Truth and Meaning

TruthandMeaning
DONALDDAVIDSON
It is conceded by most philosophers of language,and recently evenby somelinguists, that
a satisfactory theory of meaning must give an
account of how the meanings of sentences
depend upon the meanings of words. Unless
such an accountcould be supplied for a particular language, it is argued, therc would be no
explaining the fact that we can learn the language: no explaining the fact that, on mastering
a finite vocabulary and a finitely stated set of
rules, we are prcparedto produce and to understand any of a potential infinitude of sentences.
I do not disputethesevagueclaims, in which I
sense morc than a kernel of tmth.l Instead I
want to ask what it is for a theory to give an
account of the kind adumbrated.
One proposal is to begin by assigning some
entity as meaning to eachword (or other sigaificant syntactical featurc) of the sentence;thus
we might assignTheaetetusto '"Theaetetus"and
the property of flying to "flies" in the sentence
"Theaetetusflies." The problem then ariseshow
the meaning of the sentenceis generatedfrom
thesemeanings.Viewingconcatenationasa significant piece of syntax, we may assignto it the
relation of participating in or instantiating; however, it is obvious that we have herc the start of
an infinite regr€ss. Frege sought to avoid the
regressby saying that the entities corrcsponding
to prcdicates(for example)are 'unsaturated'or
'incomplete'
in contrast to the entities that cor-
respond to names, but this doctrine seems to
label a difficulty rather than solve it.
The point will emerge if we think for a
moment of complex singular terms, to which
Frcge's theory applies along with sentences.
Considerthe expression"the fatherofAnnette";
how does the meaning of the whole depend on
the meaning of the parts? The answer would
seemto be that the meaning of "the father of is
such that when this expression is prefixed to a
singular term the result refers to the father ofthe
person to whom the singular term refers. What
part is played, in this account,by the unsaturated or incomplete entity for which "the father
of' stands?All we can think to say is that this
entity 'yields' or 'gives' the father of r as value
when the argument is x, or perhaps that this
entity mapspeople onto their fathers. It may not
be clear whether the entity for which "the father
of is said to stand performs any genuine
explanatory function as long as we stick to individual exprcssions;so think insteadof the infinite classof expressionsformed by writing "the
father of" zero or more times in front of
"Annette."It is easyto supplya theorythat tells,
for an arbitrary one of these singular terms,
what it rcfers to: if the term is 'Annette" it refers
to Annette, while if the term is complex, consisting of "the father of" prcfixed to a singular
term t, then it rcfers to the father of the personto
whom t rcfers. It is obvious that no entitv corre-
From synthc*.t7 (t95711.to4-323.
copyright@ rg6z by D. Reidelpublishingcompany,Dordrecht,
Holland.Reprintedby permissionof the publisher.
rl4
T R U T HA N D M E A N I N C
spondingto "the father of" is, or needsto be,
mentionedin statingthis theory.
It would be inappropriateto complain that
this little theory asesthe words "the father of"
in giving the referenceof expressionscontaining those words. For the task was to give the
meaningof all expressionsin a certaininfinite
set on the basis of the meaningof the parts; it
wasnot in the bargainalsoto give the meanings
of the atomicparts.On the other hand,it is now
evident that a satisfactorytheory of the meanings of complex expressionsmay not require
entitiesasmeaningsof all the parts.It behooves
us thento rephraseour demandon a satisfactory
theoryof meaningso asnot to suggestthat individual words must havemeaningsat all, in any
sensethat transcendsthe fact that they have a
systematiceffect on the meaningsof the sentencesin which they occur. Actually, for the
caseat handwe can do betterstill in statingthe
criterion of success:what we wanted.and what
we got, is a theory that entailseverysentenceof
the form "t refers to x" where 'r'is replacedby
a structuraldescription2of a singularterm, and
'-r'is replacedby that term itself. Further,our
theoryaccomplishesthis without appealto any
semanticalconceptsbeyond the basic "refers
to."Finally, the theoryclearly suggestsan effective procedurefor determining,for any singular
termin its universe,what that term refersto.
A theory with such evident merits deserves
widerapplication.Thedeviceproposedby Frege
to this end hasa brilliant simplicity: countpredicatesasa specialcaseoffunctional expressions,
andsentencesas a specialcaseofcomplex singularterms.Now, however,a difficulty looms if
we want to continue in our present(implicit)
courseof identifying the meaningof a singular
termwith its reference.The difficulty follows
uponmaking two reasonableassumptions:that
: logically equivalent singular terms have the
samereference;and that a singular term does
: notchangeits referenceif a containedsingular
the samerefer; termis replacedby anotherwith
.i:ence.
But now supposethat 'R'and 'S'abbrevii ate any two sentencesalike in truth value.
havethe satne
i Thenthefollowing four sentences
fireference:
#i
n
Ei rtl
(2)
$i
G,
G
G,
E
.f(x=.Y.R
)=i(x=x)
il5
(3) i(x=x.S)=a(a=a)
(4) S
For (l) and(2) arelogically equivalent,as are
(3) and (4), while (3) differs from (2) only in
containing the singular term f(x=x.S)'where
(2) contains 't(x=x.R)'and these refer to the
samething if S and R are alike in truth value.
Hence any two sentenceshave the samereferenceif they have the sametruth value.3And if
the meaningof a sentenceis what it refersto, all
sentencesalike in truth value must be synonymous-an intolerableresult.
Apparently we must abandon the present
approachas leading to a theory of meaning.
This is the naturalpoint at which to turn for help
to the distinction betweenmeaning and reference.The trouble,we are told, is that questions
ofreference are, in general,settledby extralinguistic facts,questionsof meaningnot, and the
facts can conflatethe referencesof expressions
that are not synonymous.If we want a theory
that gives the meaning(as distinct from reference) of eachsentence,we must start with the
meaning (as distinct from reference) of the
parts.
Up to herewe havebeenfollowing in Frege's
footsteps;thanksto him, the pathis well known
and even well worn. But now, I would like to
suggest, we have reached an impasse: the
switch from referenceto meaning leads to no
useful account of how the meanings of sentencesdependupon the meaningsof the words
(or otherstructuralfeatures)thatcomposethem.
Ask, for example,for the meaningof 'Theaetetus flies." A Fregeananswer might go something like this: given the meaningof "Theaetetus" as argument,the meaningof "flies" yields
the meaningof "Theaetetusflies" as value.The
vacuity of this answeris obvious.We wantedto
know what themeaningof '"Theaetetus
flies" is;
it is no progressto be told that it is the meaning
of '"Theaetetusflies." This much we knew
before any theory was in sight. In the bogus
accountjust given, talk of the structureof the
sentenceandof the meaningsof wordswasidle,
for it played no role in producing the given
descriptionof the meaningof the sentence.
The contrast here between a real and pretendedaccountwill be plainer still if we askfor
a theory, analogousto the miniature theory of
ll6
referenceof singulartermsjustsketched,but different in dealingwith meaningsin placeof references.What analogydemandsis a theorythat
ofthe form "s
all sentences
hasasconsequences
meansrz" where 's'is replacedby a structural
descriptionofa sentenceand'm'is replacedby
a singularterm that refersto the meaningof that
sentence;a theory, moreover,that providesan
effective methodfor arriving at the meaningof
an arbitrary sentencestructurally described.
Clearly somemore articulateway of referringto
meaningsthan any we have seenis essentialif
thesecriteria are to be met.4Meaningsas entities, or the relatedconceptof synonymy,allow
us to formulate the following rule relating sentences and their parts: sentencesare synonymous whose correspondingparts are synonymous ("corresponding"here needsspellingout
of course).And meaningsasentitiesmay,in theoriessuchasFrege's,do duty,on occasionasreferences,thus losing their statusas entitiesdistinct from references.Paradoxically,the one
thing meaningsdo not seem to do is oil the
wheelsof a theoryof meaning-at leastas long
aswe requireof sucha theorythat it nontrivially
give the meaningof every sentencein the language.My objectionto meaningsin the theory
of meaningis not that they are abstractor that
their identity conditions are obscure,but that
they haveno demonstrateduse.
This is the place to scotch anotherhopeful
thought.Supposewe havea satisfactorytheory
of syntax for our language,consisting of an
effective method of telling, for an arbitrary
expression,whether or not it is independently
meaningful (i.e., a sentence),and assumeas
usual that this involves viewing each sentence
as composed,in allowable ways, out of elementsdrawnfrom a fixed finite stockof atomic
syntactical elements (roughly, words). The
hopeful thought is that syntax, so conceived,
will yield semanticswhen a dictionary giving
the meaning of each syntactic atom is added.
Hopes will be dashed,however,if semanticsis
to comprisea theory of meaningin our sense,
for knowledgeof the structural characteristics
that make for meaningfulnessin a sentence,
plus knowledgeof the meaningsof the ultimate
parts, does not add up to knowledgeof what a
sentencemeans.The point is easily illustrated
T R U T HA N D M E A N I N G
by belief sentences.Their syntax is relatively
unproblematic.Yet, adding a dictionary does
not touchthe standardsemanticproblem,which
is that we cannot accountfor even as much as
the truth conditions of such sentenceson the
basisof what we know of the meaningsof the
words in them. The situation is not radically
altered by refining the dictionary to indicate
which meaning or meanings an ambiguous
expressionbearsin eachofits possiblecontexts;
the problem of belief sentencespersistsafter
ambiguitiesare resolved.
The fact that recursivesyntaxwith dictionary
addedis not necessarilyrecursivesemanticshas
been obscuredin some recent writing on linguisticsby the intrusionof semanticcriteriainto
the discussionof purportedlysyntactictheories.
The matter would boil down to a harmlessdifferenceover terminologyif the semanticcriteria
were clear; but they are not. While there is
agreementthat it is the centraltask of semantics
to give the semanticinterpretation(the meaning) ofevery sentencein the language,nowhere
in thelinguistic literaturewill one find, so far as
I know,a straightforwardaccountof how a theory performsthis task,or how to tell when it has
beenaccomplished.The contrastwith syntaxis
striking. The main job of a modestsyntaxis to
characterizemeaningfulness(or sentencehood).
We may have as much confidencein the correctnessof sucha characterizationaswe havein
the representativeness
of our sample and our
ability to say when particular expressionsare
meaningful(sentences).What clear and analogoustask and test exist for semantics?s
We decideda while back not to assumethat
partsof sentenceshave meaningsexceptin the
ontologicallyneutralsenseof making a systematic contribution to the meaning of the sentencesin which they occur. Since postulating
meaningshas netted nothing, let us return to
that insight.Onedirection in which it pointsis a
certain holistic view of meaning.If sentences
dependfor their meaningon their structure,and
we understandthe meaningof eachitem in the
structureonly as an abstractionfrom the totality
of sentencesin which it features,then we can
give themeaningof any sentence(or word) only
by giving the meaning of every sentence(and
word) in the language.Frege said that only in
T R U T HA N D M E A N I N G
117
the context of a sentencedoes a word have
tencesgot from schemaZ when 's' is replaced
meaning;in the samevein he might haveadded
by a structuraldescriptionofa sentenceofZ and
'p'by that sentence.
that only in the context of the languagedoes a
sentence(andthereforea word) havemeaning.
Any two predicatessatisfyingthis condition
This degreeof holism was alreadyimplicit in
have the same extension,6so if the metalanguageis rich enough,nothingstandsin the way
the suggestionthat an adequatetheoryof meaning must entall all sentencesof the form "s
of putting what I am calling a theory of meaning
meansm." But now, havingfound no more help
into the form of an explicit definition of a predilhan in meaningsof
in meaningsof sentences
icate "is 7." But whether explicitly defined or
words, let us ask whetherwe can get rid of the
recursivelycharacterized,
it is clearthat the sentroublesomesingulartermssupposedto replace
tencesto which the predicate"is I" applieswill
'm' andto refer to meanings.In a way, nothing
bejust the true sentences
of I,, for the condition
could be easier:just write "s meansthatp," and
we have placed on satisfactory theories of
imagine p'replaced by a sentence.Sentences, meaning is in essenceTarski's Convention Z
as we have seen,cannot name meanings,and
that tests the adequacyof a formal semantical
definition of truth.T
sentenceswith "that" prefixed are not namesat
The path to this point has beentortuous,but
all, unlesswe decideso. It looks as though we
the conclusionmay be statedsimply: a theoryof
are in trouble on another count, however,for it
is reasonableto expectthat in wrestlingwith the
meaning for a languageL shows "how the
meaningsof sentencesdependupon the meanlogic of the apparentlynonextensional"means
ings of words" if it containsa (recursive)definithat" we will encounterproblemsashard as,or
perhapsidenticalwith, the problemsour theory
tion of truth-in-L. And, so far at least,we have
no other idea how to turn the trick. It is worth
is out to solve.
The only way I know to deal with this diffiemphasizingthat the conceptof truth playedno
ostensiblerole in statingour original problem.
culty is simple,and radical.Anxiety that we are
That problem,upon refinement,led to the view
enmeshedin the intensionalspringsfrom using
the words "means that" as filling between
that an adequatetheory of meaning must chardescriptionof sentenceand sentence,but it may
acteize a predicatemeetingcertainconditions.
be that the successof our venturedependsnot
It was in the nature of a discovery that such a
predicatewould apply exactly to the frue senon the filling but on what it fills. The theorywill
havedoneits work if it provides,for every sentences.I hope that what I am doing may be
tences in the languageunder study,a matching
describedin part as defendingthephilosophical
(to replace'p') that,in someway yet to
sentence
importance of Tarski's semanticalconcept of
be made clear, 'gives the meaning' of s. One
truth. But my defenseis only distantlyrelated,if
obviouscandidatefor matchingsentenceisjust
at all, to the questionwhethertheconceptThrski
s itself, ifthe objectlanguageis containedin the
hasshownhow to defineis the (or a) philosophmetalanguage;
otherwisea translationof s in the
ically interesting conception of truth, or the
metalanguage.
questionwhetherTarskihascastanylight on the
As a final bold step, let us try
treatingthe position occupiedby p'extensionordinary use of such words as "true" and
ally: to implementthis, sweepawaythe obscure
"truth." It is a misfornrne that dust from futile
"meansthat,"providethe sentencethat replaces
and confusedbattles over thesequestionshas
'p'
with a propersententialconnective,and suppreventedthose with a theoretical interest in
ply the descriptionthat replaces's'with its own
language-philosophers, logicians, psycholopredicate.The plausibleresult is
gists, and linguists alike-from recognizingin
the semanticalconceptof truth (underwhatever
(I) s is T if andonly if p.
name) the sophisticatedand powerfirl foundaWhat we require of a theory of meaning for a
tion of a competenttheory of meaning.
languaget is that without appeal to any (furThere is no need to suppress,of course,the
ther)semanticalnotionsit place enoughrestricobvious connection between a definition of
tions on the predicate"is Z" to entail all sentruth of the kind Tarski has shown how to con-
ll8
struct,and the conceptof meaning.It is this: the
definition works by giving necessaryand sufficient conditionsfor the truth of every sentence,
and to give truth conditionsis a way of giving
the meaningof a sentence.To know the semantic concept of truth for a languageis to know
what it is for a sentence-any sentence-to be
true, and this amounts,in one good sensewe
can give to the phrase,to understandingthe language.This at any rate is my excusefor a feature ofthe presentdiscussionthat is apt to shock
old hands: my freewheelinguse of the word
"meaning,"for what I call a theory of meaning
hasafter all turnedout to makeno useof meanings, whetherof sentencesor of words. Indeed
since a Tarski+ypetruth definition suppliesall
we have askedso far of a theory of meaning, it
is clear that such a theory falls comfortably
within what Quine terms the "theory of reference" as distinguished from what he terms the
"theory of meaning."So much to the good for
what I call a theory of meaning,and so much,
perhaps,againstmy so calling it.8
A theory of meaning (in my mildly perverse
sense)is an empiricaltheory and its ambitionit
to account for the workings of a natural language.Like anytheory it may be testedby comparing someof its consequences
with the facts.
In the presentcasethis is easy,for the theoryhas
beencharacterizedasissuingin an infinite flood
of sentenceseachgiving the truth conditionsof
a sentence;we only need to ask, in selected
cases,whetherwhat the theory aversto be the
truth conditionsfor a sentencereally are.A typical test case might involve deciding whether
the sentence"Snow is white" is true if and only
if snow is white. Not all caseswill be so simple
(for reasonsto be sketched),but it is evidentthat
this sort oftest doesnot invite countingnoses.A
sharpconceptionofwhat constitutesa theoryin
this domain fumishes an exciting context for
raising deep questionsabout when a theory of
languageis conect andhow it is to be tried. But
the difficulties are theoretical,not practical.In
application, the trouble is to get a theory that
comes close to working; anyone can tell
whetherit is right.eOne can seewhy this is so.
The theory revealsnothing new about the conditions under which an individual sentenceis
true: it does not make those conditions anv
T R U T HA N D M E A N I N G
clearerthan the sentenceiself does.The work
of the theory is in relating the known truth conditions of each sentence to those aspects
('words') ofthe sentencethat recurin othersentences,and can be assignedidentical roles in
Empirical power in sucha theother sentences.
ory dependson successin recoveringthe structure of a very complicatedability-the ability to
speakand understanda language.We can tell
easily enoughwhen particularpronouncements
of the theorycomportwith our understandingof
the language;this is consistentwith a feeble
insight into the design of the machineryof our
linguistic accomplishments.
The remarks of the last paragraph apply
directly only to the special case where it is
assumedthat the languagefor which truth is
being characterizedis part of the languageused
and understood by the characterizer. Under
thesecircumstances,the framer of a theory will
as a matterof courseavail himself when he can
of the builrin convenienceof a metalanguage
with a sentenceguaranteedequivalentto each
sentencein the object language.Still, this fact
ought not to con us into thinking a theory any
morecorrectthat entails"'Snow is white' is true
if and only if snow is white" than one that
entailsinstead:
(,9) "Snowis white" is trueif andonly if grass
is green,
provided,of course,we are as sureof the truth
of (S) as we are of that of its more celebrated
predecessor.Yet (,9) may not encouragethe
same confidence that a theory that entails it
deservesto be called a theory of meaning.
The threatenedfailure of nerve may be counteractedas follows. The grotesqueness
of (S) is
in itself nothingagainsta theoryof which it is a
providedthe theorygivesthe corconsequence,
rect resultsfor every sentence(on the basisof its
structure,there being no other way). It is not
easy to seehow (,9)could be party to such an
enterprise,but if it were-if, that is, (.I) followed from a characterizationof the predicate
"is true" that led to the invariable pairing of
truths with truths and falsehoodswith falsehoods-then there would not, I think, be anything essential.to the idea of meaning that
remainedto be captured.
T R U T HA N D M E A N I N G
t
What appearsto the right of thebiconditional
't
in sentencesof the form is true if and only if
p," when such sentencesare consdquences
ofa
theory of truth, plays its role in determining the
meaningof r not by pretendingsynonymybut
by adding one more brush-stroketo the picture
which, taken as a whole, tells what there is to
know of the meaning of s; this stroke is added
by viroe of the fact that the sentencethat
replacesp'is true ifand only ifs is.
It may help to reflect that (,S)is acceptable,if
it is, becausewe are independently sure of the
truth of "snow is white" and "grassis green";
but in caseswhere we are unsureof the truth of
a sentence,we can haveconfidencein a characterization of the truth predicate only if it pairs
that sentencewith one we havegood reasonto
believeequivalent.It would be ill advisedfor
someonewho had any doubts aboutthe color of
snowor grassto accepta tlleory that yielded (.9),
evenif his doubts were of equal degree,unless
he thought the color of the one was tied to the
color of the other. Omnisciencecan obviously
afford more bizarre theories of meaning than
ignorance;but then, omnisciencehas less need
of communication.
It must be possible,of course,for the speaker
ofone languageto constructa theoryofmeaning
for the speakerof another,though in this casethe
empirical test of the correctrressof the theory
will no longer be trivial. As before,the aim of
theorywill be an infinite conelatioh of sentences
alike in ruth. But this time the theory-builder
mustnot be assumedto have direct insight into
Iikelyequivalences
betweenhis own tongueand
thealien.What he must do is find out, however
hecan,what sentencesthe alieh holds true in his
own tongue (or better, to what degreehe holds
themtrue). The linguist then will attemptto construct a characterization of truth-for-the-alien
i,which yields, so far as possible,a mapping of
i'sentences
held true (or false) by the alien onto
sentencesheld true (or false) by the linguis;q.
Supposingno perfect fit is found, the residue of
held true translatedby sentences
held
(andvice vena) is the margin for error (foror domestic). Charity in interpreting the
and thoughtsof othersis unavoidablein
directionaswell: just as we must maxiagreement,or risk not making senseof
119
what the alien is talking aboui,so we must maximize the self-consistencywe attribute to him,
on pain of not understanding ftin. No single
principle of optimum chariryemerges;the constraints therefore determine no single theory. In
a theory of radical translation (as Quine calls it)
there is no complbtelydisentanglingquestions
of what the alien meansfrom questionsof what
he believes. lVe do not know what someone
meansunlesswe know what he believes;we do
not know what someonebelieves unless we
know what he means.In radical translation we
are able to break into this circle, if only incompletely, because we can sometimes tell
that a person accedesto a sentencewe do not
understand.lo
In the past few pagesI have been asking how
a theory of meaning that takes the form of a
truth definition can be empirically tested, and
haveblithely ignoredtheprior questionwhether
thereis any seriouschancesucha theorycan be
given for a natural language. What are the
prospects for a formal semantical theory of a
natural lahgUage? Very poor, according to
Tarski; and I believe most logicians, philosophersof language,and linguistsagree.ltl-et me
do what I can to dispel the pessimism.What I
can in a gerieral and programmatic way, of
course; for lidre the proof of the pudding will
certainly be ih the proof of the right theorems.
Tarski concludesthe first sectionof his classic
essayon the concept of truth in formalized languageswith the following remarks, which he
italicizes:
Theverypossibilityof a consistent
useof theexpression'truesentence'which
is in harmonywith thelaws
of logicand the spiritof everydaylanguageseemsto
be very questionable,and consequentlythe same
doubtanachesto thepossibilityofconstructinga correctdefnition of thisexpression.r2
I-ate in the sameessay,he returns to the subject:
the conceptof truth(aswell asotherscmanticalconcepts)whenappliedto colloquiallanguagein conjunction with the normal laws of logic leads
inevitablyto confusionsandcontradictions.
Whoever
wishes,in spite of all difficulties,to pursuethe
semanticsof colloquial languagewith the help of
120
exactmethodswill be drivenfint to undertakethe
thanklesstaskof a reformof this language.He will
to defineits structure,to overcome
find it necessary
the ambiguityof the termswhich occurin it, and
intoa seriesof languages
finallyto splitthelanguage
of greaterandgreaterextent,eachof which standsin
the samerelationto the nextin which a formalized
It may,however
languagestandsto its metalanguage.
be doubtedwhetherthe languageof everydaylife,
'rationalized'in this way,wouldstill preafterbeing
andwhetherit would not rather
serveits naturalness
featuresof the formalized
takeon the characrcristic
languages.l3
Tlvo themesemerge:that the universal character of natural languagesleadsto contradiction
(the semantic paradoxes),and that natural languagesaretoo confusedand amorphousto permit the direct application of formal methods.
The first point deservesa seriousanswer,and I
wish I had one.As it is, I will say only why I
think we are justified in carrying on without
havingdisinfectedthis particularsourceofconceptual anxiety. The semantic paradoxes arise
when the range of the quantifiers in the object
languageis too generousin certainways.But it
is not really clear how unfair to Urdu or to Hindi
it would be to view the rangeoftheir quantifiers
as insufficientto yield an explicit definition of
'true-in-Urdu'or 'true-in-Hindi'. Or, to put the
matter in another,if not more serious way, there
may in the natureof the casealways be somethe languageof
thing we graspin understanding
(the
of
truth)
that
we cannot
concept
another
communicateto him. In any case,most of the
problemsof generalphilosophicalinterestarise
within a fragment of the relevant natural languagethat may be conceivedascontainingvery
little set theory. Of coursethesecommentsdo
not meet the claim that natural languages are
universal.But it seemsto me this claim, now
that we know such universalityleads to paradox, is susPect.
Tarski'ssecondpoint is thatwe would haveto
reform a naturallanguageout of all recognition
beforewe could apply formal semanticalmethods.If this is true,it is fatal to my project,for the
task of a theory of meaningas I conceiveit is
not to change,improve or reform a language,
but to describeand understandit. Let us look at
the positive side.Thrski has shown the way to
TRUTHAND MEANINd;
giving a theoryfor interpretedformat tanguageS'
of variouskinds; pick one as much like English
as possible.Since this new languagehasbeen'
explainedin EnglishandcontainsmuchEnglish
we not only may,but I think must,view it aspart
of Englishfor thosewho understandit. For this
fragment of English we have, ex hypothesi,a
theory of the required sort. Not only that, but in
interpretingthis adjunctof English in old English we necessarilygave hints connectingold
and new. Wherever there are sentencesof old
English with the sametruth conditionsas sentencesin the adjunctwe may extendthe theory
to cover them.Much of what is calledfor is just
to mechanizeas far aspossiblewhat we now do
by art when we put ordinaryEnglish into oneor
anothercanonicalnotation.The point is not that
canonical notation is better than the rough original idiom. but rather that if we know what
idiom the canonicalnotation is canonicalpr,
we haveas good a theory for the idiom asfor its
kept companion.
Philosophershavelong beenat the hard work
of applying theory to ordinary languageby the
device of matchingsentencesin the vernacular
with sentencesfor which they have a theory.
Frege'smassivecontribution was to show how
"all," "some," "every," "each," "none," and
associatedpronouns, in some of their uses,
could be tamed;for the first time, it was possible to dream of a formal semanticsfor a significant part of a natural language.This dream
came true in a sharp way with the work of
Tarski. It would be a shameto miss the fact that
as a result of these two magnificent achievements,Frege'sand Tarski's, we have gaineda
deep insight into the structure of our mother
tongues. Philosophersof a logical bent have
tended to start where the theory was and work
out towards the complicationsof natural language.Contemporarylinguists,with an aim that
cannot easily be seento be different, start with
the ordinary and work toward a general theory.
If either party is successful,there must be a
meeting.Recentwork by Chomsky and others
is doing much to bring the complexitiesof natural languages within the scope of serious
semantic theory. To give an example: suppose
successin giving the nuth conditionsfor some
significant range of sentencesin the active
A N DM E A N I N G
TRUTH
voice. Then with a formal procedurefor transforming each such sentenceinto a corresponding sentencein the passivevoice, the theoryof
truth could be extendedin an obvious way to
this new setof sentences.la
Oneproblemtouchedon in passingby Tarski
doesnot, at leastin all its manifestations,haveto
be solvedto get aheadwith theory: theexistence
in naturallanguagesof "ambiguousterms."As
long as ambiguity does not affect grammatical
form, andcanbe translated,ambiguityfor ambiguity, into the metalanguage,a truth definition
will not tell us any lies. The trouble,for systematic semantics,with the phrase"believesthat" in
English is not its vagueness,ambiguity, or
unsuitabilityfor incorporationin a seriousscience:let our metalanguagebe English, and all
theseproblemswill be translatedwithout loss or
gaininto themetalanguage.
But thecentralproblem of the logical grammar of "believesthat"
will remainto hauntus.
The exampleis suitedto illustrating another,
and related,point, for the discussionof belief
hasbeenplaguedby failureto observe
sentences
a fundamentaldistinctionbetweentasks:uncovering the logical grammiu or form of sentences
(which is in the provinceof a theoryof meaning
as I construeit), and the analysisof individual
wordsor expressions(which aretreatedasprimitive by thetheory).ThusCamap,in the first edition of Meaning and Necessiry,suggestedwe
render"John believesthat the earthis round" as
"John responds affirmatively to "the earth is
round'as an English sentence."He gavethis up
whenMatespointedout thatJohnmight respond
affirmativelyto one sentenceand not to another
no matterhow close in meaning.But there is a
confusion here from the start. The semantic
structureof a belief sentence,accordingto this
ideaof Carnap's,is given by a three-placepredicatewith placesreservedfor expressions
referring to a person,a sentence,anda language.It is
a different sort of problem entirely to attempt an
analysisof this predicate,perhapsalong betpvioristic lines. Not least among the merits of
Tarski'sconceptionof a theory of truth is that the
purity of methodit demandsof us follows from
theformulationof the problem itself, not from
theself-imposedrestraintof someadventitious
puritanism.
Philosophical
'l2l
I think it is hard to exaggeratethe advantages
to philosophy of languageof bearing in mind
this distinction between questions of logical
form or grammar, and the analysisof individual
concepts.Another examplemay help advertise
the point.
If we supposequestionsof logical grammar
settled,sentenceslike "Bardot is good" raiseno
specialproblemsfor a truth definition.The deep
differencesbetweendescriptiveand evaluative
(emotive, expressive,etc.) terms do not show
here. Even if we hold there is some important
sensein which moral or evaluativesentences
do
not have a truth value (for example, because
they cannotbe 'verified'), we ought not to boggle at "'Bardot is good' is true if andonly if Bardot is good"; in a theory of truth, this consequence should follow with the rest, keeping
track, as must be done,of the semanticlocation
of suchsentencesin the languageas a wholeof their relation to generalizations,their role in
such compound sentencesas "Bardot is good
and Bardot is foolish," and so on. What is special to evaluativewords is simply not touched:
the mystery is transferredfrom the word "good"
in the object languageto its Eanslationin the
metalanguage.
But "good" as it featuresin "Bardot is a good
actress"is anothermatter.The problem is not
that the translationof this sentenceis not in the
metalanguage-letus supposeit is. The problem
is to frame a truth definition suchthat "'Bardot
is a good actress'is true if andonly if Bardotis a
good actress"-and all other sentenceslike itare consequences.Obviously "good actress"
doesnot mean"good and an actress."We might
think oftaking "is a good actress"as an unanalyzed predicate.This would obliterateall connection between"is a good acfress"and "is a
good mother,"andit would give us no excuseto
think of "good," in these uses, as a word or
semanticelement.But worse, it would bar us
from framing a truth definition at all, for there is
no end to the predicateswe would have to treat
as logically simple (and hence accomodatein
separateclausesin thedefinitionofsatisfaction):
"is a good companionto dogs," "is a good 28year-old conversationalist,"and so forth. The
problemis not peculiarto the case:it is the problem of attributiveadjectivesgenerally.
T R U T HA N D M E A N I N G
.
It is consistentwith the attitude taken here to
deem it usually a strategic error to undertake
philosophicalanalysisof words or expressions
which is not precededby or at any rate accompaniedby the attempt to get the logical grammar
snaight.For how can we haveanyconfidencein
our analysesof words like "right," "ought,"
"can," and "obliged," or the phraseswe use to
talk ofactions, events,and causes,when we do
not know what (logical, semantical)parts of
speechwe haveto dealwith? I would say much
the sameaboutstudiesof the 'logic'of theseand
other words,andthe sentencescontainingthem.
Whether the effort and ingenuity that has gone
into the study of deontic logics, modal logics,
imperativeand erotetic logics has been largely
futile or not cannot be known until we have
acceptablesemanticanalysesof the sentences
such systemspurport to treat. Philosophersand
logicians sometimestalk or work asif they were
free to choosebetween,say,the truth-functional
conditional and others, or free to introduce nontruth-functional sententialoperatorslike "Let it
be the casethat" or "It ought to be the casethat."
But in fact the decision is crucial. When we
depart from idioms we can accomodate in a
truth definition, we lapse into (or create) languagefor which we haveno coherentsemantical account-that is, no accountat all of how
such talk can be integrated into the languageas
a whole.
To retum to our main theme: we have recognized that a theory of the kind proposedleaves
the whole matter of what individual words mean
exactly where it was. Even when the metalanguageis differentfrom the object language,the
theory exertsno pressurefor improvement,clarification or analysisof individual words,except
when, by accident of vocabulary, sraighrforward translation fails. Just as synonomy, as
between expressions,goes generally untreated,
so also synonomyof sentences,and analyticity.
Even such sentencesas 'A vixen is a female
fox" bearno specialtag unlessit is our pleasure
to provide it. A truth definition doesnot distinguish between analytic sentencesand others,
exceptfor sentencesthat owe their truth to the
presencealoneofthe constantsthatgive the theory its grip on structure: the theory entails not
only that these sentencesare Eue but that they
will remaintrue underall significantrewritings
of their nonlogical parts. A notion of logical
truth thus given limited application, related
notions of logical equivalenceand entailment
will tag along. It is hard to imagine how a theory of meaningcould fail to reada logic into is
objectlanguageto this degree;and to the extent
that it does, our intuitions of logical ruth,
equivalence,andentailmentmay be calledupon
in constructingand testingthe theory.
I tum now to one more, and very large, fly in
tJle ointment: the fact that the same sentence
may at one time or in one mouth be true and at
anothertime or in anothermouth be false.Both
logicians and those critical of formal methods
here seemlargely (thoughby no meansuniversally) agreedthat formal semanticsand logic
are incompetentto deal with the disturbances
causedby demonstratives.
Logicianshaveoften
reactedby downgradingnatural languageand
trying to showhow to get along without demonstratives; their critics react by downgrading
logic and formal sbmantics.None of this can
makeme happy:clearly,demonstratives
cannot
be eliminatedfrom a natural languagewithout
loss or radical change,so thereis no choicebut
to accommodatetheoryto them.
No logical errors result if we simply treat
demonstrativesas constantsl5;neither do any
problemsarisefor giving a semantictruth definition. "'I am wise' is true if and only if I am
wise," with its bland ignoring of the demonstrative elementin "I" comesoff the assemblyline
alongwith "'Socratesis wise' is true if andonly
if Socratesis wise" with irs bland indifference
to the demonstrativeelementin "is wise" (the
tense).
What suffersin this treatmentof demonstrativesis not the definitionof a truth predicate,but
the plausibility of the claim that what has been
definedis truth.For this claim is acceptableonly
if the speakerand circumstancesof utteranceof
each sentencementioned in the definition is
matched by the speaker and circumstancesof
utteranceof the truth definition itself. It could
also be fairly pointed out that part of understandingdemonstratives
is knowing therulesby
which they adjust their reference to circumstance;assimilatingdemonstrativesto constant
termsobliteratesthis feature.Thesecomplaints
can be met, I think, though only by a fairly farreachingrevision in the theory of truth. I shall
123
T R U T HA N D M E A N I N G
barely suggesthow this could be done,but bare
suggestionis all that is needed:the idea is technically trivial, and quite in line with work being
doneon the logic of the tenses.16
We could take truth to be a property, not of
sentences,but of utterances,or speechacts,or
times,andpersons;
orderedtriplesof sentences,
but it is simplestjust to view truth as a relation
betweena sentence,a p€rson,and a time. Under
such treatment, ordinary logic as now read
applies as usual, but only to sets of sentences
relativized to the samespeakerand time; further
logical relations between sentencesspoken at
different times and by different speakersmay be
articulatedby new axioms.Suchis not my concern. The theory of meaning undergoesa systematicbut not puzzling change:corresponding
to each expressionwith a demonsfrativeelement there must in the theory be a phrase that
relates the ruth conditions of sentencesin
which the expressionoccursto changingtimes
and speakers.Thus the theory will entail sentenceslike the following:
"I am tired" is true as(potentially)spokenby p
at t if andonly ifp is tired at t.
'"Thatbook was stolen" is true as (potentially)
spokenby p at t if and only if the book demonstratedby p at f is stolenprior to /.17
Plainly, this course does not show how to
eliminate demonstratives;for example, there is
no suggestionthat "the book demonsnatedby
the speaker"can be substitutedubiquitouslyfor
"that book" sclva veritate. The fact that demonstratives are amenable to formal treatment
ought greatly to improve hopes for a serious
semanticsof natural language,for it is likely
that many outstanding puzzles, such as the
analysisof quotationsor sentencesaboutpropositionalattitudes,can be solvedif we recognize
a concealeddemonstrativeconstruction.
Now that we have relativized truth to times
andspeakers,it is appropriate to glance back at
the problem of empirically testing a theory of
meaningfor an alien tongue.The essenceofthe
methodwas,it will be remembered,to correlate
held-truesentenceswith held-truesentences
by
wayof a truth definition, and within the bounds
of intelligible error. Now the picture must be
elaboratedto allow for the fact that sentences
aretrue, and held true, only relative to a speaker
ill
{F
s
and a time. The real task is therefore to translate
each sentenceby another that is true for the
same speakersat the same times. Sentences
obviouslyyield a very senwith demonstratives
sitivetestof thecorrectnessof a theoryofmeaning, and constitutethe most direct link between
languageand the recurrentmacroscopicobjects
of humaninterestand attention.l8
ln this paperI haveassumedthat the speakers
of a language can effectively determine the
meaningor meaningsof an arbitrary expression
(if it has a meaning),and that it is the cenfral
task of a theory of meaning to show how this is
possible.I havearguedthat a characterizationof
a truth predicate describesthe required kind of
structure, and provides a clear and testablecriterion of an adequatesemantics for a natural
language.No doubt there are other reasonable
demandsthat may be put on a theory of meaning. But a theory that doesno more than define
truth for a languagecomesfar closer to constituting a completetheoryof meaningthansuperficial analysismight suggest;so, at least,I have
urged.
Since I think there is no alternative,I have
taken an optimistic and programmatic view of
the possibilities for a formal characterizationof
a truth predicate for a natural language. But it
mustbe allowedthat a staggeringlist of diffrcultiesandconundrumsremains.To namea few: we
do not know the logical form of counterfactual
nor of sentences
about
or subjunctivesentences,
probabilitiesandaboutcausalrelations;we have
no good idea what the logical role ofadverbsis,
nor the role of attributive adjectives;we haveno
theory for mass terms like "fire," "water," and
"snow," nor for sentencesabout belief, perception, and intention, nor for verbs of action that
imply purpose.And finally, there are all the sentencesthat seemnot to havetruth valuesat all:
the imperatives,optatives,interrogatives,and a
hostmore.A comprehensivetheory of meaning
for a natural languagemust cope successfully
with eachof theseproblems.
ACKNOWLEDGMENTS
An earlier version of this paper was read at the Eastem
Division meeting of the American Philosophical Association in Decernber, 1966; the main theme traces back to
an unpublished paper delivered to the Pacific Division of
the American Philosophical Association in 1953. hesent
124
formulations owe much to John Wallace, with whom I
have discussed these matters since 1962. My research
was supported by the National Science Foundation.
NOTES
l. Elsewhere I have urged that it is a necessary condi
tion, ifa languageis to be leamable, that it have only
a finite number of semantical primitives: see "Theories of Meaning and Leamable Languages," in Proceedings of the 1964 Intentational Congress for
Logic, Metlndolog
and Philosophy of Science
(North-Holland Publishing Company, Amsterdam:
l96s), pp. 383-394.
'structural
2. A
description'ofan exprcssion describes
the exprcssion as a concatenation of elements drawn
from a fixed finite list (for example of words or letters).
3. The argument is essentially Frcge's. See A. Church,
Intmduction to Mathematical logic, vol.I (hinceton: 1956), pp. 24-25. It is perhaps worth mentioning that the argument does not depend on any particular identification of the entities to which sentences
are supposed to refer.
4. It may be thought that Church, in'A Formulation of
the Logic of Sense and Denotation," in Structure,
Method and Meaning: Essays in Honor of H. M.
Shcffer,Henle, Kallen and L:nger, eds. (LiberalArts
hess, NewYork: l95l), pp.3-24, has given a theory
of meaning that makes essential use of meanings as
entities. But this is not the case: Church's logics of
sense and denotation are interpreted as being about
meanings, but they do not mention expressions and
so cannot of course be theories of meaning in the
sensenow under discussion.
5. For a recent and insmrcdve statement of the role of
semanticsin linguistics, see Noam Chomsky,'"Ibpics in the Theory of Generative Grammar," in Current Trends in Linguistics, Thomas A. Sebeok, ed.,
vol. III (Ihe Hague: 1966). In this article, Chomsky
(1) emphasizes the central importance of semantics
in linguistic theory (2) argues for the superiority of
transformational grarnmars over phrase structur€
grammars largely on the grounds that, although
phrase structure gmmmani may be adequate to
define sentencehood for (at least) some natural languages, they are inadequate as a foundation for
semantics, and (3) comments repeatedly on fte
'rather primitive
state' of the concepts of semantics
and remarks that the notion of semantic interpretation "still resists any deep analysis".
6. Assuming, of course, that the extension of these
prcdicates is limited to the sentences of Z.
7. Alfred Tarski, 'The Concept of Truth in Formalized
Languages," in Logic, Semantics, Metamathematics
(Oxford: 1956), pp. 152-278.
8. But Quine may be quoted in support of my usage:
". . . in point of meaning. . . a word may be said to
be determined to whatever extent the truth or falsehood of its contexts is determined." '"Truth by Convention," first published in 1936;now inThe Waysof
TRUTH AND MEANINC
Paradox (NewYork 1966), p. 82. Since a truth definition determines the truth value of every sentence
in the object language (relative to a sentence in the
metalanguage), it determines the meaning of every
word and sentence.This would seem to justify the
title Theory of Meaning.
9. To give a single example: it is clearly a count in favor
of a theory that it entails "'Snow is white' is true if
and only if snow is white." But to contrive a theory
t$at entails this (and works for all rclated sentences)
is not trivial. I do not know a theory that succeeds
'mass
with this very case (the problem of
terms').
10. This sketch of how a theory of meaning for an alien
tongue can be tested obviously owes its inspiration
to Quine's accountofradical translation in chapterII
of Wotd and Object (New York: I 960). In suggesting
that an acceptable theory of radical translation take
the form of a recursive characterization of truth, I go
beyond anything explicit in Quine. Toward the end
of this paper, in the discussion of demonstratives,
another strong point of agreement will turn up.
I l. So far as I am aware, there has been very little discussion of whether a formal truth definition can be
given for a natural language. But in a more general
vein, several people have urged that the concepts of
formal semantics be applied to natural language.
See,for example,the contributions ofYehoshua BarHillel and Evert Beth ta The Philosophy of Rudolph
Camap, Paul A. Schilpp, ed., (La Salle, I1l.: 1963),
and Bar-Hillel's "Logical Syntax and Semantics,"
Language 30,230-237.
12. Tarski,ibid., p. 165.
13. [bid,.,p.267.
14. The rapprochement I prospectively imagine between
bansformational grarnmar and a sound theory of
meaning has been much advanced by a recent
change in the conception of transformational grammar described by Chomsky in the article referred to
above (note 5). The structures generated by the
phrase-structurc part of the gralnmar, it has been
rcalized for some time, are those suited to semantic
interpretation; but this view is inconsistent with the
idea, held by Chomsky until recently, that recursive
operations are introduced only by the transformation
rules. Chomsky now believes the phrase-stnrcturc
rules are recursive. Since languages to which formal
semantic methods directly and naturally apply are
ones for which a (recursive) phrase-structuregrammar is appropriate,it is clear that Chomsky's present
picture of the relation between the structures generated by the phrase-structure part ofthe grammar, and
the sentencesofthe language, is very much like the
picturc many logicians and philosophers have had of
the relation betwe€n the richer formalized languages
and ordinary language. (ln these remarks I am
indebted to Bruce Vermazen.)
15. Quine has good things to say about this in Methods
of logb (NewYork: 1950). See 8.
16. For an upto-date bibliography, and discussion, see
A. N. hior, Past, Present, and Future (Oxford:
196il.