## 1. Definition and Preliminary Exposition



Declarative sentences seem to take truth-values, for we say things
like



(1)
 "Socrates is wise" is true.


But sentences are apparently not the only bearers of truth-values: for
we also seem to allow that what such sentences express, or mean, may
be true or false, saying such things as



(2)
 "Socrates is wise" means *that Socrates is
 wise*,[1]


and



 (3)
 *That Socrates is wise* is true


or



 (4)
 It is true *that Socrates is wise*.


If, provisionally, we call the things that declarative sentences
express, or mean, their *contents*--again provisionally,
these will be such things as *that Socrates is wise*--then
the identity theory of truth, in its most general form, states that
(cf. Baldwin 1991: 35):



 (5)
 A declarative sentence's content is true just if that
content is (identical with) a fact.


A fact is here to be thought of as, very generally, *a way things
are*, or *a way the world is*. On this approach, the
identity theory secures an intimate connection between language (what
language expresses) and world. Of course there would in principle be
theoretical room for a view that identified not the content of, say,
the true declarative sentence "Socrates is wise"--let
us assume from now on that this sentence is true--with the fact
*that Socrates is wise*, but rather that sentence itself. But
this is not a version of the theory that anyone has ever advanced, nor
does it appear that it would be plausible to do so (see Candlish
1999b: 200-2; Kunne 2003: 6). The early Wittgenstein does
regard sentences as being themselves facts, but they are not identical
with the facts that make them true.



Alternatively, and using a different locution, one might say that, to
continue with the same example,



 (6)
 *That Socrates is wise* is true just if *that Socrates
is wise* is the case.


The idea here is that (6) makes a connection between language and
reality: on the left-hand side we have something expressed by a piece
of language, and on the right-hand side we allude to a bit of reality.
Now (6) might look truistic, and that status has indeed been claimed
for the identity theory, at least in one of its manifestations. John
McDowell has argued that what he calls true "thinkables"
are identical with facts (1996: 27-8, 179-80). Thinkables
are things like *that Socrates is wise* regarded as possible
objects of thought. For we can think *that Socrates is wise*;
and it can also be the case *that Socrates is wise*. So the
idea is that what we can think can also be (identical with) what is
the case. That identity, McDowell claims, is truistic. On this
approach, one might prefer one's identity theory to take the
form (cf. Hornsby 1997: 2):



(7)
 All true thinkables are (identical with) facts.


On this approach the identity theory explicitly aims to secure an
intimate connection between mind (what we think) and world.



A point which has perhaps been obscured in the literature on this
topic, but which should be noticed, is that (7) asserts a relation of
subordination: it says that true thinkables are a (proper or improper)
subset of facts; it implicitly allows that there might be facts that
are not identical with true thinkables. So (7) is not to be confounded
with its converse,



(8)
 All facts are (identical with) true thinkables,


which asserts the opposite subordination, and says that facts are a
(proper or improper) subset of true thinkables, implicitly allowing,
this time, that there might be true thinkables that are not identical
with facts. (8) is therefore distinct from (7), and if (7) is
controversial, (8) is equally or more so, but for reasons that are at
least in part different. (8) denies the existence of facts that cannot
be grasped in thought. But many philosophers hold it to be evident
that there are, or at least could be, such facts--perhaps certain
facts involving indefinable real numbers, for example, or in some
other way going beyond the powers of human thought. So (8) could be
false; its status remains to be established; it can hardly be regarded
as truistic. Accordingly, one might expect that an identity theorist
who wished to affirm (7), and certainly anyone who wanted to say that
(7) (or (6)) was truistic, would--at least *qua* identity
theorist--steer clear of (8), and leave its status *sub
judice*. In fact, however, a good number of identity theorists,
both historical and contemporary, incorporate (8) as well as--or
even instead of--(7) into their statement of the theory. Richard
Cartwright, who published the first modern discussion of the theory in
1987, wrote that if one were formulating the theory, it would say
"that every true proposition is a fact and every fact a true
proposition" (1987: 74). McDowell states that



> 
> 
> true thinkables already belong just as much to the world as to minds
> [i.e., (7)], and things that are the case already belong just as much
> to minds as to the world [i.e., (8)]. It should not even seem that we
> need to choose a direction in which to read the claim of identity.
> (2005: 84)
> 
> 
> 



Jennifer Hornsby takes the theory to state that true thinkables and
facts *coincide* (1997: 2, 9, 17, 20)--they are the same
set--so that she in effect identifies that theory with the
conjunction of (7) and (8), as also, in effect, does Julian Dodd
(2008a: *passim*). Now, (8) is certainly an interesting thesis
that merits much more consideration than it has hitherto received (at
least in the recent philosophical literature), and, as indicated, some
expositions of the identity theory have as much invested in (8) as in
(5) or (7): on this point see further
 SS2
 below. Nevertheless, it will make for clarity of discussion if we
associate the identity theory of truth, more narrowly, with something
along the lines of (5) or (7), and omit (8) from this particular
 discussion.[2]
 That will be the policy here.



Whether or not (6) is truistic, both (5) and (7) involve technical or
semi-technical vocabulary; moreover, they have been advanced as moves
in a technical debate, namely one concerning the viability of the
correspondence theory of truth. For these reasons it seems difficult
to regard them as truisms (see Dodd 2008a: 179). What (5) and (7)
mean, and which of them one will prefer as one's statement of
the identity theory of truth, if one is favorably disposed to that
theory--one may of course be happy with both--will depend,
among other things, on what exactly one thinks about the nature of
such entities as *that Socrates is wise*. In order to get clear
on this point, discussion of the identity theory has naturally been
conducted in the context of the Fregean semantical hierarchy, which
distinguishes between levels of language, sense, and reference. Frege
recognized what he called "thoughts" (*Gedanken*)
at the level of sense corresponding to (presented by) declarative
sentences at the level of language. McDowell's thinkables are
meant to be Fregean thoughts: the change of terminology is intended to
stress the fact that these entities are not thoughts in the sense of
dated and perhaps spatially located individual occurrences (thinking
events), but are abstract contents that are at least in principle
available to be grasped by different thinkers at different times and
places. So a Fregean identity theory of truth would regard both such
entities as *that Socrates is wise* and, correlatively, facts
as sense-level entities: this kind of identity theory will then state
that true such entities are identical with facts. This approach will
naturally favor (7) as its expression of the identity theory.



By contrast with Frege, Russell abjured the level of sense and (at
least around 1903-4) recognized what, following Moore, he called
"propositions" as worldly entities composed of objects and
properties. A modern Russellian approach might adopt these
propositions--or something like them: the details of
Russell's own conception are quite vague--as the referents
of declarative sentences, and identity theorists who followed this
line might prefer to take a particular reading of (5) as their slogan.
So these Russellians would affirm something along the lines of:



(9)
 All true Russellian propositions are identical with facts (at the
level of reference),


by contrast with the Fregean



(10)
 All true Fregean thoughts are identical with facts (at the level
of sense).


This way of formulating the relevant identity claims has the advantage
of suggesting that it would, at least in principle, be open to a
theorist to combine (9) and (10) in a hybrid position that (i)
departed from Russell and followed Frege by admitting *both* a
level of Fregean sense *and* one of reference, and also, having
admitted both levels to the semantic hierarchy, (ii) *both*
located Fregean thoughts at the level of sense *and* located
Russellian propositions at the level of reference. Sense being mode of
presentation of reference, the idea would be that declarative
sentences refer, *via* Fregean thoughts, to Russellian
propositions (for this disposition, see Gaskin 2006: 203-20;
2008: 56-127). So someone adopting this hybrid approach would
affirm both (9) and (10). Of course, the facts mentioned in (9) would
be *categorially different* from the facts mentioned in (10),
and one might choose to avoid confusion by distinguishing them
terminologically, and perhaps also by privileging one set of facts,
ontologically, over the other. If one wanted to follow this
privileging strategy, one might say, for instance, that only
reference-level facts were *genuine* facts, the *relata*
of the identity relation at the level of sense being merely
*fact-like entities*, not *bona fide* facts. That would
be to give the combination of (9) and (10) a Russellian spin.
Alternatively, someone who took the hybrid line might prefer to give
it a Fregean spin, saying that the entities with which true Fregean
thoughts were identical were the genuine facts, and that the
corresponding entities at the level of reference that true Russellian
propositions were identical with were not facts as such, but fact-like
correlates of the genuine facts. Without more detail, of course, these
privileging strategies leave the status of the entities they are
treating as merely fact-*like* unclear; and, as far as the
Fregean version of the identity theory goes, commentators who identify
facts with sense-level Fregean thoughts usually, as we shall see,
repudiate reference-level Russellian propositions altogether, rather
than merely downgrading their ontological status, and so affirm (10)
but reject (9). We shall return to these issues in
 SS4
 below.


## 2. Historical Background



The expression "the identity theory of truth" was first
used--or, at any rate, first used in the relevant sense--by
Stewart Candlish in an article on F. H. Bradley published in 1989. But
the general idea of the theory had been in the air during the 1980s:
for example, in a discussion first published in 1985, concerning John
Mackie's theory of truth, McDowell criticized that theory for
making 



> 
> 
> truth consist in a relation of correspondence (rather than identity)
> between how things are and how things are represented as being. (1985
> [1998: 137 n. 21]) 
> 
> 
> 



The implication is that identity would be the right way to conceive
the given relation. And versions of the identity theory go back at
least to Bradley (see, e.g., Bradley 1914: 112-13; for further
discussion and references, see Candlish 1989; 1995; 1999b:
209-12; T. Baldwin 1991: 36-40), and to the founding
fathers of the analytic tradition (Sullivan 2005: 56-7 n. 4).
The theory can be found in G. E. Moore's "The Nature of
Judgment" (1899), and in the entry he wrote on
"Truth" for J. Baldwin's *Dictionary of
Philosophy and Psychology* (1902-3; reprinted Moore 1993:
4-8, 20-1; see T. Baldwin 1991: 40-3). Russell
embraced the identity theory at least during the period of his 1904
discussions of Meinong (see, e.g., 1973: 75), possibly also in his
*The Principles of Mathematics* of 1903, and for a few years
after these publications as well (see T. Baldwin 1991: 44-8;
Candlish 1999a: 234; 1999b: 206-9). Frege has a statement of the
theory in his 1919 essay "The Thought", and may have held
it earlier (Frege 1918-19: 74 [1977: 25]; see Hornsby 1997:
4-6; Milne 2010: 467-8).



Wittgenstein's *Tractatus* (1922) is usually held to
propound a correspondence rather than an identity theory of truth;
however this is questionable. In the *Tractatus*, declarative
sentences (*Satze*) are said to be facts (arrangements of
names), and states of affairs (*Sachlagen*,
*Sachverhalte*, *Tatsachen*) are also said to be facts
(arrangements of objects). If the *Tractatus* is taken to put
forward a correspondence theory of truth, then presumably the idea is
that a sentence will be true just if there is an appropriate relation
of correspondence (an isomorphism) between sentence and state of
affairs. However, the problem with this interpretation is that, in the
*Tractatus*, a relation of isomorphism between a sentence and
reality is generally conceived as a condition of the
*meaningfulness* of that sentence, not specifically of its
*truth*. False sentences, as well as true, are isomorphic with
states of affairs--only, in their case the states of affairs do
not obtain. For Wittgenstein, states of affairs may either obtain or
fail to obtain--both possibilities are, in general, available to
 them.[3]
 Correlatively, it has been suggested that the *Tractatus*
contains two different conceptions of fact, a factive and a
non-factive one. According to the former conception, facts necessarily
obtain or are the case; according to the latter, facts may fail to
obtain or not be the case. This non-factive conception has been
discerned at *Tractatus* 1.2-1.21, and at 2.1 (see
Johnston 2013: 382). Given that, in the *Tractatus*, states of
affairs (and perhaps facts) have two poles--obtaining or being
the case, and non-obtaining or not being the case--it seems to
follow that, while Wittgenstein is committed to a correspondence
theory of *meaning*, his theory of *truth* must be (some
version of) an identity theory, along the lines of 



> 
> 
> A declarative sentence is true just if what it is semantically
> correlated with is identical with an obtaining state of affairs (a
> factive fact). 
> 
> 
> 



(Identity theorists normally presuppose the factive conception of
facts, so that "factive" is redundant in the phrase
"factive facts", and that is the policy which will be
followed here.) Though a bipolar conception of facts (if indeed
Wittgenstein has it) may seem odd, the bipolar conception of states of
affairs (which, it is generally agreed, he does have) seems quite
natural: here the identity theorist says that a true proposition is
identical with an obtaining state of affairs (see Candlish &
Damnjanovic 2018: 271-2).



Peter Sullivan has suggested a different way of imputing an identity
theory to the Tractarian Wittgenstein (2005: 58-9). His idea is
that Wittgenstein's simple objects are to be identified with
Fregean senses, and that in effect the *Tractatus* contains an
identity theory along the lines of (7) or (10). Sullivan's
ground for treating Tractarian objects as senses is that, like
*bona fide* Fregean senses, they are *transparent*: they
cannot be grasped in different ways. An apparent difficulty with this
view is that there is plausibly more to Fregean sense than just the
property of transparency: after all, Russell also attached the
property of transparency to his basic objects, but it has not been
suggested that Russellian basic objects are really senses, and the
suggestion would seem to have little going for it (partly, though not
only, because Russell himself disavowed the whole idea of Fregean
sense).The orthodox position, which will be presupposed here, is that
the Tractarian Wittgenstein like Russell, finds no use for a level of
Fregean sense, so that his semantical hierarchy consists exclusively
of levels of language and reference, with nothing of a mediatory or
similar nature located between these levels. (Wittgenstein does appeal
to the *concepts* of sense and reference in the
*Tractatus*, but it is generally agreed that they do not figure
in a Fregean way, according to which both names and sentences, for
example, have both sense and reference; for Wittgenstein, by contrast,
sentences have sense but not reference, whereas names have reference
but not sense.)


## 3. Motivation



What motivates the identity theory of truth? It can be viewed as a
response to difficulties that seem to accrue to at least some versions
of the correspondence theory (cf. Dodd 2008a: 120, 124). The
correspondence theory of truth holds that truth consists in a relation
of correspondence between something linguistic or quasi-linguistic, on
the one hand, and something worldly on the other. Generally, the items
on the worldly end of the relation are taken to be facts or
(obtaining) states of affairs. For many purposes these two latter
kinds of entity (facts, obtaining states of affairs) are assimilated
to one another, and that strategy will be followed here. The exact
nature of the correspondence theory will then depend on what the other
*relatum* is taken to be. The items mentioned so far make
available three distinct versions of the correspondence theory,
depending on whether this *relatum* is taken to consist of
declarative sentences, Fregean thoughts, or Russellian propositions.
Modern correspondence theorists make a distinction between
truth-*bearers*, which would typically fall under one of these
three classifications, and
 truth-*makers*,[4]
 the worldly entities making truth-bearers true, when they are true.
If these latter entities are facts, then true declarative sentences,
Fregean thoughts, or Russellian propositions--whichever of these
one selects as the relata of the correspondence relation on the
language side of the language-world divide--correspond to
facts in the sense that facts are what make those sentences, thoughts,
or propositions true, when they are true. (Henceforth we shall
normally speak simply of thoughts and propositions, understanding
these to be Fregean thoughts and Russellian propositions respectively,
unless otherwise specified.)



That, according to the correspondence theorist (and the identity
theorist can agree so far), immediately gives us a constraint on the
shape of worldly facts. Take our sample sentence "Socrates is
wise", and recall that this sentence is here assumed to be true.
At the level of reference we encounter the object Socrates and
(assuming realism about
 properties)[5]
 the property of wisdom. Both of these may be taken to be entities in
the world, but it is plausible that neither amounts to a fact: neither
amounts to a plausible truth-maker for the sentence "Socrates is
wise", or for its expressed thought, or for its expressed
proposition. That is because the man Socrates, just as such, and the
property of wisdom, just as such, are not, so the argument goes,
propositionally structured, either jointly or severally, and so do not
amount to enough to make it true that Socrates is wise (cf. D.
Armstrong 1997: 115-16; Dodd 2008a: 7; Hofweber 2016: 288). Even
if we add in further universals, such as the relation of
instantiation, and indeed the instantiation of instantiation to any
degree, the basic point seems to be unaffected. In fact it can
plausibly be maintained (although some commentators disagree; Merricks
2007: ch. 1, *passim*, and pp. 82, 117, 168; Asay 2013:
63-4; Jago 2018: *passim*, e.g., pp. 73, 84, 185, 218,
250, though cf. p. 161) that the man Socrates, just as such, is not
even competent to make it true that Socrates exists; for that we need
the *existence* of the man Socrates. Hence, it would appear
that, if there are to be truth-makers in the world, they will have to
be structured, syntactically or quasi-syntactically, in the same
general way as declarative sentences, thoughts, and propositions. For
convenience we can refer to structure in this general sense as
"propositional structure": the point then is that neither
Socrates, nor the property of wisdom, nor (if we want to adduce it)
the relation of instantiation is, just as such, propositionally
structured. Following this line of argument through, we reach the
conclusion that nothing short of full-blown, propositionally
structured entities like the fact *that Socrates is wise* will
be competent to make the sentence "Socrates is wise", or
the thought or proposition expressed by that sentence, true. (A
question that arises here is whether tropes might be able to provide a
"thinner" alternative to such ontologically
"rich" entities as the fact *that Socrates is
wise*. One problem that seems to confront any such strategy is
that of making the proposed alternative a genuine one, that is, of
construing the relevant tropes in such a way that they do not simply
collapse into, or ontologically depend on, entities of the relatively
rich form *that Socrates is wise*. For discussion see Dodd
2008a: 7-9.)



The question facing the correspondence theorist is now: if such
propositionally structured entities are truth-makers, are they
truth-makers for sentences, thoughts, or propositions? It is at this
point that the identity theorist finds the correspondence theory
unsatisfactory. Consider first the suggestion that the worldly fact
*that Socrates is wise* is the truth-maker for the
reference-level proposition *that Socrates is wise* (see, e.g.,
Jago 2018: 72-3, and *passim*). There surely are such
facts as the fact *that Socrates is wise*: we talk about such
things all the time. The problem would seem to be not with the
existence of such facts, but rather with the relation of
correspondence which is said by the version of the correspondence
theory that we are currently considering to obtain between the fact
*that Socrates is wise* and the proposition *that Socrates
is wise*. As emerges from this way of expressing the difficulty,
there seems to be no linguistic difference between the way we talk
about propositions and the way we talk about facts, when these
entities are specified by "that" clauses. That suggests
that facts just *are* true propositions. If that is right, then
the relation between facts and true propositions is not one of
*correspondence*--which, as Frege famously observed (Frege
1918-19: 60 [1977: 3]; cf. Kunne 2003: 8; Milne 2010:
467-8), implies the distinctness of the
*relata*--but *identity*.



This line of argument can be strengthened by noting the following
point about explanation. Correspondence theorists have typically
wanted the relation of correspondence to *explain* truth: they
have usually wanted to say that it is *because* the proposition
*that Socrates is wise* corresponds to a fact that it is true,
and *because* the proposition *that Socrates is
foolish*--or rather: *It is not the case that Socrates is
wise* (after all, his merely being foolish is not enough to
guarantee that he is not wise, for he might, like James I and VI, be
both wise and foolish)--does not correspond to a fact that it is
false. But the distance between the true proposition *that Socrates
is wise* and the fact *that Socrates is wise* seems to be
too small to provide for explanatory leverage. Indeed the identity
theorist's claim is that there is no distance at all. Suppose we
ask: Why is the proposition *that Socrates is wise* true? If we
reply by saying that it is true because it is a fact *that Socrates
is wise*, we seem to have explained nothing, but merely repeated
ourselves (cf. Strawson 1971: 197; Anscombe 2000: 8; Rasmussen 2014:
39-43). So correspondence apparently gives way to identity as
the relation which must hold or fail to hold between a proposition and
a state of affairs if the proposition is to be true or false: the
proposition is true just if it is identical with an obtaining state of
affairs and false if it is not (cf. Horwich 1998: 106). And it would
seem that, if the identity theorist is right about this disposition,
explanatory pretensions will have to be abandoned: for while it will
be correct to say that a proposition is true just if it is identical
with a fact, false otherwise, it is hard to see that much of substance
has thereby been said about truth (cf. Hornsby 1997; 2; Dodd 2008a;
135).



It might be replied here that there are circumstances in which we
tolerate statements of the form "*A* because
*B*" when an appropriate identity--perhaps even
identity of sense, or reference, or both--obtains between
"*A*" and "*B*". For example, we say
things like "He is your first cousin because he is a child of a
sibling of one of your parents" (Kunne 2003: 155). But here
it is plausible that there is a definitional connection between
left-hand side and right-hand side, which seems not to hold of 



> 
> 
> The proposition *that Socrates is wise* is true because it is a
> fact *that Socrates is wise*. 
> 
> 
> 



In the latter case there is surely no question of definition; rather,
we are supposed, according to the correspondence theorist, to have an
example of metaphysical explanation, and that is just what, according
to the identity theorist, we do not have. After all, the identity
theorist will insist, it seems obvious that the relation, whatever it
is, between the proposition *that Socrates is wise* and the
fact *that Socrates is wise* must, given that the proposition
is true, be an extremely close one: what could this relation be? If
the identity theorist is right that the relation cannot be one of
metaphysical explanation (in either direction), then it looks as
though it will be hard to resist the insinuation of the linguistic
data that the relation is one of identity.



It is for this reason that identity theorists sometimes insist that
their position should not be defined in terms of an identity between
truth-bearer and truth-maker: that way of expressing the theory looks
too much in thrall to correspondence theorists' talk (cf.
Candlish 1999b: 200-1, 213). For the identity theorist, to speak
of both truth-makers and truth-bearers would imply that the things
allegedly doing the truth-making were distinct from the things that
were made true. But, since in the identity theorist's view there
are no truth-makers distinct from truth-bearers, if the latter are
conceived as propositions, and since nothing can make itself true, it
follows that there are no truth-makers *simpliciter*, only
truth-bearers. It seems to follow, too, that it would be ill-advised
to attack the identity theory by pointing out that some (or all)
truths lack truth-makers (so Merricks 2007: 181): so long as truths
are taken to be propositions, that is exactly what identity theorists
themselves say. From the identity theorist's point of view,
truth-maker theory looks very much like an exercise in splitting the
level of reference in half and then finding a bogus match between the
two halves (see McDowell 1998: 137 n. 21; Gaskin 2006: 203; 2008:
119-27). For example, when David Armstrong remarks that 



> 
> 
> What is needed is something in the world which ensures that *a*
> is *F*, some truth-maker or ontological ground for
> *a*'s being *F*. What can this be except the state of
> affairs of *a*'s being *F*? (1991: 190) 
> 
> 
> 



the identity theorist is likely to retort that *a*'s being
*F*, which according to Armstrong "ensures" that
*a* is *F*,*just is* the entity (whatever it is)
*that a is F*. The identity theorist maps conceptual
connections that we draw between the notions of proposition, truth,
falsity, state of affairs, and fact. These connections look trivial,
when spelt out--of course, an identity theorist will counter that
to go further would be to fall into error--so that to speak of an
identity *theory* can readily appear too grand (McDowell 2005:
83; 2007: 352. But cf. David 2002: 126). So much for the thesis that
facts are truth-makers and *propositions* truth-bearers; an
exactly parallel argument applies to the version of the correspondence
theory that treats facts as truth-makers and *thoughts* as
truth-bearers.



Consider now the suggestion that obtaining states of affairs, as the
correspondence theorist conceives them, make *declarative
sentences* (as opposed to propositions) true (cf. Horwich 1998:
106-7). In this case there appears to be no threat of triviality
of the sort that apparently plagued the previous version of the
correspondence theory, because states of affairs like *that
Socrates is wise* are genuinely distinct from linguistic items
such as the sentence "Socrates is wise". To that extent
friends of the identity theory need not jib at the suggestion that
such sentences have worldly truth-makers, if that is how the relation
of correspondence is being glossed. But they might question the
appropriateness of the gloss. For, they might point out, it does not
seem possible, without falsification, to draw detailed links between
sentences and bits of the world. After all, different sentences in the
same or different languages can "correspond" to the same
bit of the world, and these different sentences might have very
different (numbers of) components. The English sentence "There
are cows" contains three words: are there then three bits in the
world corresponding to this sentence, and making it true? (cf. Neale
2001: 177). The sentence "Cows
exist" contains only two words, but would not the correspondence
theorist want to say that it was made true by the same chunk of
reality? And when we take other languages into account, there seems in
principle to be no reason to privilege any particular number and say
that a sentence corresponding to the relevant segment of reality must
contain *that* number of words: why might there not, in
principle, be sentences of actual or possible languages such that, for
any *n* [?] 1, there existed a sentence comprising *n*
words and meaning the same as the English "There are
cows"? (In fact, is English not already such a language? Just
prefix and then iterate *ad lib.* a vacuous operator like
"Really".)



In a nutshell, then, the identity theorist's case against the
correspondence theory is that, when the truth-making relation is
conceived as originating in a worldly fact (or similar) and having as
its other relatum a true *sentence*, the claim that this
relation is one of correspondence cannot be made out; if, on the other
hand, the relevant relation targets a *proposition* (or
thought), then that relation must be held to be one of identity, not
correspondence.


## 4. Identity, Sense, and Reference



Identity theorists are agreed that, in the case of any particular
relevant identity, a fact will constitute the worldly *relatum*
of the relation, but there is significant disagreement among them on
the question what the item on the other end of the relation
is--whether a thought or a proposition (or both). As we have
seen, there are three possible positions here: (i) one which places
the identity relation exclusively between true thoughts and facts,
(ii) one which places it exclusively between true propositions and
facts, and (iii) a hybrid position which allows identities of both
sorts (identities obtaining at the level of sense will of course be
quite distinct from identities obtaining at the level of reference).
Which of these positions an identity theorist adopts will depend on
wider metaphysical and linguistic considerations that are strictly
extraneous to the identity theory as such.



Identity theorists who favor (i) generally do so because they want to
have nothing to do with *propositions* as such. That is to say,
such theorists eschew propositions as *reference-level
entities*: of course the *word* "proposition"
may be, and sometimes is, applied to Fregean thoughts at the level of
sense, rather than to Russellian propositions at the level of
reference. For example, Hornsby (1997: 2-3) uses
"proposition" and "thinkable" interchangeably.
So far, this terminological policy might be considered neutral with
respect to the location of propositions and thinkables in the Fregean
semantic hierarchy: that is to say, if one encounters a theorist who
talks about "thinkables" and "propositions",
even identifying them, one does not, just so far, know where in the
semantic hierarchy this theorist places these entities. In particular,
we cannot assume, unless we are specifically told so, that our
theorist locates either propositions or thinkables at the level of
*sense*. After all, someone who houses propositions at the
level of reference holds that these reference-level entities are
*thinkable*, in the sense that they are *graspable in
thought* (perhaps via thoughts at the level of sense). But they
are not *thinkables* if this latter word is taken, as it is by
McDowell and Hornsby, to be a technical term referring to entities at
the level of sense. For clarity the policy here will be to continue to
apply the word "proposition" exclusively to Russellian
propositions at the level of reference. Such propositions, it is
plausible to suppose, can be grasped in thought, but by definition
they are not thoughts or thinkables, where these two latter terms
have, respectively, their Fregean and McDowellian meanings. It is
worth noting that this point, though superficially a merely
terminological one, engages significantly with the interface between
the philosophies of language and mind that was touched on in the
opening paragraph. Anyone who holds that reference-level propositions
can, in the ordinary sense, be thought--are thinkable--is
likely to be unsatisfied with any terminology that seems to limit the
domain of the thinkable and of what is thought to the level of sense
(On this point see further below in this section, and Gaskin 2020:
101-2).



Usually, as has been noted, identity theorists who favor (i) above
have this preference because they repudiate propositions as that term
is being employed here: that is, they repudiate propositionally
structured reference-level entities. There are several reasons why
such identity theorists feel uncomfortable with propositions when
these are understood to be reference-level entities. There is a fear
that such propositions, if they existed, would have to be construed as
truth-makers; and identity theorists, as we have seen, want to have
nothing to do with truth-makers (Dodd 2008a: 112). That fear could
perhaps be defused if facts were also located at the level of
reference for true propositions to be identical with. This move would
take us to an identity theory in the style of (ii) or (iii) above.
Another reason for suspicion of reference-level propositions is that
commentators often follow Russell in his post-1904 aversion
specifically to *false* objectives, that is, to false
propositions *in re* (Russell 1966: 152; Cartwright 1987:
79-84). Such entities are often regarded as too absurd to take
seriously as components of reality (so T. Baldwin 1991: 46; Dodd 1995:
163; 1996; 2008a: 66-70, 113-14, 162-6). More
especially, it has been argued that false propositions *in re*
could not be unities, that the price of unifying a proposition at the
level of reference would be to make it true: if this point were
correct it would arguably constitute a *reductio ad absurdum*
of the whole idea of reference-level propositions, since it is
plausible to suppose that if there cannot be false reference-level
propositions, there cannot be true ones either (see Dodd 2008a: 165).
If, on the other hand, one is happy with the existence of propositions
*in re* or reference-level propositions, both true and
 false,[6]
 one is likely to favor an identity theory in the style of (ii) or
(iii). And, once one has got as far as jettisoning (i) and deciding
between (ii) and (iii), there must surely be a good case for adopting
(iii): for if one has admitted propositionally structured entities
both at the level of sense (as senses of declarative sentences) and at
the level of reference (propositions), there seems no good reason not
to be maximally liberal in allowing identities between entities of
these two types and, respectively, sense- and reference-level kinds of
fact (or fact-like entities).



Against what was suggested above about Frege
 (SS2),
 it has been objected that Frege could not have held an identity
theory of truth (Baldwin 1991: 43); the idea here is that, even if he
had acknowledged states of affairs as *bona fide* elements of
reality, Frege could not have identified true thoughts with them on
pain of confusing the levels of sense and reference. As far as the
exegetical issue is concerned, the objection might be said to overlook
the possibility that Frege identified true thoughts with facts
construed as *sense*-level entities, rather than with states of
affairs taken as *reference*-level entities; and, as we have
noted, Frege does indeed appear to have done just this (see Dodd &
Hornsby 1992). Still, the objection raises an important theoretical
issue. It would surely be a serious confusion to try to construct an
identity *across* the categorial division separating sense and
reference, in particular to attempt to identify true Fregean thoughts
with reference-level facts or states of
 affairs.[7]
 It has been suggested that McDowell and Hornsby are guilty of this
 confusion;[8]
 they have each rejected the
 charge,[9]
 insisting that, for them, facts are not reference-level entities, but
are, like Fregean thoughts, sense-level
 entities.[10]



But, if one adheres to the Fregean version of the identity theory ((i)
above), which identifies true thoughts with facts located at the level
of sense, and admits no correlative identity, in addition, connecting
true propositions located at the level of reference with facts or
fact-like entities also located at that level, it looks as though one
faces a difficult dilemma. At what level in the semantical hierarchy
is the world to be placed? Suppose first one puts it at the level of
reference (this appears to be Dodd's favored view: see 2008a:
180-1, and *passim*). In that case the world will contain
no facts or propositions, but just objects and properties hanging
loose in splendid isolation from one another, a dispensation which
looks like a version of Kantian transcendental idealism. (Simply
insisting that the properties include not merely monadic but also
polyadic ones, such as the relation of instantiation, will not in
itself solve the problem: we will still just have a bunch of separate
objects, properties, and relations.) If there are no true
propositions--no facts--or even false propositions to be
found at the level of reference, but if also, notwithstanding that
absence, the world is located there, the objects it contains will, it
seems, have to be conceived as bare objects, not as things of certain
sorts. Some philosophers of a nominalistic bias might be happy with
this upshot; but the problem is how to make sense of the idea of a
bare object--that is, an object not characterized by any
properties. (Properties not instantiated by any objects, by contrast,
will not be problematic, at least not for a realist.)



So suppose, on the other hand, that one places the world at the level
of sense, on the grounds that the world is composed of facts, and that
that is where facts are located. This ontological dispensation is
explicitly embraced by McDowell (1996: 179). The problem with this way
out of the dilemma would seem to be that, since Fregean senses are
constitutively modes of presentation of referents, the strategy under
current consideration would take the world to be made up of modes of
presentation--but of what? Of objects and properties? These are
certainly reference-level entities, but if they are presented by items
in the realm of sense, which is being identified on this approach with
the world, then again, as on the first horn of the dilemma, they would
appear to be condemned to an existence at the level of reference in
splendid isolation from one another, rather than in propositionally
structured combinations, so that once more we would seem to be
committed to a form of Kantian transcendental idealism (see Suhm,
Wagemann, & Wessels 2000: 32; Sullivan 2005: 59-61; Gaskin
2006:199-203). Both ways out of the dilemma appear to have this
unattractive consequence. The only difference between those ways
concerns where exactly in the semantic hierarchy we locate the world;
but it is plausible that that issue, in itself, is or ought to be of
less concern to metaphysicians than the requirement to avoid divorcing
objects from the properties that make those objects things of certain
sorts; and both ways out of the dilemma appear to flout this
requirement.



To respect the requirement, we need to nest reference-level objects
and properties in propositions, or proposition-like structures, also
located at the level of reference. And then some of these structured
reference-level entities--the true or obtaining ones--will,
it seems, be facts, or at least fact-like. Furthermore, once one
acknowledges the existence of facts, or fact-like entities, existing
at the level of *sense*, it seems in any case impossible to
prevent the automatic generation of facts, or fact-like entities,
residing at the level of *reference*. For sense is mode of
presentation of reference. So we need reference-level facts or
fact-like entities to be what sense-level facts or fact-like entities
*present*. One has to decide how to treat these variously
housed fact-like entities theoretically. If one were to insist that
the sense-level fact-like entities were the genuine and only
*facts*, the corresponding reference-level entities would be no
better than *fact-like*, and contrariwise. But, regardless
whether the propositionally structured entities automatically
generated in this way by sense-level propositionally structured
entities are to be thought of as proper facts or merely as fact-like
entities, it would seem perverse not to identify the world with these
 entities.[11]
 For to insist on continuing to identify the world with sense-level
rather than reference-level propositionally structured entities would
seem to fly in the face of a requirement to regard the world as
maximally objective and maximally non-perspectival. McDowell himself
hopes to avert any charge of embracing an unacceptable idealism
consequent on his location of the world at the level of sense by
relying on the point that senses present their references directly,
not descriptively, so that reference is, as it were, contained in
sense (1996: 179-80). To this it might be objected that the
requirement of maximal objectivity forces an identification of the
world with the contained, not the containing, entities in this
scenario, which in turn seems to force the upshot--if the threat
of Kantian transcendental idealism is really to be obviated--that
the contained entities be propositionally structured as such, that is,
*as contained entities*, and not simply in virtue of being
contained in propositionally structured containing entities. (For a
different objection to McDowell, see Sullivan 2005: 60 n. 6.)


## 5. Difficulties with the Theory and Possible Solutions


### 5.1 The modal problem



G. E. Moore drew attention to a point that might look (and has been
held to be) problematic for the identity theory (Moore 1953: 308; Fine
1982: 46-7; Kunne 2003: 9-10). The proposition
*that Socrates is wise* exists in all possible worlds where
Socrates and the property of wisdom exist, but in some of those worlds
this proposition is true and in others it is false. The fact *that
Socrates is wise*, by contrast, only exists in those worlds where
the proposition both exists and is true. So it would seem that the
proposition *that Socrates is wise* cannot be identical with
the fact *that Socrates is wise*. They have different modal
properties, and so by the principle of the indiscernibility of
identicals they cannot be identical.



Note, first, that this problem, if it is a problem, has nothing
especially to do with the identity theory of truth or with facts. It
seems to arise already for true propositions and propositions taken
*simpliciter* before ever we get to the topic of facts. That
is, one might think that the proposition *that Socrates is
wise* is identical with the true proposition *that Socrates is
wise* (assuming, as we are doing, that this proposition
*is* true); but we then face the objection that the proposition
taken *simpliciter* and the true proposition differ in their
modal properties, since (as one might suppose) the true proposition
*that Socrates is wise* does not exist at worlds where the
proposition *that Socrates is wise* is false, but the
proposition taken *simpliciter* does. Indeed the problem, if it
is a problem, is still more general, and purported solutions to it go
back at least to the Middle Ages (when it was discussed in connection
with Duns Scotus' formal distinction; see Gaskin 2002 [with
references to further relevant literature]). Suppose that Socrates is
a cantankerous old curmudgeon. Now grumpy Socrates, one would think,
is identical with Socrates. But in some other possible worlds Socrates
is of a sunny and genial disposition. So it would seem that Socrates
cannot be identical with grumpy Socrates after all, because in these
other possible worlds, while Socrates goes on existing, grumpy
Socrates does not exist--or so one might argue.



Can the identity theorist deal with this problem, and if so how? Here
is one suggestion. Suppose we hold, staying with grumpy Socrates for a
moment, that, against the assumption made at the end of the last
paragraph, grumpy Socrates *does* in fact exist in worlds where
Socrates has a sunny disposition. The basis for this move would be the
thought that, after all, grumpy Socrates *is* identical with
Socrates, and *Socrates* exists in these other worlds. So
grumpy Socrates exists in those worlds too; it is just that he is not
grumpy in those worlds. (Suppose Socrates is *very* grumpy;
suppose in fact that grumpiness is so deeply ingrained in his
character that worlds in which he is genial are quite far away.
Someone surveying the array of possible worlds, starting from the
actual world and moving out in circles, and stumbling at long last
upon a world with a pleasant Socrates in it, might register the
discovery by exclaiming, with relief, "Oh look! Grumpy Socrates
is not grumpy over here!".) Similarly, one might contend, the
true proposition, and fact, *that Socrates is wise* goes on
existing in the worlds where Socrates is not wise, because the true
proposition, and fact, *that Socrates is wise* just *is*
the proposition *that Socrates is wise*, and that proposition
goes on existing in these other worlds, but in those worlds that true
proposition, and fact, is not a true proposition, or a fact. (In
Scotist terms one might say that the proposition *that Socrates is
wise* and the fact *that Socrates is wise* are really
identical but formally distinct.)



This solution was, in outline, proposed by Richard Cartwright in his
1987 discussion of the identity theory (Cartwright 1987: 76-8;
cf. David 2002: 128-9; Dodd 2008a: 86-8; Candlish &
Damnjanovic 2018: 265-6). According to Cartwright, the true
proposition, and fact, *that there are subways in Boston*
exists in other possible worlds where Boston does not have subways,
even though in those worlds that fact would be not be a fact.
(Compare: grumpy Socrates exists in worlds where Socrates is genial
and sunny, but he is not grumpy there.) So even in worlds where it is
not *a* fact *that Boston has subways*, *that*
fact, namely the fact *that Boston has subways*, continues to
exist. Cartwright embellishes his solution with two controversial
points. First, he draws on Kripke's distinction between rigid
and non-rigid designation, suggesting that his solution can be
described by saying that the expression "The fact *that
Boston has subways*" is a non-rigid designator. But it is
plausible that that expression goes on referring to, or being
satisfied by (depending on how exactly one wants to set up the
semantics of definite descriptions: see Gaskin 2008: 56-81), the
fact *that Boston has subways* in possible worlds where Boston
does not have subways; it is just that, though that fact exists in
those worlds, it is not a fact there. But that upshot does not appear
to derogate from the rigidity of the expression in
question**.** Secondly, Cartwright allows for a true
reading of "The fact *that there are subways in Boston*
might not have been the fact *that there are subways in
Boston*". But it is arguable that we should say that this
sentence is just false (David 2002: 129). The fact *that there are
subways in Boston* would still have gone on being *the same
fact* in worlds where Boston has no subways, namely the fact
*that there are subways in Boston*; it is just that in those
worlds *this* fact would not have been *a* fact. You
might say: in *that* world the fact *that there are subways
in Boston* would not be correctly described as a fact, but in
talking about that world we are talking about it from the point of
view of our world, and in our world it is a fact. (Similarly with
grumpy Socrates.)



Now, an objector may want to press the following point against the
above purported solution to the difficulty. Consider again the fact
*that Socrates is wise*. Surely, it might be said, it is more
natural to maintain that that fact *does not exist* in a
possible world where Socrates is not wise, rather than that it exists
there all right, but is not a fact. After all, imagine a conversation
about a world in which Socrates is not wise and suppose that Speaker
*A* claims that Socrates is indeed wise in that world. Speaker
*B* might counter with 



> 
> 
> No, sorry, you're wrong: there is no such fact in that world;
> the purported fact *that Socrates is wise* simply does not
> exist in that world. 
> 
> 
> 



It might seem odd to insist that *B* is not allowed to say this
and must say instead 



> 
> 
> Yes, you're right that there is such a fact in that world,
> namely the fact *that Socrates is wise*, but in that world
> *that* fact is not *a* fact;. 
> 
> 
> 



How might the identity theorist respond to this objection? One
possible strategy would be to make a distinction between *fact*
and *factuality*, as follows. *Factuality*, one might
say, is a reification of facts. Once you have a fact, you also get, as
an ontological spin-off, the *factuality* of that fact. The
fact, being a proposition, exists at all possible worlds where the
proposition exists, though in some of these worlds it may not be a
fact: it will not be a fact in worlds where the proposition is false.
The factuality of that fact, by contrast, only exists at those worlds
where the fact *is* a fact--where the proposition is true.
So factuality is a bit like a trope. Compare grumpy Socrates again.
Grumpy Socrates, the identity theorist might contend, exists at all
worlds where Socrates exists, though at some of those worlds he is not
grumpy. But *Socrates' grumpiness*--that particular
trope--exists only at worlds where Socrates is grumpy. That seems
to obviate the problem, because the suggestion being canvassed here is
that grumpy Socrates is identical not with *Socrates'
grumpiness*--so that the fact that these two entities have
different modal properties need embarrass no one--but rather with
*Socrates*. Similarly, the suggestion is that the proposition
*that Socrates is wise* is identical not with the
*factuality* of the fact *that Socrates is wise*, but
just with that *fact*. So the identity theorist would
accommodate the objector's point by insisting that
*facts* exist at possible worlds where their
*factualities* do not exist.



The reader may be wondering why this problem was ever raised against
the identity theory of truth in the first place. After all, the
identity theorist does not say that propositions *simpliciter*
are identical with facts, but that *true* propositions are
identical with facts, and now true propositions and facts surely have
exactly the *same* modal properties: for regardless how things
are with the sheer proposition *that Socrates is wise*, at any
rate the *true* proposition *that Socrates is wise* must
surely be thought to exist at the same worlds as the fact *that
Socrates is wise*, whatever those worlds are. However, as against
this quick way with the purported problem, there stands the intuition,
mentioned and exploited above, that the true proposition *that
Socrates is wise* is identical with the proposition *that
Socrates is wise*. So long as that intuition is in play, the
problem does indeed seem to arise--for true propositions, in the
first instance, and then for facts by transitivity of identity. But
the identity theorist will maintain that, as explained, the problem
has a satisfactory solution.


### 5.2 The "right fact" problem



Candlish, following Cartwright, has urged that the identity theory of
truth is faced with the difficulty of getting hold of the "right
fact" (Cartwright 1987: 74-5; Candlish 1999a: 238-9;
1999b: 202-4). Consider a version of the identity theory that
states:



(11)
 The proposition *that *p** is true just if it is
identical with a
 fact.[12]


Candlish's objection is now that (11)



> 
> 
> does not specify *which* fact has to be identical with the
> proposition for the proposition to be true. But what the identity
> theory requires is not that a true proposition be identical with
> *some fact or other*, it is that it be identical with the
> *right* fact. (1999b: 203)
> 
> 
> 



In another paper Candlish puts the matter like this:



> 
> 
> But after all, any proposition might be identical with *some*
> fact or other (and there are reasons identified in the
> *Tractatus* for supposing that all propositions are themselves
> facts), and so all might be true. What the identity theory needs to
> capture is the idea that it is *by virtue of* being identical
> with the *appropriate* fact that a proposition is true. (1999a:
> 239)
> 
> 
> 



The reference to the *Tractatus* is suggestive. Of course, it
might be objected that the *Tractatus* does not have
propositions in the sense of that word figuring here: that is, it does
not recognize Russellian propositions (propositions at the level of
reference). Nor indeed does it appear to recognize Fregean thoughts.
In the *Tractatus*, as we have noted
 (SS2),
 declarative sentences (*Satze*) are facts (arrangements
of names), and states of affairs (*Sachlagen*,
*Sachverhalte*, *Tatsachen*) are also facts
(arrangements of objects). Even so, Candlish's allusion to the
*Tractatus* reminds us that propositions (in our sense)
*are* Tractarian inasmuch as they are structured
*arrangements of entities*, namely objects and properties.
(Correlatively, thoughts are structured arrangements of senses.) False
propositions (and false thoughts) will equally be arrangements of
objects and properties (respectively, senses). So the difficulty that
Cartwright and Candlish have identified can be put like this.
Plausibly *any* proposition, whether or not it is true, is
identical with *some fact or other* given that a proposition is
an arrangement of entities of the appropriate sort. But if
propositions just *are* facts, then *every* proposition
is identical with *some* fact--at the very least, with
itself--whether it is true or false. So the right-to-left
direction of (11) looks incorrect.



J. C. Beall (2000) attempts to dissolve this problem on the identity
theorist's behalf by invoking the principle of the
indiscernibility of identicals. His proposal works as follows. If we
ask, in respect of (11), what the "right" fact is, it
seems that we can answer that the "right" fact must at
least have the property of *being identical with the proposition
that *p**, and the indiscernibility principle then guarantees
that there is only one such fact. This proposal is open to an obvious
retort. Suppose that the proposition *that *p** is false.
That proposition will still be identical with itself, and if we are
saying (in Wittgensteinian spirit) that propositions are facts, then
that proposition will be identical with at least one fact, namely
itself. So it will satisfy the right-hand side of (11), its falsity
notwithstanding. But reflection on this retort suggests a patch-up to
Beall's proposal: why not say that the *right* fact is
*the fact that *p**? We would then be able to gloss (11)
with



(12)
 The proposition *that *p** is true just if (a) it is
a fact *that *p**, and (b) the proposition *that
*p** is identical with *that fact*.


Falsity, it seems, now no longer presents a difficulty, because if it
is false *that *p** then it is not a fact *that
*p**, so that (a) fails, and there is no appropriate
candidate for the proposition *that *p** to be identical
 with.[13]
 Notice that, in view of the considerations already aired in
connection with the modal problem ((i) of this section), caution is
here required. Suppose that it is true *that *p** in the
actual world, but false in some other possible world. According to the
strategy that we have been considering on the identity
theorist's behalf, it would be wrong to say that, in the
possible world where it is false *that *p**, there is no
such fact as the fact *that *p**. The strategy has it that
there is indeed such a fact, because it is (in the actual world) a
fact *that *p**, and that fact, and the true proposition,
*that *p**, go on existing in the possible world where it
is false *that *p**; it is just that *that* fact is
not *a* fact in that possible world. But (12), the identity
theorist will maintain, deals with this subtlety. In the possible
world we are considering, where it is false *that *p**,
though the fact *that *p** exists, it is not a fact
*that *p**, so (a) fails, and there is accordingly no risk
of our getting hold of the "wrong" fact. Note also that if
a Wittgensteinian line is adopted, while the (false) proposition that
*p* will admittedly be identical with *a* fact--at
the very least with itself--it will be possible, given the
failure of (a), for the identity theorist to contend with a clear
conscience that that fact is the *wrong* fact, which does not
suffice to render the proposition true.


### 5.3 The "slingshot" problem



If the notorious "slingshot" argument worked, it would
pose a problem for the identity theory of truth. The argument exists
in a number of different, though related, forms, and this is not the
place to explore all of these in
 detail.[14]
 Here we shall look briefly at what is one of the simplest and most
familiar versions of the argument, namely Davidson's. This
version of the argument aims to show that if true declarative
sentences refer to anything (for example to propositions or facts),
then they all refer to the same thing (to the "Great
Proposition", or to the "Great Fact"). This upshot
would be unacceptable to an identity theorist of a Russellian cast,
who thinks that declarative sentences refer to propositions, and that
true such propositions are identical with facts: any such theorist is
naturally going to want to insist that the propositions referred to by
different declarative sentences are, at least in general, distinct
from one another, and likewise that the facts with which distinct true
propositions are identical are also distinct from one another.
Davidson expresses the problem that the slingshot argument purportedly
throws up as follows:



> 
> 
> The difficulty follows upon making two reasonable assumptions: that
> logically equivalent singular terms have the same reference; and that
> a singular term does not change its reference if a contained singular
> term is replaced by another with the same reference. But now suppose
> that "*R*" and "*S*" abbreviate any
> two sentences alike in truth value. (1984: 19)
> 
> 
> 



He then argues that the following four sentences have the same
reference:



(13)
 \(R\)


(14)
 \(\hat{z}(z\! =\! z \amp R) = \hat{z}(z\! =\! z)\)


(15)
 \(\hat{z}(z\! =\! z \amp S) = \hat{z}(z\! =\! z \))


(16)
 \(S\)


(The hat over a variable symbolizes the description operator: so
"\(\hat{z}\)" means *the \(z\) such that ...*)
This is because (13) and (14) are logically equivalent, as are (15)
and (16), while the only difference between (14) and (15) is that (14)
contains the expression (Davidson calls it a "singular
term") "\(\hat{z} (z\! =\! z \amp R)\)" whereas (15)
contains "\(\hat{z} (z\! =\! z \amp S)\)",



> 
> 
> and these refer to the same thing if *S* and *R* are alike
> in truth value. Hence any two sentences have the same reference if
> they have the same truth value. (1984: 19)
> 
> 
> 



The difficulty with this argument, as a number of writers have pointed
out (see, e.g., Yourgrau 1987; Gaskin 1997: 153 n. 17; Kunne
2003: 133-41), and the place where the identity theorist is
likely to raise a cavil, lies in the first assumption on which it
depends. Davidson calls this assumption "reasonable", but
it has been widely questioned. It states "that logically
equivalent singular terms have the same reference". But
intuitively, the ideas of logical equivalence and reference seem to be
quite distinct, indeed to have, as such, little to do with one
another, so that it would be odd if there were some *a priori*
reason why the assumption had to hold. And it is not difficult to
think of apparent counterexamples: the sentence "It is
raining" is logically equivalent to the sentence "It is
raining and (either Pluto is larger than Mercury or it is not the case
that Pluto is larger than Mercury)", but the latter sentence
seems to carry a referential payload that the former does not. Of
course, if declarative sentences refer to truth-values, as Frege
thought, then the two sentences will indeed be co-referential, but to
assume that sentences refer to truth-values would be question-begging
in the context of an argument designed to establish that all true
sentences refer to the same thing.


### 5.4 The congruence problem



A further objection to the identity theory, going back to an
observation of Strawson's, takes its cue from the point that
canonical names of propositions and of facts are often not
straightforwardly congruent with one another: they are often not
intersubstitutable *salva congruitate* (or, if they are, they
may not be intersubstitutable *salva veritate*) (Strawson 1971:
196; cf. Kunne 2003: 10-12). For example, we say that
propositions are true, not that they obtain, whereas we say that facts
obtain, not that they are true. How serious is this point? The
objection in effect presupposes that for two expressions to be
co-referential, or satisfied by one and the same thing, they must be
syntactically congruent, have the same truth-value potential, and
match in terms of general contextual suitability. The assumption of
the syntactic congruence of co-referential expressions is
controversial, and it may be possible for the identity theorist simply
to deny it (see Gaskin 2008: 106-10, for argument on the point,
with references to further literature; cf. Dodd 2008a: 83-6.).
Whether co-referential expressions must be syntactically congruent
depends on one's conception of reference, a matter that cannot
be further pursued here (for discussion see Gaskin 2008: ch. 2; 2020:
chs. 3-5).



There has been a good deal of discussion in the literature concerning
the question whether an identification of facts with true propositions
is undermined not specifically by phenomena of *syntactic*
incongruence but rather by failure of relevant intersubstitutions to
preserve *truth-values* (see, e.g., King 2007: ch. 5; King in
King, Soames, & Speaks 2014: 64-70, 201-8; Hofweber
2016: 215-23; Candlish & Damnjanovic 2018: 264). The
discussion has focused on examples like the following:



(17)
 Daniel remembers the fact that this is a leap year;


(18)
 Daniel remembers the true proposition that this is a leap
year;


(19)
 The fact that my local baker has shut down is just
appalling;


(20)
 The true proposition that my local baker has shut down is just
appalling.


The problem here is said to be that the substitution of "true
proposition" for "fact" or vice versa generates
different readings (in particular, readings with different
truth-values). Suppose Daniel has to memorize a list of true
propositions, of which one is the proposition that this is a leap
year. Then it is contended that we can easily imagine a scenario in
which (17) and (18) differ in truth-value. Another way of putting the
same point might be to say that (17) is equivalent to



(21)
 Daniel remembers that this is a leap year,


but that (18) is not equivalent to (21), because--so the argument
goes--(18) but not (21) would be true if Daniel had memorized his
list of true propositions without realizing that they *were*
true. Similar differences can be argued to apply, *mutatis
mutandis*, to (19) and (20). Can the identity theorist deal with
this difficulty?



In the first place one might suggest that the alleged mismatch between
(17) and (18) is less clear than the objector claims. (17) surely does
have a reading like the one that is said to be appropriate for (18).
Suppose Daniel has to memorize a list of facts. (17) could then
diverge in truth-value from



(22)
 Daniel remembers the fact that this is a leap year *as a
fact*.


For there is a reading of (17) on which, notwithstanding (17)'s
truth, (22) is false: this is the reading on which Daniel has indeed
memorized a list of facts, but without necessarily realizing that the
things he is memorizing *are* facts. He has memorized the
relevant fact (that this is a leap year), we might say, but not
*as* a fact. That is parallel to the reading of (18) according
to which Daniel has memorized the true proposition that this is a leap
year, but not *as* a true proposition. The identity theorist
might then aver that, perhaps surprisingly, the same point actually
applies to the simple (21), on the grounds that this sentence can mean
that Daniel remembers the propositional object *that this is a leap
year* (from a list of such objects, say, that he has been asked to
memorize), with no implication that he remembers it either *as a
proposition* or *as a fact*. So, according to this
response, the transparent reading of (18)--which has Daniel
remember the propositional object, namely *that this is a leap
year*, but not necessarily remember it *as* a fact, or even
as the propositional object *that this is a leap year* (he
remembers it under some other mode of presentation)--is also
available for (17) and for (21).



What about the opaque reading of either (17) or (21), which implies
that Daniel knows *for a fact* that this is a leap
year--is that reading available for (18) too? The identity
theorist might maintain that this reading is indeed available, and
then explain why we tend not to use sentences like (18) in the
relevant sense, preferring sentences of the form of (17) or (21), on
the basis of the relative technicality of the vocabulary of (18). The
idea would be that it is just an accident of language that we prefer
either (17) or (21) to (18) where what is in question is the sense
that implies that Daniel has propositional knowledge that this is a
leap year (is acquainted with that fact as a fact), as opposed to
having mere acquaintance, under some mode of presentation or other,
with the propositional object which happens to be *(the fact) that
this is a leap year*. And if we ask why we prefer (17) or (21)
to



(23)
 Daniel remembers the proposition that this is a leap year,


then the answer will be the Gricean one that (23) conveys less
information than (17) or (21), under the reading of these two
sentences that we are usually interested in, according to which Daniel
remembers the relevant fact as a fact, for (23) is compatible with the
falsity of "This is a leap year". Hence to use (23) in a
situation where one was in a position to use (17) or (21) would carry
a misleading conversational implicature. That, at any rate, is one
possible line for the identity theorist to take. (It is worth noting
here that, if the identity theorist is right about this, it will
follow that the "know that" construction will be subject
to a similar ambiguity as the "remember that"
construction, given that remembering is a special case of knowing.
That is: "*A* knows *that *p**" will mean
either "*A* is acquainted with the fact *that
*p**, and is acquainted with it *as a fact*" or
merely "*A* is acquainted with the fact *that
*p**, but not necessarily with it *as
such*--either as a fact or even as a propositional
object".)


### 5.5 The individuation problem



It might appear that we individuate propositions more finely than
facts: for example, one might argue that the fact *that Hesperus is
bright* is the same fact as the fact *that Phosphorus is
bright*, but that the propositions in question are different (see
on this point Kunne 2003: 10-12; Candlish & Damnjanovic
2018: 266-7). The identity theorist has a number of strategies
in response to this objection. One would be simply to deny it, and
maintain that facts are individuated as finely as propositions: if one
is a supporter of the Fregean version of the identity theory, this is
likely to be one's response (see, e.g., Dodd 2008a: 90-3).
Alternatively, one might respond by saying that, if there is a good
point hereabouts, at best it tells only against the Fregean and
Russellian versions of the identity theory, not against the hybrid
version. The identity theory in the hybrid version can agree that we
sometimes think of facts as extensional, reference-level entities and
sometimes also individuate propositions or proposition-like entities
intensionally. Arguably, these twin points do indeed tell against
either a strict Fregean or a strict Russellian version of the identity
theory: they tell against the strict Fregean position because, as well
as individuating facts intensionally, we also, sometimes, individuate
facts extensionally; and they tell against the strict Russellian
position because, as well as individuating facts extensionally, we
also, sometimes, individuate facts intensionally. But it is plausible
that the hybrid version of the identity theory is not touched by the
objection, because that version of the theory accommodates
propositionally structured and factual entities at both levels of
sense and reference, though different sorts of these entities at these
different levels--either propositions at the level of sense and
correlative proposition-like entities at the level of reference or
*vice versa*, and similarly, *mutatis mutandis*, for
facts and fact-like entities. It will follow, then, for this version
of the identity theory, that Fregean thoughts and Russellian
propositions are available, if true, to be identical with the factual
entities of the appropriate level (sense and reference, respectively),
and the individuation problem will not then, it seems, arise.
Propositions or propositionally structured entities will be
individuated just as finely as we want them to be individuated, and at
each level of resolution there will be facts or fact-like entities,
individuated to the same resolution, for them to be identical with, if
 true.[15]


### 5.6 Truth and Intrinsicism



The solutions to these problems, if judged satisfactory, seem to
direct us to a conception of truth that has been called
"intrinsicist" (Wright 1999: 207-9), and
"primitivist" (Candlish 1999b: 207). This was a conception
recognized by Moore and Russell who, in the period when they were
sympathetic to the identity theory, spoke of truth as a simple and
unanalysable property (Moore 1953: 261; 1993: 20-1; Russell
1973: 75; Cartwright 1987: 72-5; Johnston 2013: 384). The point
here would be as follows. There are particular, individual
explanations of the truth of many propositions. For example, the true
proposition that there was a fire in the building will be explained by
alluding to the presence of combustible material, enough oxygen, a
spark caused by a short-circuit, etc. So, case by case, we will (at
least often) be able to provide explanations why given propositions
are true, and science is expanding the field of such explanations all
the time. But according to the intrinsicist, there is no prospect of
providing a *general* explanation of truth, in the sense of an
account that would explain, in utterly general terms, why *any*
true proposition was true. At that general level, according to the
intrinsicist, there is nothing interesting to be said about what makes
true propositions true: there are only the detailed case-histories. An
intrinsicist may embrace one or another version of the identity theory
of truth: what has to be rejected is the idea that the truth of a true
proposition might consist in a relation to a *distinct*
fact--that the truth of the true proposition *that Socrates is
wise*, for example, might consist in *anything other than*
identity with the fact *that Socrates is wise*. On this
approach, truth is held to be both intrinsic to propositions, and
 primitive.[16]
 Intrinsicism was not a popular position, at least until recently:
Candlish described it as "so implausible that almost no one else
[apart from Russell, in 1903-4] has been able to take it
seriously" (1999b: 208); but it may be gaining in popularity now
(see, e.g., Asay 2013).



Candlish (1999b: 208) thinks that intrinsicism and the identity theory
are competitors, but perhaps that view is not mandatory. Intrinsicism
says that truth is a simple and unanalysable property of propositions;
the identity theory says that a true proposition is identical with a
fact (and with the right fact). These statements will seem to clash
only if the identity theory is taken to propound a heavy-duty analysis
of truth. But if, following recent exponents of the theory, we take it
rather to be merely spelling out a connection between two entities
that we have in our ontology anyway, namely true propositions and
facts, and which turn out (like Hesperus and Phosphorus) to be
identical, on the basis of a realization that an entity like *that
Socrates is wise* is both a true proposition and a fact, then any
incipient clash between intrinsicism and the identity theory will, it
seems, be averted. On this approach, a natural thing to say will be
that the identity theory describes the *way in which* truth is
a simple and unanalysable property.