The identity theory of truth was influential in the formative years ofmodern analytic philosophy, and has come to prominence again recently.Broadly speaking, it sees itself as a reaction against correspondencetheories of truth, which maintain that truth-bearers aremadetrue by facts. The identity theory maintains, against this, thatat least some truth-bearers are not made true by, but areidentical with, facts. The theory is normally applied not atthe level of declarative sentences, but to what such sentencesexpress. It is these items—or, again, some of them—thatare held to be identical with facts. Identity theorists diverge overthe details of this general picture, depending on what exactly theytake declarative sentences to express, whether Fregean thoughts (atthe level of sense), Russellian propositions (at the level ofreference), or both, and depending also on how exactly facts areconstrued. But, to give a precise illustration, an identity theoristwho thinks that declarative sentences express Russellian propositionswill typically hold that true such propositions are identical withfacts. The significance of the identity theory, for its supporters, isthat it appears to make available the closing of a certain gap thatmight otherwise be thought to open up between language and worldand/or between mind and world. If its supporters are right about this,the identity theory of truth potentially has profound consequencesboth in metaphysics and in the philosophies of mind and language.

• 1. Definition and Preliminary Exposition
• 2. Historical Background
• 3. Motivation
• 4. Identity, Sense, and Reference
• 5. Difficulties with the Theory and Possible Solutions
  • 5.1 The modal problem
  • 5.2 The “right fact” problem
  • 5.3 The “slingshot” problem
  • 5.4 The congruence problem
  • 5.5 The individuation problem
  • 5.6 Truth and Intrinsicism
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Definition and Preliminary Exposition

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

(1)

“Socrates is wise” is true.

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

(2)

“Socrates is wise” meansthat Socrates is wise,^[1]

and

(3)

That Socrates is wise is true

or

(4)

It is truethat Socrates is wise.

If, provisionally, we call the things that declarative sentencesexpress, or mean, theircontents—again provisionally,these will be such things asthat Socrates is wise—thenthe 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 thatcontent is (identical with) a fact.

A fact is here to be thought of as, very generally,a way thingsare, ora way the world is. On this approach, theidentity theory secures an intimate connection between language (whatlanguage expresses) and world. Of course there would in principle betheoretical room for a view that identified not the content of, say,the true declarative sentence “Socrates is wise”—letus assume from now on that this sentence is true—with the factthat Socrates is wise, but rather that sentence itself. Butthis is not a version of the theory that anyone has ever advanced, nordoes it appear that it would be plausible to do so (see Candlish1999b: 200–2; Künne 2003: 6). The early Wittgenstein doesregard sentences as being themselves facts, but they are not identicalwith the facts that make them true.

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

(6)

That Socrates is wise is true just ifthat Socratesis wise is the case.

The idea here is that (6) makes a connection between language andreality: on the left-hand side we have something expressed by a pieceof 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 claimedfor the identity theory, at least in one of its manifestations. JohnMcDowell has argued that what he calls true “thinkables”are identical with facts (1996: 27–8, 179–80). Thinkablesare things likethat Socrates is wise regarded as possibleobjects of thought. For we can thinkthat Socrates is wise;and it can also be the casethat Socrates is wise. So theidea is that what we can think can also be (identical with) what isthe case. That identity, McDowell claims, is truistic. On thisapproach, one might prefer one’s identity theory to take theform (cf. Hornsby 1997: 2):

(7)

All true thinkables are (identical with) facts.

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

A point which has perhaps been obscured in the literature on thistopic, but which should be noticed, is that (7) asserts a relation ofsubordination: it says that true thinkables are a (proper or improper)subset of facts; it implicitly allows that there might be facts thatare not identical with true thinkables. So (7) is not to be confoundedwith 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 identicalwith facts. (8) is therefore distinct from (7), and if (7) iscontroversial, (8) is equally or more so, but for reasons that are atleast in part different. (8) denies the existence of facts that cannotbe grasped in thought. But many philosophers hold it to be evidentthat there are, or at least could be, such facts—perhaps certainfacts involving indefinable real numbers, for example, or in someother way going beyond the powers of human thought. So (8) could befalse; its status remains to be established; it can hardly be regardedas truistic. Accordingly, one might expect that an identity theoristwho wished to affirm (7), and certainly anyone who wanted to say that(7) (or (6)) was truistic, would—at leastqua identitytheorist—steer clear of (8), and leave its statussubjudice. In fact, however, a good number of identity theorists,both historical and contemporary, incorporate (8) as well as—oreven instead of—(7) into their statement of the theory. RichardCartwright, who published the first modern discussion of the theory in1987, wrote that if one were formulating the theory, it would say“that every true proposition is a fact and every fact a trueproposition” (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 muchto minds as to the world [i.e., (8)]. It should not even seem that weneed to choose a direction in which to read the claim of identity.(2005: 84)

Jennifer Hornsby takes the theory to state that true thinkables andfactscoincide (1997: 2, 9, 17, 20)—they are the sameset—so that she in effect identifies that theory with theconjunction of (7) and (8), as also, in effect, does Julian Dodd(2008a:passim). Now, (8) is certainly an interesting thesisthat merits much more consideration than it has hitherto received (atleast in the recent philosophical literature), and, as indicated, someexpositions of the identity theory have as much invested in (8) as in(5) or (7): on this point see further§2 below. Nevertheless, it will make for clarity of discussion if weassociate the identity theory of truth, more narrowly, with somethingalong 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 orsemi-technical vocabulary; moreover, they have been advanced as movesin a technical debate, namely one concerning the viability of thecorrespondence theory of truth. For these reasons it seems difficultto regard them as truisms (see Dodd 2008a: 179). What (5) and (7)mean, and which of them one will prefer as one’s statement ofthe identity theory of truth, if one is favorably disposed to thattheory—one may of course be happy with both—will depend,among other things, on what exactly one thinks about the nature ofsuch entities asthat Socrates is wise. In order to get clearon this point, discussion of the identity theory has naturally beenconducted in the context of the Fregean semantical hierarchy, whichdistinguishes between levels of language, sense, and reference. Fregerecognized what he called “thoughts” (Gedanken)at the level of sense corresponding to (presented by) declarativesentences at the level of language. McDowell’s thinkables aremeant to be Fregean thoughts: the change of terminology is intended tostress the fact that these entities are not thoughts in the sense ofdated and perhaps spatially located individual occurrences (thinkingevents), but are abstract contents that are at least in principleavailable to be grasped by different thinkers at different times andplaces. So a Fregean identity theory of truth would regard both suchentities asthat Socrates is wise and, correlatively, factsas sense-level entities: this kind of identity theory will then statethat true such entities are identical with facts. This approach willnaturally favor (7) as its expression of the identity theory.

By contrast with Frege, Russell abjured the level of sense and (atleast around 1903–4) recognized what, following Moore, he called“propositions” as worldly entities composed of objects andproperties. A modern Russellian approach might adopt thesepropositions—or something like them: the details ofRussell’s own conception are quite vague—as the referentsof declarative sentences, and identity theorists who followed thisline 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 thelevel of reference),

by contrast with the Fregean

(10)

All true Fregean thoughts are identical with facts (at the levelof sense).

This way of formulating the relevant identity claims has the advantageof suggesting that it would, at least in principle, be open to atheorist to combine (9) and (10) in a hybrid position that (i)departed from Russell and followed Frege by admittingboth alevel of Fregean senseand one of reference, and also, havingadmitted both levels to the semantic hierarchy, (ii)bothlocated Fregean thoughts at the level of senseand locatedRussellian propositions at the level of reference. Sense being mode ofpresentation of reference, the idea would be that declarativesentences refer,via Fregean thoughts, to Russellianpropositions (for this disposition, see Gaskin 2006: 203–20;2008: 56–127). So someone adopting this hybrid approach wouldaffirm both (9) and (10). Of course, the facts mentioned in (9) wouldbecategorially different from the facts mentioned in (10),and one might choose to avoid confusion by distinguishing themterminologically, and perhaps also by privileging one set of facts,ontologically, over the other. If one wanted to follow thisprivileging strategy, one might say, for instance, that onlyreference-level facts weregenuine facts, therelataof the identity relation at the level of sense being merelyfact-like entities, notbona fide facts. That wouldbe to give the combination of (9) and (10) a Russellian spin.Alternatively, someone who took the hybrid line might prefer to giveit a Fregean spin, saying that the entities with which true Fregeanthoughts were identical were the genuine facts, and that thecorresponding entities at the level of reference that true Russellianpropositions were identical with were not facts as such, but fact-likecorrelates of the genuine facts. Without more detail, of course, theseprivileging strategies leave the status of the entities they aretreating as merely fact-like unclear; and, as far as theFregean version of the identity theory goes, commentators who identifyfacts with sense-level Fregean thoughts usually, as we shall see,repudiate reference-level Russellian propositions altogether, ratherthan merely downgrading their ontological status, and so affirm (10)but reject (9). We shall return to these issues in§4 below.

2. Historical Background

The expression “the identity theory of truth” was firstused—or, at any rate, first used in the relevant sense—byStewart Candlish in an article on F. H. Bradley published in 1989. Butthe general idea of the theory had been in the air during the 1980s:for example, in a discussion first published in 1985, concerning JohnMackie’s theory of truth, McDowell criticized that theory formaking

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 conceivethe given relation. And versions of the identity theory go back atleast to Bradley (see, e.g., Bradley 1914: 112–13; for furtherdiscussion and references, see Candlish 1989; 1995; 1999b:209–12; T. Baldwin 1991: 36–40), and to the foundingfathers of the analytic tradition (Sullivan 2005: 56–7 n. 4).The theory can be found in G. E. Moore’s “The Nature ofJudgment” (1899), and in the entry he wrote on“Truth” for J. Baldwin’sDictionary ofPhilosophy and Psychology (1902–3; reprinted Moore 1993:4–8, 20–1; see T. Baldwin 1991: 40–3). Russellembraced the identity theory at least during the period of his 1904discussions of Meinong (see, e.g., 1973: 75), possibly also in hisThe Principles of Mathematics of 1903, and for a few yearsafter these publications as well (see T. Baldwin 1991: 44–8;Candlish 1999a: 234; 1999b: 206–9). Frege has a statement of thetheory in his 1919 essay “The Thought”, and may have heldit earlier (Frege 1918–19: 74 [1977: 25]; see Hornsby 1997:4–6; Milne 2010: 467–8).

Wittgenstein’sTractatus (1922) is usually held topropound a correspondence rather than an identity theory of truth;however this is questionable. In theTractatus, declarativesentences (Sätze) are said to be facts (arrangements ofnames), and states of affairs (Sachlagen,Sachverhalte,Tatsachen) are also said to be facts(arrangements of objects). If theTractatus is taken to putforward a correspondence theory of truth, then presumably the idea isthat a sentence will be true just if there is an appropriate relationof correspondence (an isomorphism) between sentence and state ofaffairs. However, the problem with this interpretation is that, in theTractatus, a relation of isomorphism between a sentence andreality is generally conceived as a condition of themeaningfulness of that sentence, not specifically of itstruth. False sentences, as well as true, are isomorphic withstates of affairs—only, in their case the states of affairs donot obtain. For Wittgenstein, states of affairs may either obtain orfail to obtain—both possibilities are, in general, available to them.^[3] Correlatively, it has been suggested that theTractatuscontains two different conceptions of fact, a factive and anon-factive one. According to the former conception, facts necessarilyobtain or are the case; according to the latter, facts may fail toobtain or not be the case. This non-factive conception has beendiscerned atTractatus 1.2–1.21, and at 2.1 (seeJohnston 2013: 382). Given that, in theTractatus, states ofaffairs (and perhaps facts) have two poles—obtaining or beingthe case, and non-obtaining or not being the case—it seems tofollow that, while Wittgenstein is committed to a correspondencetheory ofmeaning, his theory oftruth must be (someversion of) an identity theory, along the lines of

A declarative sentence is true just if what it is semanticallycorrelated with is identical with an obtaining state of affairs (afactive fact).

(Identity theorists normally presuppose the factive conception offacts, so that “factive” is redundant in the phrase“factive facts”, and that is the policy which will befollowed here.) Though a bipolar conception of facts (if indeedWittgenstein has it) may seem odd, the bipolar conception of states ofaffairs (which, it is generally agreed, he does have) seems quitenatural: here the identity theorist says that a true proposition isidentical with an obtaining state of affairs (see Candlish &Damnjanovic 2018: 271–2).

Peter Sullivan has suggested a different way of imputing an identitytheory to the Tractarian Wittgenstein (2005: 58–9). His idea isthat Wittgenstein’s simple objects are to be identified withFregean senses, and that in effect theTractatus contains anidentity theory along the lines of (7) or (10). Sullivan’sground for treating Tractarian objects as senses is that, likebona fide Fregean senses, they aretransparent: theycannot be grasped in different ways. An apparent difficulty with thisview is that there is plausibly more to Fregean sense than just theproperty of transparency: after all, Russell also attached theproperty of transparency to his basic objects, but it has not beensuggested that Russellian basic objects are really senses, and thesuggestion would seem to have little going for it (partly, though notonly, because Russell himself disavowed the whole idea of Fregeansense).The orthodox position, which will be presupposed here, is thatthe Tractarian Wittgenstein like Russell, finds no use for a level ofFregean sense, so that his semantical hierarchy consists exclusivelyof levels of language and reference, with nothing of a mediatory orsimilar nature located between these levels. (Wittgenstein does appealto theconcepts of sense and reference in theTractatus, but it is generally agreed that they do not figurein a Fregean way, according to which both names and sentences, forexample, have both sense and reference; for Wittgenstein, by contrast,sentences have sense but not reference, whereas names have referencebut not sense.)

3. Motivation

What motivates the identity theory of truth? It can be viewed as aresponse to difficulties that seem to accrue to at least some versionsof the correspondence theory (cf. Dodd 2008a: 120, 124). Thecorrespondence theory of truth holds that truth consists in a relationof correspondence between something linguistic or quasi-linguistic, onthe one hand, and something worldly on the other. Generally, the itemson the worldly end of the relation are taken to be facts or(obtaining) states of affairs. For many purposes these two latterkinds of entity (facts, obtaining states of affairs) are assimilatedto one another, and that strategy will be followed here. The exactnature of the correspondence theory will then depend on what the otherrelatum is taken to be. The items mentioned so far makeavailable three distinct versions of the correspondence theory,depending on whether thisrelatum is taken to consist ofdeclarative sentences, Fregean thoughts, or Russellian propositions.Modern correspondence theorists make a distinction betweentruth-bearers, which would typically fall under one of thesethree 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 theseone selects as the relata of the correspondence relation on thelanguage side of the language–world divide—correspond tofacts in the sense that facts are what make those sentences, thoughts,or propositions true, when they are true. (Henceforth we shallnormally speak simply of thoughts and propositions, understandingthese to be Fregean thoughts and Russellian propositions respectively,unless otherwise specified.)

That, according to the correspondence theorist (and the identitytheorist can agree so far), immediately gives us a constraint on theshape of worldly facts. Take our sample sentence “Socrates iswise”, 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 inthe world, but it is plausible that neither amounts to a fact: neitheramounts to a plausible truth-maker for the sentence “Socrates iswise”, or for its expressed thought, or for its expressedproposition. That is because the man Socrates, just as such, and theproperty of wisdom, just as such, are not, so the argument goes,propositionally structured, either jointly or severally, and so do notamount to enough to make it true that Socrates is wise (cf. D.Armstrong 1997: 115–16; Dodd 2008a: 7; Hofweber 2016: 288). Evenif we add in further universals, such as the relation ofinstantiation, and indeed the instantiation of instantiation to anydegree, the basic point seems to be unaffected. In fact it canplausibly be maintained (although some commentators disagree; Merricks2007: 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 noteven competent to make it true that Socrates exists; for that we needtheexistence of the man Socrates. Hence, it would appearthat, if there are to be truth-makers in the world, they will have tobe structured, syntactically or quasi-syntactically, in the samegeneral way as declarative sentences, thoughts, and propositions. Forconvenience we can refer to structure in this general sense as“propositional structure”: the point then is that neitherSocrates, nor the property of wisdom, nor (if we want to adduce it)the relation of instantiation is, just as such, propositionallystructured. Following this line of argument through, we reach theconclusion that nothing short of full-blown, propositionallystructured entities like the factthat Socrates is wise willbe competent to make the sentence “Socrates is wise”, orthe thought or proposition expressed by that sentence, true. (Aquestion that arises here is whether tropes might be able to provide a“thinner” alternative to such ontologically“rich” entities as the factthat Socrates iswise. One problem that seems to confront any such strategy isthat of making the proposed alternative a genuine one, that is, ofconstruing the relevant tropes in such a way that they do not simplycollapse into, or ontologically depend on, entities of the relativelyrich formthat Socrates is wise. For discussion see Dodd2008a: 7–9.)

The question facing the correspondence theorist is now: if suchpropositionally structured entities are truth-makers, are theytruth-makers for sentences, thoughts, or propositions? It is at thispoint that the identity theorist finds the correspondence theoryunsatisfactory. Consider first the suggestion that the worldly factthat Socrates is wise is the truth-maker for thereference-level propositionthat Socrates is wise (see, e.g.,Jago 2018: 72–3, andpassim). There surely are suchfacts as the factthat Socrates is wise: we talk about suchthings all the time. The problem would seem to be not with theexistence of such facts, but rather with the relation ofcorrespondence which is said by the version of the correspondencetheory that we are currently considering to obtain between the factthat Socrates is wise and the propositionthat Socratesis wise. As emerges from this way of expressing the difficulty,there seems to be no linguistic difference between the way we talkabout propositions and the way we talk about facts, when theseentities are specified by “that” clauses. That suggeststhat facts justare true propositions. If that is right, thenthe relation between facts and true propositions is not one ofcorrespondence—which, as Frege famously observed (Frege1918–19: 60 [1977: 3]; cf. Künne 2003: 8; Milne 2010:467–8), implies the distinctness of therelata—butidentity.

This line of argument can be strengthened by noting the followingpoint about explanation. Correspondence theorists have typicallywanted the relation of correspondence toexplain truth: theyhave usually wanted to say that it isbecause the propositionthat Socrates is wise corresponds to a fact that it is true,andbecause the propositionthat Socrates isfoolish—or rather:It is not the case that Socrates iswise (after all, his merely being foolish is not enough toguarantee that he is not wise, for he might, like James I and VI, beboth wise and foolish)—does not correspond to a fact that it isfalse. But the distance between the true propositionthat Socratesis wise and the factthat Socrates is wise seems to betoo small to provide for explanatory leverage. Indeed the identitytheorist’s claim is that there is no distance at all. Suppose weask: Why is the propositionthat Socrates is wise true? If wereply by saying that it is true because it is a factthat Socratesis wise, we seem to have explained nothing, but merely repeatedourselves (cf. Strawson 1971: 197; Anscombe 2000: 8; Rasmussen 2014:39–43). So correspondence apparently gives way to identity asthe relation which must hold or fail to hold between a proposition anda state of affairs if the proposition is to be true or false: theproposition is true just if it is identical with an obtaining state ofaffairs and false if it is not (cf. Horwich 1998: 106). And it wouldseem that, if the identity theorist is right about this disposition,explanatory pretensions will have to be abandoned: for while it willbe correct to say that a proposition is true just if it is identicalwith a fact, false otherwise, it is hard to see that much of substancehas thereby been said about truth (cf. Hornsby 1997; 2; Dodd 2008a;135).

It might be replied here that there are circumstances in which wetolerate statements of the form “A becauseB” when an appropriate identity—perhaps evenidentity of sense, or reference, or both—obtains between“A” and “B”. For example, we saythings like “He is your first cousin because he is a child of asibling of one of your parents” (Künne 2003: 155). But hereit is plausible that there is a definitional connection betweenleft-hand side and right-hand side, which seems not to hold of

The propositionthat Socrates is wise is true because it is afactthat 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 anexample of metaphysical explanation, and that is just what, accordingto the identity theorist, we do not have. After all, the identitytheorist will insist, it seems obvious that the relation, whatever itis, between the propositionthat Socrates is wise and thefactthat Socrates is wise must, given that the propositionis true, be an extremely close one: what could this relation be? Ifthe identity theorist is right that the relation cannot be one ofmetaphysical explanation (in either direction), then it looks asthough it will be hard to resist the insinuation of the linguisticdata that the relation is one of identity.

It is for this reason that identity theorists sometimes insist thattheir position should not be defined in terms of an identity betweentruth-bearer and truth-maker: that way of expressing the theory lookstoo much in thrall to correspondence theorists’ talk (cf.Candlish 1999b: 200–1, 213). For the identity theorist, to speakof both truth-makers and truth-bearers would imply that the thingsallegedly doing the truth-making were distinct from the things thatwere made true. But, since in the identity theorist’s view thereare no truth-makers distinct from truth-bearers, if the latter areconceived as propositions, and since nothing can make itself true, itfollows that there are no truth-makerssimpliciter, onlytruth-bearers. It seems to follow, too, that it would be ill-advisedto attack the identity theory by pointing out that some (or all)truths lack truth-makers (so Merricks 2007: 181): so long as truthsare taken to be propositions, that is exactly what identity theoriststhemselves say. From the identity theorist’s point of view,truth-maker theory looks very much like an exercise in splitting thelevel of reference in half and then finding a bogus match between thetwo 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 thataisF, some truth-maker or ontological ground fora’s beingF. What can this be except the state ofaffairs ofa’s beingF? (1991: 190)

the identity theorist is likely to retort thata’s beingF, which according to Armstrong “ensures” thata isF,just is the entity (whatever it is)that a is F. The identity theorist maps conceptualconnections 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 thatto go further would be to fall into error—so that to speak of anidentitytheory can readily appear too grand (McDowell 2005:83; 2007: 352. But cf. David 2002: 126). So much for the thesis thatfacts are truth-makers andpropositions truth-bearers; anexactly parallel argument applies to the version of the correspondencetheory that treats facts as truth-makers andthoughts astruth-bearers.

Consider now the suggestion that obtaining states of affairs, as thecorrespondence theorist conceives them, makedeclarativesentences (as opposed to propositions) true (cf. Horwich 1998:106–7). In this case there appears to be no threat of trivialityof the sort that apparently plagued the previous version of thecorrespondence theory, because states of affairs likethatSocrates is wise are genuinely distinct from linguistic itemssuch as the sentence “Socrates is wise”. To that extentfriends of the identity theory need not jib at the suggestion thatsuch sentences have worldly truth-makers, if that is how the relationof correspondence is being glossed. But they might question theappropriateness of the gloss. For, they might point out, it does notseem possible, without falsification, to draw detailed links betweensentences and bits of the world. After all, different sentences in thesame or different languages can “correspond” to the samebit of the world, and these different sentences might have verydifferent (numbers of) components. The English sentence “Thereare cows” contains three words: are there then three bits in theworld corresponding to this sentence, and making it true? (cf. Neale2001: 177). The sentence “Cowsexist” contains only two words, but would not the correspondencetheorist want to say that it was made true by the same chunk ofreality? And when we take other languages into account, there seems inprinciple to be no reason to privilege any particular number and saythat a sentence corresponding to the relevant segment of reality mustcontainthat number of words: why might there not, inprinciple, be sentences of actual or possible languages such that, foranyn ≥ 1, there existed a sentence comprisingnwords and meaning the same as the English “There arecows”? (In fact, is English not already such a language? Justprefix and then iteratead lib. a vacuous operator like“Really”.)

In a nutshell, then, the identity theorist’s case against thecorrespondence theory is that, when the truth-making relation isconceived as originating in a worldly fact (or similar) and having asits other relatum a truesentence, the claim that thisrelation is one of correspondence cannot be made out; if, on the otherhand, the relevant relation targets aproposition (orthought), then that relation must be held to be one of identity, notcorrespondence.

4. Identity, Sense, and Reference

Identity theorists are agreed that, in the case of any particularrelevant identity, a fact will constitute the worldlyrelatumof the relation, but there is significant disagreement among them onthe question what the item on the other end of the relationis—whether a thought or a proposition (or both). As we haveseen, there are three possible positions here: (i) one which placesthe identity relation exclusively between true thoughts and facts,(ii) one which places it exclusively between true propositions andfacts, and (iii) a hybrid position which allows identities of bothsorts (identities obtaining at the level of sense will of course bequite distinct from identities obtaining at the level of reference).Which of these positions an identity theorist adopts will depend onwider metaphysical and linguistic considerations that are strictlyextraneous to the identity theory as such.

Identity theorists who favor (i) generally do so because they want tohave nothing to do withpropositions as such. That is to say,such theorists eschew propositions asreference-levelentities: of course theword “proposition”may be, and sometimes is, applied to Fregean thoughts at the level ofsense, rather than to Russellian propositions at the level ofreference. For example, Hornsby (1997: 2–3) uses“proposition” and “thinkable” interchangeably.So far, this terminological policy might be considered neutral withrespect to the location of propositions and thinkables in the Fregeansemantic hierarchy: that is to say, if one encounters a theorist whotalks about “thinkables” and “propositions”,even identifying them, one does not, just so far, know where in thesemantic hierarchy this theorist places these entities. In particular,we cannot assume, unless we are specifically told so, that ourtheorist locates either propositions or thinkables at the level ofsense. After all, someone who houses propositions at thelevel of reference holds that these reference-level entities arethinkable, in the sense that they aregraspable inthought (perhaps via thoughts at the level of sense). But theyare notthinkables if this latter word is taken, as it is byMcDowell and Hornsby, to be a technical term referring to entities atthe level of sense. For clarity the policy here will be to continue toapply the word “proposition” exclusively to Russellianpropositions at the level of reference. Such propositions, it isplausible to suppose, can be grasped in thought, but by definitionthey are not thoughts or thinkables, where these two latter termshave, respectively, their Fregean and McDowellian meanings. It isworth noting that this point, though superficially a merelyterminological one, engages significantly with the interface betweenthe philosophies of language and mind that was touched on in theopening paragraph. Anyone who holds that reference-level propositionscan, in the ordinary sense, be thought—are thinkable—islikely to be unsatisfied with any terminology that seems to limit thedomain 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) abovehave this preference because they repudiate propositions as that termis being employed here: that is, they repudiate propositionallystructured reference-level entities. There are several reasons whysuch identity theorists feel uncomfortable with propositions whenthese are understood to be reference-level entities. There is a fearthat such propositions, if they existed, would have to be construed astruth-makers; and identity theorists, as we have seen, want to havenothing to do with truth-makers (Dodd 2008a: 112). That fear couldperhaps be defused if facts were also located at the level ofreference for true propositions to be identical with. This move wouldtake us to an identity theory in the style of (ii) or (iii) above.Another reason for suspicion of reference-level propositions is thatcommentators often follow Russell in his post-1904 aversionspecifically tofalse objectives, that is, to falsepropositionsin re (Russell 1966: 152; Cartwright 1987:79–84). Such entities are often regarded as too absurd to takeseriously as components of reality (so T. Baldwin 1991: 46; Dodd 1995:163; 1996; 2008a: 66–70, 113–14, 162–6). Moreespecially, it has been argued that false propositionsin recould not be unities, that the price of unifying a proposition at thelevel of reference would be to make it true: if this point werecorrect it would arguably constitute areductio ad absurdumof the whole idea of reference-level propositions, since it isplausible to suppose that if there cannot be false reference-levelpropositions, there cannot be true ones either (see Dodd 2008a: 165).If, on the other hand, one is happy with the existence of propositionsin 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 decidingbetween (ii) and (iii), there must surely be a good case for adopting(iii): for if one has admitted propositionally structured entitiesboth at the level of sense (as senses of declarative sentences) and atthe level of reference (propositions), there seems no good reason notto be maximally liberal in allowing identities between entities ofthese two types and, respectively, sense- and reference-level kinds offact (or fact-like entities).

Against what was suggested above about Frege (§2), it has been objected that Frege could not have held an identitytheory of truth (Baldwin 1991: 43); the idea here is that, even if hehad acknowledged states of affairs asbona fide elements ofreality, Frege could not have identified true thoughts with them onpain of confusing the levels of sense and reference. As far as theexegetical issue is concerned, the objection might be said to overlookthe possibility that Frege identified true thoughts with factsconstrued assense-level entities, rather than with states ofaffairs taken asreference-level entities; and, as we havenoted, Frege does indeed appear to have done just this (see Dodd &Hornsby 1992). Still, the objection raises an important theoreticalissue. It would surely be a serious confusion to try to construct anidentityacross the categorial division separating sense andreference, in particular to attempt to identify true Fregean thoughtswith 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, butare, 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 levelof sense, and admits no correlative identity, in addition, connectingtrue propositions located at the level of reference with facts orfact-like entities also located at that level, it looks as though onefaces a difficult dilemma. At what level in the semantical hierarchyis the world to be placed? Suppose first one puts it at the level ofreference (this appears to be Dodd’s favored view: see 2008a:180–1, andpassim). In that case the world will containno facts or propositions, but just objects and properties hangingloose in splendid isolation from one another, a dispensation whichlooks like a version of Kantian transcendental idealism. (Simplyinsisting that the properties include not merely monadic but alsopolyadic ones, such as the relation of instantiation, will not initself solve the problem: we will still just have a bunch of separateobjects, properties, and relations.) If there are no truepropositions—no facts—or even false propositions to befound at the level of reference, but if also, notwithstanding thatabsence, the world is located there, the objects it contains will, itseems, have to be conceived as bare objects, not as things of certainsorts. Some philosophers of a nominalistic bias might be happy withthis upshot; but the problem is how to make sense of the idea of abare object—that is, an object not characterized by anyproperties. (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 levelof sense, on the grounds that the world is composed of facts, and thatthat is where facts are located. This ontological dispensation isexplicitly embraced by McDowell (1996: 179). The problem with this wayout of the dilemma would seem to be that, since Fregean senses areconstitutively modes of presentation of referents, the strategy undercurrent consideration would take the world to be made up of modes ofpresentation—but of what? Of objects and properties? These arecertainly reference-level entities, but if they are presented by itemsin the realm of sense, which is being identified on this approach withthe world, then again, as on the first horn of the dilemma, they wouldappear to be condemned to an existence at the level of reference insplendid isolation from one another, rather than in propositionallystructured combinations, so that once more we would seem to becommitted to a form of Kantian transcendental idealism (see Suhm,Wagemann, & Wessels 2000: 32; Sullivan 2005: 59–61; Gaskin2006:199–203). Both ways out of the dilemma appear to have thisunattractive consequence. The only difference between those waysconcerns where exactly in the semantic hierarchy we locate the world;but it is plausible that that issue, in itself, is or ought to be ofless concern to metaphysicians than the requirement to avoid divorcingobjects from the properties that make those objects things of certainsorts; and both ways out of the dilemma appear to flout thisrequirement.

To respect the requirement, we need to nest reference-level objectsand properties in propositions, or proposition-like structures, alsolocated at the level of reference. And then some of these structuredreference-level entities—the true or obtaining ones—will,it seems, be facts, or at least fact-like. Furthermore, once oneacknowledges the existence of facts, or fact-like entities, existingat the level ofsense, it seems in any case impossible toprevent the automatic generation of facts, or fact-like entities,residing at the level ofreference. For sense is mode ofpresentation of reference. So we need reference-level facts orfact-like entities to be what sense-level facts or fact-like entitiespresent. One has to decide how to treat these variouslyhoused fact-like entities theoretically. If one were to insist thatthe sense-level fact-like entities were the genuine and onlyfacts, the corresponding reference-level entities would be nobetter thanfact-like, and contrariwise. But, regardlesswhether the propositionally structured entities automaticallygenerated in this way by sense-level propositionally structuredentities are to be thought of as proper facts or merely as fact-likeentities, it would seem perverse not to identify the world with these entities.^[11] For to insist on continuing to identify the world with sense-levelrather than reference-level propositionally structured entities wouldseem to fly in the face of a requirement to regard the world asmaximally objective and maximally non-perspectival. McDowell himselfhopes to avert any charge of embracing an unacceptable idealismconsequent on his location of the world at the level of sense byrelying on the point that senses present their references directly,not descriptively, so that reference is, as it were, contained insense (1996: 179–80). To this it might be objected that therequirement of maximal objectivity forces an identification of theworld with the contained, not the containing, entities in thisscenario, which in turn seems to force the upshot—if the threatof Kantian transcendental idealism is really to be obviated—thatthe contained entities be propositionally structured as such, that is,as contained entities, and not simply in virtue of beingcontained in propositionally structured containing entities. (For adifferent 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 beenheld to be) problematic for the identity theory (Moore 1953: 308; Fine1982: 46–7; Künne 2003: 9–10). The propositionthat Socrates is wise exists in all possible worlds whereSocrates and the property of wisdom exist, but in some of those worldsthis proposition is true and in others it is false. The factthatSocrates is wise, by contrast, only exists in those worlds wherethe proposition both exists and is true. So it would seem that thepropositionthat Socrates is wise cannot be identical withthe factthat Socrates is wise. They have different modalproperties, and so by the principle of the indiscernibility ofidenticals they cannot be identical.

Note, first, that this problem, if it is a problem, has nothingespecially to do with the identity theory of truth or with facts. Itseems to arise already for true propositions and propositions takensimpliciter before ever we get to the topic of facts. Thatis, one might think that the propositionthat Socrates iswise is identical with the true propositionthat Socrates iswise (assuming, as we are doing, that this propositionis true); but we then face the objection that the propositiontakensimpliciter and the true proposition differ in theirmodal properties, since (as one might suppose) the true propositionthat Socrates is wise does not exist at worlds where thepropositionthat Socrates is wise is false, but theproposition takensimpliciter does. Indeed the problem, if itis a problem, is still more general, and purported solutions to it goback at least to the Middle Ages (when it was discussed in connectionwith Duns Scotus’ formal distinction; see Gaskin 2002 [withreferences to further relevant literature]). Suppose that Socrates isa cantankerous old curmudgeon. Now grumpy Socrates, one would think,is identical with Socrates. But in some other possible worlds Socratesis of a sunny and genial disposition. So it would seem that Socratescannot be identical with grumpy Socrates after all, because in theseother possible worlds, while Socrates goes on existing, grumpySocrates does not exist—or so one might argue.

Can the identity theorist deal with this problem, and if so how? Hereis one suggestion. Suppose we hold, staying with grumpy Socrates for amoment, that, against the assumption made at the end of the lastparagraph, grumpy Socratesdoes in fact exist in worlds whereSocrates has a sunny disposition. The basis for this move would be thethought that, after all, grumpy Socratesis identical withSocrates, andSocrates exists in these other worlds. Sogrumpy Socrates exists in those worlds too; it is just that he is notgrumpy in those worlds. (Suppose Socrates isvery grumpy;suppose in fact that grumpiness is so deeply ingrained in hischaracter that worlds in which he is genial are quite far away.Someone surveying the array of possible worlds, starting from theactual world and moving out in circles, and stumbling at long lastupon a world with a pleasant Socrates in it, might register thediscovery by exclaiming, with relief, “Oh look! Grumpy Socratesis not grumpy over here!”.) Similarly, one might contend, thetrue proposition, and fact,that Socrates is wise goes onexisting in the worlds where Socrates is not wise, because the trueproposition, and fact,that Socrates is wise justisthe propositionthat Socrates is wise, and that propositiongoes on existing in these other worlds, but in those worlds that trueproposition, and fact, is not a true proposition, or a fact. (InScotist terms one might say that the propositionthat Socrates iswise and the factthat Socrates is wise are reallyidentical but formally distinct.)

This solution was, in outline, proposed by Richard Cartwright in his1987 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 trueproposition, and fact,that there are subways in Bostonexists 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 genialand sunny, but he is not grumpy there.) So even in worlds where it isnota factthat Boston has subways,thatfact, namely the factthat Boston has subways, continues toexist. Cartwright embellishes his solution with two controversialpoints. First, he draws on Kripke’s distinction between rigidand non-rigid designation, suggesting that his solution can bedescribed by saying that the expression “The factthatBoston has subways” is a non-rigid designator. But it isplausible that that expression goes on referring to, or beingsatisfied by (depending on how exactly one wants to set up thesemantics of definite descriptions: see Gaskin 2008: 56–81), thefactthat Boston has subways in possible worlds where Bostondoes not have subways; it is just that, though that fact exists inthose worlds, it is not a fact there. But that upshot does not appearto derogate from the rigidity of the expression inquestion. Secondly, Cartwright allows for a truereading of “The factthat there are subways in Bostonmight not have been the factthat there are subways inBoston”. But it is arguable that we should say that thissentence is just false (David 2002: 129). The factthat there aresubways in Boston would still have gone on beingthe samefact in worlds where Boston has no subways, namely the factthat there are subways in Boston; it is just that in thoseworldsthis fact would not have beena fact. Youmight say: inthat world the factthat there are subwaysin Boston would not be correctly described as a fact, but intalking about that world we are talking about it from the point ofview of our world, and in our world it is a fact. (Similarly withgrumpy Socrates.)

Now, an objector may want to press the following point against theabove purported solution to the difficulty. Consider again the factthat Socrates is wise. Surely, it might be said, it is morenatural to maintain that that factdoes not exist in apossible world where Socrates is not wise, rather than that it existsthere all right, but is not a fact. After all, imagine a conversationabout a world in which Socrates is not wise and suppose that SpeakerA claims that Socrates is indeed wise in that world. SpeakerB might counter with

No, sorry, you’re wrong: there is no such fact in that world;the purported factthat Socrates is wise simply does notexist in that world.

It might seem odd to insist thatB is not allowed to say thisand must say instead

Yes, you’re right that there is such a fact in that world,namely the factthat Socrates is wise, but in that worldthat fact is nota fact;.

How might the identity theorist respond to this objection? Onepossible strategy would be to make a distinction betweenfactandfactuality, as follows.Factuality, one mightsay, is a reification of facts. Once you have a fact, you also get, asan ontological spin-off, thefactuality of that fact. Thefact, being a proposition, exists at all possible worlds where theproposition exists, though in some of these worlds it may not be afact: it will not be a fact in worlds where the proposition is false.The factuality of that fact, by contrast, only exists at those worldswhere the factis 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 allworlds where Socrates exists, though at some of those worlds he is notgrumpy. ButSocrates’ grumpiness—that particulartrope—exists only at worlds where Socrates is grumpy. That seemsto obviate the problem, because the suggestion being canvassed here isthat grumpy Socrates is identical not withSocrates’grumpiness—so that the fact that these two entities havedifferent modal properties need embarrass no one—but rather withSocrates. Similarly, the suggestion is that the propositionthat Socrates is wise is identical not with thefactuality of the factthat Socrates is wise, butjust with thatfact. So the identity theorist wouldaccommodate the objector’s point by insisting thatfacts exist at possible worlds where theirfactualities do not exist.

The reader may be wondering why this problem was ever raised againstthe identity theory of truth in the first place. After all, theidentity theorist does not say that propositionssimpliciterare identical with facts, but thattrue propositions areidentical with facts, and now true propositions and facts surely haveexactly thesame modal properties: for regardless how thingsare with the sheer propositionthat Socrates is wise, at anyrate thetrue propositionthat Socrates is wise mustsurely be thought to exist at the same worlds as the factthatSocrates is wise, whatever those worlds are. However, as againstthis quick way with the purported problem, there stands the intuition,mentioned and exploited above, that the true propositionthatSocrates is wise is identical with the propositionthatSocrates is wise. So long as that intuition is in play, theproblem does indeed seem to arise—for true propositions, in thefirst instance, and then for facts by transitivity of identity. Butthe identity theorist will maintain that, as explained, the problemhas a satisfactory solution.

5.2 The “right fact” problem

Candlish, following Cartwright, has urged that the identity theory oftruth is faced with the difficulty of getting hold of the “rightfact” (Cartwright 1987: 74–5; Candlish 1999a: 238–9;1999b: 202–4). Consider a version of the identity theory thatstates:

(11)

The propositionthatp is true just if it isidentical with a fact.^[12]

Candlish’s objection is now that (11)

does not specifywhich fact has to be identical with theproposition for the proposition to be true. But what the identitytheory requires is not that a true proposition be identical withsome fact or other, it is that it be identical with theright fact. (1999b: 203)

In another paper Candlish puts the matter like this:

But after all, any proposition might be identical withsomefact or other (and there are reasons identified in theTractatus for supposing that all propositions are themselvesfacts), and so all might be true. What the identity theory needs tocapture is the idea that it isby virtue of being identicalwith theappropriate fact that a proposition is true. (1999a:239)

The reference to theTractatus is suggestive. Of course, itmight be objected that theTractatus does not havepropositions in the sense of that word figuring here: that is, it doesnot recognize Russellian propositions (propositions at the level ofreference). Nor indeed does it appear to recognize Fregean thoughts.In theTractatus, as we have noted (§2), declarative sentences (Sätze) are facts (arrangementsof names), and states of affairs (Sachlagen,Sachverhalte,Tatsachen) are also facts(arrangements of objects). Even so, Candlish’s allusion to theTractatus reminds us that propositions (in our sense)are Tractarian inasmuch as they are structuredarrangements of entities, namely objects and properties.(Correlatively, thoughts are structured arrangements of senses.) Falsepropositions (and false thoughts) will equally be arrangements ofobjects and properties (respectively, senses). So the difficulty thatCartwright and Candlish have identified can be put like this.Plausiblyany proposition, whether or not it is true, isidentical withsome fact or other given that a proposition isan arrangement of entities of the appropriate sort. But ifpropositions justare facts, thenevery propositionis identical withsome fact—at the very least, withitself—whether it is true or false. So the right-to-leftdirection of (11) looks incorrect.

J. C. Beall (2000) attempts to dissolve this problem on the identitytheorist’s behalf by invoking the principle of theindiscernibility of identicals. His proposal works as follows. If weask, in respect of (11), what the “right” fact is, itseems that we can answer that the “right” fact must atleast have the property ofbeing identical with the propositionthatp, and the indiscernibility principle then guaranteesthat there is only one such fact. This proposal is open to an obviousretort. Suppose that the propositionthatp is false.That proposition will still be identical with itself, and if we aresaying (in Wittgensteinian spirit) that propositions are facts, thenthat proposition will be identical with at least one fact, namelyitself. So it will satisfy the right-hand side of (11), its falsitynotwithstanding. But reflection on this retort suggests a patch-up toBeall’s proposal: why not say that theright fact isthe fact thatp? We would then be able to gloss (11)with

(12)

The propositionthatp is true just if (a) it isa factthatp, and (b) the propositionthatp is identical withthat fact.

Falsity, it seems, now no longer presents a difficulty, because if itis falsethatp then it is not a factthatp, so that (a) fails, and there is no appropriatecandidate for the propositionthatp to be identical with.^[13] Notice that, in view of the considerations already aired inconnection with the modal problem ((i) of this section), caution ishere required. Suppose that it is truethatp in theactual world, but false in some other possible world. According to thestrategy that we have been considering on the identitytheorist’s behalf, it would be wrong to say that, in thepossible world where it is falsethatp, there is nosuch fact as the factthatp. The strategy has it thatthere is indeed such a fact, because it is (in the actual world) afactthatp, and that fact, and the true proposition,thatp, go on existing in the possible world where itis falsethatp; it is just thatthat fact isnota fact in that possible world. But (12), the identitytheorist will maintain, deals with this subtlety. In the possibleworld we are considering, where it is falsethatp,though the factthatp exists, it is not a factthatp, so (a) fails, and there is accordingly no riskof our getting hold of the “wrong” fact. Note also that ifa Wittgensteinian line is adopted, while the (false) proposition thatp will admittedly be identical witha fact—atthe very least with itself—it will be possible, given thefailure of (a), for the identity theorist to contend with a clearconscience that that fact is thewrong fact, which does notsuffice to render the proposition true.

5.3 The “slingshot” problem

If the notorious “slingshot” argument worked, it wouldpose a problem for the identity theory of truth. The argument existsin a number of different, though related, forms, and this is not theplace to explore all of these in detail.^[14] Here we shall look briefly at what is one of the simplest and mostfamiliar versions of the argument, namely Davidson’s. Thisversion of the argument aims to show that if true declarativesentences refer to anything (for example to propositions or facts),then they all refer to the same thing (to the “GreatProposition”, or to the “Great Fact”). This upshotwould be unacceptable to an identity theorist of a Russellian cast,who thinks that declarative sentences refer to propositions, and thattrue such propositions are identical with facts: any such theorist isnaturally going to want to insist that the propositions referred to bydifferent declarative sentences are, at least in general, distinctfrom one another, and likewise that the facts with which distinct truepropositions are identical are also distinct from one another.Davidson expresses the problem that the slingshot argument purportedlythrows up as follows:

The difficulty follows upon making two reasonable assumptions: thatlogically equivalent singular terms have the same reference; and thata singular term does not change its reference if a contained singularterm is replaced by another with the same reference. But now supposethat “R” and “S” abbreviate anytwo sentences alike in truth value. (1984: 19)

He then argues that the following four sentences have the samereference:

(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“\(\hat{z}\)” meansthe \(z\) 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 “singularterm”) “\(\hat{z} (z\! =\! z \amp R)\)” whereas (15)contains “\(\hat{z} (z\! =\! z \amp S)\)”,

and these refer to the same thing ifS andR are alikein truth value. Hence any two sentences have the same reference ifthey have the same truth value. (1984: 19)

The difficulty with this argument, as a number of writers have pointedout (see, e.g., Yourgrau 1987; Gaskin 1997: 153 n. 17; Künne2003: 133–41), and the place where the identity theorist islikely to raise a cavil, lies in the first assumption on which itdepends. Davidson calls this assumption “reasonable”, butit has been widely questioned. It states “that logicallyequivalent singular terms have the same reference”. Butintuitively, the ideas of logical equivalence and reference seem to bequite distinct, indeed to have, as such, little to do with oneanother, so that it would be odd if there were somea priorireason why the assumption had to hold. And it is not difficult tothink of apparent counterexamples: the sentence “It israining” is logically equivalent to the sentence “It israining and (either Pluto is larger than Mercury or it is not the casethat Pluto is larger than Mercury)”, but the latter sentenceseems to carry a referential payload that the former does not. Ofcourse, if declarative sentences refer to truth-values, as Fregethought, then the two sentences will indeed be co-referential, but toassume that sentences refer to truth-values would be question-beggingin the context of an argument designed to establish that all truesentences refer to the same thing.

5.4 The congruence problem

A further objection to the identity theory, going back to anobservation of Strawson’s, takes its cue from the point thatcanonical names of propositions and of facts are often notstraightforwardly congruent with one another: they are often notintersubstitutablesalva congruitate (or, if they are, theymay not be intersubstitutablesalva veritate) (Strawson 1971:196; cf. Künne 2003: 10–12). For example, we say thatpropositions are true, not that they obtain, whereas we say that factsobtain, not that they are true. How serious is this point? Theobjection in effect presupposes that for two expressions to beco-referential, or satisfied by one and the same thing, they must besyntactically congruent, have the same truth-value potential, andmatch in terms of general contextual suitability. The assumption ofthe syntactic congruence of co-referential expressions iscontroversial, and it may be possible for the identity theorist simplyto 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 congruentdepends on one’s conception of reference, a matter that cannotbe 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 concerningthe question whether an identification of facts with true propositionsis undermined not specifically by phenomena ofsyntacticincongruence but rather by failure of relevant intersubstitutions topreservetruth-values (see, e.g., King 2007: ch. 5; King inKing, Soames, & Speaks 2014: 64–70, 201–8; Hofweber2016: 215–23; Candlish & Damnjanovic 2018: 264). Thediscussion 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 leapyear;

(19)

The fact that my local baker has shut down is justappalling;

(20)

The true proposition that my local baker has shut down is justappalling.

The problem here is said to be that the substitution of “trueproposition” for “fact” or vice versa generatesdifferent readings (in particular, readings with differenttruth-values). Suppose Daniel has to memorize a list of truepropositions, of which one is the proposition that this is a leapyear. Then it is contended that we can easily imagine a scenario inwhich (17) and (18) differ in truth-value. Another way of putting thesame 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 argumentgoes—(18) but not (21) would be true if Daniel had memorized hislist of true propositions without realizing that theyweretrue. Similar differences can be argued to apply,mutatismutandis, to (19) and (20). Can the identity theorist deal withthis 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 doeshave a reading like the one that is said to be appropriate for (18).Suppose Daniel has to memorize a list of facts. (17) could thendiverge in truth-value from

(22)

Daniel remembers the fact that this is a leap yearas afact.

For there is a reading of (17) on which, notwithstanding (17)’struth, (22) is false: this is the reading on which Daniel has indeedmemorized a list of facts, but without necessarily realizing that thethings he is memorizingare facts. He has memorized therelevant fact (that this is a leap year), we might say, but notas a fact. That is parallel to the reading of (18) accordingto which Daniel has memorized the true proposition that this is a leapyear, but notas a true proposition. The identity theoristmight then aver that, perhaps surprisingly, the same point actuallyapplies to the simple (21), on the grounds that this sentence can meanthat Daniel remembers the propositional objectthat this is a leapyear (from a list of such objects, say, that he has been asked tomemorize), with no implication that he remembers it eitheras aproposition oras a fact. So, according to thisresponse, the transparent reading of (18)—which has Danielremember the propositional object, namelythat this is a leapyear, but not necessarily remember itas a fact, or evenas the propositional objectthat this is a leap year (heremembers it under some other mode of presentation)—is alsoavailable for (17) and for (21).

What about the opaque reading of either (17) or (21), which impliesthat Daniel knowsfor a fact that this is a leapyear—is that reading available for (18) too? The identitytheorist might maintain that this reading is indeed available, andthen explain why we tend not to use sentences like (18) in therelevant sense, preferring sentences of the form of (17) or (21), onthe basis of the relative technicality of the vocabulary of (18). Theidea would be that it is just an accident of language that we prefereither (17) or (21) to (18) where what is in question is the sensethat implies that Daniel has propositional knowledge that this is aleap year (is acquainted with that fact as a fact), as opposed tohaving mere acquaintance, under some mode of presentation or other,with the propositional object which happens to be(the fact) thatthis 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 lessinformation than (17) or (21), under the reading of these twosentences that we are usually interested in, according to which Danielremembers the relevant fact as a fact, for (23) is compatible with thefalsity of “This is a leap year”. Hence to use (23) in asituation where one was in a position to use (17) or (21) would carrya misleading conversational implicature. That, at any rate, is onepossible line for the identity theorist to take. (It is worth notinghere that, if the identity theorist is right about this, it willfollow that the “know that” construction will be subjectto a similar ambiguity as the “remember that”construction, given that remembering is a special case of knowing.That is: “A knowsthatp” will meaneither “A is acquainted with the factthatp, and is acquainted with itas a fact” ormerely “A is acquainted with the factthatp, but not necessarily with itassuch—either as a fact or even as a propositionalobject”.)

5.5 The individuation problem

It might appear that we individuate propositions more finely thanfacts: for example, one might argue that the factthat Hesperus isbright is the same fact as the factthat Phosphorus isbright, but that the propositions in question are different (seeon this point Künne 2003: 10–12; Candlish & Damnjanovic2018: 266–7). The identity theorist has a number of strategiesin response to this objection. One would be simply to deny it, andmaintain that facts are individuated as finely as propositions: if oneis a supporter of the Fregean version of the identity theory, this islikely to be one’s response (see, e.g., Dodd 2008a: 90–3).Alternatively, one might respond by saying that, if there is a goodpoint hereabouts, at best it tells only against the Fregean andRussellian versions of the identity theory, not against the hybridversion. The identity theory in the hybrid version can agree that wesometimes think of facts as extensional, reference-level entities andsometimes also individuate propositions or proposition-like entitiesintensionally. Arguably, these twin points do indeed tell againsteither a strict Fregean or a strict Russellian version of the identitytheory: they tell against the strict Fregean position because, as wellas individuating facts intensionally, we also, sometimes, individuatefacts extensionally; and they tell against the strict Russellianposition because, as well as individuating facts extensionally, wealso, sometimes, individuate facts intensionally. But it is plausiblethat the hybrid version of the identity theory is not touched by theobjection, because that version of the theory accommodatespropositionally structured and factual entities at both levels ofsense and reference, though different sorts of these entities at thesedifferent levels—either propositions at the level of sense andcorrelative proposition-like entities at the level of reference orvice versa, and similarly,mutatis mutandis, forfacts and fact-like entities. It will follow, then, for this versionof the identity theory, that Fregean thoughts and Russellianpropositions are available, if true, to be identical with the factualentities of the appropriate level (sense and reference, respectively),and the individuation problem will not then, it seems, arise.Propositions or propositionally structured entities will beindividuated just as finely as we want them to be individuated, and ateach 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 todirect us to a conception of truth that has been called“intrinsicist” (Wright 1999: 207–9), and“primitivist” (Candlish 1999b: 207). This was a conceptionrecognized by Moore and Russell who, in the period when they weresympathetic to the identity theory, spoke of truth as a simple andunanalysable property (Moore 1953: 261; 1993: 20–1; Russell1973: 75; Cartwright 1987: 72–5; Johnston 2013: 384). The pointhere would be as follows. There are particular, individualexplanations of the truth of many propositions. For example, the trueproposition that there was a fire in the building will be explained byalluding to the presence of combustible material, enough oxygen, aspark caused by a short-circuit, etc. So, case by case, we will (atleast often) be able to provide explanations why given propositionsare true, and science is expanding the field of such explanations allthe time. But according to the intrinsicist, there is no prospect ofproviding ageneral explanation of truth, in the sense of anaccount that would explain, in utterly general terms, whyanytrue proposition was true. At that general level, according to theintrinsicist, there is nothing interesting to be said about what makestrue propositions true: there are only the detailed case-histories. Anintrinsicist may embrace one or another version of the identity theoryof truth: what has to be rejected is the idea that the truth of a trueproposition might consist in a relation to adistinctfact—that the truth of the true propositionthat Socrates iswise, for example, might consist inanything other thanidentity with the factthat Socrates is wise. On thisapproach, 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 itseriously” (1999b: 208); but it may be gaining in popularity now(see, e.g., Asay 2013).

Candlish (1999b: 208) thinks that intrinsicism and the identity theoryare competitors, but perhaps that view is not mandatory. Intrinsicismsays that truth is a simple and unanalysable property of propositions;the identity theory says that a true proposition is identical with afact (and with the right fact). These statements will seem to clashonly if the identity theory is taken to propound a heavy-duty analysisof truth. But if, following recent exponents of the theory, we take itrather to be merely spelling out a connection between two entitiesthat we have in our ontology anyway, namely true propositions andfacts, and which turn out (like Hesperus and Phosphorus) to beidentical, on the basis of a realization that an entity likethatSocrates is wise is both a true proposition and a fact, then anyincipient clash between intrinsicism and the identity theory will, itseems, be averted. On this approach, a natural thing to say will bethat the identity theory describes theway in which truth isa simple and unanalysable property.

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Other Internet Resources

• Candlish, Stewart and Damnjanovic, Nic, “The Identity Theoryof Truth”,The Stanford Encyclopedia of Philosophy(Spring 2011 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2011/entries/truth-identity/>. [This was the previous entry on the identity theory of truth in theStanford Encyclopedia of Philosophy—see theversion history.]
• Pluralist Theories of Truth, by Douglas Edwards, entry in theInternet Encyclopedia ofPhilosophy.
• George Edward Moore (1873–1958), by Aaron Preston, entry in theInternet Encyclopedia ofPhilosophy.

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