The Correspondence Theory of Truth (Stanford Encyclopedia of Philosophy) Cite this entry Search the SEP • Advanced Search • Tools • RSS FeedTable of Contents• What's New• Archives• Projected ContentsEditorial Information• About the SEP• Editorial Board• How to Cite the SEP• Special CharactersSupport the SEPContact the SEP ©Metaphysics Research Lab,CSLI,Stanford University  Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia FreeThe Correspondence Theory of TruthFirst published Fri May 10, 2002; substantive revision Mon Jul 25, 2005Narrowly speaking, the correspondence theory of truth is the view thattruth is correspondence to a fact—a view that was advocated byRussell and Moore early in the 20th century. But the labelis usually applied much more broadly to any view explicitly embracingthe idea that truth consists in a relation to reality, i.e., thattruth is a relational property involving a characteristic relation (tobe specified) to some portion of reality (to be specified). This basicidea has been expressed in many ways, giving rise to an extendedfamily of theories and, more often, theory sketches. The members ofthe family employ various concepts for the relevant relation(correspondence, conformity, congruence, agreement, accordance,copying, picturing, signification, representation, reference,satisfaction) and/or various concepts for the relevant portion ofreality (facts, states of affairs, situations, events, objects,sequences of objects, sets, properties, tropes). The resultingmultiplicity of versions and reformulations of the theory is due to ablend of substantive and terminological differences.The correspondence theory of truth is often associated withmetaphysical realism. Its traditional competitors, coherentist,pragmatist, and verificationist theories of truth, are oftenassociated with idealism, anti-realism, or relativism. In recentyears, the traditional competitors have been virtually replaced (atleast from publication-space) by deflationary theories oftruth—and to a lesser extent by the identity theory—whichnow lead the attack against correspondence theories.1. History of the Correspondence Theory2. Truth and Truthbearers3. Simple Versions of the Correspondence Theory4. Arguments for the Correspondence Theory5. Objections to the Correspondence Theory6. Correspondence as Isomorphism7. Modified Versions of the Correspondence Theory 7.1 Logical Atomism7.2 Logical “Subatomism”7.3 Relocating Correspondence8. The Correspondence Theory and Its Competitors9. More Objections to the Correspondence Theory 9.1 The Big Fact9.2 No Independent AccessBibliographyOther Internet ResourcesRelated Entries1. History of the Correspondence TheoryThe correspondence theory is often traced back to Aristotle'swell-known definition of truth (Metaphysics 1011b25):“To say of what is that it is not, or of what is not that it is,is false, while to say of what is that it is, and of what is not thatit is not, is true”—but virtually identical formulationscan be found in Plato (Cratylus 385b2, Sophist263b). It is noteworthy that this definition does not highlight thebasic correspondence intuition. Although it does invoke a relation(saying something of something) to reality (whatis), the relation is not made very explicit, and there is nospecification of what on the part of reality is responsible for thetruth of a saying. The definition offers a muted, relatively minimalversion of a correspondence theory. (For this reason it has also beeninterpreted as an impure precursor of deflationary theories of truth.)Aristotle sounds much more like a genuine correspondence theorist inthe Categories (12b11, 14b14), where he talks of“underlying things” that make statements true and impliesthat these “things” (pragmata) are logicallystructured situations or facts (viz., his sitting, his notsitting). Most influential is his claim in De Interpretatione(16a3) that thoughts are “likenessess”(homoiosis) of things. Although he nowhere defines truth interms of a thought's likeness to a thing or fact, it is clear thatsuch a definition would fit well into his overall philosophy ofmind.In medieval authors we find a division between“metaphysical” and “semantic” versions of thecorrespondence theory. The former are indebted to thetruth-as-likeness theme suggested by Aristotle's overall views, thelatter are modeled on Aristotle's more austere definition.The best known is the metaphysical version presented by ThomasAquinas: “Veritas est adaequatio rei etintellectus”—Truth is the equation of thing andintellect—which he restates as: “A judgment is said to betrue when it conforms to the external reality” (DeVeritate Q.1, A.1&3; cf. Summa TheologiaeQ.16). Aquinas credits the Neoplatonist Isaac Israeli with thisdefinition; but there is no such definition in Isaac. It can be tracedback to Carneades, 2nd century B.C., whom Sextus Empiricus(Adversos Mathematicos, vii, 168) reports as having taughtthat a presentation “is true when it is in accord(symphonos) with the object presented, and false when it isin discord with it”. Similar definitions can be found in variousearly commentators on Aristotle (cf. K¨nne 2003, chap. 3.1) and inAvicenna and Averroes (Tahafut 103, 302); they wereintroduced to the scholastics by William of Auxerre (cf. Boehner 1958;Wolenski 1994).Aquinas' balanced formula “equation of thing andintellect” is intended to leave room for the idea that“true” can be applied not only to thoughts and judgmentsbut also to things (e.g., a true friend). Aquinas explains that athought is said to be true because it conforms to reality, whereas athing is said to be true because it conforms to a thought (a friend istrue insofar as, and because, he conforms to our, or God's, conceptionof what a friend ought to be). This notion of thing-truth, whichplayed an important role in ancient and medieval thinking, isdisregarded by modern and analytic philosophers but survives to someextent in existentialist and continental philosophy.Medieval authors who prefer a semantic version of the correspondencetheory often use a peculiarly truncated formula to render Aristotle'sdefinition: A (mental) sentence is true iff, as it signifies, so it is(sicut significat, ita est). This emphasizes the semanticrelation of signification while remaining maximally elusive about whatit is that is signified by a true sentence. Foreshadowing a favoriteapproach of the 20th century, medieval semanticists likeOckham (Summa Logicae, II) and Buridan (Sophismata,II) give exhaustive lists of different truth-conditional clauses forsentences of different grammatical categories; they systematicallyrefrain from associating true sentences in general with a singleontological category.Authors of the modern period generally convey the impression that thecorrespondence theory of truth is far too obvious to merit much, orany, discussion. Brief statements of some version or other can befound in almost all major writers; see e.g., Descartes 1639, ATII 597;Spinoza, Ethics, axiom vi; Locke, Essay, IV.v.i;Leibniz, New Essays, IV.v.ii; Hume, Treatise, 3.1.1;and Kant 1787, B82—Berkeley, who does not seem to offer anyaccount of truth, is a potentially significant exception. Due to theinfluence of Thomism, metaphysical versions of the theory are morepopular with the moderns than semantic versions. But since the modernsgenerally subscribe to a representational theory of the mind (thetheory of ideas), they would seem to be committed to spelling outrelations like correspondence or conformity in terms of apsycho-semantic representation relation holding between ideas, orsequences of ideas, and appropriate portions of reality.One should distinguish between object-based andfact-based versions of correspondence theories(cf. Künne 2003, chap. 3). The former assume that thetruth-bearing item has subject-predicate structure; e.g.,: A judgmentis true iff it/its predicate corresponds to its object—note thatthis actually involves two relations to an object: areference relation (presupposed), holding between the predicativejudgment and the object the judgment is about; and a correspondencerelation (highlighted), holding between that object and the predicateof the judgment. Object-based correspondence was the norm untilrelatively recently (with some remarks in Aristotle being a possibleexception, see above). Fact-based correspondence, which does not needto assume that truth-bearing items have subject-predicate structure,became prominent only in the 20th century.The now classical formulation of a fact-based correspondence theoryappears in Moore (1910-11, chap. 15) and Russell: “Thus a beliefis true when there is a corresponding fact, and is false when there isno corresponding fact” (1912, 129; cf. also his 1906 and1913). The self-conscious emphasis on facts as the correspondingportions of reality—and a more serious concern withfalsehood—distinguishes this version from itsprecursors. Russell and Moore's forceful advocacy of truth ascorrespondence to a fact was, at that time, an integral part of theirdefense of metaphysical realism. Their formulation is indebted to oneof their idealist opponents, H. H. Joachim (1906), an early advocateof the coherence theory, who had set up a slightly more involvedcorrespondence-to-fact account of truth as the main target of hisattack on realism. Later, Wittgenstein (1921) and Russell (1918)developed “logical atomism”, which introduces an importantmodification of the fact-based correspondence approach. Furthermodifications, bringing a return to more overtly semantic and broadlyobject-based versions, was influenced by Tarski's (1935) technicalwork on truth (cf. Field 1972, Popper 1972).2. Truth and TruthbearersCorrespondence theories of truth have been given for beliefs,thoughts, ideas, judgments, statements, assertions, utterances,sentences, and propositions. It has become customary to talk of“truthbearers” whenever one wants to stay neutral betweenthese choices. Two points should be kept in mind: (i) The term issomewhat misleading; it is intended to refer to bearers of truth orfalsehood (or alternatively, to things of which it makes sense to askwhether they are true or false, thus allowing for the possibility thatsome of them might be neither); (ii) One distinguishes betweensecondary and primary truthbearers. Secondary truthbearers are thosewhose truth-values (truth or falsehood) are derived from thetruth-values of primary truthbearers, whose truth-values are notderived from any other truthbearers. It is often unproblematic toadvocate one theory of truth for bearers of one type and anothertheory for bearers of a different type (e.g., a deflationary theory, oran identity theory, of truth for propositions could be a component ofa correspondence theory of truth for sentences): different theoriesapplied to bearers of different types do not automaticallycompete. The standard segregation of truth theories into competingcamps proceeds under the assumption, or pretense, that they areintended for primary truthbearers. Confusingly, there is littleagreement as to which entities are properly taken to be primarytruthbearers. Nowadays, the main contenders are public languagesentences, sentences of the language of thought (mentalrepresentations), and propositions.3. Simple Versions of the Correspondence TheorySome simple forms of correspondence definitions of truth should bedistinguished (“iff” means “if and only if”;“x” refers to whatever truthbearers are taken asprimary; the notion of correspondence might be replaced by variousrelated notions):(1)x is true iff x corresponds to some fact; x is false iff x does not correspond to anyfact;(2)x is true iff x corresponds to some state ofaffairs that obtains; x is false iff x corresponds to some state ofaffairs that does not obtain.Both forms invoke portions of reality—facts/states ofaffairs—that are denoted by that-clauses or by sententialgerundives, viz. the fact/state of affairs that snow iswhite, or the fact/state of affairs of snow's beingwhite. (2)'s definition of falsehood is committed to there beingentities of this sort that do not obtain; (1)'s definition offalsehood is not so committed (to say that a fact does not obtainmeans, at best, that there is no such fact). It should be noted thatthis terminology is not standardized: some authors use “state ofaffairs” much like “fact” is used here(e.g., Armstrong 1997). The question whether non-obtaining entities ofthe relevant sort are to be accepted is the substantive issue behindsuch terminological variations. The difference between (2) and (1) isakin to the difference between Platonism about properties (embracesuninstantiated properties) and Aristotelianism (rejects uninstantiatedproperties).Advocates of (2) typically hold that facts are states of affairs thatobtain, i.e., they hold that their account of truth is in effect ananalysis of (1)'s account of truth. So disagreement turns largely onthe treatment of falsehood, which (1) simply identifies with theabsence of truth.The following points can be made for preferring (2) over (1): (a) Form(2) does not imply that things outside the category of truthbearersare false just because they don't correspond to facts. (b) Form (2)allows for items within the category of truthbearers that are neithertrue nor false, i.e., it allows for the failure of bivalence. (c) Ifthe primary truthbearers are sentences or mental states, then statesof affairs can be their meanings or contents, and the correspondencerelation in (2) can be understood, accordingly, as the relation ofrepresentation, signification, meaning, or having-as-content. Facts,on the other hand, cannot be identified with the meanings or contentsof sentences or mental states, on pain of the absurd consequence thatfalse sentences and beliefs have no meaning or content. (d) Take atruth of the form ‘p or q’, where‘p’ is true and ‘q’false. What are the constituents of the corresponding fact? Since‘q’ is false, they cannot both be facts. (2)allows that the corresponding fact is a disjunctive state of affairscomposed of a state of affairs that obtains and a state of affairsthat does not obtain.The main point in favor of (1) over (2) is that (1) is not committedto counting non-obtaining states of affairs, like the state of affairsthat snow is green, as constituents of reality.Both forms, (1) and (2), should be distinguished from (3) x istrue iff x corresponds to some fact that exists; x is false iff x corresponds to some fact that doesnot exist,which is a confused version of (1), or a confused version of (2), or,if unconfused, implies commitment to Meinongianism, i.e., the thesisthat there are things/facts that do not exist. The lure of (3) stemsfrom the desire to give a good account of falsehood while avoidingcommitment to non-obtaining states of affairs. Moore sometimessuccumbs to (3)'s temptations (1910-11, 269). It can also be found inWittgenstein (1921, 4.25), who uses “Sachverhalt”to refer to (atomic) facts. The problem of falsehood (How can we thinkwhat is not the case?), which is related to the problem ofnonexistence (How can we think of what does not exist?), was broughtout nicely in Plato's Theaetetus (188c-89).A fourth simple form of correspondence definition was popular for atime (cf. Russell 1918, secs. 1 & 3; Broad 1933, IV.2.23; Austin1950, fn. 23) but seems to have fallen out of favor: (4) x istrue iff x corresponds with some fact; x is false iff x mis-corresponds with some fact.This formulation attempts to avoid (2)'s commitment to non-obtainingstates of affairs and (3)'s commitment to non-existent facts byinvoking the relation of mis-correspondence to account forfalsehood. It differs from (1) in that it attempts to keep itemsoutside the intended category of x's from being false:supposedly, tables and dogs cannot mis-correspond with a fact. Mainworries about (4) are: (a) its invocation of an additional,potentially mysterious, relation, and (b) that this additionalrelation seems difficult to tame: Which fact is the one thatmis-corresponds with a given falsehood? and What keeps a truth, whichby definition corresponds with some fact, from also mis-correspondingwith some other facts?In the following, I will treat definitions (1) and (2) as paradigmatic.4. Arguments for the Correspondence TheoryThe main positive argument given by advocates of the correspondencetheory of truth is its obviousness. Descartes: “I have never hadany doubts about truth, because it seems a notion so transcendentallyclear that nobody can be ignorant of it...the word‘truth’, in the strict sense, denotes the conformity ofthought with its object” (1639, AT II 597); Kant: “Thenominal definition of truth, that it is the agreement of [a cognition]with its object, is assumed as granted” (1787, B82); WilliamJames: “Truth, as any dictionary will tell you, is a property ofcertain of our ideas. It means their ‘agreement’, asfalsity means their disagreement, with ‘reality’”(1907, 96); The Oxford English Dictionary: “Truth,n. Conformity with fact; agreement with reality”. Since the(relatively recent) arrival of apparently competing theories,correspondence theorists have added negative arguments to theirarsenal, defending their view against objections and attacking(sometimes ridiculing) competing views.5. Objections to the Correspondence TheoryObjection 1: Definitions like (1) or (2) aretoo broad; although they apply to truths from some domains ofdiscourse, e.g., the domain of science, they fail for others, e.g.,the domain of morality: there are no moral facts.The objection recognizes moral truths, but rejects the idea thatreality contains moral facts. Logic provides another example of adomain that has been “flagged” in this way: the logicalpositivists recognized logical truths but rejected logical facts.There are four possible responses to objections of this sort: (a)Error theory, which says that all claims from the flagged domain arefalse; (b) Noncognitivism, which says that, despite appearances to thecontrary, claims from the flagged domain are not truth-evaluable tobegin with, they are commands or emotions disguised as truthbearers;(c) Reductionism, which says that truths from the flagged domaincorrespond to facts of a different domain regarded as unproblematic,e.g., moral truths correspond to social-behavioral facts, logicaltruths correspond to facts about linguistic conventions; (d) Standingfirm, i.e., embracing facts of the flagged domain. The last option canbe supported by the following observation. The objection in effectmaintains that there are different brands of truth (not justdifferent brands of truths) for the different domains. This makes ithard to explain why there are many obviously valid arguments combiningpremises from flagged and unflagged domains.Objection 2: Correspondence theories are tooobvious; they are trivial, vacuous, engaging in mere platitudes.Locutions from the “corresponds to the facts”-family areused regularly in everyday language as idiomatic substitutes for“true”. Such common turns of phrase should not be taken toindicate commitment to a correspondence theory in any serioussense. Definitions like (1) or (2) merely condense some trivial idiomsinto handy formulas; they don't deserve the grand label“theory”: there is no theoretical weight behind them (cf.Woozley 1949, chap. 6; Davidson 1969; Blackburn 1984, chap. 7.1).In response, one could point out: (a) Definitions like (1) or (2) are“mini-theories”—mini-theories are quite common inphilosophy, and it is not obvious that they are vacuous merely becausethey are modeled on common usage; (b) There are correspondencetheories that go beyond these definitions; (c) The complaint impliesthat definitions like (1) or (2) are generally accepted and are,moreover, so shallow that they are compatible with any deeper theoryof truth. This makes it difficult to explain why a considerablenumber of thinkers emphatically reject all correspondenceformulations. Moreover, the suggestion that the correspondence ofS's belief to a fact could be said to consist in, e.g., itscoherence with S's belief system is quite implausible, evenon the most shallow understanding of “correspondence” and“fact”.Objection 3: Correspondence theories aretoo obscure.Objections of this sort, which are the most common, protest that thecentral notions of a correspondence theory carry unacceptablecommitments and/or cannot be accounted for in any respectable manner.They might be divided into objections primarily aimed at thecorrespondence relation, or its relatives, and objections primarilyaimed at the notions of fact or state of affairs:3.C1: The correspondence relation must be some sort of resemblancerelation. But truthbearers don't resemble anything in the world exceptother truthbearers—echoing Berkeley's “an idea can be likenothing but an idea”.3.C2: The correspondence relation is very mysterious: it seems toreach into the most distant regions of space (faster than light?) andtime (past and future). How could such a relation possibly beaccounted for within a naturalistic framework? What physical relationcould it possibly be?3.F1: Given the great variety of complex truthbearers, acorrespondence theory will be committed to all sorts of complex“funny facts” that are ontologically disreputable:negative, disjunctive, conditional, universal, probabilistic,subjunctive, and counterfactual facts have all given cause forcomplaint on this score.3.F2: All facts, even the most simple ones, are disreputable.Fact-talk, being wedded to that-clauses, is entirely parasitic ontruth-talk. Facts are too much like truthbearers. Facts are fictions,spurious sentence-like slices of reality, “projected from truesentences for the sake of correspondence” (Quine 1987, 213; cf.Strawson 1950).6. Correspondence as IsomorphismA correspondence theory is usually expected to go beyond a meredefinition like (1) or (2) and discharge a triple task: it should tellus about the workings of the correspondence relation, about the natureof facts, and about the conditions that determine which truthbearerscorrespond to which facts. It is natural to tackle this by construingcorrespondence as an isomorphism between truthbearers andfacts (cf. Kirkham 1992, chap. 4). The basic idea is that truthbearersand facts are both complex structured entities: truthbearers arecomposed of words, or concepts, and other truthbearers; facts arecomposed of things, properties, relations, and other facts or statesof affairs. The aim is to show how the correspondence relation isgenerated from underlying relations between the ultimate constituentsof truthbearers and the ultimate constituents of their correspondingfacts. One part of the project will be concerned with thesecorrespondence-generating relations: it will lead into a theory thataddresses the question how simple words, or concepts, can beabout things, properties, and relations; i.e., it will mergewith semantics or psycho-semantics (depending on what the truthbearersare taken to be). The other part of the project, the specificallyontological part, will have to provide identity criteria for facts andexplain how their simple constituents combine into complex wholes.Putting all this together should yield an account of the conditionsdetermining which truthbearers correspond to which facts.The isomorphism approach offers an answer to objection 3.C1.Although the truth that the cat is on the mat does not resemble the cator the mat (the truth doesn't smell, etc.), it does resemble the factthat the cat is on the mat. This is not a qualitative resemblance; itis a more abstract, structural resemblance.The approach also puts objection 3.C2 in some perspective. Thecorrespondence relation is supposed to reduce to underlying relationsbetween words, or concepts, and reality. Consequently, acorrespondence theory is little more than a spin-off from semanticsand/or psycho-semantics (the theory of intentionality). This remindsus that, as a relation, correspondence is no more—but also noless—mysterious than semantic relations in general. Suchrelations have some curious features, and they raise a host of puzzlesand difficult questions—most notoriously: Can they be explainedin terms of natural (causal) relations, or do they have to be regardedas irreducibly non-natural aspects of reality? Some philosophers haveclaimed that semantic relations are too mysterious to be takenseriously, usually on the grounds that they are not explainable innaturalistic terms. But one should bear in mind that this is a verygeneral and extremely radical attack on semantics as a whole, on thevery idea that words and concepts can be about things. Thecommon practice to aim it specifically at the correspondence theoryseems misleading. As far as the intelligibility of the correspondencerelation is concerned, the correspondence theory will stand, or fall,with the general theory of reference and intentionality.On a straightforward implementation of the isomorphism approach,correspondence will be a one-one relation between truths andcorresponding facts, which leaves the approach vulnerable toobjections against funny facts (3.F1): each true truthbearer, nomatter how complex, will be assigned a matching fact. Moreover, sincethe approach assigns corresponding entities to all (relevant)constituents of truthbearers, complex facts will contain objectscorresponding to the logical constants (“not”,“or”, “if-then”, etc.), and these“logical objects” will have to be regarded as constituentsof the world. Many philosophers have found it hard to believe in theexistence of all these funny facts and objects.The isomorphism approach has never been advocated in a fullynaïve form, assigning corresponding objects to each and everywrinkle of our verbal or mental utterings. Instead, proponents try toisolate the “relevant” constituents of truthbearersthrough meaning analysis, aiming to uncover the logical form, or deepstructure, behind ordinary language and thought. This deep structuremight then be expressed in an ideal-language (typically, thelanguage of predicate logic) whose syntactic structure is designed tomirror perfectly the ontological structure of reality. The resultingview—correspondence as isomorphism between properly analyzedtruthbearers and facts—avoids assigning strange objects to suchphrases as “the average husband”, “the present kingof France”, or “the sake of”; but the view remainscommitted to logically complex facts and to logical objectscorresponding to the logical constants.Austin (1950) rejects the isomorphism approach on the grounds thatit reads the structure of our language into the world. On his versionof the correspondence theory (a more elaborated variant of (4) appliedto statements), a statement as a whole is correlated to a state ofaffairs by arbitrary linguistic conventions without mirroring the innerstructure of its correlate. This approach appears vulnerable to theobjection that it avoids funny facts at the price of neglectingsystematicity. Language does not provide separate linguisticconventions for each statement: that would require too vast a number ofconventions. Rather, it seems that the truth-values of statements aresystematically determined, via a relatively small set of conventions,by the semantic values (relations to reality) of their simplerconstituents. Recognition of this systematicity is built right into theisomorphism approach.7. Modified Versions of the Correspondence Theory7.1 Logical AtomismWittgenstein (1921) and Russell (1918) propose a modified (fact-based)correspondence account of truth as part of their program of“logical atomism”. Such an account proceeds in two stages:(A) the basic truth-definition, say (1), is restricted to a specialsubclass of truthbearers, the so-called elementary, or atomic,truthbearers; (B) the truth-values of non-elementary, or molecular,truthbearers are explained recursively in terms of theirlogical structure and the truth-values of their simpler constituents:for example, a sentence of the form ‘not-p’ istrue iff ‘p’ is false; a sentence of the form‘p and q’ is true iff‘p’ is true and ‘q’ is true;a sentence of the form ‘p or q’ is trueiff ‘p’ is true or ‘q’ istrue, etc. These recursive clauses (called “truthconditions”) can be reapplied until the truth of a molecularsentence of arbitrary complexity is reduced to the truth or falsehoodof its atomic constituents. Definition (1), restricted to atomictruthbearers, serves as the base-clause for the truth-conditionalrecursions.Such an account of truth is designed to go with the ontological viewthat the world is the totality of atomic facts (cf. Wittgenstein 1921,2.04); i.e., atomic facts are all the facts there are—althoughatomists tend to allow conjunctive facts, regarding them as mereaggregates of atomic facts. An atomic truth is true because itcorresponds to an atomic fact: correspondence is still isomorphism,but it holds exclusively between atomic truths and atomicfacts. Molecular truths are not assigned any matching facts: strictlyspeaking, they do not correspond to facts at all; but theirtruth-values are explained in terms of logical structure andcorrespondence of atomic constituents. One-one correspondence isrestricted to the atomic level; above that level, there is no one-onecorrelation between truths and facts (e.g., ‘p’,‘p or q’, and ‘p orr’ might all be true merely because‘p’ corresponds to a fact). The trick foravoiding logically complex facts lies in not assigning any entities tothe logical constants. Logical complexity, so the idea goes, belongsto the structure of language and/or thought; it is not a feature ofthe world.While Wittgenstein and Russell seem to have held that the constituentsof atomic facts are to be determined on the basis of a prioriconsiderations, Armstrong (1997, 2004) advocates an aposteriori form of logical atomism. On his view, atomic facts arecomposed of particulars and simple universals (properties andrelations). The latter are objective features of the world that groundthe objective resemblances between particulars and explain theircausal powers. Accordingly, what particulars and universals there arewill have to be determined on the basis of total science.Logical atomism is not easy to sustain and has rarely been held in apure form. Among its difficulties are the following: (a) There aremolecular truthbearers, like subjunctives and counterfactuals, thattend to provoke the funny-fact objection but cannot be handled bysimple truth-conditional clauses because their truth-values do notseem to be determined by the truth-values of their atomicconstituents. (b) Are there universal facts corresponding to trueuniversal generalizations? Wittgenstein (1921) disapproves ofuniversal facts; apparently, he wants to reanalyze universalgeneralizations as infinite conjunctions of their instances. Russell(1918) and Armstrong (1997, 2004) reject this analysis; they admituniversal facts. (c) Negative truths are the most notorious problemcase, because they clash with an appealing principle, the“truthmaker principle” (Armstrong 1997, 2004), which saysthat for every truth there must be something in the world that makesit true, i.e., every true truthbearer must have a truthmaker. Suppose‘p’ is elementary. On the account given above,‘not-p’ is true iff ‘p’ isfalse iff ‘p’ does not correspond to any fact;hence, ‘not-p’ is not made true by any fact: itdoes not seem to have a truthmaker. Russell finds himself driven toadmit negative facts, regarded by many as paradigmaticallydisreputable portions of reality. Wittgenstein (cf. 1921, 2.06)sometimes talks of atomic facts that do not exist and calls their verynonexistence a negative fact—but this is hardly an atomic factitself. Armstrong (1997, chap. 8.7; 2004, chaps. 5-6) holds thatnegative truths are made true by a second-order “totalityfact” which says of all the (positive) first-order facts thatthey are all the first-order facts.Logical atomism is designed to address objections to funny facts(3.F1). It is not designed to address objections to facts in general(3.F2). Here logical atomists will respond by defending (atomic)facts. According to one defense, facts are needed because mereobjects are not sufficiently articulated to serve astruthmakers. If a were the sole truthmaker of‘a is F’, then the latter should imply‘a is G’, for any‘G’. So the truthmaker for ‘a isF’ needs at least to involve a andFness. But since Fness is a universal, it could beinstantiated in another object, b, hence the mere existenceof a and Fness is not sufficient for making true theclaim ‘a is F’: a andFness need to be tied together in the fact of a's beingF. Armstrong (1997) and Olson (1987) also maintain that facts areneeded to make sense of the tie that binds particular objects touniversals. In this context it is usually emphasized that facts do notsupervene on, hence, are not reducible to, their constituents. Factsare entities over and above the particulars and universals ofwhich they are composed: a's loving b andb's loving a are not the same fact even though theyhave the very same constituents. Another defense, surprisingly rare,would point out that many facts are observable: one can see that thecat is on the mat; and this is different from seeing the cat, or themat, or both. One might object that many facts are not observable;this invites the rejoinder that many objects are not observableeither. See also Vision (2004, chap. 3) for responses to anti-factarguments.Some logical atomists propose a version of (1) without facts becausethey regard facts as too sentence-like slices of reality. Instead,they propose events and/or objects-plus-tropes (a.k.a. modes,particularized qualities, moments) as the corresponding portions ofreality. It is claimed that these items are more “thingy”than facts but still sufficiently articulated—and sufficientlyabundant—to serve as adequate truthmakers (cf. Mulligan, Simons,and Smith 1984).7.2 Logical “Subatomism”Logical atomism aims at getting by without complex truthmakers byrestricting definitions like (1) or (2) to atomic truthbearers andaccounting for the truth-values of molecular truthbearers recursivelyin terms of their logical structure and atomic truthmakers (atomicfacts, events, objects-plus-tropes). More radical modifications of thecorrespondence theory push the recursive strategy even further,entirely discarding definitions like (1) or (2), and hence the needfor atomic truthmakers, by going, as it were,“subatomic”.Such accounts analyze truthbearers, e.g., sentences, into theirsubsentential constituents and dissolve the relation of correspondenceinto appropriate semantic subrelations: names refer to, ordenote, objects; predicates (open sentences) apply to, or aresatisfied by objects. Satisfaction of complex predicates canbe handled recursively in terms of logical structure and satisfactionof simpler constituent predicates: an object o satisfies‘x is not F’ iff o does notsatisfy ‘x is F’; o satisfies‘x is F or x is G’ iffo satisfies ‘x is F’ oro satisfies ‘x is G’; and soon. These recursions are anchored in a base-clause addressing thesatisfaction of primitive predicates: e.g., osatisfies ‘x is F’ iff oinstantiates the property expressed by‘F’—some would prefer a more nominalisticbase-clause for satisfaction, hoping to get by without seriouslyinvoking properties. Truth for singular sentences, consisting of aname and an arbitrarily complex predicate, is defined thus: A singularsentence is true iff the object denoted by the name satisfies thepredicate. Logical machinery provided by Tarski (1935) can be used toturn this simplified sketch into a more general definition oftruth—a definition that handles sentences containing relationalpredicates and quantifiers and covers molecular sentences aswell. (Whether Tarski's own definition of truth can be regarded as acorrespondence definition even in this modified sense is under debate;cf. Popper 1972; Field 1972, 1986; Kirkham 1992, chaps. 5-6; Soames1999; Künne 2003, chap. 4)Subatomism constitutes a return to (broadly) object-basedcorrespondence. Since it promises to avoid facts and all similarlyarticulated, sentence-like slices of reality, correspondence theoristswho take seriously objection 3.F2 favor this approach: not even atomictruthbearers are assigned any matching truthmakers. The correspondencerelation itself has given way to two semantic relations betweenconstituents of truthbearers and objects: denotation andsatisfaction—relations central to any semantic theory. Someadvocates envision causal accounts of denotation and satisfaction (cf.Field 1972; Devitt 1982, 1984; Schmitt 1995; Kirkham 1992,chaps. 5-6). It turns out that relational predicates require talk ofsatisfaction by ordered sequences of objects. Davidson (1969,1977) maintains that satisfaction by sequences is all that remains ofthe traditional idea of correspondence to facts; he regards denotationand satisfaction as “theoretical constructs” not in needof causal, or any, explanation.Problems: (a) The subatomistic approach accounts for the truth-valuesof molecular truthbearers in the same way as the atomistic approach;consequently, molecular truthbearers that are not truth-functionalpose similar problems. (b) Belief attributions and modal claims posespecial problems; e.g., it seems that “believes” is arelational predicate, so that “John believes that snow iswhite” is true iff “believes” is satisfied by Johnand the object denoted by “that snow is white”; but thelatter appears to be a proposition or state of affairs, whichthreatens to let in through the back-door the very sentence-likeslices of reality the subatomic approach was supposed to avoid; (c)The phenomenon of referential indeterminacy threatens to undermine theidea that the truth-values of atomic truthbearers are alwaysdetermined by the denotation and/or satisfaction of theirconstituents; e.g., pre-relativistic uses of the term“mass” are plausibly taken to lack determinate reference(referring determinately neither to relativistic mass nor to restmass); yet a claim like “The mass of the earth is greater thanthe mass of the moon” seems to be determinately true even whenmade by Newton (cf. Field 1973).Problems for both versions of modified correspondence theories: (a) Itis not known whether an entirely general recursive definition oftruth, one that covers all truthbearers, can be made available. Thisdepends on unresolved issues concerning the extent to whichtruthbearers are amenable to the kind of structural analyses that arepresupposed by the recursive clauses. The more an account of truthwants to exploit the internal structure of truthbearers, the more itwill be hostage to the (limited) availability of appropriatestructural analyses of the relevant truthbearers. (b) Any account oftruth that employs recursions may be virtually committed to takingsentences (maybe sentences of the language of thought) as primarytruthbearers. After all, the recursive clauses rely heavily on whatappears to be the logico-syntactic structure of truthbearers, and itis unclear whether anything but sentences can plausibly be said topossess this kind of structure. The thesis that sentences of any sortcan be regarded as primary truthbearers is contentious. (c) If clauseslike “‘p or q’ is true iff‘p’ is true or ‘q’ istrue” are to be used in a recursive account of ournotion of truth, as opposed to some other notion, it has tobe presupposed that ‘or’ expresses disjunction:one cannot define ‘or’ and ‘true’ at the sametime. To avoid circularity, a modified correspondence theory (be itatomic or subatomic) must hold that the logical connectives can beunderstood without reference to correspondence truth.7.3 Relocating CorrespondenceAccording to definitions like (1) and (2), the truthbearer itself isthe item that corresponds with a fact. There are views that rejectthis assumption, proposing to account for the truth of a truthbearerby way of the correspondence to a fact of another item, which containsthe truthbearer. The state of believing that p (or theactivity of judging that p) is not, strictly speaking, trueor false; rather, what is true or false is the proposition thatp. Nevertheless, on this view, the state of believing thatp can be said to correspond with a fact. So truth/falsehoodof a proposition can be defined in the following manner: x isa true/false proposition iff there is a belief state B suchthat x is the content of B and Bcorresponds/fails to correspond to a fact.Such a modification of fact-based correspondence can be found in Moore(1927, 83) and Armstrong (1973, 4.iv & 9). It can be adapted toatomistic (Armstrong) and subatomistic views, and to views on whichsentences (of the language of thought) are the primary bearers oftruth and falsehood. It entails that there are no truths/falsehoodsthat are not believed by someone. Most advocates of propositions asprimary bearers of truth and falsehood will regard this as a seriousweakness. Armstrong (1973) combines the view with an instrumentalistattitude towards propositions, on which propositions are mereabstractions from mental states that should not be taken seriously,ontologically speaking. 8. The Correspondence Theory and Its CompetitorsA. Against the traditionalcompetitors—coherentist, pragmatist, and verificationist andother epistemic theories of truth—correspondence theorists raisetwo main sorts of objections. First, such accounts tend tolead into relativism. Take, e.g., a coherentist account oftruth. Since it is possible that ‘p’ coheres withthe belief system of S while ‘not-p’coheres with the belief system of S*, the coherentist accountseems to imply, absurdly, that contradictories,‘p’ and ‘not-p’, could bothbe true. To avoid embracing contradictions, coherentists often committhemselves (if only covertly) to the objectionable relativistic viewthat ‘p’ is true-for-S and‘not-p’ is true-for-S*. Second,the competing accounts tend to lead into some form of idealism oranti-realism. E.g., it is possible for the belief that p tocohere with someone's belief system even though it is not a fact thatp; also, it is possible for it to be a fact that peven if no one believes that p, or if the belief thatp does not cohere with anyone's belief system. Cases of thisform are frequently cited as counterexamples to coherentist accountsof truth. Coherentists tend to reject such counterexamples byinsisting that they are not possible after all—a reaction thatcommits them to the anti-realist view that the facts are (largely)determined by what we believe.B. According to the identity theory oftruth, true propositions do not correspond to facts, they are(identical with) facts: the true proposition that snow is white = thefact that snow is white. This non-traditional competitor of thecorrespondence theory threatens to collapse the correspondencerelation into identity. In response, a correspondence theorist mightpoint out: First, the identity theory is defensible only forpropositions as truthbearers, and only if propositions are construedin a certain way, namely as having objects and properties asconstituents rather than ideas or concepts of objects andproperties. Hence, even if the identity theory of truth were acceptedfor propositions (so construed), there would still be ample room (andneed) for correspondence accounts of truth with respect to other typesof truthbearers. Second, the identity theory rests on the assumptionthat that-clauses always denote propositions, so that the that-clausein “the fact that snow is white” denotes the propositionthat snow is white. The assumption can be questioned. That-clauses canbe understood as ambiguous names, sometimes denoting propositions andsometimes denoting facts. The descriptive phrases “theproposition…” and “the fact…” can beregarded as serving to disambiguate the succeeding ambiguousthat-clauses—much like the descriptive phrases in “thephilosopher Socrates” and “the soccer-playerSocrates” serve to disambiguate the ambiguous name“Socrates” (cf. David 2002).C. At present the most noticeable competitors tocorrespondence theories are deflationary accounts of truth(or ‘true’). Deflationists maintain that correspondencetheories need to be deflated; that their central notions,correspondence and fact (and relatives), play no legitimate role in anadequate account of truth and can be excised without loss. Acorrespondence-type formulation like(5) “Snow is white” is true iff it correspondsto the fact that snow is white,is to be deflated to(6) “Snow is white” is true iff snow iswhite,which, according to deflationists, says all there is to be said aboutthe truth of “Snow is white” without superfluousembellishments (cf. Quine 1987, 213).Correspondence theorists protest that (6) cannot lead to anythingdeserving to be regarded as an account or theory of truth because itresists generalization. (6) is a substitution instance of theschema(7) “p” is true iffp,which does not say anything itself and cannot be turned into a genuinegeneralization about truth; moreover, no genuine generalizations abouttruth can be accounted for on the basis of (7). Correspondencedefinitions, on the other hand, i.e., definitions like (1) or (2), doyield genuine generalizations about truth.It should be noted that (5), which lends itself to deflatingexcisions, misrepresents the correspondence theory. According to (5),corresponding to the fact that snow is white is sufficient andnecessary for “Snow is white” to be true. Yet,according to (1) and (2), this is sufficient but not necessary:“Snow is white” will be true as long as it corresponds tosome fact or other. The genuine article, (1) or (2), is not as easilydeflated as (5).The debate turns crucially on the question whether anything deservingto be called an “account” or “theory” of truthought to take the form of a genuine generalization (and ought to beable to account for genuine generalizations involving truth).Correspondence theorists tend to regard this as a (minimal)requirement. Deflationists argue that truth is a shallow (sometimes“logical”) notion—a notion that has no seriousexplanatory role to play: as such it does not require a full-fledgedaccount, a real theory, that would have to take the form of a genuinegeneralization.(Cf. Quine 1970; Devitt 1984; Field 1986; Horwich 1990 &19982; Kirkham 1992; Gupta 1993; David 1994; Schmitt 1995;Künne 2003, chap. 4; and the essays in Blackburn and Simmons1999, and in Schantz 2002.)9. More Objections to the Correspondence TheoryTwo final objections to the correspondence theory should be mentioned. 9.1 The Big FactInspired by an allegedly similar argument of Frege's, Davidson (1969)argues that the correspondence theory is bankrupt because it cannotavoid the consequence that all true sentences correspond to the samefact: the Big Fact.The argument is based on two crucial assumptions: (i) Logicallyequivalent sentences can be substituted salva veritate in thecontext ‘the fact that...’; and (ii) If two singular termsdenoting the same thing can be substituted for each other in a givensentence salva veritate, they can still be so substituted ifthat sentence is embedded within the context ‘the factthat...’. In the version below, the relevant singular terms willbe the following: ‘(the x such that x=Diogenes& p)’ and ‘(the x such thatx=Diogenes & q)’. Now, assume that a givensentence, s, corresponds to the fact that p; andassume that ‘p’ and ‘q’ aresentences with the same truth-value. We have: s corresponds to the fact thatp which, by (i), impliess corresponds to the fact that (the x such thatx=Diogenes & p) = (the x such thatx=Diogenes), which, by (ii), impliess corresponds to the fact that (the x such thatx=Diogenes & q) = (the x such thatx=Diogenes), which, by (i), impliess corresponds to the fact that q. Since the only restriction on ‘q’ was that ithave the same truth-value as ‘p’, it would followthat any sentence s that corresponds to any fact correspondsto every fact; so that all true sentences correspond to the samefacts, thereby proving the emptiness of the correspondencetheory—the conclusion of the argument is taken as tantamount tothe conclusion that every true sentence corresponds to the totality ofall the facts, i.e, the Big Fact, i.e., the world as a whole.This argument, which is a variation on the so-called “slingshotargument”, has been criticized repeatedly. Critics point to thetwo assumptions on which it relies, (i) and (ii), and maintain that itis far from obvious why a correspondence theorist should be tempted byeither one of them. Opposition to assumption (ii) rests on theobservation that the (alleged) singular terms used in the argument aredefinite description: their status as genuine singular termsis in doubt, and it is well-known that they behave rather differentlythan proper names for which assumption (ii) is probably valid(cf. Olson 1987; Neale 2001).9.2 No Independent AccessThe objection that may well have been the most effective in causingdiscontent with the correspondence theory is based on anepistemological concern. In a nutshell, the objection is that acorrespondence theory of truth must inevitably lead into skepticismabout the external world because the required correspondence betweenour thoughts and reality is not ascertainable. Ever since Berkeley'sattack on the representational theory of the mind, objections of thissort have enjoyed considerable popularity. It is typically pointed outthat we cannot step outside our own minds to compare our thoughts withmind-independent reality. Yet—so the objectioncontinues—on the correspondence theory of truth, this isprecisely what we would have to do to gain knowledge. We would have toaccess reality as it is in itself, independently of our cognition ofit, and determine whether our thoughts correspond to it. Since this isimpossible, since all our access to the world is mediated by ourcognition, the correspondence theory makes knowledge impossible(cf. Kant 1800, intro vii). Assuming that the resulting skepticism isunacceptable, the correspondence theory has to be rejected.This type of objection brings up a host of issues in epistemology, thephilosophy of mind, and general metaphysics. All that can be done hereis to hint at a few pertinent points (cf. Searle 1995, chap. 7; David2004, 6.7). The objection makes use of the following line ofreasoning: “If truth is correspondence, then, since knowledgerequires truth, we have to know that our beliefs correspond toreality, if we are to know anything about reality”. There aretwo assumptions implicit in this line of reasoning, both of themdebatable.(i) It isassumed that S knows x only if S knows thatx is true—a requirement not underwritten by standarddefinitions of knowledge, which tell us that S knowsx only if x is true and S is justified inbelieving x. The assumption may rest on confusing requirementsfor knowing x with requirements for knowing that one knowsx.(ii) It is assumed that, if truth = F, then S knowsthat x is true only if S knows that x hasF. This seems highly implausible. By the same standard itwould follow that no one who does not know that water isH2O can know that the Nile contains water—which wouldmean, of course, that until fairly recently nobody knew that the Nilecontained water (that there were stars in the sky, whales in the sea,or that the sun gives light). Moreover, even if one does know thatWater is H2O, one's strategy for finding out whether theliquid in one's glass is water does not have to involve chemicalanalysis. Similarly, it seems the correspondence theory does notentail that we have to know that a belief corresponds to a fact inorder to know that it is true, or that our method of finding outwhether a belief is true has to involve a strategy of actuallycomparing a belief with a fact—although the theory does ofcourse entail that obtaining knowledge amounts to obtaining a beliefthat corresponds to a fact.More generally, one might question whether the objection still hasmuch bite once the metaphors of “accessing” and“comparing” are spelled out with more attention to thepsychological details of belief formation and to epistemologicalissues concerning the conditions under which beliefs are justified orwarranted. For example, it is quite unclear how the metaphor of“comparing” applies to knowledge gained through perceptualbelief-formation. 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D., 1949, Theory of Knowledge, London:Hutchinson.Other Internet ResourcesTruth and Correspondence, by Laurence BonJour(Chapter 3, Ph.D. dissertation, Princeton, 1969)Related Entries Aristotle | language of thought hypothesis | Meinong, Alexius | Moore, George Edward | propositions | realism | Russell, Bertrand | Tarski, Alfred | tropes | truth: coherence theory of | truth: deflationary theory of | truth: identity theory of | Wittgenstein, Ludwig Copyright © 2005 byMarian David<david.1@nd.edu> |
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