conservativeness arises from making too
much of the metaphor of "insubstantiality" and that it
fails to see what the function of the truth predicate really amounts
to. Their leading idea is that, from a deflationist's
perspective, the logico-linguistic function of the truth predicate is
to simulate sentential and predicate quantification in a first-order
setting (cf. Horwich 1998a, 4, n. 1). They maintain that, for a
deflationist, in conjunction with first-order quantifiers, the truth
predicate has the same function as sentential and predicate
quantifiers. So, we should not expect the deflationist's truth
theory to conservatively extend its base theory.


### 4.7 Normativity



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



The first thing to note is that there is certainly a sense in which
deflationism is consistent with the idea that truth is a norm of
assertion. To illustrate this, notice (as we saw in examining
truth's putative explanatory role) that we can obtain an
intuitive understanding of this idea without mentioning truth at all,
so long as we focus on a particular case. Suppose that for whatever
reason Mary sincerely believes that snow is green, has good evidence
for this belief, and on the basis of this belief and evidence asserts
that snow is green. We might say that there is a norm of assertion
that implies that Mary is still open to criticism in this case. After
all, since snow is not green, there must be something
*incorrect* or *defective* about Mary's assertion
(and similarly for her belief). It is this incorrectness or
defectiveness that the idea that truth is a norm of assertion (and
belief) is trying to capture.



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



(13)
If someone asserts that snow is green when snow is not green, then
that assertion is open to criticism.


To generalize on this, what we want to do is generalize on the
positions occupied by 'snow is green' and express
something 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 same
issue first raised in Section 1.3, and the solution by now should be
familiar. To state the norm in general we would need to be able to do
something we seem unable to do in ordinary language, namely, employ
sentential variables and quantifiers for them. But this is where the
notion of truth comes in. Because (ES) gives us its
contraposition,



(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 \(p\) is
not true, then that assertion is open to criticism.


But since the variable '\(p\)' occurs only in nominalized
contexts in (15), we can replace it with an object variable,
'\(x\)', and bind this with an ordinary objectual
quantifier, 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 the
notion of truth to *express* a norm of assertion; on the
contrary, the concept of truth seems required to state that very
generalization.



If deflationists can account for the fact that we must apply the
notion of truth to express a norm of assertion, then does normativity
pose any problem for deflationism? Crispin Wright (1992, 15-23)
argues that it does, claiming that deflationism is inherently unstable
because there is a distinctive norm for assertoric practice that goes
beyond the norms for warranted assertibility - that the norms of
truth and warranted assertibility are potentially extensionally
divergent. This separate norm of truth, he claims, is already implicit
just in acceptance of the instances of (ES). He points out that not
having warrant to assert some sentence does not yield having warrant
to assert its negation. However, because (ES) gives us (ES-con), we
have, in each instance, an inference (going from right to left) from
the 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 sentence
to an ascription of truth to that negated sentence. Thus, some
sentence not being true *does* yield that the negation of the
sentence is true, in contrast with warranted assertibility. This
difference, Wright (ibid., 18) claims, reveals that, by
deflationism's own lights, the truth predicate expresses a
distinct norm governing assertion, which is incompatible with the
deflationary contention "that 'true' is only
grammatically a predicate whose role is not to attribute a substantial
characteristic".



Rejecting Wright's argument for the instability of deflationism,
Ian Rumfitt (1995, 103) notes that if we add the ideas of denying
something and of having warrant for doing so
("anti-warrant") to Wright's characterization of
deflationism, this would make 'is not true' simply a
device of rejection governed by the norm that "[t]he predicate
'is not true' may be applied to any sentence for which one
has an anti-warrant". But then truth-talk's behavior with
negation would not have to be seen as indicating that it marks a
distinct norm beyond justified assertibility *and justifiable
deniability*, which would be perfectly compatible with
deflationism.



Field (1994a, 264-5) offers a deflationary response to
Wright's challenge (as well as to a similar objection regarding
normativity from Putnam (1983a, 279-80)), pointing again to the
generalizing role of the truth predicate in such normative desires as
one to utter only true sentences or one to have only true beliefs.
Field agrees with Wright that truth-talk expresses a norm beyond
warranted assertibility, but he (1994a, 265) also maintains that
"there is no difficulty in desiring that all one's beliefs
be disquotationally true; and not only can each of us desire such
things, there can be a general practice of badgering other to into
having such desires". Horwich (1996, 879-80) argues that
Wright's rejection of deflationism does not follow from showing
that one can use the truth predicate to express a norm beyond
warranted assertibility. Like Field, Horwich claims that Wright missed
the point that, in the expression of such a norm, the truth predicate
is just playing its generalizing role. For other objections to
deflationism 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 a
little-known doctrine about truth that G.E. Moore held at the
beginning of the 20th Century. Richard Cartwright (1987, 73) describes
the view as follows: "a true proposition is one that has a
certain simple unanalyzable property, and a false proposition is one
that lacks the property". This doctrine about truth is to be
understood as the analogue for the doctrine that Moore held about
goodness, namely that goodness is a simple, unanalyzable quality.



The potential problem that this Moorean view about truth presents for
deflationism might best be expressed in the form of a question: What
is the difference between the Moorean view and deflationism? One might
reply that, according to deflationary theories, the concept of truth
has an important logical role, i.e., expressing certain
generalizations, whereas the concept of goodness does not. However,
this doesn't really answer our question. For one thing, it
isn't clear that Moore's notion of truth does not also
capture generalizations, since it too will yield all of the instances
of (ES). For another, the idea that the concept of truth plays an
important logical role doesn't distinguish the metaphysics of
deflationary conceptions from the metaphysics of the Moorean view, and
it is the metaphysics of the matter that the present objection really
brings into focus. Alternatively, one might suggest that the
distinction between truth according to Moore's view and
deflationary conceptions of truth is the distinction between having a
simple unanalyzable nature, and not having any underlying nature at
all. But what is that distinction? It is certainly not obvious that
there is any distinction between having a nature about which nothing
can be said and having no nature at all.



How might a deflationist respond to this alleged problem? The key move
will be to focus on the property of being true. For the Moorean, this
property is a simple unanalyzable one. But deflationists need not be
committed to this. As we have seen, some deflationists think that
there is no truth property at all. And even among deflationists who
accept that there is some insubstantial truth property, it is not
clear 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 a
fundamental property. One might understand this in something like the
sense that Lewis proposes, i.e., as a property that is sparse and
perfectly natural. Or one might understand a fundamental property as
one that is groundable but not grounded in anything. But deflationists
need not understand a purported property of being true in either of
these ways. As noted in Section 1.2, they may think of it as an
abundant property rather than a sparse one, or as one that is
ungroundable. In this way, there are options available for
deflationists who want to distinguish themselves from the Moorean view
of truth.


### 4.9 Truth and Meaning



The final objection that we will consider concerns the relation
between deflationism and theories of meaning, i.e., theories about how
sentences get their meanings.



The orthodox approach to this last question appeals to the notion of
truth, suggesting, roughly, that a sentence \(S\) means that \(p\)
just in case \(S\) is true if and only if \(p\). This approach to
meaning, known widely as "truth-conditional semantics", is
historically associated with
 Donald Davidson's
 (1967) thesis that the "(T)-sentences" (i.e., the
instances of the (T)-schema) generated by a Tarski-truth-definition
for a language give the meanings of the sentences they mention, by
specifying their truth conditions. In contemporary linguistics, a
prominent approach to sentence meaning explains it in terms of
propositions, understood (following Lewis 1970 and Stalnaker 1970) as
sets of possible worlds, which amount to encapsulations of truth
conditions (Elbourne 2011, 50-51).



This has led a number of philosophers to argue that, on pain of
circularity, deflationism cannot be combined with theories of meaning
that make use of the notion of truth to explain meaning - in
other words, that deflationism is incompatible with truth-conditional
theories of meaning. This assessment of deflationism stems from
Dummett's (1959 [1978, 7]) claim that the (T)-sentences (or the
instances of any other version of (ES)) cannot both tell us what the
sentences they nominalize mean and give us an account of
'true'. As Horwich (1998a, 68) puts it, "we would be
faced with something like a single equation and two unknowns"
(cf. Davidson 1990, 1996; Horwich 1998b, Kalderon 1999, Collins
2002).



The first thing to say regarding this objection is that, even if
deflationism were inconsistent with truth-conditional theories of
meaning, this would not *automatically* constitute an objection
to deflationism. After all, there are alternative theories of meaning
available, and most deflationists reject truth-conditional semantics
in favor of some "truth-free" alternative. The main
alternatives available include Brandom's (1994) inferentialism,
developed following
 Wilfrid Sellars
 (1974, 1979); Horwich's (1998b) use-theory of meaning, inspired
by 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 regarded
as adequate. Devitt 2001 makes this point in rejecting all of these
alternative approaches to meaning, claiming that the only viable
approach is (referential/)truth-conditional semantics.



While the orthodoxy of truth-conditional accounts of meaning adds
weight to this challenge to deflationism, it is still, contra Devitt,
an open question whether any non-truth-conditional account of meaning
will 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 more
problem with a truth-conditional theory of meaning than any other
approach to truth does. Others have gone further, arguing positively
that there is no incompatibility between deflationism and
truth-conditional theories. Alexis Burgess (2011, 407-410)
argues that at least some versions of deflationism are compatible with
mainstream model-theoretic semantics in linguistics (understood as
providing explanations of truth conditions) and the recognition of
"the manifest power and progress of truth-conditional
semantics". Claire Horisk (2008) argues that
"circularity" arguments for incompatibility (or, as she
prefers, "immiscibility") fail. The only circularity
involved here, she claims, is a harmless kind, so long as one is (like
some 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 an
anaphoric reading of 'is true' (as in Brandom 1988, 1994)
is independent of, and thus compatible with, any underlying account of
meaning, including a truth-conditional one. Williams 1999 likewise
claims that the role of truth in meaning theories for particular
languages is just the expressive role that deflationists claim
exhausts the notion of truth's function. Of course, all of these
claims have been contested, but they seem to show that the thesis that
deflationism is inconsistent with a truth-conditional theory of
meaning is neither a forgone conclusion nor necessarily an objection
to deflationism, even if the thesis is correct. (For further
discussion of this issue, see Gupta 1993b, Field 2005, Gupta and
Martinez-Fernandez 2005, Patterson 2005, and Horisk 2007.) That said,
one outstanding question that remains regarding the viability of any
deflationary approach to truth is whether that approach can be squared
with an adequate account of meaning.