This Essay Is Going To Argue Semantics

The formal approach to meaning:
Formal semantics and its recentdevelopments

 [This paper is inJournal of Foreign Languages (Shanghai),119:1 (January 1999), 2-20.]

Barbara Abbott
Michigan State University
June 1998

Like Spanish moss on a live oak tree, the scientific study of meaningin language has expanded in the last 100 years, and continues to expandsteadily. In this essay I want to chart some central themes in that expansion,including their histories and their important figures. Our attention willbe directed toward what is called 'formal semantics', which is the adaptationto natural language of analytical techniques from logic.[1] Thefirst, background, section of the paper will survey the changing attitudesof linguists toward semantics into the last third of the century. The secondand third sections will examine current formal approaches to meaning. Inthe final section I will summarize some of the common assumptions of theapproaches examined in the middle sections of the paper, sketch a few alternatives,and make some daring predictions.

'Meaning' is a broad term that can encompass any aspect of the potentialfor cognitive or emotive impact of speech on interlocutors. However inlinguistic semantics these days the cognitive aspects are the center offocus. On the other hand the traditional distinction between semantics,as the study of the relation between linguistic expressions and what theyare used to talk about (people and things, events and situations, etc.)and pragmatics, as the study of anything involving the use of language,has become less certain and is in fact lost in several different currentapproaches.

1. Background

1.1 The Bloomfieldian era. Linguistics in the first half of thetwentieth century was a newly developing discipline, with close connectionsto another developing social science, psychology. In the United States(and elsewhere) dominant figures in psychology were striving to implementthe principles of British empiricist philosophy, and especially logicalpositivism, which stressed attention to objective observable data in formulatingscientific theories. Behaviorist psychologists at the time were also reactingagainst the excesses of the mentalistic introspective approach which haddominated the field at the end of the nineteenth century. Leonard Bloomfield,who was the most influential figure in linguistics in the United Statesin the first half of the twentieth century, was strongly influenced bybehaviorism. The beginning of the chapter of his classic text Languagewhich is titled 'Meaning' reveals this influence:Bloomfield's 'stimulus-response' model of meaning was as impractical asit was suited to his theoretical orientation. As Bar-Hillel described it,Bloomfield 'deplored the mentalistic mud into which the study of meaningshad fallen, and tried to reconstruct [the field of linguistics] on a purelyformal-structural basis' (Bar-Hillel 1954, 234-235).

Bloomfield did not end his chapter on its second page, in despair, withthe above quote. He did find a way to talk, however briefly and informally,about the arbitrariness of meaning, polysemy and homonymy, semantic features,narrowing and broadening of word meaning, connotations of style and slang,and taboo words, though not always using these terms. (It is significantthat Bloomfield had nothing at all to say about sentence meaning.) Howeverthe constraints of the crude behaviorist view of meaning he shared withother linguists of the time did prove to be a strong barrier to the developmentof linguistic semantics, a barrier which continued into the Chomskyan era.

1.2 The Chomskyan revolution. In 1957 a little book named SyntacticStructures was published by an obscure Dutch press, but was reviewedglowingly and at great length (33 pages, to be exact) by Robert B. Leesin Language -- the journal of the Linguistic Society of America.Noam Chomsky's revolution in linguistics had begun. Probably Chomsky'smost important contribution, from the perspective of the future developmentof linguistic semantics, was the institution of the generative conceptionof grammar, on which the goal of the grammarian was not to simply catalogelements from a corpus, or fixed quantity, of observed utterances, butrather to construct a completely explicit formula that would generate,or characterize exactly, all, and most importantly only, the infinitudeof sentences of the language. Besides the notable consequence of puttingsyntax at the center of linguistics, where formerly it had stood quietlyat the back door, this change in goals would eventually help to draw theattention of semanticists toward the problem of describing explicitly howthe meanings of sentences are derived from the meanings of the words thatmake them up. However that development would have to wait for a few years,since the scientific study of semantics was still in the vexed state ithad been in in Bloomfield's day. The primary issue about meaning at thetime was whether or not intuitions about meaning should play any role indetermining grammatical (= syntactic, morphological, or phonological) analysis.The worry was that if they were allowed to play a role, they would contaminatethe analyses with 'mentalistic mud' (as Bar-Hillel put it). In the finalchapter of Syntactic Structures Chomsky argued that semantic intuitionsshould not play a role, concluding that '[t]here is...little evidence that"intuition about meaning" is at all useful in the actual investigationof linguistic form' (Chomsky 1957, 94).

In the decades following, linguists found themselves unable to resistlooking at meaning. Already in the review article mentioned above, Leeshad speculated about whether 'it could be shown that all or most of whatis "meant" by a sentence is contained in the kernel sentences from whichit is derived' (Lees 1957, 394). A couple of developments in syntacticanalysis[2] made possiblethe main tenet of the school of thought called generative semantics: thatthe deep structure of a sentence constitutes a representation of its meaning.Following the work of linguists such as Fillmore, Postal, McCawley, Ross,and G. and R. Lakoff, deep structures took on some of the aspects of arepresentation in first order predicate logic, though in tree form. Negation,quantifiers, and adverbs were analyzed as sentence operators ('higher predicates'),in order to represent ambiguities such as those in (1)-(3):

(1) Every woman loves one man.

    a. There is one man that every woman loves.
    b. Every woman loves some man or other.

(2) Everyone didn't enjoy the play.

    a. At least one person did not enjoy the play.
    b. No one enjoyed the play.

(3) Mary isn't working in the garden because it's sunny.

    a. Because it's sunny, Mary isn't working in thegarden.
    b. It is not because it's sunny that Mary is workingin the garden (but for some other reason).

Thus (1), for example, would be assigned two deep structures, roughlyas in (4).

(4) a. [[one man]y [[every woman]x [x loves y]]]
    b. [[every woman]x [[one man]y [x loves y]]]

However generative semanticists at the time did not worry about thetask of assigning explicit truth conditions to deep structures. Ratherthe devising and justification of particular deep structures was seen asthe end of the job of semantics.

Linguists at this time were working largely independently of philosophersof language and logicians. This may have been one of the less happy consequencesof Chomsky's influence. In the article cited above, Bar-Hillel suggestedthat linguists pay attention to developments in logic and try to incorporatea formal account of semantics into their grammar, but Chomsky's rathersharp reply the following year asserted that 'the relevance of logicalsyntax and semantics' to the study of natural languages 'is very dubious'(Chomsky 1955, 36). This reaction of Chomsky's was explicitly based onthe not uncommon idea that natural languages and formal languages are fundamentallydifferent from each other, but it was also very much in tune with his largerproject of overthrowing empiricist philosophy of language and mind in favorof a return to Cartesian rationalism, as well as his personal style ofpublicly expressed arrogance and disdain for the work of others. Chomsky'sfirst crops of linguistics Ph.D.'s began to appear in the mid 1960's, andthereafter increasing numbers of American linguists were taught by linguistswho had been taught by Chomsky himself. These students, and their students,tended to inherit the idea that little of substantial value had been saidabout language in the centuries immediately prior to Chomsky. In the late1960's and early 1970's several developments altered this picture.

1.3. Montague and formal semantics. The just mentioned assumptionthat natural languages like English and Chinese are fundamentally differentfrom the formal languages devised by logicians was a cornerstone of a twentiethcentury dispute within British empiricist philosophy between formalists,who held that natural languages were too riddled with vagueness and ambiguityto be useful philosophical tools, and ordinary language philosophers, whoheld that natural languages not only could be excellent tools if used carefully,but also were rich repositories of the wisdom of generations of speakers.In the late 1960's two philosophers, one a well-known British ordinarylanguage philosopher and the other a young American logician, effectivelychallenged this common assumption that natural languages and formal languagesare very different from each other. H. Paul Grice, in his William Jameslecture series delivered at Harvard University in 1967, presented a systematicaccount of what he argued were only apparent divergences between a numberof logical expressions and their natural language counterparts. At roughlythe same time[3] RichardMontague, in a series of papers with titles like 'English as a formal language'and 'Universal grammar', was making good on the following bold statement:'There is in my opinion no important theoretical difference between naturallanguages and the artificial languages of logicians; indeed, I considerit possible to comprehend the syntax and semantics of both kinds of languageswithin a single natural and mathematically precise theory' (Montague 1970b,222).[4]

Montague's papers are highly formal and condensed,very difficult for ordinary humans (even logicians!) to read with comprehension.Fortunately it happened that a young linguist named Barbara Partee, anexceptionally intelligent and clear-thinking as well as personable individualwho was in Chomsky's first (1965) class of Linguistics Ph.D.'s from MIT,took a job at UCLA, met Montague there, and developed an interest in hisapproach to natural language and its contrast with Chomskyan transformationalgrammar. In lectures in the early 1970's, especially following Montague'suntimely death early in 1971, Partee presented his work in such a way asto make it both comprehensible and appealing. 1974 was the fiftieth anniversaryof the Linguistic Society of America and that summer a special Golden AnniversaryLinguistic Institute was held at the University of Massachusetts at Amherst,where Partee was now on the faculty. Partee's class on Montague Grammarwas one of the highlights of this stellar Institute, and was attended bymany prominent linguists. Her 100 page article 'Montague Grammar and TransformationalGrammar', which contained a kind of 'do it yourself' kit for learning formalsemantics, appeared in Linguistic Inquiry in 1975, and served asa kind of introductory text until the excellent volume by Dowty, Wall &Peters appeared in 1981.

Linguists were not entirely ignorant of relevant work in logic and philosophyof language at this time, but there was not the kind of interaction thatthere is today. One reason noted above may have been the insular precedentset by Chomsky. Another may have been the personalities of the generativesemanticists, who would have been expected to be the linguists most interestedin developments in logic and philosophy of language. In August of 1969the philosophers Donald Davidson and Gilbert Harman organized a small colloquiumof logicians and linguists in an effort to promote more fruitful interactions,but Quine (one of the participants) remarked in his condensed autobiographythat '[t]he colloquium was a fiasco at bridge building' (Quine 1986, 38),and suggested that the personalities involved were the cause. However thevolume that resulted from this small conference, Davidson & Harman1972, contained many classic articles (including contributions from bothPartee and Montague) which were widely read by linguists as well as philosophers,and ultimately the work of Montague and Partee along with linguisticallyinclined philosophers like David Lewis and Robert Stalnaker had and continueto have a tremendous impact on the field.

Probably the most important byproduct of this interaction was that linguistsbecame very aware of the fact that simply to represent meaning is not togive an analysis of it. This point was made most effectively by David Lewis,who criticized Katz and Postal's system of semantic representation in termsof semantic features which they called 'markers' (Katz & Postal 1964).Lewis pointed out that Katz and Postal were merely giving rules for translatingEnglish into an artificial language that might be called 'Markerese', andhe said:By studying ordinary predicate logic as well as Montague's more specializedwork linguists became familiar with truth conditional model-theoretic semantics,in which interpretations for expressions, including truth conditions forsentences, are assigned relative to a model.

From the early 1970's to the present time, linguists and philosophershave worked closely and fruitfully together, attending and presenting papersat each other's conferences and publishing in each other's journals, andwork in semantics, and especially formal semantics, has flourished in theUnited States. The journal Linguistics and Philosophy, which describesitself as focusing 'on issues related to structure and meaning in naturallanguage as addressed in the philosophy of language, linguistic semantics,syntax and related disciplines', published its first issue in 1977 andis now in its 21st volume. Other journals devoted to semantics have alsobegun to appear -- Journal of Semantics (which started in 1984),NaturalLanguage Semantics (1993) -- as well as the prestigious conferenceseries Semantics and Linguistic Theory (SALT), which publishes the proceedingsof its annual meetings and is now (1998) in its eighth year. A number oflinguists and philosophers have joint academic appointments in Linguisticsand Philosophy (among them Richmond Thomason, Barbara Partee, and myself)and the linguistics program at MIT is housed in the Department of Linguisticsand Philosophy, though it should be noted that Chomsky's resistance toformal semantics has continued unabated.

2. Current formal semantics: quantification.

We will begin our investigation of the current scene in American linguisticsemantics with a closer work at Montague's work, including some of theproblems he was able to formalize solutions to. In this work interpretationof noun phrases takes center stage, and that will continue when we lookat other analyses of quantification in natural language. Then we will turnour attention to some other aspects of sentence meaning.

2.1. Montague Grammar. The papers of Montague's cited above dealwith 'fragments' of English. Montague's aim was not to construct a grammarfor the whole language, but rather to give a complete (and completely explicit)syntax and semantics for an infinite subpart of the language which containedsome constructions which pose interesting challenges for the semantician.Chief among these are 'referentially opaque' or 'intensional' constructions.'Referential opacity' is the term coined by Quine 1953 for the failureof substitution of coreferential expressions (expressions which refer tothe same thing) to preserve truth in certain contexts. (See also Quine1956 for an excellent introduction to this problem.) One major group ofreferentially opaque contexts consists of sentences about propositionalattitudes, or people's psychological attitudes (such as belief, desire,hope, fear, knowledge) towards situations or states of affairs. (5a) belowcan be true and (5c) false, despite the fact that the truth of (5b) meansthat the NPs Jocasta and Oedipus's mother are coreferential.

(5) a. Oedipus wanted to marry Jocasta.
    b. Jocasta was Oedipus's mother.
    c. Oedipus wanted to marry his mother.

Frege 1892 had argued that associated with expressions is a sense (Sinn)as well as a reference or denotation (Bedeutung), and that in referentiallyopaque contexts expressions denote their sense instead of their customaryreference. Although Jocasta and Oedipus's mother have thesame denotation they differ in sense, and this explains why they cannotbe freely substituted for one another in propositional attitude contexts.Montague's semantics formalized Frege's solution using the notion 'intension',which is a formal analysis of the Fregean concept of sense developed byCarnap, Kripke, Montague and others. Intensions are functions from possibleworlds, or possible states of affairs, to denotations or referents (thelatter also known as extensions).[5]

'Montague Grammar' came to denote the style ofgrammar presented in Montague 1973, which has three components: a syntaxgenerating a fragment of English (which in Montague 1973 included sentencesabout propositional attitudes), a complete syntax and model-theoretic semanticsfor a tensed intensional logic, and a set of translation rules mappingparsed English expressions to expressions of the intensional logic. Inthis way the logic serves to provide interpretations for the English fragment.The intensional logic was included in this paper for perspicuity; in 'Englishas a formal language', Montague interpreted an English fragment directly.

2.2. Generalized quantifiers. Chomsky has impressed linguistswith the importance of accounting for what he calls the 'creative' aspectof human language -- the fact that we are able to produce and comprehendan unlimited number of novel utterances, sentences that we have never heardbefore. Compositionality is the semantic property of linguistic expressionsthat we assume is an essential part of the explanation for this miraculousability. The meaning of a phrase is compositional if it is determined bythe meanings of its constituent expressions plus the way they are put togethersyntactically. Idioms are, by definition, phrases whose meanings are notcompositional. If all of language were idiomatic in this sense, then languagewould have no creative aspect in Chomsky's sense.

The formal languages of logic are strongly compositional, which meansthat expressions of a given syntactic category all receive the same typeof interpretation and contribute in the same way to the interpretationof larger expressions of which they form a part. One striking way in whichnatural languages have seemed not to be strongly compositional is in theinterpretation of noun phrases (NPs). NPs that are proper names, like Mary,have the same distributional properties as quantified NPs like everystudent, and sentences like those in (6) share their syntactic structure:

(6) a. Mary talks.
    b. Every student talks.

However, while it is natural to say of (6a) that it is true just incase the individual denoted by the name Mary belongs to the setof entities that talk, a parallel analysis is not possible for (6b), andtraditionally sentences like (6a) have received very different translationsinto first order predicate logic from sentences like (6b), as seen in (7).

(7) a. Talks(m)
    b. " x [Student(x) ->Talks(x)]

Probably the most impressive and far-reaching innovation in Montague'ssemantics came about because of his need to solve this problem, and thatwas the introduction of the generalized quantifier analysis of NPs. A generalizedquantifier (GQ) is (an expression denoting) a set of subsets of some domain;on this view the traditional existential quantifier would be interpretedas the set of all non-empty subsets of the domain of discourse. TakingNPs to denote GQs, Mary would be interpreted as the set containingall and only those sets which have the person Mary as a member, and Everystudent would denote the set containing all and only supersets of theset of students. In this way the subject NPs of (6a) and (6b) can bothbe seen as taking the predicate as an argument, and each sentence is trueif and only if the set of entities that talk belongs to the GQ denotedby the subject NP.[6]

Besides enabling Montague to solve the strong compositionalityproblem, the GQ analysis of NPs allows a number of other improvements.Some of these were observed and made use of by Montague; for example thegeneralization of conjunction and disjunction, which in ordinary predicatelogic are strictly sentence operators, to apply also to NPs (as well asverb phrases). Following Montague's death other linguists and philosophers,beginning with the seminal work of Barwise & Cooper 1981, exploredother avenues opened by the GQ approach and many papers and books haveappeared detailing the results (see e.g. Gärdenfors 1987 and Bachet al. 1995, and the works cited there). A major thrust of this work isa change of focus from the NP to the determiner, which under the GQ approachcan be easily treated categorematically (unlike the traditional logic syncategorematicanalysis of quantifier expressions) and analyzed as denoting a functionfrom sets (common noun denotations) to sets of sets (GQs) or, equivalently,as expressing a relation between sets -- the set denoted by the commonnoun it combines with and the set denoted by the predicate. This shiftin focus is very much in tune with current trends in syntax, where increasinglyfunction morphemes have taken center stage, so that clauses are now takento be complements of complementizers and so part of a CP category, andnominal phrases are complements of determiners and so part of a DP category.

A number of formal semantic properties of quantified NPs came to lightunder the GQ approach. One of the most widely cited concerns 'entailingness'or monotonicity. In general an operator is upward entailing if a sentencecontaining it entails a sentence where the operator's argument is replacedwith superset of its original argument, and downward entailing if the entailmentgoes in the other direction. Viewing quantificational determiners as functionsfrom sets to GQs, and GQs as functions from sets to truth values, we havetwo operators to consider -- the determiner and the GQ. The determinereveryis downward entailing, as shown by the fact that (8a) entails (8b):

(8) a. Every dog barks.
    b. Every spotted dog barks.

On the other hand the GQ Every dog is upward entailing, as seenby the fact that (9b) entails (9a):

(9) a. Every dog barks.
    b. Every dog barks loudly.

Both some and some dog are upward entailing, while noand no dog are both downward entailing, as the reader may confirmby substituting them for every in the examples in (8) and (9).

Negative polarity items are expressions like any and everthat are limited in their occurrence; they occur naturally in negativesentences, and in some other environments, but an exact statement of theconstraint has proved elusive. An appealing hypothesis is that they occurexactly in downward entailing environments (see Ladusaw 1983), and thisis confirmed by the examples in (10) - (12).[7]

(10) a. *Some dog who ever smiles barks.
        b. *Some dog barks at anyone.

(11) a. No dog who ever smiles barks.
        b. No dog barks at anyone.

(12) a. Every dog who ever smiles barks.
        b. *Every dog barks at anyone.

Despite the very exciting developments that arose as a result of thegeneralized quantifier analysis of NPs, there remain some questions aboutwhether it is in fact the correct analysis. One challenge which we willlook at in the next subsection has come, in part, from one of Partee'sown students, and in connection with a new approach which considerablyblurs the traditional distinction between semantics, as the study of words-worldrelations abstracting away from contexts of utterance, and pragmatics,as the study of the effects of context on interpretation.

2.3. Discourse representation and file change semantics. In theearly 1980s a rather different approach to natural language quantificationwas proposed independently by Irene Heim, at the time one of Barbara Partee'sstudents at the University of Massachusetts at Amherst, and by Hans Kamp,a philosopher and logician. (See Heim 1982, 1983, and Kamp 1984.) One problemwhich Kamp and Heim were concerned with was providing an adequate analysisof what are called 'donkey sentences', as in (13):[8]

(13) Every farmer who owns a donkey beats it.

Such sentences actually present two problems. The first concerns theinterpretation of the pronoun it. If we represent a donkeyin traditional predicate logic, using the existential quantifier, thenthe it (represented by the final occurrence of y in (14)will be outside the scope of that quantifier and will not be appropriatelybound:

(14) " x [[Farmer(x) & $y [Donkey(y) & Own(x,y)]] -> Beat(x,y)]

If, on the other hand, we use a universal quantifier for a donkeyas in (15),

(15) " x " y[[Farmer(x)& Donkey(y) & Own(x,y)] -> Beat(x,y)]

we get a correct representation of the meaning of (13) but we have toexplain how a donkey should sometimes be represented with a universalquantifier, but not other times, e.g. (16):

(16) Mary owns a donkey.

Discourse Representation Semantics (DRS) (Kamp) and File Change Semantics(FCS) (Heim) both solved this problem with an approach to semantics whichviews the meaning of a sentence in terms of the impact an utterance ofit has on the discourse of which it is a part, in other words in termsof its context change potential. This is an approach that had earlier beenurged by Stalnaker, in connection with the problem of presuppositions andpresupposition projection. (See Stalnaker 1974, 1978.) Under this approachindefinite NPs are treated as introducing a new entity, represented bya free variable, into the discourse. (Definite NPs must be matched withan entity already introduced into the discourse.) When they occur in simplesentences like (17) they receive an existential interpretation in viewof the semantic rule for interpreting the entire discourse -- roughly,the discourse is true if there is a sequence of individuals meeting allthe conditions that have been mentioned. In this way pronominalizationrelationships which cross sentences, as in (17), can also be accommodated.

(17) Mary owns a donkey. It always brays when itwants to be fed.

The pronouns in (17) are beyond the capability of traditional formalsemantics, which follows traditional logic in providing interpretationssentence by sentence.

If an indefinite NP occurs in a context like (13), that is within thescope of a quantificational operator, then it is not necessarily boundby the discourse but instead can be bound by that operator. Lets look moreclosely to see how this happens. In the discourse oriented view of semantics,quantification breaks down into a three part, or tripartite, structure.The first element of the structure is the quantificational operator, thesecond element includes any restriction on the range of quantification,and the third element (often called the 'scope') is the actual assertionassociated with the quantifier. If indefinite NPs fall within the restrictiveportion of a quantificational structure, they inherit binding by whateverquantificational operator is involved. So (13) receives a representationas in (18), where Q stands for 'Quantificational operator', R stands for'Restriction', and S stands for 'Scope':

(18) Q[every: x, y] R[Farmer(x), Donkey(y), Owns(x,y)] S[Beats(x,y)]

One of the attractive features of this approach is that it can alsohandle examples of adverbial and adjectival quantification which were pointedout by David Lewis (see Lewis 1975). Notice that (19) below means the samething as (13), and would also be represented by (18), but this time theuniversal quantification is expressed by the adverb, and there are twoindefinite NPs -- a farmer and a donkey -- to fall withinits scope.

(19) Invariably, if a farmer owns a donkey he beats it.

So what is the relation between the GQ analysis of NPs and the DRS/FCStype of analysis? Barbara Partee, ever the unifier, argued that both arecorrect, but possibly for different kinds of NPs and different kinds ofcontexts. In Partee 1986 she argued that indefinite NPs in fact need threedifferent types of representations, depending on the context in which theyoccur. Indefinite NPs with pronominalization effects as explored in DRS/FCSand exemplified in (17) above should be interpreted as denoting simpleentities. Indefinites that function as predicate nominals, as in (20),should be analyzed as denoting sets of things, here, the set of students.

(20) Mary is a student.

And the indefinite NP in (21) needs to be regarded as denoting a GQ,since it is conjoined with a quantificational NP:

(21) One student and all the teachers appeared at the rally.

This is not the end of the story, however; see Bach et al. 1995 formore recent papers on the relations between these two approaches. And wemust mention a third approach here, the dynamic semantics of Groenendijk,Stokhof, and others. (See Groenendijk & Stokhof 1991, Groenendijk,Stokhof & Veltman 1996.) Expressing a concern about the lack of attentionto compositionality in the DRS/FCS approaches, Groenendijk and Stokhofhave explored a modification of traditional predicate logic which willbe able to interpret donkey sentences and cross-sentence anaphora. It ispossible to equate the interpretation of a sentence in traditional predicatelogic with the set of assignments of values to variables which will satisfyit. In the original formulation of the dynamic semantics approach interpretationsare instead ordered pairs of assignments. Successive sentences in a discoursecarry over information from previous assignments, so that examples like(17) receive the proper interpretation. In conditional sentences, whichdonkey sentences are formally, the same property holds between antecedentand consequent, so that in a logical form like (14) the rightmost occurrenceof the y variable will be bound by the existential quantifier. Thisbasic approach is modified and elaborated in Groenendijk et al. 1996.

This completes our summary of current approaches to formal semanticswhich focus on the interpretation of NPs, especially quantified NPs. Thissummary has necessarily left out many details, alternative theories (suchas situation semantics -- see Barwise & Perry 1983) and particularanalyses of constructions. For more information, see the many excellentpapers in Lappin 1996. We turn now to look at some other aspects of sentenceinterpretation.

3. Aspects of eventualities.

As noted above, by far the most attention in formal semantics has beenpaid to the interpretation of NPs. However philosophers and linguists havealso been drawn to consider other aspects of sentence interpretation andnow we will look at some of these. We will begin with a problem noticedby Donald Davidson, and that will lead us to consider the nature of differentkinds of eventualities as well as some more complexities of NP interpretation.

3.1. Davidson's 'event' semantics. Davidson (1967) consideredthe fanciful example in (22):

(22) Jones buttered the toast with a knife in the bathroom at midnight.

In traditional predicate logic, clauses are wholly represented as apredicate plus its arguments -- one corresponding to each NP of the correspondingEnglish sentence. There are 5 NPs in (22) (Jones, the toast,aknife, the bathroom, midnight); hence to represent thissentence in traditional logic we would have to have a 5-place predicate,something like Butter-with-in-at, to go with five arguments correspondingto these five NPs. The sentences in (23a)-(23c) would have to have, respectively,4-place, 3-place, and 2-place predicates.

(23) a. Jones buttered the toast with a knife in the bathroom.
        b. Jones buttered the toastwith a knife.
        c. Jones buttered the toast.

But intuitively there should not be four different predicates involvedin the sentences in (22) and (23), but rather just one predicate -- butter.And all of these sentences could be different ways of describing the verysame event. To put the problem in more formal terms (the way Davidson describedit), (22) entails each of the sentences in (23) (and they each entail theones below them), but these semantic relations could not be captured intraditional predicate logic.

What Davidson proposed by way of a solution was to recognize eventsas a kind of entity -- that is, to add events to the other things (people,dogs, chairs, etc.) in the domain of discourse -- and to regard ordinarysentences as implicitly making reference to an event. Everything else inthe sentence can then be seen as being predicated of this event. So (22)would introduce an event which is a 'Jones buttering the toast' type ofevent, and this very event has other properties -- it occurred with a knifeand in the bathroom, etc. The logical form of (22), according to Davidson,is something like (24),[9] wheree is a special variable over events:

(24) $e [Butter(Jones, the toast,e)& With(a knife, e) & In(the bathroom, e) & At(midnight,e)]

The logical form for (23c) would be (25).

(25) $e [Butter(Jones, the toast,e)]

(25) is entailed by (24) as well as by the Davidsonian logical formsfor (23a) and (23b).

Linguists were not aware of Davidson's proposals for a while after theywere introduced, but more recently they have received a great deal of attention.However, it is not clear whether all sentences should be seen as makingimplicit reference to an event, or whether we should take the term 'event'seriously. Not all sentences describe events. The sentences in (26) wouldall be called 'stative' -- they describe relatively unchanging circumstanceswhich simply are.

(26) a. Joyce knows Arabic.
        b. Four divided by two equalstwo.
        c. Dogs make good companions.

Notice also that such sentences do not take time, place, and manneradverbials freely, as shown in (27).

(27) a. ?Joyce knows Arabic at midnight.
        b. ?Four divided by twoequals two in the bathroom.
        c. ?Dogs make good companionswith a knife.

Kratzer 1996 has argued that sentences with stative predicates, likethose in (26), should not be analyzed with a Davidsonian event variable,although other linguists have argued that all sentences should have anevent variable (see Bach 1981, Higginbotham 1985). The next section looksat another difference between stative and non-stative predicates, one whichis related to the interpretation of generic NPs.

3.2. Generic NPs. Sentences like those in (28) present an interestingpuzzle:

(28) a. Dogs are excellent companions.
        b. Dogs are barking outsidemy window.

Though the same word -- dogs -- functions as subject in bothit seems to refer to two different things. (28a) is a statement about dogsin general, perhaps all dogs, while (28b) talks about some specific dogs,perhaps only two or three. Greg Carlson (another of Barbara Partee's students!)had a crucial insight in proposing a solution to this puzzle. He shiftedattention from the subject to the predicate and saw that the apparent distinctionin NP interpretation correlated well with a difference in whether the verbphrase expressed a permanent property, or instead a more temporary property,of the subject. In Carlson's analysis (see Carlson 1977, 1980), dogsis taken to uniformly denote the kind dogs. Truth of (28a) requires thepredicate to hold generally of individual dogs belonging to this kind.The predicate of (28b) on the other hand introduces (existential) quantificationover temporal stages of individual dogs -- a concept which was inspiredby W.V. Quine 1960.

Although particular aspects of this analysis have been disputed (seeCarlson & Pelletier 1995 for some current views of generics), Carlson'sdistinction between individual level and stage level predication has provedto have far reaching significance. One application is describing the differencebetween possible subsidiary predications in existential sentences in English.(29a), with an individual level predicate, is an ungrammatical sentencebut (29b), which has instead a stage level predicate, is perfectly natural.

(29) a. *There are dogs excellent companions.
        b. There are dogs barkingoutside my window.

Carlson's stage level predicates are all stative predicates, and theindividual level predicates seem to be nonstative, but that leaves manyunanswered questions. Are there just two types of eventualities? If not,what other kinds are there, and how are the different categories defined?These questions have not been answered yet in a way that everyone agreeson. We will look at some proposals in the next section.

3.3. Types of eventualities. The German word Aktionsarten (singularAktionsart) is commonly now used in the study of different types of eventualities,to distinguish aspect in this sense from the aspectual markers found onverbs in inflecting languages. Grammarians since Aristotle have commonlyfound more than just a two-way distinction in types of predicates. Aristotlehimself pointed to a three way distinction among states like knowing Arabic,which are relatively unchanging, processes like running, in which thereis activity of some kind going on, and actions like building a house, whichhave a natural culmination or termination point. The latter are now commonlyreferred to as telic eventualities.

Zeno Vendler, one of the earliest philosophers to pay serious attentionto the kinds of linguistic evidence that motivates linguists, divided Aristotle'stelic eventualities into two subcategories -- accomplishments like buildinga house, which are volitional and take some time to bring about, and whathe called achievements like noticing a mistake or dying, which are nonvolitionaland are referred to as though they were instantaneous. (See Vendler 1967.)Some of the grammatical distinctions in these four categories are illustratedin the following examples, where know Arabic represents stativepredicates, push a cart represents processes, build a houserepresents accomplishments, and notice a mistake represents achievements.

(30) a. *Mary is knowing Arabic/noticing a mistake.
        b. Mary is pushing a cart/buildinga house.

(31) a. Mary knew Arabic/pushed a cart for a year.
        b. *Mary built a house/noticeda mistake for a year.

(32) a. *Mary knew Arabic/pushed a cart within day.
        b. Mary built a house/noticeda mistake within a day.

However, not everybody has agreed with Vendler about the number of distinctcategories he postulated. In the formal semantics for Aktionsarten presentedin Parsons 1990, there are just two operators: Cul ('culminate') to representVendler's accomplishments and achievements, and Hold, for sentences representingeither states or processes. Bach 1986, on the other hand, subdivided eventualitiesinto six different subcategories, including two different types of states(dynamic and static), in addition to processes and several kinds of teliceventualities. There are other complications too; Verkuyl has stressedthe importance of the effect different types of NP arguments can have onthe aspect of a sentence. (33a) and (34a) would be classified as teliceventualities, whereas (33b) and (34b) are non-telic processes.

(33) a. Mary painted a picture (*for a year).
        b. Mary painted pictures(for a year).

(34) a. A guest arrived (*for an hour).
        b. Guests arrived (for anhour).

Verkuyl 1993 proposes a formal semantics in which NPs as well as verbsare taken into account, and eventuality types are determined compositionallyfor the sentence as a whole.

4. Summary, conclusions and prognostications.

4.1. Commonalities. All of the formal analyses described andsummarized here have shared some common assumptions about the goals ofsemantics. One is that any proposed analysis of the semantic interpretationfor a language, or a portion thereof, must be given in rigorous and explicitterms. Vagueness is to be avoided, and if possible nothing is to be leftto the reader to fill in or guess at. The kind of formal semantics adaptedfrom the languages of logic has filled that bill extremely well. This explainsthe frequent use of special symbols in formal semantics. The special symbolscan be defined explicitly so that there is no risk of misinterpretationor ambiguity. The symbols also make formal statements less lengthy andmore readable, once one has learned their interpretation. Although theheavy use of special symbols initially presents somewhat of a formidableseeming barrier to formal semantics, ultimately it has more than enoughvalue in clarity to make climbing over this barrier well worth while.

Another common assumption was referred to above in the contradictory-soundingstatement from David Lewis: 'Semantics without truth conditions is notsemantics' (Lewis 1972, 169). Truth conditional semantics takes the coreof meaning for a sentence to be given by some kind of explicit statementabout what it would take for a sentence to be true. There are many argumentsfor this assumption. One is that it makes clear how language is relatedto the things in the outside world that it is used to talk about. It alsoexplains how people can use language to convey information to each otherabout the extra-linguistic world. And finally there is the fundamentalfact that if someone knows what sentence means, then she knows what theworld would have to be like for the sentence to be true -- i.e. the truthconditions of the sentence. Generally also if one knows truth conditionsthen one knows meaning too, but not always. Necessarily true sentenceslike the truths of mathematics all have the same truth conditions -- theyare true under any circumstances or in every possible world. Neverthelessthese sentences don't all mean the same thing. Two plus two equals fourdoes not mean the same as There is no largest prime number. So thereis more to meaning besides truth conditions, but formal semanticians agreethat giving truth conditions is an essential core to describing meaning.

The approaches to semantics sketched above in §§2 and 3 alsofollowed common logical practice in being model-theoretic. Model-theoreticsemantics is a generalization of the truth conditional approach accordingto which truth conditions are given relative to a model. The semanticsfor a given language will specify what a model for the language must consistof -- what kinds of things it must have and how the language is to be relatedto them. Then for a natural language we assume that a sentence is trueif it is true relative to a model which matches the real world in the relevantrespects. (See Kalish 1967 for discussion and historical notes.)

4.2. Alternatives, formal & informal. Not all truth conditionalsemantics is model-theoretic. Donald Davidson has proposed a differentstyle of semantics for natural language, which is also based on modernlogic, but which takes the task of semantics for a language as divisinga system which will generate specific statements of truth conditions whichare called 'T-sentences'. T-sentences were introduced by Tarski (see Tarski1944), but the 'T' stands for 'truth' not for 'Tarski'! A T-sentence forthe English sentence Snow is white is given in (35).

(35) Snow is white is true if and only if snow is white.

(35) looks fairly vacuous, but part of that vacuous look is becausethe object language -- the language we are talking about the semanticsof, is the same as the metalanguage -- the language we are using to dothe semantics with. When the object language is different from the metalanguage,the T-sentence looks more significant:

(36) Xuê shì baí de is true if and only ifsnow is white.

Tarski proposed as a minimal condition on the adequacy of the semanticrules for a language, that they should allow the derivation (that is, theproof, in the logical sense) of the correct T-sentences for all the sentencesof the object language. Larson & Segal 1995 have undertaken the taskof working out the formal details of the T-sentence approach for a largefragment of English which includes generalized quantifiers, referentiallyopaque sentences, tense and aspect features, and many other interestingand challenging constructions. Their work is presented as a textbook forgraduate students, but it is of great interest to professional linguistsand philosophers of language as well.

There are few alternatives to the approaches falling under the headingof formal semantics, and none that offer the same comprehensiveness. Probablythe most well known is the approach of Jackendoff -- see Jackendoff 1990,1997. Jackendoff's specialty is lexical semantics, about which formal semanticistshave had the least to say, and his work, which offers many insights intothe nature of word meaning, deserves careful attention. Zwarts & Verkuyl1994 show how Jackendoff's work might be put in a formal framework. Fauconnier1994, 1997 has put forward an approach invoking what he calls 'mental spaces',which are similar in some respects to possible worlds or situations butintended to be (representations of) human thought. This work focuses inparticular on unusual cases of reference such as those illustrated in (36).

(36) a. Bill [meaning Bill's car] is parked on the next street.
        b. If I were you I wouldtreat myself/me with a little more respect.

Fauconnier's work tends to be less carefully worked out than Jackendoff's,and neither approach reaches the level of explicit comprehensiveness ofthe formal theories we have been looking at.

4.3. Future prospects. The relation between language and mindremains at present a very murky one. Chomsky's mentalistic revolution inlinguistics put the study of language, at least theoretically and accordingto Chomsky, under the umbrella of psychology. However in practice developmentsin linguistics and findings of psycholinguists have not always fit togethercomfortably, and I regret to have to report that linguists have sometimesseemed to turn their back on psycholinguists in such cases. Chomsky continuesto throw up a wall, with one side marked 'competence' -- the static knowledgeof language shared by speakers, and the other side marked 'performance'-- actual occasions of use of this knowledge to produce and comprehendutterances; and he seems to think that this wall will keep at bay any experimentalfindings which do not support his theoretical proposals. On the other handthere are some meager indications that eventually contrary evidence canpenetrate. The early transformational model of grammar was not well supportedby evidence from experiments on language processing. While this evidenceseemed to be ignored for many years, gradually Chomsky has replaced thetransformational model with another, and it is possible that the psycholinguisticevidence played a role in this replacement.

Another issue is the relation of semantics to the rest of the grammar,on the one hand, and to the rest of cognition on the other. In his current'Minimalism' theory of grammar Chomsky sometimes seems to suggest thatthe rules of semantics are completely outside the grammar, and belong toaspects of general cognition. On other occasions, though, Chomsky usesexamples of word meaning to argue for the highly specialized nature oflinguistic competence and for its innateness. (See Chomsky 1995a,b.) Thisambivalence is matched by other long standing controversies -- the controversyover whether word meanings are specialized and distinguished from generalknowledge about the world (the 'dictionary' view) or whether they are holisticand global, and encompass everything related to extensions (the 'encyclopedia'view), as well as the many disputes about whether certain aspects of sentencemeaning (in a broad sense of 'meaning') belong to semantics or pragmatics-- aspects such as presupposition, conversational implicature, and illocutionaryforce.

I predict that these issues will be resolved within the next fifty years,and that findings from the rest of the new field of cognitive science --especially the subfields of psycholinguistics and language processing,neurolinguistics, and computational linguistics -- will be helpful in thisresolution. I also believe that the evidence will ultimately indicate thatthe framework for semantic interpretation will share the unique naturethat the rest of language seems to have, and that there will be a distinctionbetween the linguistic lexicon and the encyclopedia of world knowledge.I base this projection in part on the fact that the principles of meaning,whether at the word level or at the sentence level, seem to be as illusiveand inaccessible to conscious reflection as the principles of syntacticstructure or phonological interpretation, and in part on my belief thatGrice and Montague were right, that the logical approach to language, inwhich semantic and syntactic representations mirror each other, is justifiedfor natural as well as formalized languages.[10]


[1] According to CarnapOn this characterization it may seem like the phrase 'formal semantics'should be a contradiction in terms! At the time Carnap and others believedthat relations of meaning among sentences, such as entailment and contradiction,could and should be given an account in purely formal, that is syntactic,terms. However with the development by Tarski and others of rigorous methodsof semantic interpretation, on the one hand, and the proof by Gödelof the nonequivalence of syntactic and semantic notions of logical consequence,on the other, 'logic' has come to encompass both syntax and semantics,and 'formal' has come to mean something like 'rigorous and explicit; modeledon methods in logic'. In some ways the term is a counterpart to Chomsky'sterm 'generative'.  [return]

[2] One of these developments was the discoveryby Fillmore of the cyclic principle of transformational rule application(Fillmore 1963), which allowed the abandonment of generalized transformationsand the incorporation of recursive rules in the phrase structure component.The other was the development by Katz and Postal of arguments for deepstructure triggers of otherwise meaning changing transformations -- mostnotably the negation and question rules (Katz & Postal 1964).  [return]

[3] The earliest of these papers were publishedin 1970, but reference notes make clear that the ideas were already beginningto be presented in lectures as early as January and February of 1966 (cf.Montague 1970a, 188).   [return]

[4] The reader may have guessed from this quotationthat the phrase 'universal grammar' had quite a different meaning for Montaguethan it has for Chomsky. While for Chomsky 'universal grammar' denotesthe innate human language faculty, for Montague that phrase denoted themathematical study of syntax and semantics. Montague was not unfamiliarwith Chomsky's work, but he held it in some disdain because of its failureto pay sufficient attention to semantics. Cf. e.g. Montague 1973, 247.  [return]

[5] Frege's solution to the problem of referentialopacity, as formalized by Montague and others, has not proved to be completelysuccessful. One difficulty is posed by the fact that proper names do notseem to have a sense, the way descriptive expressions like Oedipus'smother do. (Kripke 1972 argued this at length and quite convincingly.)Nevertheless proper names cannot be substituted for each other in referentiallyopaque contexts, as seen in by the fact that (ia) can be true and (ic)false, despite the truth of (ib):

(i) a. Ruth knows that Mark Twain wrote Tom Sawyer.
    b. Mark Twain was Samuel Clemens.
    c. Ruth knows that Samuel Clemens wrote Tom Sawyer.

There is a huge literature on this topic, which stretches back at leastto the middle ages and continues to the present day. See Linsky 1971 forsome of the standard 'classical' references on this topic, including Quine1953 and Quine 1956, and Anderson & Owens 1990 and Künne, Newen& Anduschus 1997 for some recent papers.   [return]

[6] Although generalized quantifiers had been discoveredprior to Montague's work (see Barwise & Cooper 1981, 159), he was apparentlyunaware of this and did not use the term 'generalized quantifier' in hisown papers. Also, because of the intensionality in his approach, ratherthan interpreting NPs as sets of sets he actually interpreted them as propertiesof properties, but I am ignoring that complication for this presentation.  [return]

[7] Despite the appealing nature of Ladusaw's hypothesisabout negative polarity items there are problems with this explanation.See Israel 1996 for a review of much of the literature on polarity, andan alternative hypothesis.   [return]

[8] Geach 1962 was the first to draw the attentionof modern philosophers and linguists to the problems presented by suchsentences, though he cited a medieval literature on the subject.  [return]

[9] Of course the real logical form for (22) wouldhave the NPs unpacked in familiar quantificational ways, which have beenomitted here for clarity's sake.   [return]

[10] I would like to thank Aldo Antonelli, JianguoChen, Yen-Hwei Lin, Dick Stanley, and Luding Tong for help in connectionwith this paper.   [return]


1. Two kinds of theory of meaning

In “General Semantics,” David Lewis wrote

I distinguish two topics: first, the description of possible languages or grammars as abstract semantic systems whereby symbols are associated with aspects of the world; and, second, the description of the psychological and sociological facts whereby a particular one of these abstract semantic systems is the one used by a person or population. Only confusion comes of mixing these two topics. (Lewis 1970, 19)

Lewis was right. Even if philosophers have not consistently kept these two questions separate, there clearly is a distinction between the questions ‘What is the meaning of this or that symbol (for a particular person or group)?’ and ‘In virtue of what facts about that person or group does the symbol have that meaning?’

Corresponding to these two questions are two different sorts of theory of meaning. One sort of theory of meaning—a semantic theory—is a specification of the meanings of the words and sentences of some symbol system. Semantic theories thus answer the question, ‘What is the meaning of this or that expression?’ A distinct sort of theory—a foundational theory of meaning—tries to explain what about some person or group gives the symbols of their language the meanings that they have. To be sure, the shape of a correct semantic theory may place constraints on the correct foundational theory of meaning, or vice versa; but that does not change the fact that semantic theories and foundational theories are simply different sorts of theories, designed to answer different questions.

To see the distinction between semantic theories and foundational theories of meaning, it may help to consider an analogous one. Imagine an anthropologist specializing in table manners sent out to observe a distant tribe. One task the anthropologist clearly might undertake is to simply describe the table manners of that tribe—to describe the different categories into which members of the tribe place actions at the table, and to say which sorts of actions fall into which categories. This would be analogous to the task of the philosopher of language interested in semantics; her job is say what different sorts of meanings expressions of a given language have, and which expressions have which meanings.

But our anthropologist might also become interested in the nature of manners; he might wonder how, in general, one set of rules of table manners comes to be the system of etiquette governing a particular group. Since presumably the fact that a group obeys one system of etiquette rather than another is traceable to something about that group, the anthropologist might put his new question by asking, ‘In virtue of what facts about a person or group does that person or group come to be governed by a particular system of etiquette, rather than another?’ Our anthropologist would then have embarked upon the analogue of the construction of a foundational theory of meaning: he would then be interested, not in which etiquette-related properties particular action types have in a certain group, but rather the question of how action-types can, in any group, come to acquire properties of this sort.[1] Our anthropologist might well be interested in both sorts of questions about table manners; but they are, pretty clearly, different questions. Just so, semantic theories and foundational theories of meaning are, pretty clearly, different sorts of theories.

The term ‘theory of meaning’ has, in the recent history of philosophy, been used to stand for both semantic theories and foundational theories of meaning. As this has obvious potential to mislead, in what follows I’ll avoid the term which this article is meant to define and stick instead to the more specific ‘semantic theory’ and ‘foundational theory of meaning.’ ‘Theory of meaning’ simpliciter is to be understood as ambiguous between these two interpretations.

Before turning to discussion of these two sorts of theories, it is worth noting that one prominent tradition in the philosophy of language denies that there are facts about the meanings of linguistic expressions. (See, for example, Quine 1960 and Kripke 1982; for critical discussion, see Soames 1997.) If this sort of skepticism about meaning is correct, then there is neither a true semantic theory nor a true foundational theory of meaning to be found, since the relevant sort of facts simply are not around to be described or analyzed. Discussion of these skeptical arguments is beyond the scope of this entry, so in what follows I’ll simply assume that skepticism about meaning is false.

2. Semantic theories

The task of explaining the main approaches to semantic theory in contemporary philosophy of language might seem to face an in-principle stumbling block. Given that no two languages have the same semantics—no two languages are comprised of just the same words, with just the same meanings—it may seem hard to say how we can say anything about different views about semantics in general, as opposed to views about the semantics of this or that language. This problem has a relatively straightforward solution. While it is of course correct that the semantics for English is one thing and the semantics for French something else, most assume that the various natural languages should all have semantic theories of (in a sense to be explained) the same form. The aim of what follows will, accordingly, be to introduce the reader to the main approaches to natural language semantics—the main views about the right form for a semantics for a natural language to take—rather than a detailed examination of the various views about the semantics of some particular expression. (For some of the latter, see names, descriptions, propositional attitude reports, and natural kinds.)

One caveat before we get started: before a semantic theorist sets off to explain the meanings of the expressions of some language, she needs a clear idea of what she is supposed to explain the meaning of. This might not seem to present much of a problem; aren’t the bearers of meaning just the sentences of the relevant language, and their parts? This is correct as far as it goes; but the task of explaining what the semantically significant parts of a sentence are, and how those parts combine to form the sentence, is an enterprise which is both far from trivial, and has important consequences for semantic theory. Indeed, most disputes about the right semantic treatment of some class of expressions are intertwined with questions about the syntactic form of sentences in which those expressions figure. Unfortunately, discussion of theories of this sort, which attempt to explain the logical form, or syntax, of natural language sentences, is well beyond the scope of this entry. As a result, figures like Richard Montague, whose work on syntax and its connection to semantics has been central to the development of semantic theory over the past few decades, are passed over in what follows. (Montague’s essays are collected in Montague 1974; for a discussion of the importance of his work, see §3.3 of Soames 2010.)

Most philosophers of language these days think that the meaning of an expression is a certain sort of entity, and that the job of semantics is to pair expressions with the entities which are their meanings. For these philosophers, the central question about the right form for a semantic theory concerns the nature of these entities. Because the entity corresponding to a sentence is called a proposition, I’ll call these propositional semantic theories. However, not all philosophers of language think that the meanings of sentences are propositions, or even believe that there are such things. Accordingly, in what follows, I’ll divide the space of approaches to semantics into propositional and non-propositional semantic theories. Following discussion of the leading approaches to theories of each type, I’ll conclude in §2.3 by discussing a few general questions which semantic theorists take which are largely orthogonal to one’s view about the form which a semantic theory ought to take.

2.1 Propositional semantic theories

The easiest way to understand the various sorts of propositional semantic theories is by beginning with another sort of theory: a theory of reference.

2.1.1 The theory of reference

A theory of reference is a theory which, like a propositional semantic theory, pairs the expressions of a language with certain values. However, unlike a semantic theory, a theory of reference does not pair expressions with their meanings; rather, it pairs expressions with the contribution those expressions make to the determination of the truth-values of sentences in which they occur. (Though later we will see that this view of the reference of an expression must be restricted in certain ways.)

This construal of the theory of reference is traceable to Gottlob Frege’s attempt to formulate a logic sufficient for the formalization of mathematical inferences (see especially Frege 1879 and 1892.) The construction of a theory of reference of this kind is best illustrated by beginning with the example of proper names. Consider the following sentences:

  • (1)Barack Obama is the 44th president of the United States.
  • (2)John McCain is the 44th president of the United States.

(1) is true, and (2) is false. Obviously, this difference in truth-value is traceable to some difference between the expressions ‘Barack Obama’ and ‘John McCain.’ What about these expressions explains the difference in truth-value between these sentences? It is very plausible that it is the fact that ‘Barack Obama’ stands for the man who is in fact the 44th president of the United States, whereas ‘John McCain’ stands for a man who is not. This indicates that the reference of a proper name—its contribution to the determination of truth conditions of sentences in which it occurs—is the object for which that name stands.

Given this starting point, it is a short step to some conclusions about the reference of other sorts of expressions. Consider the following pair of sentences:

  • (3)Barack Obama is a Democrat.
  • (4)Barack Obama is a Republican.

Again, the first of these is true, whereas the second is false. We already know that the reference of ‘Barack Obama’ is the man for which the name stands; so, given that reference is power to affect truth-value, we know that the reference of predicates like ‘is a Democrat’ and ‘is a Republican’ must be something which combines with an object to yield a truth-value. Accordingly, it is natural to think of the reference of predicates of this sort as functions from objects to truth-values. The reference of ‘is a Democrat’ is that function which returns the truth-value ‘true’ when given as input an object which is a member of the Democratic party (and the truth-value ‘false’ otherwise), whereas the reference of ‘is a Republican’ is a function which returns the truth-value ‘true’ when given as input an object which is a member of the Republican party (and the truth-value ‘false’ otherwise). This is what explains the fact that (3) is true and (4) false: Obama is a member of the Democratic party, and is not a member of the Republican party.

Matters get more complicated, and more controversial, as we extend this sort of theory of reference to cover more and more of the types of expressions we find in natural languages like English. (For an introduction, see Heim and Kratzer 1998.) But the above is enough to give a rough idea of how one might proceed. For example, some predicates, like ‘loves’ combine with two names to form a sentence, rather than one. So the reference of two-place predicates of this sort must be something which combines with a pair of objects to determine a truth-value—perhaps, that function from ordered pairs of objects to truth-values which returns the truth-value ‘true’ when given as input a pair of objects whose first member loves the second member, and ‘false’ otherwise.

2.1.2 Theories of reference vs. semantic theories

So let’s suppose that we have a theory of reference for a language, in the above sense. Would we then have a satisfactory semantic theory for the language?

Some plausible arguments indicate that we would not. To adopt an example from Quine (1970), let’s assume that the set of animals with hearts (cordates) is the same as the set of animals with kidneys (renates). Now, consider the pair of sentences:

  • (5)All cordates are cordates.
  • (6)All cordates are renates.

Given our assumption, both sentences are true. Moreover, from the point of view of the theory of reference, (5) and (6) are just the same: they differ only in the substitution of ‘renates’ for ‘cordates’, and these expressions have the same reference (because they stand for the same function from objects to truth-values).

All the same, there is clearly an intuitive difference in meaning between (5) and (6); the sentences seem, in some sense, to say different things. The first seems to express the trivial, boring thought that every creature with a heart is a creature with a heart, whereas the second expresses the non-trivial, potentially informative claim that every creature with a heart also has a kidney. This suggests that there is an important difference between (5) and (6) which our theory of reference simply fails to capture.

Examples of the same sort can be generated using pairs of expressions of other types which share a reference, but intuitively differ in meaning; for example, ‘Clark Kent’ and ‘Superman,’ or (an example famously discussed by Frege (1892/1960)), ‘the Morning Star’ and ‘the Evening Star.’

This might seem a rather weak argument for the incompleteness of the theory of reference, resting as it does on intuitions about the relative informativeness of sentences like (5) and (6). But this argument can be strengthened by embedding sentences like (5) and (6) in more complex sentences, as follows:

  • (7)John believes that all cordates are cordates.
  • (8)John believes that all cordates are renates.

(7) and (8) differ only with respect to the underlined expressions and, as we noted above, these expressions have the same reference. Despite this, it seems clear that (7) and (8) could differ in truth-value: someone could know that all cordates have a heart without having any opinion on the question of whether all cordates have a kidney. But that means that the references of expressions don’t even do the job for which they were introduced: they don’t explain the contribution that expressions make to the determination of the truth-value of all sentences in which they occur. (One might, of course, still think that the reference of an expression explains its contribution to the determination of the truth-value of a suitably delimited class of simple sentences in which the expression occurs.) If we are to be able to explain, in terms of the properties of the expressions that make them up, how (7) and (8) can differ in truth-value, then expressions must have some other sort of value, some sort of meaning, which goes beyond reference.

(7) and (8) are called belief ascriptions, for the obvious reason that they ascribe a belief to a subject. Belief ascriptions are one sort of propositional attitude ascription—other types include ascriptions of knowledge, desire, or judgement. As will become clear in what follows, propositional attitude ascriptions have been very important in recent debates in semantics. One of the reasons why they have been important is exemplified by (7) and (8). Because these sentences can differ in truth-value despite the fact that they differ only with respect to the underlined words, and these words both share a reference and occupy the same place in the structure of the two sentences, we say that (7) and (8) contain a non-extensional context: roughly, a ‘location’ in the sentence which is such that substitution of terms which share a reference in that location can change truth-value. (They’re called ‘non-extensional contexts’ because ‘extension’ is another term for ‘reference.’)

We can give a similar argument for the incompleteness of the theory of reference based on the substitution of whole sentences. A theory of reference assigns to subsentential expressions values which explain their contribution to the truth-values of sentences; but to those sentences, it only assigns ‘true’ or ‘false.’ But consider a pair of sentences like

  • (9)Mary believes that Barack Obama is the president of the United States.
  • (10)Mary believes that John Key is the prime minister of New Zealand.

Because both of the underlined sentences are true, (9) and (10) are a pair of sentences which differ only with respect to substitution of expressions (namely, the underlined sentences) with the same reference. Nonetheless, (9) and (10) could plainly differ in truth-value.

This seems to show that a semantic theory should assign some value to sentences other than a truth-value. Another route to this conclusion is the apparent truth of claims of the following sort:

There are three things that John believes about Indiana, and they are all false.

There are many necessary truths which are not a priori, and my favorite sentence expresses one of them.

To get an A you must believe everything I say.

Sentences like these seem to show that there are things which are the objects of mental states like belief, the bearers of truth and falsity as well as modal properties like necessity and possibility and epistemic properties like a prioricity and posterioricity, and the things expressed by sentences. What are these things? The theory of reference provides no answer.

Friends of propositions aim both to provide a theory of these entities, and, in so doing, also to solve the two problems for the theory of reference discussed above: (i) the lack of an explanation for the fact that (5) is trivial and a priori while (6) is not, and (ii) the fact (exemplified by (7)/(8) and (9)/(10)) that sentences which differ only in the substitution of expressions with the same reference can differ in truth-value.

A theory of propositions thus does not abandon the theory of reference, as sketched above, but simply says that there is more to a semantic theory than the theory of reference. Subsentential expressions have, in addition to a reference, a content. The contents of sentences—what sentences express—are known as propositions.

2.1.3 The relationship between content and reference

The natural next question is: What sorts of things are contents? Below I’ll discuss some of the leading answers to this question. But in advance of laying out any theory about what contents are, we can say some general things about the role that contents are meant to play.

First, what is the relationship between content and reference? Let’s examine this question in connection with sentences; here it amounts to the question of the relationship between the proposition a sentence expresses and the sentence’s truth-value. One point brought out by the example of (9) and (10) is that two sentences can express different propositions while having the same truth-value. After all, the beliefs ascribed to Mary by these sentences are different; so if propositions are the objects of belief, the propositions corresponding to the underlined sentences must be different. Nonetheless, both sentences are true.

Is the reverse possible? Can two sentences express the same proposition, but differ in truth-value? It seems not, as can be illustrated again by the role of propositions as the objects of belief. Suppose that you and I believe the exact same thing—both of us believe the world to be just the same way. Can my belief be true, and yours false? Intuitively, it seems not; it seems incoherent to say that we both believe the world to be the same way, but that I get things right and you get them wrong. (Though see the discussion of relativism in §2.3.2 below for a dissenting view.) So it seems that if two sentences express the same proposition, they must have the same truth value.

In general, then, it seems plausible that two sentences with the same content—i.e., which express the same proposition—must always have the same reference, though two expressions with the same reference can differ in content. This is the view stated by the Fregean slogan that sense determines reference (‘sense’ being the conventional translation of Frege’s Sinn, which was his word for what we are calling ‘content’).

If this holds for sentences, does it also hold for subsentential expressions? It seems that it must. Suppose for reductio that two subsentential expressions, e and e*, have the same content but differ in reference. It seems plausible that two sentences which differ only by the substitution of expressions with the same content must have the same content. (While plausible, this principle is not uncontroversial; see compositionality.) But if this is true, then sentences which differ only in the substitution of e and e* would have the same content. But such a pair of sentences could differ in truth-value, since, for any pair of expressions which differ in reference, there is some pair of sentences which differ only by the substitution of those expressions and differ in truth-value. So if there could be a pair of expressions like e and e*, which differ in their reference but not in their content, there could be a pair of sentences which have the same content—which express the same proposition—but differ in truth-value. But this is what we argued above to be impossible; hence there could be no pair of expressions like e and e*, and content must determine reference for subsentential expressions as well as sentences.

This result—that content determines reference—explains one thing we should, plausibly, want a semantic theory to do: it should assign to each expression some value—a content—which determines a reference for that expression.

2.1.4 Character and content, context and circumstance

However, there is an obvious problem with the idea that we can assign a content, in this sense, to all of the expressions of a language like English: many expressions, like ‘I’ or ‘here’, have a different reference when uttered by different speakers in different situations. So we plainly cannot assign to ‘I’ a single content which determines a reference for the expression, since the expression has a different reference in different situations. These ‘situations’ are typically called contexts of utterance, or just contexts, and expressions whose reference depends on the context are called indexicals or context-dependent expressions.

The obvious existence of such expressions shows that a semantic theory must do more than simply assign contents to every expression of the language. Expressions like ‘I’ must also be associated with rules which determine the content of the expression, given a context of utterance. These rules, which are (or determine) functions from contexts to contents, are called characters. (The terminology here, as well as the view of the relationship between context, content, and reference, is due to Kaplan (1989).) So the character of ‘I’ must be some function from contexts to contents which, in a context in which I am the speaker, delivers a content which determines me as reference; in a context in which Barack Obama is the speaker, delivers a content which determines Barack Obama as reference; and so on.

Figure 1.

Here we face another potentially misleading ambiguity in ‘meaning.’ What is the real meaning of an expression—its character, or its content (in the relevant context)? This is an empty terminological question. Expressions have characters which, given a context, determine a content. We can talk about either character or content, and both are important. Nothing is to be gained by arguing that one rather than the other deserves the title of ‘meaning.’ The important thing is to be clear on the distinction, and to see the reasons for thinking that expressions have both a character and (relative to a context) a content.

How many indexical expressions are there? There are some obvious candidates—‘I’, ‘here’, ‘now’, etc.—but beyond the obvious candidates, it is very much a matter of dispute; for discussion, see §2.3.1 below.

But there is a kind of argument which seems to show that almost every expression is an indexical. Consider an expression which does not seem to be context-sensitive, like ‘the second-largest city in the United States.’ This does not seem to be context-sensitive, because it seems to refer to the same city—Los Angeles—whether uttered by me, you, or some other English speaker. But now consider a sentence like

  • (11)100 years ago, the second-largest city in the United States was Chicago.

This sentence is true. But for it to be true, ‘the second-largest city in the United States’ would have to, in (11), refer to Chicago. But then it seems like this expression must be an indexical—its reference must depend on the context of utterance. In (11), the thought goes, the phrase ‘one hundred years ago’ shifts the context: in (11), ‘the second-largest city in the United States’ refers to that city that it would have referred to if uttered one hundred years ago.

However, this can’t be quite right, as is shown by examples like this one:

  • (12)In 100 years, I will not exist.

Let’s suppose that this sentence, as uttered by me, is true. Then, if what we said about (11) was right, it seems that ‘I’ must, in, (12), refer to whoever it would refer to if it were uttered 100 years in the future. So the one thing we know is that (assuming that (12) is true), it does not refer to me—after all, I won’t be around to utter anything. But, plainly, the ‘I’ in (12) does refer to me when this sentence is uttered by me—after all, it is a claim about me. What’s going on here?

What examples like (12) are often taken to show is that the reference of an expression must be relativized, not just to a context of utterance, but also to a circumstance of evaluation—roughly, the possible state of the world relevant to the determination of the truth or falsity of the sentence. In the case of many simple sentences, context and circumstance coincide; details aside, they both just are the state of the world at the time of the utterance, with a designated speaker and place. But sentences like (12) show that they can come apart. Phrases like ‘In 100 years’ shift the circumstance of evaluation—they change the state of the world relevant to the evaluation of the truth or falsity of the sentence—but don’t change the context of utterance. That’s why when I utter (12), ‘I’ refers to me—despite the fact that I won’t exist to utter it in 100 years time.

Figure 2.

This is sometimes called the need for double-indexing semantics—the two indices being contexts of utterance and circumstances of evaluation.

The classic explanation of a double-indexing semantics is Kaplan (1989); another important early discussion is Kamp (1971). For a different interpretation of the framework, see Lewis (1980).

Double-indexing explains how we can regard the reference of ‘the second-largest city in the United States’ in (11) to be Chicago, without taking ‘the second-largest city in the United States’ to be an indexical like ‘I.’ On this view, ‘the second-largest city in the United States’ does not vary in content depending on the context of utterance; rather, the content of this phrase is such that it determines a different reference with respect to different circumstances of evaluation. In particular, it has Los Angeles as its reference with respect to the present state of the actual world, and has Chicago as its reference with respect to the state of actual world 100 years ago, in 1910.[2] Because ‘the second-largest city in the United States’ refers to different things with respect to different circumstances, it is not a rigid designator—these being expressions which (relative to a context of utterance) refer to the same object with respect to every circumstance of evaluation at which that object exists, and never refer to anything else with respect to another circumstance of evaluation. (The term ‘rigid designator’ is due to Kripke (1972).)

(Note that this particular example assumes the highly controversial view that circumstances of evaluation include, not just possible worlds, but also times. For a discussion of different views about the nature of circumstances of evaluation and their motivations, see §2.3.2 below.)

2.1.5 Possible worlds semantics

So we know that expressions are associated with characters, which are functions from contexts to contents; and we know that contents are things which, for each circumstance of evaluation, determine a reference. We can now raise a central question of (propositional) semantic theories: what sorts of things are contents? The foregoing suggests a pleasingly minimalist answer to this question: perhaps, since contents are things which together with circumstances of evaluation determine a reference, contents just are functions from circumstances of evaluation to a reference.

This view sounds abstract but is, in a way, quite intuitive. The idea is that the meaning of an expression is not what the expression stands for in the relevant circumstance, but rather a rule which tells you what the expression would stand for were the world a certain way. So, on this view, the content of an expression like ‘the tallest man in the world’ is not simply the man who happens to be tallest, but rather a function from ways the world might be to men—namely, that function which, for any way the world might be, returns as a referent the tallest man in that world (if there is one, and nothing otherwise). This fits nicely with the intuitive idea that to understand such an expression one needn’t know what the expression actually refers to—after all, one can understand ‘the tallest man’ without knowing who the tallest man is—but must know how to tell what the expression would refer to, given certain information about the world (namely, the heights of all the men in it).

These functions, or rules, are called (following Carnap (1947)) intensions. Possible worlds semantics is the view that contents are intensions (and hence that characters are functions from contexts to intensions, i.e. functions from contexts to functions from circumstances of evaluation to a reference). (‘Intension’ is sometimes used more generally, as a synonym for ‘content.’ This usage is misleading, and the term is better reserved for functions from contexts to referents. It is then controversial whether, as the proponent of possible worlds semantics thinks, contents are intensions.)

Figure 3.

For discussion of the application of the framework of possible world semantics to natural language, see Lewis (1970). The intension of a sentence—i.e., the proposition that sentence expresses, on the present view—will then be a function from worlds to truth-values. In particular, it will be that function which returns the truth-value ‘true’ for every world with respect to which that sentence is true, and ‘false’ otherwise. The intension of a simple predicate like ‘is red’ will be a function from worlds to the function from objects to truth-values which, for each world, determines the truth-value ‘true’ if the thing in question is red, and false otherwise. In effect, possible worlds semantics takes the meanings of expressions to be functions from worlds to the values which would be assigned by a theory of reference to those expressions at the relevant world: in that sense, intensions are a kind of ‘extra layer’ on top of the theory of reference.

This extra layer promises to solve the problem posed by non-extensional contexts, as illustrated by the example of ‘cordate’ and ‘renate’ in (7) and (8). Our worry was that, since these expressions have the same reference, if meaning just is reference, then it seems that any pair of sentences which differ only in the substitution of these expressions must have the same truth-value. But (7) and (8) are such a pair of sentences, and needn’t have the same truth-value. The proponent of possible worlds semantics solves this problem by identifying the meaning of these expressions with their intension rather than their reference, and by pointing out that ‘cordate’ and ‘renate’, while they share a reference, seem to have different intensions. After all, even if in our world every creature with a heart is a creature with a kidney (and vice versa), it seems that the world could have been such that some creatures had a heart but not a kidney. Since with respect to that circumstance of evaluation the terms will differ in reference, their intensions—which are just functions from circumstances of evaluations to referents—must also differ. Hence possible worlds semantics leaves room for (7) and (8) to differ in truth value, as they manifestly can.

The central problem facing possible worlds semantics, however, concerns sentences of the same form as (7) and (8): sentences which ascribe propositional attitudes, like beliefs, to subjects. To see this problem, we can begin by asking: according to possible worlds semantics, what does it take for a pair of sentences to have the same content (i.e., express the same proposition)? Since contents are intensions, and intensions are functions from circumstances of evaluation to referents, it seems that two sentences have the same content, according to possible worlds semantics, if they have the same truth-value with respect to every circumstance of evaluation. In other words, two sentences express the same proposition if and only if it is impossible for them to differ in truth-value.

The problem is that there are sentences which have the same truth-value in every circumstance of evaluation, but seem to differ in meaning. Consider, for example

  • (13)2+2=4.
  • (14)There are infinitely many prime numbers.

(13) and (14) are in a way reminiscent of (5) and (6): the first seems to be a triviality which everyone knows, and the second seems to be a more substantial claim of which one might well be ignorant. However, both are necessary truths: like any truths of mathematics, neither depends on special features of the actual world, but rather both are true with respect to every circumstance of evaluation. Hence (13) and (14) have the same intension and, according to possible worlds semantics, must have the same content.

This is highly counterintuitive. The problem (just as with (5) and (6)) can be sharpened by embedding these sentences in propositional attitude ascriptions:

  • (15)John believes that 2+2=4.
  • (16)John believes that there are infinitely many prime numbers.

As we have just seen, the proponent of possible worlds semantics must take the underlined sentences, (13) and (14), to have the same content; hence the proponent of possible worlds semantics must take (15) and (16) to be a pair of sentences which differ only in the substitution of expressions with the same content. But then it seems that the proponent of possible worlds semantics must take this pair of sentences to express the same proposition, and have the same truth-value; but (15) and (16) (like (7) and (8)) clearly can differ in truth-value, and hence clearly do not express the same proposition.

Indeed, the problem, as shown in Soames (1988), is worse than this. Consider a pair of sentences like

  • (17)Grass is green.
  • (18)Grass is green and there are infinitely many prime numbers.

The second of these is just the first conjoined with a necessary truth; hence the second is true if and only if the first is true. But then they have the same intension and, according to possible worlds semantics, have the same content. Hence the following two sentences cannot differ in truth-value:

  • (19)John believes that grass is green.
  • (20)John believes that grass is green and there are infinitely many prime numbers.

since they differ only by the substitution of (17) and (18), and these are (according to possible worlds semantics) expressions with the same content. Furthermore, it seems that belief distributes over conjunction, in this sense: anyone who believes the conjunction of a pair of propositions must also believe each of those propositions. But then if (20) is true, so must be (16). So it follows that (19) implies (16), and anyone who believes that grass is green must also believe that there are infinitely many primes. This line of argument generalizes to show that anyone who believes any propositions at all must believe every necessary truth. This is, at best, a highly counterintuitive consequence of the possible worlds semanticist’s equation of contents with intensions. All things being equal, it seems that we should seek an approach to semantics which does not have this consequence.

For an attempt to reply to the argument from within the framework of possible worlds semantics, see Stalnaker (1984); for discussion of a related approach to semantics which aims to avoid these problems, see situations in natural language semantics.

2.1.6 Russellian propositions

What we need, then, is an approach to semantics which can explain how sentences like (13) and (14), and hence also (15) and (16), can express different propositions. That is, we need a view of propositions which makes room for the possibility that a pair of sentences can be true in just the same circumstances but nonetheless have genuinely different contents.

A natural thought is that (13) and (14) have different contents because they are about different things; for example, (14) makes a general claim about the set of prime numbers whereas (13) is about the relationship between the numbers 2 and 4. One might want our semantic theory to be sensitive to such differences: to count two sentences as expressing different propositions if they are have different subject matters, in this sense. One way to secure this result is to think of the contents of subsentential expressions as components of the proposition expressed by the sentence as a whole. Differences in the contents of subsentential expressions would then be sufficient for differences in the content of the sentence as a whole; so, for example, since (14) but not (13) contains an expression which refers to prime numbers, these sentences will express different propositions.

Proponents of this sort of view think of propositions as structured: as having constituents which include the meanings of the expressions which make up the sentence expressing the relevant proposition. (See, for more discussion, structured propositions.) One important question for views of this sort is: what does it mean for an abstract object, like a proposition, to be structured, and have constituents? But this question would take us too far afield into metaphysics. (See §2.3.3 below for a brief discussion.) The fundamental semantic question for proponents of this sort of structured proposition view is: what sorts of things are the constituents of propositions?

The answer to this question given by a proponent of Russellian propositions is: objects, properties, relations, and functions. (The view is called ‘Russellianism’ because of its resemblance to the view of content defended in Chapter IV of Russell (1903).) So described, Russellianism is a general view about what sorts of things the constituents of propositions are, and does not carry a commitment to any views about the contents of particular types of expressions. However, most Russellians also endorse a particular view about the contents of proper names which is known as Millianism: the view that the meaning of a simple proper name is the object (if any) for which it stands.

Russellianism has much to be said for it. It not only solves the problems with possible worlds semantics discussed above, but fits well with the intuitive idea that the function of names is to single out objects, and the function of predicates is to (what else?) predicate properties of those objects.

However, Millian-Russellian semantic theories also face some problems. Some of these are metaphysical in nature, and are based on the premise that propositions which have objects among their constituents cannot exist in circumstances in which those objects do not exist. (For discussion, see singular propositions, §§4–5.) Of the semantic objections to Millian-Russellian semantics, two are especially important.

The first of these problems involves the existence of empty names: names which have no referent. It is a commonplace that there are such names; an example is ‘Vulcan,’ the name introduced for the planet between Mercury and the sun which was causing perturbations in the orbit of Mercury. Because the Millian-Russellian says that the content of a name is its referent, the Millian-Russellian seems forced into saying that empty names lack a content. But this is surprising; it seems that we can use empty names in sentences to express propositions and form beliefs about the world. The Millian-Russellian owes some explanation of how this is possible, if such names genuinely lack a content. An excellent discussion of this problem from a Millian point of view is provided in Braun (1993).

Perhaps the most important problem facing Millian-Russellian views, though, is Frege’s puzzle. Consider the sentences

  • (21)Clark Kent is Clark Kent.
  • (22)Clark Kent is Superman.

According to the Millian-Russellian, (21) and (22) differ only in the substitution of expressions with have the same content: after all, ‘Clark Kent’ and ‘Superman’ are proper names which refer to the same object, and the Millian-Russellian holds that the content of a proper name is the object to which that name refers. But this is a surprising result. These sentences seem to differ in meaning, because (21) seems to express a trivial, obvious claim, whereas (22) seems to express a non-trivial, potentially informative claim.

This sort of objection to Millian-Russellian views can (as above) be strengthened by embedding the intuitively different sentences in propositional attitude ascriptions, as follows:

  • (23)Lois believes that Clark Kent is Clark Kent.
  • (24)Lois believes that Clark Kent is Superman.

The problem posed by (23) and (24) for Russellian semantics is analogous to the problem posed by (15) and (16) for possible worlds semantics. Here, as there, we have a pair of belief ascriptions which seem as though they could differ in truth-value despite the fact that these sentences differ only with respect to expressions counted as synonymous by the relevant semantic theory.

Russellians have offered a variety of responses to Frege’s puzzle. Many Russellians think that our intuition that sentences like (23) and (24) can differ in truth-value is based on a mistake. This mistake might be explained at least partly in terms of a confusion between the proposition semantically expressed by a sentence in a context and the propositions speakers would typically use that sentence to pragmatically convey (Salmon 1986; Soames 2002), or in terms of the fact that a single proposition may be believed under several ‘propositional guises’ (again, see Salmon 1986), or in terms of a failure to integrate pieces of information stored using distinct mental representations (Braun and Saul (2002)).[3] Alternatively, a Russellian might try to make room for (23) and (24) to genuinely differ in truth-value by giving up the idea that sentences which differ only in the substitution of proper names with the same content must express the same proposition (Taschek 1995, Fine 2007).

2.1.7 Fregean propositions

However, these are not the only responses to Frege’s puzzle. Just as the Russellian responded to the problem posed by (15) and (16) by holding that two sentences with the same intension can differ in meaning, one might respond to the problem posed by (23) and (24) by holding that two names which refer to the same object can differ in meaning, thus making room for (23) and (24) to differ in truth-value. This is to endorse a Fregean response to Frege’s puzzle, and to abandon the Russellian approach to semantics (or, at least, to abandon Millian-Russellian semantics).

Fregeans, like Russellians, think of the proposition expressed by a sentence as a structured entity with constituents which are the contents of the expressions making up the sentence. But Fregeans, unlike Russellians, do not think of these propositional constituents as the objects, properties, and relations for which these expressions stand; instead, Fregeans think of the contents as modes of presentation, or ways of thinking about, objects, properties, and relations. The standard term for these modes of presentation is sense. (As with ‘intension,’ ‘sense’ is sometimes also used as a synonym for ‘content.’ But, as with ‘intension,’ it avoids confusion to restrict ‘sense’ for ‘content, as construed by Fregean semantics.’ It is then controversial whether there are such things as senses, and whether they are the contents of expressions.) Frege explained his view of senses with an analogy:

The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon itself to the reference; it is the object of the observation, mediated by the real image projected by the object glass in the interior of the telescope, and by the retinal image of the observer. The former I compare to the sense, the latter is like the idea or experience. The optical image in the telescope is indeed one-sided and dependent upon the standpoint of observation; but it is still objective, inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image. (Frege 1892/1960)

Senses are then objective, in that more than one person can express thoughts with a given sense, and correspond many-one to objects. Thus, just as Russellian propositions correspond many-one to intensions, Fregean propositions correspond many-one to Russellian propositions. This is sometimes expressed by the claim that Fregean contents are more fine-grained than Russellian contents (or intensions).

Indeed, we can think of our three propositional semantic theories, along with the theory of reference, as related by this kind of many-one relation, as illustrated by the chart below:

Figure 4.

The principal argument for Fregean semantics (which also motivated Frege himself) is the neat solution the view offers to Frege’s puzzle: the view says that, in cases like (23) and (24) in which there seems to be a difference in content, there really is a difference in content: the names share a reference, but differ in their sense, because they differ in their mode of presentation of their shared reference.

The principal challenge for Fregeanism is the challenge of giving a non-metaphorical explanation of the nature of sense. This is a problem for the Fregean in a way that it is not for the possible worlds semanticist or the Russellian since the Fregean, unlike these two, introduces a new class of entities to serve as meanings of expressions rather than merely appropriating an already recognized sort of entity—like a function, or an object, property, or relation—to serve this purpose.[4]

A first step toward answering this challenge is provided by a criterion for telling when two expressions differ in meaning, which might be stated as follows. In his 1906 paper, ‘A Brief Survey of My Logical Doctrines,’ Frege seems to endorse the following criterion:

Frege’s criterion of difference for senses
Two sentences S and S* differ in sense if and only if some rational agent who understood both could, on reflection, judge that S is true without judging that S* is true.

One worry about this formulation concerns the apparent existence of pairs of sentences, like ‘If Obama exists, then Obama=Obama’ and ‘If McCain exists, McCain=McCain’ which are such that any rational person who understands both will take both to be true. These sentences seem intuitively to differ in content—but this is ruled out by the criterion above. One idea for getting around this problem would be to state our criterion of difference for senses of expressions in terms of differences which result from substituting one expression for another:

Two expressions e and e* differ in sense if and only if there are a pair of sentences, S and S* which (i) differ only in the substitution of e for e* and (ii) are such that some rational agent who understood both could, on reflection, judge that S is true without judging that S* is true.

This version of the criterion has Frege’s formulation as a special case, since sentences are, of course, expressions; and it solves the problem with obvious truths, since it seems that substitution of sentences of this sort can change the truth value of a propositional attitude ascription. Furthermore, the criterion delivers the wanted result that coreferential names like ‘Superman’ and ‘Clark Kent’ differ in sense, since a rational, reflective agent like Lois Lane could think that (21) is true while withholding assent from (22).

But even if this tells us when names differ in sense, it does not quite tell us what the sense of a name is. Here is one initially plausible way of explaining what the sense of a name is. We know that, whatever the content of a name is, it must be something which determines as a reference the object for which the name stands; and we know that, if Fregeanism is true, this must be something other than the object itself. A natural thought, then, is that the content of a name—its sense—is some condition which the referent of the name uniquely satisfies. Coreferential names can differ in sense because there is always more than one condition which a given object uniquely satisfies. (For example, Superman/Clark Kent uniquely satisfies both the condition of being the superhero Lois most admires, and the newspaperman she least admires.) Given this view, it is natural to then hold that names have the same meanings as definite descriptions—phrases of the form ‘the so-and-so.’ After all, phrases of this sort seem to be designed to pick out the unique object, if any, which satisfies the condition following the ‘the.’ (For more discussion, see descriptions.) This Fregean view of names is called Fregean descriptivism.

However, as Saul Kripke argued in Naming and Necessity, Fregean descriptivism faces some serious problems. Here is one of the arguments he gave against the view, which is called the modal argument. Consider a name like ‘Aristotle,’ and suppose for purposes of exposition that the sense I associate with that name is the sense of the definite description ‘the greatest philosopher of antiquity.’ Now consider the following pair of sentences:

  • (25)Necessarily, if Aristotle exists, then Aristotle is Aristotle.
  • (26)Necessarily, if Aristotle exists, then Aristotle is the greatest philosopher of antiquity.

If Fregean descriptivism is true, and ‘the greatest philosopher of antiquity’ is indeed the description I associate with the name ‘Aristotle,’ then it seems that (25) and (26) must be a pair of sentences which differ only via the substitution of expressions (the underlined ones) with the same content. If this is right, then (25) and (26) must express the same proposition, and have the same truth-value. But this seems to be a mistake; while (25) appears to be true (Aristotle could hardly have failed to be himself), (26) appears to be false (perhaps Aristotle could have been a shoemaker rather than a philosopher; or perhaps if Plato had worked a bit harder, he rather than Aristotle could have been the greatest philosopher of antiquity).

Fregean descriptivists have given various replies to Kripke’s modal and other arguments; see especially Plantinga (1978), Dummett (1981), and Sosa (2001). For rejoinders to these Fregean replies, see Soames (1998, 2002) and Caplan (2005). For a brief sketch of Kripke’s other arguments against Fregean descriptivism, see names, §2.4.

Kripke’s arguments provide a strong reason for Fregeans to deny Fregean descriptivism, and hold instead that the senses of proper names are not the senses of any definite description associated with those names by speakers. The main problem for this sort of non-descriptive Fregeanism is to explain what the sense of a name might be such that it can determine the reference of the name, if it is not a condition uniquely satisfied by the reference of the name. Non-descriptive Fregean views are defended in McDowell (1977) and Evans (1981); for a version of the view which gives up the idea that the sense of a name determines its reference, see Chalmers (2004, 2006).

Two other problems for Fregean semantics are worth mentioning. The first calls into question the Fregean’s claim to have provided a plausible solution to Frege’s puzzle. The Fregean resolves instances of Frege’s puzzle by positing differences in sense to explain apparent differences in truth-value. But this sort of solution, if pursued generally, seems to lead to the surprising result that no two expressions can have the same content. For consider a pair of expressions which really do seem to have the same content, like ‘catsup’ and ‘ketchup.’ (The example, as well as the argument to follow, are borrowed from Salmon (1990).) Now consider Bob, a confused condiment user, who thinks that the tasty red substance standardly labeled ‘catsup’ is distinct from the tasty red substance standardly labeled ‘ketchup’, and consider the following pair of sentences:

  • (27)Bob believes that catsup is catsup.
  • (28)Bob believes that catsup is ketchup.

(27) and (28) seem quite a bit like (23) and (24): these each seem to be pairs of sentences which differ in truth-value, despite differing only in the substitution of the underlined expressions. So, for consistency, it seems that the Fregean should explain the apparent difference in truth-value between (27) and (28) in just the way he explains the apparent difference in truth-value between (23) and (24): by positing a difference in meaning between the underlined expressions. But, first, it is hard to see how expressions like ‘catsup’ and ‘ketchup’ could differ in meaning; and, second, it seems that an example of this sort could be generated for any alleged pair of synonymous expressions. (A closely related series of examples is developed in much more detail in Kripke (1979).)

The example of ‘catsup’ and ‘ketchup’ is related to a second worry for the Fregean, which is the reverse of the Fregean’s complaint about Russellian semantics: a plausible case can be made that Frege’s criterion of difference for sense slices contents too finely, and draws distinctions in content where there are none. One way of developing this sort of argument involves (again) propositional attitude ascriptions. It seems plausible that if I utter a sentence like ‘Hammurabi thought that Hesperus was visible only in the morning,’ what I say is true if and only if one of Hammurabi’s thoughts has the same content as does the sentence ‘Hesperus was visible only in the morning,’ as used by me. On a Russellian view, this places a reasonable constraint on the truth of the ascription; it requires only that Hammurabi believe of a certain object that it instantiates the property of being visible in the morning. But on a Fregean view, this sort of view of attitude ascriptions would require that Hammurabi thought of the planet Venus under the same mode of presentation as I attach to the term ‘Hesperus.’ This seems implausible, since it seems that I can truly report Hammurabi’s beliefs without knowing anything about the mode of presentation under which he thought of the planets. (For a recent attempt to develop a Fregean semantics for propositional attitude ascriptions which avoids this sort of problem by integrating aspects of a Russellian semantics, see Chalmers (2011).)

2.2 Non-propositional theories

So, while there are powerful motivations for propositional semantic theories, each theory of this sort also faces some difficult challenges. These challenges have led some to think that the idea behind propositional semantics—the idea that the job of a semantic theory is to systematically pair expressions with the entities which are their meanings—is fundamentally misguided. Wittgenstein was parodying just this idea when he wrote “You say: the point isn’t the word, but its meaning, and you think of the meaning as a thing of the same kind as the word, though also different from the word. Here the word, there the meaning. The money, and the cow that you can buy with it” (§120).

While Wittgenstein himself did not think that systematic theorizing about semantics was possible, this anti-theoretical stance has not been shared by all subsequent philosophers who share his aversion to “meanings as entities.” This section is intended to provide some idea of how semantics might work in a framework which eschews propositions and their constituents, by explaining the basics of two representative theories within this tradition.

The difference between these theories is best explained by recalling the sort of theory of reference sketched in §2.1.1 above. Recall that propositional theories supplement this theory of reference with an extra layer—with a theory which assigns a content, as well as a reference, to each meaningful expression. One alternative to propositional theories—Davidsonian truth-conditional theories—takes this extra layer to be unnecessary, and holds that a theory of reference is all the semantic theory we need. A second, more radical alternative to propositional theories—Chomskyan internalist theories—holds not that a theory of reference is not enough, but rather that it is too much; on this view, the meanings of expressions of a natural language neither are, nor determine, a reference.

2.2.1 The Davidsonian program

One of the most important sources of opposition to the idea of “meanings as entities” is Donald Davidson. Davidson thought that semantic theory should take the form of a theory of truth for the language of the sort which Alfred Tarski showed us how to construct. (See Tarski 1936 and Tarski’s truth definitions.)

For our purposes, it will be convenient to think of a Tarskian truth theory as a variant on the sorts of theories of reference introduced in §2.1.1. Recall that theories of reference of this sort specified, for each proper name in the language, the object to which that name refers, and for every simple predicate in the language, the set of things which satisfy that predicate. If we then consider a sentence which combines a proper name with such a predicate, like

Amelia sings

the theory tells us what it would take for that sentence to be true: it tells us that this sentence is true if and only if the object to which ‘Amelia’ refers is a member of the set of things which satisfy the predicate ‘sings’—i.e., the set of things which sing. So we can think of a full theory of reference for the language as implying, for each sentence of this sort, a T-sentence of the form

“Amelia sings” is T (in the language) if and only if Amelia sings.

Suppose now that we expand our theory of reference so that it implies a T-sentence of this sort for every sentence of the language, rather than just for simple sentences which result from combining a name and a monadic predicate. We would then have a Tarskian truth theory for our language. Tarski’s idea was that such a theory would define a truth predicate (‘T’) for the language; Davidson, by contrast, thought that we find in Tarskian truth theories “the sophisticated and powerful foundation of a competent theory of meaning” (Davidson 1967).

This claim is puzzling: why should a a theory which issues T-sentences, but makes no explicit claims about meaning or content, count as a semantic theory? Davidson’s answer was that knowledge of such a theory would be sufficient to understand the language. If Davidson were right about this, then he would have a plausible argument that a semantic theory could take this form. After all, it is plausible that someone who understands a language knows the meanings of the expressions in the language; so, if knowledge of a Tarskian truth theory for the language were sufficient to understand the language, then knowledge of what that theory says would be sufficient to know all the facts about the meanings of expressions in the language, in which case it seems that the theory would state all the facts about the meanings of expressions in the language.

One advantage of this sort of approach to semantics is its parsimony: it makes no use of the intensions, Russellian propositions, or Fregean senses assigned to expressions by the propositional semantic theories discussed above. Of course, as we saw above, these entities were introduced to provide a satisfactory semantic treatment of various sorts of linguistic constructions, and one might well wonder whether it is possible to provide a Tarskian truth theory of the sort sketched above for a natural language without making use of intensions, Russellian propositions, or Fregean senses. The Davidsonian program obviously requires that we be able to do this, but it is still very much a matter of controversy whether a truth theory of this sort can be constructed. Discussion of this point is beyond the scope of this entry; one good way into this debate is through the debate about whether the Davidsonian program can provide an adequate treatment of propositional attitude ascriptions. See the discussion of the paratactic account and interpreted logical forms in the entry on propositional attitude reports. (For Davidson’s initial treatment of attitude ascriptions, see Davidson (1968); for further discussion see, among other places, Burge 1986; Schiffer 1987; LePore and Loewer 1989; Larson and Ludlow 1993; Soames 2002.)

Let’s set this aside, and assume that a Tarskian truth theory of the relevant sort can be constructed, and ask whether, given this supposition, this sort of theory would provide an adequate semantics. There are two fundamental reasons for thinking that it would not, both of which are ultimately due to Foster (1976). I will follow Larson and Segal (1995) by calling these the extension problem and the informationproblem.

The extension problem stems from the fact that it is not enough for a semantic theory whose theorems are T-sentences to yield true theorems; the T-sentence

“Snow is white” is T in English iff grass is green.

is true, but tells us hardly anything about the meaning of “Snow is white.” Rather, we want a semantic theory to entail, for each sentence of the object language, exactly one interpretive T-sentence: a T-sentence such that the sentence used on its right-hand side gives the meaning of the sentence mentioned on its left-hand side. Our theory must entail at least one such T-sentence for each sentence in the object language because the aim is to give the meaning of each sentence in the language; and it must entail no more than one because, if the theory had as theorems more than one T-sentence for a single sentence S of the object language, an agent who knew all the theorems of the theory would not yet understand S, since such an agent would not know which of the T-sentences which mention S was interpretive.

The problem is that it seems that any theory which implies at least one T-sentence for every sentence of the language will also imply more than one T-sentence for every sentence in the language. For any sentences p,q, if the theory entails a T-sentence

S is T in L iff p,

then, since p is logically equivalent to p & ∼(q & ∼q), the theory will also entail the T-sentence

S is T in L iff p & ∼(q & ∼q),

which, if the first is interpretive, won’t be. But then the theory will entail at least one non-interpretive T-sentence, and someone who knows the theory will not know which of the relevant sentences is interpretive and which not; such a person therefore would not understand the language.

The information problem is that, even if our semantic theory entails all and only interpretive T-sentences, it is not the case that knowledge of what is said by these theorems would suffice for understanding the object language. For, it seems, I can know what is said by a series of interpretive T-sentences without knowing that they are interpretive. I may, for example, know what is said by the interpretive T-sentence

“Londres est jolie” is T in French iff London is pretty

but still not know the meaning of the sentence mentioned on the left-hand side of the T-sentence. The truth of what is said by this sentence, after all, is compatible with the sentence used on the right-hand side being materially equivalent to, but different in meaning from, the sentence mentioned on the left. This seems to indicate that knowing what is said by a truth theory of the relevant kind is not, after all, sufficient for understanding a language. (For replies to these criticisms, see Davidson (1976), Larson and Segal (1995) and Kölbel (2001); for criticism of these replies, see Soames (1992) and Speaks (2006).)

2.2.2 Chomskyan internalist semantics

There is another alternative to propositional semantics which is at least as different from the Davidsonian program as that program is from various propositional views. This view is sometimes called ‘internalist semantics’ by contrast with views which locate the semantic properties of expressions in their relation to elements of the external world. An internalist approach to semantics is associated with the work of Noam Chomsky (see especially Chomsky (2000)).

It is easy to say what this approach to semantics denies. The internalist denies an assumption common to all of the approaches above: the assumption that in giving the content of an expression, we are primarily specifying something about that expression’s relation to things in the world which that expression might be used to say things about. According to the internalist, expressions as such don’t bear any semantically interesting relations to things in the world; names don’t, for example, refer to the objects with which one might take them to be associated. Sentences are not true or false, and do not express propositions which are true or false; the idea that we can understand natural languages using a theory of reference as a guide is mistaken. On this sort of view, we occasionally use sentences to say true or false things about the world, and occasionally use names to refer to things; but this is just one thing we can do with names and sentences, and is not a claim about the meanings of those expressions.

It is more difficult, in a short space, to say what the internalist says the meanings of linguistic expressions are. According to McGilvray (1998), “[t]he basic thesis is that meanings are contents intrinsic to expressions …and that they are defined and individuated by syntax, broadly conceived” (225). This description is sufficient to show the difference between this view of meaning and those sketched above: it is not just that the focus is not on the relationship between certain syntactic items and non-linguistic reality, but that, according to this view, syntactic and semantic properties of expressions are held to be inseparable. McGilvray adds that “[t]his unusual approach to meaning has few contemporary supporters,” which is probably true—though less so now than in 1998, when this was written. For defenses and developments of this view, see McGilvray (1998), Chomsky (2000), and Pietroski (2003, 2005).

2.3 General questions facing semantic theories

As mentioned above, the aim of §2 of this entry is to discuss issues about the form which a semantic theory should take which are at a higher level of abstraction than issues about the correct semantic treatment or particular expression-types. (Also as mentioned above, some of these may be found in the entries on conditionals, descriptions, names, propositional attitude reports, and tense and aspect.) But there are some general issues in semantics which, while more general than questions about how, for example, the semantics of adverbs should go, are largely (though not wholly) orthogonal to the question of whether our semantics should be developed in accordance with a possible worlds, Russellian, Fregean, Davidsonian, or Chomskyan framework. The present subsection introduces a few of these.

2.3.1 How much context-sensitivity?

Above, in §2.1.4, I introduced the idea that some expressions might be context-sensitive, or indexical. Within a propositional semantics, we’d say that these expressions have different contents relative to distinct contexts; but the phenomenon of context-sensitivity is one which any semantic theory must recognize. A very general question which is both highly important and orthogonal to the above distinctions between types of semantic theories is: How much context-sensitivity is there in natural languages?

Virtually everyone recognizes a sort of core group of indexicals, including ‘I’, ‘here’, and ‘now.’ Most also think of demonstratives, like (some uses of) ‘this’ and ‘that’, as indexicals. But whether and how this list should be extended is a matter of controversy. Some popular candidates for inclusion are:

  • devices of quantification
  • gradable adjectives
  • alethic modals, including counterfactual conditionals
  • ‘knows’ and epistemic modals
  • propositional attitude ascriptions
  • ‘good’ and other moral terms

Many philosophers and linguists think that one or more of these categories of expressions are indexicals. Indeed, some think that virtually every natural language expression is context-sensitive.

Questions about context-sensitivity are important, not just for semantics, but for many areas of philosophy. And that is because some of the terms thought to be context-sensitive are terms which play a central role in describing the subject matter of other areas of philosophy.

Perhaps the most prominent example here is the role that the view that ‘knows’ is an indexical has played in recent epistemology. This view is often called ‘contextualism about knowledge’; and in general, the view that some term F is an indexical is often called ‘contextualism about F.’ Contextualism about knowledge is of interest in part because it promises to provide a kind of middle ground between two opposing epistemological positions: the skeptical view that we know hardly anything about our surroundings, and the dogmatist view that we can know that we are not in various Cartesian skeptical scenarios. (So, for example, the dogmatist holds that I can know that I am not a brain in a vat which is, for whatever reason, being made to have the series of experiences subjectively indistinguishable from the experiences I actually have.) Both of these positions can seem unappealing—skepticism because it does seem that I can occasionally know, e.g., that I am sitting down, and dogmatism because it’s hard to see how I can rule out the possibility that I am in a skeptical scenario subjectively indistinguishable from my actual situation.

But the disjunction of these positions can seem, not just unappealing, but inevitable; for the proposition that I am sitting entails that I am not a brain in a vat, and it’s hard to see—presuming that I know that this entailment holds—how I could know the former without thereby being in a position to know the latter. The contextualist about ‘knows’ aims to provide the answer: the extension of ‘knows’ depends on features of the context of utterance. Perhaps—to take one among several possible contextualist views—a pair of a subject and a proposition p will be in the extension of ‘knows’ relative to a context only if that subject is able to rule out every possibility which is both (i) inconsistent with p and (ii) salient in C. The idea is that ‘I know that I am sitting down’ can be true in a normal setting, simply because the possibility that I am a brain in a vat is not normally salient; but typically ‘I know that I am not a brain in a vat’ will be false, since discussion of skeptical scenarios makes them salient, and (if the skeptical scenario is well-designed) I will lack the evidence needed to rule them out. See for discussion, among many other places, the entry on epistemic contextualism, Cohen (1986), DeRose (1992), and Lewis (1996).

Having briefly discussed one important contextualist thesis, let’s return to the general question which faces the semantic theorist, which is: How do we tell when an expression is context-sensitive? Contextualism about knowledge, after all, can hardly get off the ground unless ‘knows’ really is a context-sensitive expression. ‘I’ and ‘here’ wear their context-sensitivity on their sleeves; but ‘knows’ does not. What sort of argument would suffice to show that an expression is an indexical?

Philosophers and linguists disagree about the right answers to this question. The difficulty of coming up with a suitable diagnostic is illustrated by considering one intuitively plausible test, defended in Chapter 7 of Cappelen & LePore (2005). This test says that an expression is an indexical iff it characteristically blocks disquotational reports of what a speaker said in cases in which the original speech and the disquotational report are uttered in contexts which differ with respect to the relevant contextual parameter. (Or, more cautiously, that this test provides evidence that a given expression is, or is not, context-sensitive.)

This test clearly counts obvious indexicals as such. Consider ‘I.’ Suppose that Mary utters

I am hungry.

One sort of disquotational report of Mary’s speech would use the very sentence Mary uttered in the complement of a ‘says’ ascription. So suppose that Sam attempts such a disquotational report of what Mary said, and utters

Mary said that I am hungry.

The report is obviously false; Mary said that Mary is hungry, not that Sam is. The falsity of Sam’s report suggests that ‘I am hungry’ has a different content out of Mary’s mouth than out of Sam’s; and this, in turn, suggests that ‘I’ has a different content when uttered by Mary than when uttered by Sam. Hence, it suggests that ‘I’ is an indexical.

It isn’t just that this test gives the right result in many cases; it’s also that the test fits nicely with the plausible view that an utterance of a sentence of the form ‘A said that S’ in a context C is true iff the content of S in C is the same as the content of what the referent of ‘A’ said (on the relevant occasion).

The interesting uses of this test are not uses which show that ‘I’ is an indexical; we already knew that. The interesting use of this test, as Cappelen and LePore argue, is to show that many of the expressions which have been taken to be indexicals—like the ones on the list given above—are not context-sensitive. For we can apparently employ disquotational reports of the above sort to report utterances using quantifiers, gradable adjectives, modals, ‘knows,’ etc. This test thus apparently shows that no expressions beyond the obvious ones—‘I’, ‘here’, ‘now,’ etc.—are genuinely context-sensitive.

But, as Hawthorne (2006) argues, naive applications of this test seem to lead to unacceptable results. Terms for relative directions, like ‘left’, seem to be almost as obviously context-sensitive as ‘I’; the direction picked out by simple uses of ‘left’ depends on the orientation of the speaker of the context. But we can typically use ‘left’ in disquotational ‘says’ reports of the relevant sort. Suppose, for example, that Mary says

The coffee machine is to the left.

Sam can later truly report Mary’s speech by saying

Mary said that the coffee machine was to the left.

despite the fact that Sam’s orientation in the context of the ascription differs from Mary’s orientation in the context of the reported utterance. Hence our test seems to lead to the absurd result that ‘left’ is not context-sensitive.

One interpretation of this puzzling fact is that our test using disquotational ‘says’ ascriptions is a bit harder to apply than one might have thought. For, to apply it, one needs to be sure that the context of the ascription really does differ from the context of the original utterance in the value of the relevant contextual parameter . And in the case of disquotational reports using ‘left’, one might think that examples like the above show that the relevant contextual parameter is sometimes not the orientation of the speaker, but rather the orientation of the subject of the ascription at the time of the relevant utterance.

This is but one criterion for context-sensitivity. But discussion of this criterion brings out the fact that the reliability of an application of a test for context-sensitivity will in general not be independent of the space of views one might take about the contextual parameters to which a given expression is sensitive. For an illuminating discussion of ways in which we might revise tests for context-sensitivity using disquotational reports which are sensitive to the above data, see Cappelen & Hawthorne (2009). For a critical survey of other proposed tests for context-sensitivity, see Cappelen & LePore (2005), Part I.

2.3.2 How many indices?

Above, in §2.1.5, I introduced the idea of an expression determining a reference, relative to a context, with respect to a particular circumstance of evaluation. But I left the notion of a circumstance of evaluation rather underspecified. One might want to know more about what, exactly, these circumstances of evaluation involve—and hence about what sorts of things the reference of an expression can (once we’ve fixed a context) vary with respect to.

One way to focus this question is to stay at the level of sentences, and imagine that we have fixed on a sentence S, with a certain character, and context C. If sentences express propositions relative to contexts, then S will express some proposition P relative to C. If the determination of reference in general depends not just on character and context, but also on circumstance, then we know that P might have different truth-values relative to different circumstances of evaluation. Our question is: exactly what must we specify in order to determine P’s truth-value?

Let’s say that an index is the sort of thing which, for some proposition P, we must at least sometimes specify in order to determine P’s truth-value. Given this usage, we can think of circumstances of evaluation—the things which play the theoretical role outlined in §2.1.5—as made up of indices.

The most uncontroversial candidate for an index is a world, because most advocates of a propositional semantics think that propositions can have different truth-values with respect to different possible worlds. The main question is whether circumstances of evaluation need contain any indices other than a possible world.

The most popular candidate for a second index is a time. The view that propositions can have different truth-values with respect to different times—and hence that we need a time index—is often called ‘temporalism.’ The negation of temporalism is eternalism.

The motivations for temporalism are both metaphysical and semantic. On the metaphysical side, A-theorists about time (see the entry on time) think that corresponding to predicates like ‘is a child’ are A-series properties which a thing can have at one time, and lack at another time. (Hence, on this view, the property corresponding to ‘is a child’ is not a property like being a child in 2014, since that is a property which a thing has permanently if at all, and hence is a B-series rather than A-series property.) But then it looks like the proposition expressed by ‘Violet is a child’—which predicates this A-series property of Violet—should have different truth-values with respect to different times. And this is enough to motivate the view that we should have an index for a time.

On the semantic side, as Kaplan (1989) notes, friends of the idea that tenses are best modeled as operators have good reason to include a time index in circumstanes of evaluation. After all, operators operate on contents, so if there are temporal operators, they will only be able to affect truth-values if those contents can have different truth-values with respect to different times.

A central challenge for the view that propositions can change truth-value over time is whether the proponent of this view can make sense of retention of propositional attitudes over time. For suppose that I believe in 2014 that Violet is a child. Intuitively, I might hold fixed all of my beliefs about Violet for the next 40 years, without its being true, in 2054, that I have the obviously false belief that Violet is still a child. But the temporalist, who thinks of the proposition that Violet is a child as something which incorporates no reference to a time and changes truth-value over time, seems stuck with this result. Problems of this sort for temporalism are developed in Richard (1981); for a response see Sullivan (2014).

Motivations for eternalism are also both metaphysical and semantic. Those attracted to B-theories of time will take propositions to have their truth-values eternally, which makes inclusion of a time index superfluous. And those who think that tenses are best modeled in terms of quantification over times rather than using tense operators will, similarly, see no use for a time index. For a defense of the quantificational over the operator analysis of tense, see King (2003).

Is there a case to be made for including any indices other than a world and a time? There is; and this has spurred much of the recent interest in relativist semantic theories. Relativist semantic theories hold that our indices should include not just a world and (perhaps) a time, but also a context of assessment. Just as propositions can have different truth values with respect to different worlds, so, on this view, they can vary in their truth depending upon features of the conversational setting in which they are considered. (Though this way of putting things assumes that the relativist should be a ‘truth relativist’ rather than a ‘content relativist’; I ignore this in what follows. See for discussion Weatherson and Egan (2011), § 2.3.)

The motivations for this sort of view can be illustrated by a type of example whose importance is emphasized in Egan et. al. (2005). Suppose that, at the beginning of a murder investigation inquiry, I say

The murderer might have been on campus at midnight.

It looks like the proposition expressed by this sentence will be true, roughly, if we don’t know anything which rules out the murderer having been on campus at midnight. But now suppose that more information comes in, some of which rules out the murderer having been on campus at midnight. At this point, it seems, I could truly say

What I said was false—the murderer couldn’t have been on campus at midnight.

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