contexts in formal semantics

Contexts in Formal Semantics

Christopher Gauker*University of Cincinnati

Abstract

Recent philosophical literature has debated the question of how much context-relativity needs tobe countenanced in precise semantic theories for natural languages and has displayed different con-ceptions of the way in which it might be accommodated. This article presents reasons to thinkthat context-relativity is a phenomenon that semantic theory must accommodate and identifiessome of the issues concerning how it ought to be accommodated.

In many ways, the truth values of sentences may vary with the contexts in which theyare uttered. For instance, ‘Everyone is present’ may be true in a context in which every-one who matters is present, even if not everyone in the universe is present. ‘Dumbo issmall’ might be true in a context in which the relevant standard is the average size ofelephants but false in a context in which the relevant standard is the average sizeof animals in the zoo. The purpose of this article is, first, to explain why these kinds ofcontext-relativity are matters that a formal semantic theory of natural language needs toattend to, and, second, to review some of the issues that arise in attending to them. Forinstance, should we think of contexts as abstract structures of some kind or as concretesituations? And should we think of the context that pertains to an utterance as deter-mined by the speaker’s intentions or in some other way? For each such question, I willbriefly, not conclusively, defend one sort of answer over others.

1. Some Candidate Context-Relativities

I begin with some representative examples of the kinds of context-relativities that seman-tics might potentially have to deal with. Prospectively, I will call these semantics-involvingcontext-relativities to distinguish them from other ways in which the interpretation of aspeaker’s act of speech may depend on features of the situation in which he or shespeaks.

Demonstratives: Relative to one context, ‘that’ may refer to the Matterhorn; relative toa different context, ‘that’ might refer to a cucumber.Indexicals: Relative to a context in which I am the speaker, ‘I’ will refer to me;whereas relative to a context in which you are the speaker, ‘I’ will refer to you.Quantifiers: Relative to a context in which the domain of discourse is the pieces of fur-niture for sale in a certain shop, ‘Everything is made of wood’ might be true, whereasin other domains it might be false.Modalities: The truth of ‘Holmes might be in Paris’ is relative to a contextually deter-mined domain of possibilities.Gradable adjectives: The truth of ‘Dumbo is small’ is relative to a contextually deter-mined standard, such as the average size of elephants.

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Incomplete adjectives: The truth of ‘Tipper is ready’ is relative to a contextually deter-mined specification of an activity, such as going to the convention center, for whichTipper might or might not be ready.Discourse particles: The truth of ‘Dennis too is having dinner in London tonight’ dependson whether for some x „ Dennis in a contextually determined set of people, theproposition that x is having dinner in London tonight belongs to a contextually deter-mined set of presuppositions.Possessives: Whether ‘Sandra is in her car’ is true depends on whether Sandra stands inthe contextually determined relation of possession, which could be, for example, own-ing, or renting, or borrowing for the day.

Despite this variety, it is not the case that whenever a speaker’s meaning can be said to‘depend on the context’ that is a kind of semantics-involving context-relativity. Forexample, conversational implicature falls outside the realm of semantic context-relativities. Aspeaker who utters the sentence, ‘There’s a gas station around the corner’ might therebyconversationally imply that the gas station is open and has gas to sell, although the speaker’swords do not mean that. A case of conversational implicature is a case in which a speakerin some sense means more by what he or she says than what his or her words literallymean in context, whereas the context-relativities that a semantic theory has to contendwith are only those that have a place somewhere in an account of what the speaker’swords literally mean in context. (See Grice, Levinson, and Gauker for several points ofview on conversational implicature.)

Further, the resolution of ambiguity is often thought of not as a matter of choosing aninterpretation of a given form of words but as a matter of determining which words orsentences have been used (even if that decision has to be made in light of potential inter-pretations). So when we decide that a speaker who says ‘bank’ meant financial institution,not embankment on a body of water, that decision is construed as a decision concerningwhich of two same-sounding words the speaker spoke. And when we decide that some-one who says ‘Every member of congress did not support the President’ meant that notevery member of congress supported the President and did not mean that no member of congresssupported the President, that decision is construed as a question concerning which sentencethe speaker actually spoke, not a question of how the interpretation of the speaker’s sen-tence depends on the context.

2. The Need for Contexts in Formal Semantics

Not everyone agrees that semantics ought to deal with everything that I have calleda ‘semantics-involving context-relativity’. Advocates of what is called minimalism insemantics (Borg; Cappelen and Lepore) argue that the kinds of context-relativity thathave to be accommodated in a precise semantic theory are strictly limited. According tothe minimalist, instead of countenancing many context-dependent aspects of semanticinterpretation, we can suppose that a sentence merely expresses a minimal propositioninstead. For instance, the sentence ‘Tipper is ready’ expresses the minimal proposition thatTipper is ready (Cappelen and Lepore), or is true, as uttered in a context, if and only ifTipper is ready for something in that context (Borg). If it seems to us that a semantictheory ought to ascribe something more to a sentence in context, then that is because weare confusing the proposition semantically expressed by the sentence in context with thecontent of the various speech acts that a speaker might perform by means of utteringthe sentence.

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Other theorists, whom I will call partialists (Recanati; Bach; Carston), avoid semantics-involving context-relativities not by positing minimal propositions or truth conditions butby denying that utterances typically express complete propositions. According to thesetheorists, a semantic theory cannot be expected to determine for each sentence, togetherwith a contextually determined interpretation of certain elements, a complete proposition.What semantics assigns to many sentences is only a proposition radical (Bach) or linguisticallyencoded meaning (Carston). To identify the proposition that a speaker expresses on anygiven occasion of utterance we have to look to features of the situation in which thespeaker spoke. The ways in which the sentence and the speaker’s situation determine acomplete proposition go well beyond anything that semantics will deal with.

There are at least two good reasons to think that, contrary to both the minimalists andthe partialists, the range of semantics-involving context-relativities is rather broad. Thefirst of these has to do with logic. Whatever else we expect from a semantic theory, weexpect it to explicate the logical relations between sentences. Many of the purportedlysemantics-involving context-relativities in the list in Section 1 do seem to have a bearingon the logical properties of sentences.

For example, ‘The moon is not made of wood’ logically implies ‘Something is notmade of wood’, but ‘Everything is made of wood’ seems not to imply ‘The moon ismade of wood’, because everything in the contextually determined domain of discoursemight be made of wood, although the moon is not in that domain (see my paper on thisin Erkenntnis). For another example, ‘Tipper is not ready’ seems to imply ‘There is some-thing that Tipper is not ready for’, but ‘Tipper is ready for something’ arguably does notimply ‘Tipper is ready’, because Tipper might be ready for something without beingready for the contextually specified activity (see my paper on this forthcoming in Nous).For yet another example, the sentence, ‘Tiny is big, Dumbo is small, and Dumbo is big-ger than Tiny’ would seem to be contradictory, true in no single context, because forany contextually specified standard, nothing big can be smaller than anything small.

It is hard to see how minimalists can account for such facts, since their best candidatesfor the minimal propositions expressed do not seem to corroborate such observations (asMontminy, MacFarlane, Kissine, and I, in my paper in Nous, have all observed). As forthe partialists, it is hard to see how they can countenance logical relations betweensentences at all, since they think that many sentences do not express propositions relativeto any context. One can imagine various answers on their behalf (that logic deals withpropositions, not sentences, that logic deals with sentence forms not propositionsexpressed, that logic deals with what follows no matter how the partial propositionexpressed is completed), but they have not addressed the issue themselves in print. Incontrast, a semantics that explicitly relativizes sentence truth to context might in principleaccount for such logical properties by identifying a class of arguments that are valid in thesense that for every context in which the premises are true, the conclusion is true andidentifying a class of sentences that are contradictory in the sense that there is no singlecontext in which they are true.

The other reason to hold that the range of semantics-involving context-relativities isbroad has to do with what we might call relations of paraphrase, although there has been lit-tle study of this. Suppose that in a certain situation, a speaker A utters a sentence p. Lateron, in a different situation, another person B may want to utter a sentence q that ‘says’what A ‘said’ in A’s situation. What we expect of B’s sentence q may not be so little as thatit be the same as A’s sentence p, but we may also not expect so much as that it be anexpression of everything A meant by what he or she said. We expect it to be an equivalentparaphrase adjusted to accommodate the differences between the context that pertains to

570 Contexts in Formal Semantics


A’s utterance and the context that pertains to B’s utterance. For example, if p was ‘Every-thing is made of wood’, q may be ‘Everything in the shop was made of wood’. If p was‘Tipper is ready’, q may be ‘Tipper was ready for dinner’. It is hard to see how minimalistsor partialists might account for such facts. In contrast, from a theory of semantics-involvingcontext-relativities we can expect an account of what q has to be, or can be, given p, thecontext pertinent to A’s utterance and the context pertinent to B’s utterance.

3. Absolute Truth for Utterances or Context-Relative Truth for Sentences?

It is often supposed that explicit relativization of truth to context can be avoided insemantic theory by taking truth to be a property of particular utterances. Thus, one mightpropose semantic theses along the following lines:

(1) If in an utterance u of ‘This is nice’, the utterance of ‘this’ refers to x, then u istrue if and only if x is nice.

(2) If in an utterance u of ‘Dumbo is small’, the utterance of ‘small’ refers to things thatare smaller than standard s, then u is true if and only if Dumbo is smaller than s.

Statements along these lines can be found in works by Weinstein, Higginbotham, Larsonand Segal, Gross, Borg (2004, p. 165), and Lepore and Ludwig (p. 116).

However, this strategy does not ultimately obviate the need to treat truth as a relationbetween sentences and contexts. Since a theory should be something one can actuallystate, a semantic theory for a language, regardless of the form of the theory, should besomething that in principle we could write out completely, although it might fill amultivolume encyclopedia. Consequently, we cannot require a separate statement of truthconditions for each of the infinitely many sentences of the language. Rather, the truthconditions of, for example, negations ought to follow from a general thesis about allnegations and theses about the sentences negated. For example, (3), below, should be aconsequence of (1) and something like (4):

(3) If in an utterance u of ‘This is not nice’, the utterance of ‘this’ refers to x, then u istrue if and only if x is not nice.

(4) If u is an utterance of a sentence s and v is an utterance of the negation of s, then vis true if and only if u is not true.

The trouble is that thesis (4) tells us the truth conditions of a negation only on the condi-tion that the sentence negated has been uttered. But it is not in general true that all of thecomponents of an utterance in terms of which we need to define its truth value havebeen uttered. It might happen that ‘This is not nice’ has been uttered, but ‘This is nice’has never been uttered. Even if ‘This is nice’ has been uttered, the utterance of ‘this’ inthat utterance may not refer to the same thing as the utterance of ‘this’ in the utteranceof ‘This is not nice’, in which case (4) may be false. Even if there is a sense in which inuttering a negation one also utters the sentence negated, it is certainly not the case that inuttering a universal quantification one utters every instance; so we will still have aproblem of this sort when we go to write the general thesis about the truth conditions ofuniversal quantifications.

Accordingly, at least some of the authors who have proposed theses like (1) and (2)have recognized that such theses have to be consequences of a recursive definition ofsentence-truth relative to a context. Thus, instead of (1) and (4), we might have:



(1¢) The sentence ‘This is nice’ is true relative to context c if and only if for some x‘this’ refers to x in c and x is nice.

(4¢) If r is the negation of sentence s, then r is true in context c if and only if s is nottrue in c.

Since sentences, unlike utterances, are abstract entities, there is no doubt that if the nega-tion of a sentence exists then so does the sentence negated. From (1¢) and (4¢), we canderive the truth-in-a-context conditions of the sentence ‘This is not nice’. Moreover, asLarson and Segal (208–9) show, we can derive (1) from (1¢) if we add, first, that if anutterance t of ‘this’ is part of an utterance u of ‘This is nice’, then the context that per-tains to u is the context that pertains to t, and, second, that if a context c pertains to theutterance u of an expression e, then the value of u equals the value of e in c. (There is asimilar derivation in Weinstein.) Inasmuch as one popular attempt to detour around therelativization of sentence truth to context leads us straight back to it, we might begin tofeel that the relativization to context is inevitable.

4. What is a Context?

The conception of contexts in David Kaplan’s classic paper, ‘Demonstratives’, inspires amore capacious conception that might be suitable for our purposes. For Kaplan, contextsare structures that assign values to a variety of contextually variable parameters. Kaplanconceived of contexts as affecting only the interpretation of indexicals and demonstratives,but we can extend his conception by allowing contexts to contain some kind of structurefor each kind of context-relativity that we want to accommodate. For example, toaccommodate the context-relativity of quantifications, we might build into a context acontextually determined domain of quantification.

Some philosophers have thought that we could dispense with most of the complexityin a Kaplan-style context by simply identifying contexts with the situations in which anutterance takes place. For instance, in a paper from 1980, David Lewis identifies contextswith spatio-temporal locations in a possible world. Their assumption is that such things asthe referents of demonstratives, domains of discourse, and so forth, can all be recognizedas features of a particular situation. The trouble with this identification of contexts withsituations is that it stands in the way of our aspirations for logic. As I pointed out in Sec-tion 1, we may take an interest in the class of arguments that are valid in the sense thatfor every context in which the premises are true, the conclusion is true. But to identifythis class of arguments, we have to be able to define the class of contexts in a generalway, as all set-theoretic structures (built up from certain non-set atoms) meeting certainconditions, and our definition has to build enough structure into contexts to allow us toprove, in the case of the valid arguments, that if the premises are all true in an arbitrarilychosen context, then so is the conclusion. Further, we should be able to demonstrate thatan argument is not valid by actually specifying a context in which the premise is true andthe conclusion is not. For example, we should be able to show that ‘Everything is madeof wood; therefore, the moon is made of wood’ is not valid by specifying a context inwhich the domain of discourse consists of things made of wood and excludes the moon.So a context will have to be a structure containing one of each of the sorts of things wemight have to specify in demonstrating that an argument is not valid.

Another conception of context, due to Robert Stalnaker, also provides a structure tocontexts. Stalnaker holds that a context can be identified with a set of propositions,which we may think of as the common ground between the interlocutors. But a context



of Stalnaker’s kind will do the requisite job for logic only if it in effect specifies the valuesof various parameters in just the way a Kaplanian context does. What Stalnaker adds toKaplan’s conception, in thinking of the context as the common ground, is a thesis con-cerning the determinants of context, which is the topic I turn to next.

5. What Determines which Context Pertains to an Utterance?

Given that contexts are to be conceived, for purposes of formal semantics, as structuresspecifying the values of various parameters, contexts are, strictly speaking, entities of a dif-ferent kind from the concrete situations in which speakers speak. Nonetheless, there willbe an important relation between contexts and such situations. An utterance u of a sen-tence s will be true (absolutely) if and only if s is true relative to the context that pertainsto u. More generally, an utterance u of an expression will have a value v if and only if ehas value v relative to the context that pertains to u. Presumably, it is something about thesituation in which an utterance takes place that determines which context is the contextthat pertains to the utterance. So we may ask: What is it about the situation in which anutterance takes place that does that? (If one prefers to use ‘context’ for what I am callingsituations, then one could use ‘index’ for what I am calling context, as does Predelli.)

It is commonly assumed (for instance, by King and Stanley) that something about aspeaker’s intention is what determines which context pertains to a given utterance. Forsome expressions, there may be conventional constraints on what the contextually deter-mined referent can be. For instance, ‘now’ may typically have to refer to the time ofutterance, and ‘that cat’ may have to refer to some cat or other. But among the possibili-ties left open by such constraints, it is the speaker’s intention that is supposed to be deter-minative. For instance, an utterance of the bare demonstrative ‘that’ refers to whateverthe speaker intends it to refer to. That is just what Stalnaker’s conception of the contextas common ground tells us about demonstratives as well in light of his account of whatmakes it the case that a proposition concerning the referent of a demonstrative belongs tothe common ground (pp. 109–10). There are several reasons to question this consensus.

First, it is not very obvious how we should characterize the pertinent intentions. Itwould be question-begging to say that a demonstrative refers to the object that thespeaker intends it to refer to. In the case of demonstratives, we could say instead that ademonstrative refers to that to which the speaker intends to draw the hearer’s attention. Buthow are we to identify a domain of discourse in terms of the speaker’s intention? Itwould be question-begging to say that the domain of discourse for an utterance of aquantified sentence is the set of things that the speaker intends to be the domain of discoursefor the utterance. We could say without circularity that the domain of discourse is the setof things that the speaker intends the hearer to think of. But that seems insufficient. Thedomain is not just any set the speaker intends the hearer to think of; it is specifically thatset that the speaker intends the hearer to think of as the domain of discourse. But thatanswer takes us back to the question: What does it mean for something to be the domainof discourse for an utterance?

Moreover, we cannot expect people to be mind-readers. For the most part, we knowvery little about what other people are thinking apart from our interpretation of whatthey say. How, in particular, could a hearer know what a speaker intended to draw thehearer’s attention to in uttering ‘that’? One way would be for the hearer to discover,independently of the speaker’s intention, what ‘that’ refers to and then make the reason-able assumption that the speaker intended it to refer to that to which it did refer. But ifthat is our answer, then we have to suppose that something other than the speaker’s



intention determines the reference of ‘that’. Alternatively, we might suppose that a hearerfirst obtains as much of an interpretation of a speaker’s words as he or she can obtainwithout identifying the context and then uses that much of his or her interpretation toidentify the speaker’s intention. But it is not clear that the aspects of interpretation thatcan be achieved apart from the pertinent context (in my sense) will be sufficient to enablethe hearer to discern the speaker’s intention.

Finally, it is hard to see how it could be the speaker’s intention that determines thecontext pertinent to an utterance if mental representations exhibit the same kind of con-text-relativity that we find in spoken language. In fact, there are good reasons to supposethat the truth value of a token mental representation depends on which context pertainsto it in just the way that the truth value of a spoken utterance of a sentence does. Butwe cannot, without regress, maintain that the context that pertains to a token mentalrepresentation is determined by an underlying intention in the speaker. So since some-thing other than speaker’s intention determines the context pertinent to a token mentalrepresentation, we may expect that that same sort of thing, whatever it is, will determinethe context pertinent to a spoken utterance of a sentence. (For further exposition of thisissue, see chapter 4 of my book, Words without Meaning.)

The alternative to the supposition that the speaker’s intention determines the contextpertinent to the speaker’s utterance is to suppose that there are objective features of theenvironment in which the utterance occurs that determines the pertinent context. Theterm ‘salient’ is often used to describe the features of a situation that determine the con-text, but that is not a very helpful description, since the pertinent features of a situationmay not be the most salient in any plain and literal sense. Nonetheless, there are manyother features of a situation that we might in principle appeal to: Pointing and gestures,parallel syntactic structures, the relevance, in various senses, of the elements of the situa-tion, and the reasonableness of what we would interpret a speaker as saying. Still, therewill not be any algorithm for identifying the context based on these factors, and so wemay have to acknowledge that the context that pertains to an utterance is the object ofsome kind of all-things-considered judgment. (For further discussion of these issues, seemy paper in Synthese.)

6. Do Contexts Only Make Assignments?

Jason Stanley has claimed that the role of a context in the interpretation of a sentence isexclusively to assign some kind of value to a lexical item in the sentence. If no suitablelexical item appears in a sentence as spoken, then we have to suppose that there is a suit-able lexical item in the explicit representation of the grammatical structure that in somesense underlies the sentence spoken. For instance, what the sentence ‘Every girl answeredevery question’ means in context might be that each girl x in Mrs Kaplinger’s class answeredevery question on x’s exam. To get this reading, according to Stanley, we have to supposethat the lexical constituency of this sentence is something like ‘For every j in Ægirl, f(i)æ,for every k in Æquestion, g(j)æ, j answered k’. To generate the desired reading, what con-text assigns to ‘i’ might be Mrs Kaplinger, what context assigns to ‘f’ might be a functionthat takes Mrs Kaplinger into the set of students in Mrs Kaplinger’s class, and what con-text assigns to ‘g’ might be a function that takes each student in Mrs Kaplinger’s class intothe set of questions on that student’s exam. The expression ‘Ægirl, f(i)æ’ denotes the inter-section of the set of girls (all girls anywhere) with the set thus assigned to ‘f(i)’, and, foreach j, ‘Æquestion, g(j)æ’ denotes the intersection of the set of all questions with the set ofitems obtained by applying g to j.



To see that there might be a problem with Stanley’s philosophy of context-relativity,consider the following sentence:

(5) He is happy and he is not happy.

It is plausible that (5) is consistent in the sense that there is a single context in which it istrue. One way to allow that (5) might be true in some context is to suppose that the firstoccurrence of ‘he’ in this sentence is actually a different lexical item from the secondoccurrence (although it is the same word). Thus, we may make the lexical constituency of(5) more explicit by writing:

(5¢) He1 is happy and he2 is not happy.

The reason (5¢) may be true in a single context is that a single context may assign a happyperson to ‘he1’ and an unhappy person to ‘he2’. It is plausible that a context can assigndifferent people to different occurrences of ‘he’ in a single context because there arewell-recognized, conventional means by which speakers can indicate how the differentoccurrences are to be interpreted. For instance, as the speaker utters ‘he1’, she can pointto its referent, and as she utters ‘he2’, she can point to its different referent, or the speakercan expect the first ‘he’ to pick up the reference of the first of two earlier noun phrasesand the second ‘he’ to pick up the reference of the second of the two.

But now compare the following sentence:

(6) Every student is happy and some student is not happy.

On Stanley’s theory, the lexical constituency of (6) may be represented somewhat as fol-lows:

(6¢) Every Æstudent, f(i)æ is happy and some Æstudent, g(j)æ is not happy.

Thus, the sentence may be true in a context that assigns different sets to ‘f(i)’ and ‘g(j)’.The problem with that conclusion is that in fact it is not very plausible that (6) is true

in some single context (as I have argued in a paper forthcoming in the Journal of Seman-tics). The indexical expressions in (6¢) are not actually spoken; so the speaker cannot drawthe hearer’s attention to them; and most people will not even be aware of their existence.More generally, setting aside the details of Stanley’s representation, one cannot by con-ventional means indicate distinct domains associated with the first occurrence of ‘student’and the second occurrence of ‘student’. Certainly, we can imagine a situation in which aspeaker utters (6) and thereby communicates something true. A principal in a schoolmight utter the first half of (6) while gesturing toward a classroom on one side of the halland utter the second half of (6) while gesturing toward a classroom on the other side ofthe hall. Nonetheless, we do not have to agree that the sentence (6) is true relative to asingle context that pertains to her entire utterance. The answer to the example of theprincipal is not to say that the context shifts between the utterance of the first conjunctand the utterance of the second; our theory of the pertaining relation between contextsand situations will probably not allow contexts to shift at will in this way. But what wecan say is that, even if the principal’s utterance is false, a hearer might manage to figureout that what the principal has in mind is something true, such as that every student inthis classroom is happy and some student in that classroom is not happy.



If Stanley’s philosophy of context-relativity may be rejected on such grounds, thenperhaps we do not have to think of each element of the context as assigned to some lexi-cal item in the logical structure of the sentence. Rather, we may simply think of eachelement of the context as an entity to which we make some reference in a recursivespecification of the truth-in-a-context conditions. For instance, the clause for quantifierswill make reference to a contextually determined domain.

7. A Semantics for Context-Relativity will be Three-Valued

In light of context-relativity we seem to obtain various counterexamples to the principleof contraposition, according to which p implies q if and only if the negation of q impliesthe negation of p. For example, the argument ‘The moon is not made of wood; there-fore, something is not made of wood’ is valid, but ‘Everything is made of wood;therefore, the moon is made of wood’ is not. Likewise, ‘Tipper is not ready; therefore,there is something that Tipper is not ready for’ is valid, whereas ‘Tipper is ready forsomething; therefore, Tipper is ready’ appears not to be. (For an example resting on thecontext-relativity of conditionals, see my book, Conditionals in Context, pp. 62–3.)

The principle of contraposition inevitably holds in a bivalent semantics. Any counter-example to the argument from p to q will likewise be a counterexample to the argumentfrom not-q to not-p. But the principle of contraposition may fail in a three-valued seman-tics. The argument from p to q may fail, because p may be true in some context whereasq is neither true nor false in that context; and yet the argument from not-q to not-p maybe valid nonetheless, because the case in which not-q is neither true nor false in a contextand not-p is false in that context is no counterexample. Thus, these failures of contraposi-tion indicate that a semantic theory allowing context-relativity must be a three-valuedsemantics. Relative to a context, a sentence may be either true, false or neither. In a con-text in which ‘Everything is made of wood’ is true, still ‘The moon is made of wood’may be neither true nor false, perhaps because the moon is an irrelevant object in the sit-uation to which the context pertains. It may be surprising to hear that ‘The moon ismade of wood’ may not be false in some contexts, but that just goes to show that truth-in-a-context and falsehood-in-a-context are not to be equated with absolute truth andfalsehood.

8. Are Contexts Too Complex?

A possible objection to the conception of contexts that I have developed here is that itmakes contexts too complex. (Lewis objects to a similar conception on those grounds.)There are many kinds of context-relativity, and on the present conception we will haveto build into each context something for each of them. Moreover, for each kind of con-text-relativity there will be many expressions that are subject to that kind of relativity.There are many incomplete adjectives, many gradable adjectives, and, if we have to countdemonstratives as I proposed in Section 6, then we may have to countenance infinitelymany of them.

Part of the answer may be that the contexts that pertain to many utterances may simplyleave many variables unevaluated. Although there are infinitely many demonstratives, acontext may assign nothing to all but a few. A context pertaining to a conversation inwhich the sizes of things will not be at issue need not assign any standard to ‘small’.

But part of the answer also is what I said in Section 5 about the determinants of thepertinent context. So long as we imagine that the context pertinent to an utterance has



to be determined by a speaker’s state of mind, it may seem implausible that a contextcould address all of the context-relativities that matter in a given conversation. But if thecontext that pertains to an utterance is, broadly speaking, a matter of what is objectivelyrelevant, then we may suppose that the values of many variables are determined by whatis objectively relevant quite apart from whether any interlocutor has the values of thosevariables in mind.

Acknowledgements

The author thanks Michael Glanzberg, Kent Bach and an anonymous referee for veryuseful comments on earlier drafts of this article. During its composition, the author wassupported by a grant from the Taft Research Center of the University of Cincinnati.

Short Biography

Christopher Gauker works in both the philosophy of mind and the philosophy of lan-guage. He is skeptical about conceptions of linguistic communication that explicate it asthe expression of mental states, and about semantic theories formulated in terms of theconcept of reference. He aims to develop an alternative conception of communicationand semantics that treats language as fundamentally a tool by which people coordinatetheir activities.

Note

* Correspondence: Department of Philosophy, University of Cincinnati, Cincinnati, OH 45221-0374, USA.Email: [email protected].

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