## 1. The neo-classical theories of truth



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



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



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


### 1.1 The correspondence theory



Perhaps the most important of the neo-classical theories for the
contemporary literature is the correspondence theory. Ideas that sound
strikingly like a correspondence theory are no doubt very old. They
might well be found in Aristotle or Aquinas. When we turn to the late
19th and early 20th centuries where we pick up the story of the
neo-classical theories of truth, it is clear that ideas about
correspondence were central to the discussions of the time. In spite
of their importance, however, it is strikingly difficult to find an
accurate citation in the early 20th century for the received
neo-classical view. Furthermore, the way the correspondence theory
actually emerged will provide some valuable reference points for the
contemporary debate. For these reasons, we dwell on the origins of the
correspondence theory in the late 19th and early 20th centuries at
greater length than those of the other neo-classical views, before
turning to its contemporary neo-classical form. For an overview of the
correspondence theory, see David (2018).


### 1.1.1 The origins of the correspondence theory



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



Let us pick up the thread of this story in the years between 1898 and
about 1910. These years are marked by Moore and Russell's
rejection of idealism. Yet at this point, they do not hold a
correspondence theory of truth. Indeed Moore (1899) sees the
correspondence theory as a source of idealism, and rejects it. Russell
follows Moore in this regard. (For discussion of Moore's early
critique of idealism, where he rejects the correspondence theory of
truth, see Baldwin (1991). Hylton (1990) provides an extensive
discussion of Russell in the context of British idealism. An overview
of these issues is given by Baldwin (2018).)



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



The identity theory Moore and Russell espoused takes truth to be a
property of propositions. Furthermore, taking up an idea familiar to
readers of Moore, the property of truth is a simple unanalyzable
property. Facts are understood as simply those propositions which are
true. There are true propositions and false ones, and facts just are
true propositions. There is thus no "difference between truth
and the reality to which it is supposed to correspond" (Moore,
1902, p. 21). (For further discussion of the identity theory of truth,
see Baldwin (1991), Candlish (1999), Candlish and Damnjanovic (2018),
Cartwright (1987), Dodd (2000), and the entry on the
 identity theory of truth.)



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



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



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



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



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



Views like this are held by Moore (1953) and Russell (1910b; 1912). Of
course, to understand such a theory, we need to understand the crucial
relation of correspondence, as well as the notion of a fact to which a
belief corresponds. We now turn to these questions. In doing so, we
will leave the history, and present a somewhat more modern
reconstruction of a correspondence theory. (For more on facts and
proposition in this period, see Sullivan and Johnston (2018).)


### 1.1.2 The neo-classical correspondence theory



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



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



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



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



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



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



\[\begin{matrix}
\text{proposition that} & \text{Ramey} & \text{sings} \\
 & \downarrow & \downarrow \\
\text{fact} & \langle Ramey, & Singing \rangle
\end{matrix}\]


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



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



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



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



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



For more on the correspondence theory, see David (1994, 2018) and the
entry on the
 correspondance theory of truth.


### 1.2 The coherence theory



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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


### 1.3 Pragmatist theories



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



> 
> Truth is the end of inquiry.
> 



(See, for instance Hartshorne et al., 1931-58, SS3.432.)
Both Peirce and James are associated with the slogan that:



> 
> Truth is satisfactory to believe.
> 



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



In her reconstruction (upon which we have relied heavily), Haack
(1976) notes that the pragmatists' views on truth also make room
for the idea that truth involves a kind of correspondence, insofar as
the scientific method of inquiry is answerable to some independent
world. Peirce, for instance, does not reject a correspondence theory
outright; rather, he complains that it provides merely a
'nominal' or 'transcendental' definition of
truth (e.g Hartshorne et al., 1931-58, SS5.553,
SS5.572), which is cut off from practical matters of experience,
belief, and doubt (SS5.416). (See Misak (2004) for an extended
discussion.)



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



For more on pragmatist theories of truth, see Misak (2018).
James' views are discussed further in the entry on
 William James.
 Peirce's views are discussed further in the entry on
 Charles Sanders Peirce.


## 2. Tarski's theory of truth



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



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



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


### 2.1 Sentences as truth-bearers



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



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



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



In some places (e.g., Tarski, 1944), Tarski refers to his view as the
'semantic conception of truth'. It is not entirely clear
just what Tarski had in mind by this, but it is clear enough that
Tarski's theory defines truth for sentences in terms of concepts
like reference and satisfaction, which are intimately related to the
basic semantic functions of names and predicates (according to many
approaches to semantics). For more discussion, see Wolenski
(2001). 


### 2.2 Convention T



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



> 
> An adequate theory of truth for \(\mathbf{L}\) must imply, for
> each sentence \(\phi\) of \(\mathbf{L}\)
> 



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



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



Convention T draws our attention to the biconditionals of the form



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



which are usually called the *Tarski biconditionals* for a
language \(\mathbf{L}\).


### 2.3 Recursive definition of truth



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



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


1. Base clauses:
	1. 'Snow is white' is true if and only if snow is
	white.
	2. 'Grass is green' is true if and only if grass is
	green.
2. Recursion clauses. For any sentences \(\phi\) and \(\psi\) of
\(\mathbf{L}\):
	1. \(\ulcorner \phi \vee \psi \urcorner\) is true if
	and only if \(\ulcorner \phi \urcorner\) is true or
	\(\ulcorner \psi \urcorner\) is true.
	2. \(\ulcorner \neg \phi \urcorner\) is true if and
	only if it is not the case that \(\ulcorner \phi \urcorner\) is true.



This theory satisfies Convention T.


### 2.4 Reference and satisfaction



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



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



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


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



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



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



For more, see Ray (2018) and the entries on
 axiomatic theories of truth,
 the
 Liar paradox,
 and
 Tarski's truth definitions.


## 3. Correspondence revisited



The correspondence theory of truth expresses the very natural idea
that truth is a content-to-world or word-to-world relation: what we
say or think is true or false in virtue of the way the world turns out
to be. We suggested that, against a background like the metaphysics of
facts, it does so in a straightforward way. But the idea of
correspondence is certainly not specific to this framework. Indeed, it
is controversial whether a correspondence theory should rely on any
particular metaphysics at all. The basic idea of correspondence, as
Tarski (1944) and others have suggested, is captured in the slogan
from Aristotle's *Metaphysics* G 7.27, "to
say of what is that it is, or of what is not that it is not, is
true" (Ross, 1928). 'What is', it is natural enough
to say, is a fact, but this natural turn of phrase may well not
require a full-blown metaphysics of facts. (For a discussion of
Aristotle's views in a historical context, see Szaif
(2018).)



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


### 3.1 Correspondence without facts



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



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



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



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


1. 'Snow' refers to snow.
2. \(a\) satisfies 'is white' if and only if
\(a\) is white.



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



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


### 3.2 Representation and Correspondence



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



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



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



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


### 3.3 Facts again



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



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



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



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



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



For more on facts, see the entry on
 facts.


### 3.4 Truthmakers



The truthmaker principle is often put as the schema:



> 
> If \(\phi\), then there is an \(x\) such that necessarily, if
> \(x\) exists, then \(\phi\).
> 



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



The truthmaker principle expresses the *ontological* aspect of
the neo-classical correspondence theory. Not merely must truth obtain
in virtue of word-to-world relations, but there must be a thing that
makes each truth true. (For one view on this, see Merricks
(2007).)



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



As we saw in discussing the neo-classical correspondence theory,
truthmaker theories, and fact theories in particular, raise a number
of issues. One which has been discussed at length, for instance, is
whether there are *negative facts*. Negative facts would be the
truthmakers for negated sentences. Russell (1956) notoriously
expresses ambivalence about whether there are negative facts.
Armstrong (1997) rejects them, while Beall (2000) defends them. (For
more discussion of truthmakers, see Cameron (2018) and the papers in
Beebee and Dodd (2005).)


## 4. Realism and anti-realism



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



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


### 4.1 Realism and truth



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



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


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



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



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



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



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



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



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



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


### 4.2 Anti-realism and truth



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



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



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



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



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



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



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



For more on anti-realism and truth, see Shieh (2018) and the papers in
Greenough and Lynch (2006) and the entry on
 realism.


### 4.3 Anti-realism and pragmatism



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



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



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



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


### 4.4 Truth pluralism



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



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



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



For more on pluralism about truth, see Pedersen and Lynch (2018) and
the entry on
 pluralist theories of truth.


## 5. Deflationism



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



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


### 5.1 The redundancy theory



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



> 
> \(\ulcorner \ulcorner \phi \urcorner\)
> is true \(\urcorner\) has the same meaning as \(\phi\).
> 



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



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



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



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



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



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


### 5.2 Minimalist theories



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



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


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



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



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


### 5.3 Other aspects of deflationism



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



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



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



For more on deflationism, see Azzouni (2018) and the entry on the
 deflationary theory of truth.


## 6. Truth and language



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


### 6.1 Truth-bearers



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



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



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



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



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



For more on these issues, see King (2018).


### 6.2 Truth and truth conditions



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



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



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



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



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



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


### 6.3 Truth conditions and deflationism



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



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



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



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



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


### 6.4 Truth and the theory of meaning



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



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


### 6.5 The coherence theory and meaning



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



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



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



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



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


### 6.6 Truth and assertion



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



> 
> Truth is the aim of assertion.
> 



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



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



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



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



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



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