## 1. History of the Correspondence Theory




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


### 1.1 Metaphysical and Semantic Versions




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




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




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




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




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


### 1.2 Object-Based and Fact-Based Versions




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




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



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




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




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




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



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




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


## 2. Truthbearers, Truthmakers, Truth


### 2.1 Truthbearers




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


1. The term "truthbearer" is somewhat misleading. It is
intended to refer to bearers of truth or falsehood
(truth-value-bearers), or alternatively, to things of which it makes
sense to ask whether they are true or false, thus allowing for the
possibility that some of them might be neither.
2. One distinguishes between
*secondary* and *primary* truthbearers. Secondary
truthbearers are those whose *truth-values* (truth or
falsehood) are derived from the truth-values of primary truthbearers,
whose truth-values are not derived from any other
truthbearers. Consequently, the term "true" is usually
regarded as ambiguous, taking its primary meaning when applied to
primary truthbearers and various secondary meanings when applied to
other truthbearers. This is, however, not a brute ambiguity, since the
secondary meanings are supposed to be derived, i.e. definable from,
the primary meaning together with additional relations. For example,
one might hold that propositions are true or false in the primary
sense, whereas sentences are true or false in a secondary sense,
insofar as they *express* propositions that are true or false
(in the primary sense). The meanings of "true", when
applied to truthbearers of different kinds, are thus connected in a
manner familiar from what Aristotelians called
"analogical" uses of a term--nowadays one would call
this "focal meaning"; e.g., "healthy" in
"healthy organism" and "healthy food", the
latter being defined as healthy in the secondary sense of contributing
to the healthiness (primary sense) of an organism.
3. It is often unproblematic to advocate one theory of truth for
bearers of one kind and another theory for bearers of a different kind
(e.g., a deflationary theory of truth, or an identity theory, applied
to propositions, could be a component of some form of correspondence
theory of truth for sentences). Different theories of truth applied to
bearers of different kinds do not automatically compete. The standard
segregation of truth theories into competing camps (found in
textbooks, handbooks, and dictionaries) proceeds under the
assumption--really a pretense--that they are intended for
primary truthbearers of the same kind.
4. Confusingly, there is little agreement as to which entities are
properly taken to be primary truthbearers. Nowadays, the main
contenders are public language sentences, sentences of the language of
thought (sentential mental representations), and propositions. Popular
earlier contenders--beliefs, judgments, statements, and
assertions--have fallen out of favor, mainly for two reasons:
	1. The problem of *logically complex truthbearers*. A
	subject, S, may hold a disjunctive belief (the baby will be a boy or
	the baby will be a girl), while believing only one, or neither, of the
	disjuncts. Also, S may hold a conditional belief (if whales are fish,
	then some fish are mammals) without believing the antecedent or the
	consequent. Also, S will usually hold a negative belief (not everyone
	is lucky) without believing what is negated. In such cases, the
	truth-values of S's complex beliefs depend on the truth-values
	of their constituents, although the constituents may not be believed
	by S or by anyone. This means that a view according to which beliefs
	are primary truthbearers seems unable to account for how the
	truth-values of complex beliefs are connected to the truth-values of
	their simpler constituents--to do this one needs to be able to
	apply truth and falsehood to belief-constituents *even when they
	are not believed*. This point, which is equally fundamental for a
	proper understanding of logic, was made by all early advocates of
	propositions (cf. Bolzano 1837, I.SSSS22, 34; Frege 1879, SSSS2-5; Husserl
	1900, I.SS11; Meinong 1902, SS6). The problem arises in much the same
	form for views that would take judgments, statements, or assertions as
	primary truthbearers. The problem is not easily evaded. Talk of
	unbelieved beliefs (unjudged judgments, unstated statements,
	unasserted assertions) is either absurd or simply amounts to talk of
	unbelieved (unjudged, unstated, unasserted) propositions or
	sentences. It is noteworthy, incidentally, that quite a few
	philosophical proposals (concerning truth as well as other matters)
	run afoul of the simple observation that there are unasserted and
	unbelieved truthbearers (cf. Geach 1960 & 1965).
	2. The duality of  *state/content*
	a.k.a. *act/object*. The noun "belief" can refer
	to *the state of believing* or to its content, i.e.,
	to *what is believed*. If the former, the state of believing,
	can be said to be true or false at all, which is highly questionable,
	then only insofar as the latter, what is believed, is true or
	false. Similarly for nouns referring to mental acts or their objects
	(contents), such as "judgment", "statement",
	and "assertion".
5. Mental sentences were the preferred primary truthbearers
throughout the medieval period. They were neglected in the first half
of the 20th century, but made a comeback in the second half through
the revival of the representational theory of the mind (especially in
the form of the language-of-thought hypothesis, cf. Fodor
1975). Somewhat confusingly (to us now), for many centuries the term
"proposition" (*propositio*) was reserved
exclusively for sentences, written, spoken or mental. This use was
made official by Boethius in the 6th century, and is still found in
Locke's *Essay* in 1705 and in
Mill's *Logic* in 1843. Some time after that, e.g., in
Moore's 1901-01, "proposition" switched sides, the
term now being used for *what is said* by uttering a sentence,
for what is believed, judged, stated, assumed (etc.)--with
occasional reversions to medieval usage, e.g. in Russell (1918,
1919).


### 2.2 Truthmakers




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


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


### 2.3 Truth




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


## 3. Simple Versions of the Correspondence Theory




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



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | *x* is true iff *x* corresponds to some fact;
> 
> *x* is false iff *x* does not correspond to any fact.
>  |
> 
> 
> 



> 
> 
> 
> |  |  |
> | --- | --- |
> | (2) | *x* is true iff *x* corresponds to some state of
> affairs that obtains; 
> *x* is false iff *x* corresponds to some state of
> affairs that does not obtain. |
> 
> 
> 




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




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




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




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




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




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



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




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




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



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




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




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


## 4. Arguments for the Correspondence Theory




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




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




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


## 5. Objections to the Correspondence Theory



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




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




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




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




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



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




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



***Objection 3*:** Correspondence theories are
too obscure.




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



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



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



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



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


## 6. Correspondence as Isomorphism




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




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



> 
> *Nonidentity:*  
>  No truth is identical with a fact
> correspondence to which is sufficient for its being a truth.
> 




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




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



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




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




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



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



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




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




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




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




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


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




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




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




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




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




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




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


## 7. Modified Versions of the Correspondence Theory


### 7.1 Logical Atomism




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




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




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




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




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



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



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




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




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




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




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


### 7.2 Logical "Subatomism"




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




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




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



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



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


### 7.3 Relocating Correspondence




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




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


## 8. The Correspondence Theory and Its Competitors


### 8.1 Traditional Competitors




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




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


### 8.2 Pluralism




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


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




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



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



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




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


### 8.3 The Identity Theory of Truth




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




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


### 8.4 Deflationism About Truth




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



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




is to be deflated to



> (6) "Snow is white" is true iff snow is
> white,




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




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



> (7) "*p*" is true iff
> *p*,




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




It should be noted that the deflationist's starting point, (5),
which lends itself to deflating excisions, actually misrepresents the
correspondence theory. According to (5), corresponding to the fact
that snow is white is sufficient *and necessary* for
"Snow is white" to be true. Yet, according to (1) and (2),
it is sufficient but not necessary: "Snow is white" will
be true as long as it corresponds to some fact or other. The genuine
article, (1) or (2), is not as easily deflated as the impostor
(5).




The debate turns crucially on the question whether anything deserving
to be called an "account" or "theory" of truth
ought to take the form of a genuine generalization (and ought to be
able to account for genuine generalizations involving
truth). Correspondence theorists tend to regard this as a (minimal)
requirement. Deflationists argue that truth is a shallow (sometimes
"logical") notion--a notion that has no serious
explanatory role to play: as such it does not require a full-fledged
account, a real theory, that would have to take the form of a genuine
generalization.




There is now a substantial body of literature on truth-deflationism in
general and its relation to the correspondence theory in particular;
the following is a small selection: Quine 1970, 1987; Devitt 1984;
Field 1986; Horwich 1990 & 19982; Kirkham 1992; Gupta
1993; David 1994, 2008; Schmitt 1995; Kunne 2003, chap. 4; Rami
2009. Relevant essays are contained in Blackburn and Simmons 1999;
Schantz 2002; Armour-Garb and Beall 2005; and Wright and Pedersen
2010. See also the entry
 the deflationary theory of truth 
in this encyclopedia.


### 8.5 Truthmaker Theory




This approach centers on the *truthmaker*
or *truthmaking* *principle*: Every truth has a
truthmaker; or alternatively: For every truth there is something that
makes it true. The principle is usually understood as an expression of
a realist attitude, emphasizing the crucial contribution the world
makes to the truth of a proposition. Advocates tend to treat
truthmaker theory primarily as a guide to ontology, asking: To
entities of what ontological categories are we committed as
truthmakers of the propositions we accept as true? Most advocates
maintain that propositions of different logical types can be made true
by items from different ontological categories: e.g., propositions of
some types are made true by facts, others just by individual things,
others by events, others by tropes (cf., e.g. Armstrong 1997). This is
claimed as a significant improvement over traditional correspondence
theories which are understood--correctly in most but by no means
all cases--to be committed to all truthmakers belonging to a
single ontological category (albeit disagreeing about which category
that is). All advocates of truthmaker theory maintain that the
truthmaking relation is not one-one but many-many: some truths are
made true by more than one truthmaker; some truthmakers make true more
than one truth. This is also claimed as a significant improvement over
traditional correspondence theories which are often portrayed as
committed to correspondence being a one-one relation. This portrayal
is only partly justified. While it is fairly easy to find real-life
correspondence theorists committing themselves to the view that each
truth corresponds to exactly one fact (at least by implication,
talking about *the* corresponding fact), it is difficult to
find real-life correspondence theorists committing themselves to the
view that only one truth can correspond to a given fact (but see Moore
1910-11, p. 256).




A truthmaker theory may be presented as a competitor to the
correspondence theory or as a version of the correspondence
theory. This depends considerably on how narrowly or broadly one
construes "correspondence theory", i.e. on terminological
issues. Some advocates would agree with Dummett (1959, p. 14) who said
that, although "we have nowadays abandoned the correspondence
theory of truth", it nevertheless "expresses one important
feature of the concept of truth...: that a statement is true only
if there is something in the world in virtue of which it is
true". Other advocates would follow Armstrong who tends to
present his truthmaker theory as a liberal form of correspondence
theory; indeed, he seems committed to the view that the truth of a
(contingent) *elementary* proposition consists in its
correspondence with some (atomic) fact (cf. Armstrong 1997; 2004,
pp. 22-3, 48-50).




It is not easy to find a substantive difference between truthmaker
theory and various brands of the sort of modified correspondence
theory treated above under the heading "Logical Atomism"
(see Section 7.1). Logical atomists, such as Russell (1918) and
Wittgenstein (1921), will hold that the truth or falsehood of every
truth-value bearer can be explained in terms of (can be derived from)
logical relations between truth-value bearers, by way of the recursive
clauses, together with the base clauses, i.e., the correspondence and
non-correspondence of elementary truth-value bearers with facts. This
recursive strategy could be pursued with the aim to *reject the
truthmaker principle*: not all truths have truthmakers, only
elementary truths have truthmakers (here understood as corresponding
atomic facts). But it could also be pursued--and this seems to
have been Russell's intention at the time--with the aim
to *secure the truthmaker principle*, even though the simple
correspondence definition has been abandoned: not every truth
corresponds to a fact, only elementary truths do, but every
truth *has* a truthmaker; where the recursive clauses are
supposed to show how truthmaking without correspondence, but grounded
in correspondence, comes about.




There is one straightforward difference between truthmaker theory and
most correspondence theories. The latter are designed to answer the
question "What is truth?". Simple (unmodified)
correspondence theories center on a *biconditional*, such as
"*x* is true iff *x* corresponds to a fact",
intended to convey a *definition* of truth (at least a
"real definition" which does not commit them to the claim
that the term "true" is synonymous with "corresponds
to a fact"--especially nowadays most correspondence
theorists would consider such a claim to be implausibly and
unnecessarily bold). Modified correspondence theories also aim at
providing a definition of truth, though in their case the definition
will be considerably more complex, owing to the recursive character of
the account. Truthmaker theory, on the other hand, centers on
the *truthmaker principle*: For every truth there is something
that makes it true. Though this principle will deliver the
biconditional "*x* is true iff something makes *x*
true" (since "something makes *x* true"
trivially implies "*x* is true"), this does not
yield a promising candidate for a definition of truth: defining truth
in terms of truthmaking would appear to be circular. Unlike most
correspondence theories, truthmaker theory is not equipped, and
usually not designed, to answer the question "What is
truth?"--at least not if one expects the answer to take the
form of a feasible candidate for a definition of truth.




There is a growing body of literature on truthmaker theory; see for
example: Russell 1918; Mullligan, Simons, and Smith 1984; Fox 1987;
Armstrong 1997, 2004; Merricks 2007; and the essays in Beebe and Dodd
2005; Monnoyer 2007; and in Lowe and Rami 2009. See also the entry
on truthmakers in this encyclopedia.


## 9. More Objections to the Correspondence Theory




Two final objections to the correspondence theory deserve separate
mention.


### 9.1 The Big Fact




Inspired by an allegedly similar argument of Frege's, Davidson
(1969) argues that the correspondence theory is bankrupt because it
cannot avoid the consequence that all true sentences correspond to the
same fact: the Big Fact. The argument is based on two crucial
assumptions: (i) Logically equivalent sentences can be
substituted *salva veritate* in the context 'the fact
that...'; and (ii) If two singular terms denoting the same thing
can be substituted for each other in a given sentence *salva
veritate*, they can still be so substituted if that sentence is
embedded within the context 'the fact that...'. In the
version below, the relevant singular terms will be the following:
'(the *x* such that *x* = Diogenes
& *p*)' and '(the *x* such
that *x* = Diogenes & *q*)'. Now, assume that
a given sentence, *s*, corresponds to the fact that *p*;
and assume that '*p*' and '*q*'
are sentences with the same truth-value. We have:


* *s* corresponds to the fact that
*p*



 which, by (i), implies


* *s* corresponds to the fact that [(the *x* such that
*x* = Diogenes & *p*) = (the *x* such that
*x* = Diogenes)],


 which, by (ii), implies


* *s* corresponds to the fact that [(the *x* such that
*x* = Diogenes & *q*) = (the *x* such that
*x* = Diogenes)],



 which, by (i), implies


* *s* corresponds to the fact that *q*.




Since the only restriction on '*q*' was that it
have the same truth-value as '*p*', it would follow
that any sentence *s* that corresponds to any fact corresponds
to every fact; so that all true sentences correspond to the same
facts, thereby proving the emptiness of the correspondence
theory--the conclusion of the argument is taken as tantamount to
the conclusion that every true sentence corresponds to the totality of
all the facts, i.e, the Big Fact, i.e., the world as a whole.




This argument belongs to a type now called "slingshot
arguments" (because a giant opponent is brought down by a single
small weapon, allegedly). The first versions of this type of argument
were given by Church (1943) and Godel (1944); it was later
adapted by Quine (1953, 1960) in his crusade against quantified modal
logic. Davidson is offering yet another adaption, this time involving
the expression "corresponds to the fact that". The
argument has been criticized repeatedly. Critics point to the two
questionable assumptions on which it relies, (i) and (ii). It is far
from obvious why a correspondence theorist should be tempted by either
one of them. Opposition to assumption (i) rests on the view that
expressibility by logically equivalent sentences may be a necessary,
but is not a sufficient condition for fact identity. Opposition to
assumption (ii) rests on the observation that the (alleged) singular
terms used in the argument are *definite descriptions*: their
status as genuine singular terms is in doubt, and it is well-known
that they behave rather differently than proper names for which
assumption (ii) is probably valid (cf. Follesdal 1966/2004; Olson
1987; Kunne 2003; and especially the extended discussion and
criticism in Neale 2001.)


### 9.2 No Independent Access to Reality




The objection that may well have been the most effective in causing
discontent with the correspondence theory is based on an
epistemological concern. In a nutshell, the objection is that a
correspondence theory of truth must inevitably lead into skepticism
about the external world, because the required correspondence between
our thoughts and reality is not ascertainable. Ever since
Berkeley's attack on the representational theory of the mind,
objections of this sort have enjoyed considerable popularity. It is
typically pointed out that we cannot step outside our own minds to
compare our thoughts with mind-independent reality. Yet--so the
objection continues--on the correspondence theory of truth, this
is precisely what we would have to do to gain knowledge. We would have
to access reality as it is in itself, independently of our cognition,
and determine whether our thoughts correspond to it. Since this is
impossible, since all our access to the world is mediated by our
cognition, the correspondence theory makes knowledge impossible
(cf. Kant 1800, intro vii). Assuming that the resulting skepticism is
unacceptable, the correspondence theory has to be rejected, and some
other account of truth, an epistemic (anti-realist) account of some
sort, has to be put in its place (cf., e.g., Blanshard 1941.)




This type of objection brings up a host of issues in epistemology, the
philosophy of mind, and general metaphysics. All that can be done here
is to hint at a few pertinent points (cf. Searle 1995, chap. 7; David
2004, 6.7). The objection makes use of the following line of
reasoning: "If truth is correspondence, then, since knowledge
requires truth, we have to know that our beliefs correspond to
reality, if we are to know anything about reality". There are
two assumptions implicit in this line of reasoning, both of them
debatable.




(i) It is assumed that *S* knows *x*, only if *S*
knows that
*x* is true--a requirement not underwritten by standard
definitions of knowledge, which tell us that *S* knows
*x*, only if *x* is true and *S* is justified in
believing *x*. The assumption may rest on confusing requirements
for knowing *x* with requirements for knowing that one knows
*x*.




(ii) It is assumed that, if truth = *F*, then *S* knows
that *x* is true, only if *S* knows that *x* has
*F*. This is highly implausible. By the same standard it
would follow that no one who does not know that water is
H2O can know that the Nile contains water--which would
mean, of course, that until fairly recently nobody knew that the Nile
contained water (and that, until fairly recently, nobody
knew that there were stars in the sky, whales in the sea, or that the
sun gives light). Moreover, even if one does know that water is
H2O, one's strategy for finding out whether the liquid in
one's glass is water does not have to involve chemical analysis: one
could simply taste it, or ask a reliable informant. Similarly, as far
as knowing that *x* is true is concerned, the
correspondence theory does not entail that we have to know that a
belief corresponds to a fact in order to know that it is true, or that
our method of finding out whether a belief is true has to involve a
strategy of actually comparing a belief with a fact--although the
theory does of course entail that one obtains knowledge only if
one obtains a belief that corresponds to a fact.




More generally, one might question whether the objection still has
much bite once the metaphors of "accessing" and
"comparing" are spelled out with more attention to the
psychological details of belief formation and to epistemological
issues concerning the conditions under which beliefs are justified or
warranted. For example, it is quite unclear how the metaphor of
"comparing" applies to knowledge gained through perceptual
belief-formation. A perceptual belief that p may be true, and by
having acquired that belief, one may have come to know that p, without
having "compared" (the content of) one's belief with
anything.




One might also wonder whether its competitors actually enjoy any
significant advantage over the correspondence theory, once they are
held to the standards set up by this sort of objection. For example,
why should it be easier to find out whether one particular belief
coheres with *all* of one's other beliefs than it is to
find out whether a belief corresponds with a fact?




In one form or other, the "No independent access to
reality"-objection against correspondence theoretic approaches
has been one of the, if not the, main source and motivation for
idealist and anti-realist stances in philosophy (cf. Stove
1991). However, the connection between correspondence theories of
truth and the metaphysical realism vs. anti-realism (or idealism)
debate is less immediate than is often assumed. On the one hand,
deflationists and identity theorists can be, and typically are,
metaphysical realists while rejecting the correspondence theory. On
the other hand, advocates of a correspondence theory can, in
principle, be metaphysical idealists (e.g. McTaggart 1921) or
anti-realists, for one might advocate a correspondence theory while
maintaining, at the same time, (*a*) that all facts are
constituted by mind or (*b*) that what facts there are depends
somehow on what we believe or are capable of believing, or
(*c*) that the correspondence relation between true
propositions and facts depends somehow on what we believe or are
capable of believing (claiming that the correspondence relation
between true beliefs or true sentences and facts depends on what we
believe can hardly count as a commitment to anti-realism). Keeping
this point in mind, one can nevertheless acknowledge that advocacy of
a correspondence theory of truth comes much more naturally when
combined with a metaphysically realist stance and usually signals
commitment to such a stance.