Vague Terms, Indexicals, and Vague Indexicals

Vague Terms, Indexicals, and Vague IndexicalsAuthor(s): Joshua GertSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 140, No. 3 (Sep., 2008), pp. 437-445Published by: SpringerStable URL: http://www.jstor.org/stable/27734307 .

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Philos Stud (2008) 140:437-445

DOI 10.1007/s 11098-007-9154-4

Vague terms, indexicals, and vague indexicals

Joshua Gert

Published online: 5 September 2007

? Springer Science+Business Media B.V. 2007

Abstract Jason Stanley has criticized a contextualist solution to the sorites par adox that treats vagueness as a kind of indexicality. His objection rests on a feature

of indexicals that seems plausible: that their reference remains fixed in verb phrase

ellipsis. But the force of Stanley's criticism depends on the undefended assumption that vague terms, if they are a special sort of indexical, must function in the same

way that more paradigmatic indexicals do. This paper argues that there can be more

than one sort of indexicality, that one term might easily have both sorts, and that

therefore, and despite Stanley's worries, vagueness might easily be assimilated to

one form.

Keywords Vagueness Sorites Indexicality Contextualism

Jason Stanley (2003) has criticized one kind of contextualist solution to the sorites

paradox. The paradox, in one standard sort of incarnation, depends on the apparent

undeniability of premises of the form 'If thatn is a heap, then thatn+1 is also', where

the subscripts indicate that the demonstrative is being used to pick out, respectively, two adjacent collections of grains of sand, and where each collection in the

sequence has one less grain than the last. If 'that]' indicates a collection that is

clearly large enough to count as a heap, and if our sequence is long enough to reach a collection with, say, only one grain, then we seem forced, by an unobjectionable

series of inferences, to the false conclusion that a lone grain of sand makes a heap. One kind of contextualist solution to this paradox depends on the following two

ideas. First: vague terms, such as 'heap', function like indexicals in that their

J. Gert (S) Florida State University, Tallahassee, FL 32306, USA

e-mail: [email protected]

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438 J. Gert

content, on particular occasions of use, is determined by features of the context.1 Second: when we consider two similar objects (here, collections of grains of sand), and the question of whether or not the vague predicate applies to them, this very process of consideration itself affects a relevant feature of the context. The particular contextual feature of relevance is a state of the speaker: a disposition to classify objects in terms of the predicate. Consideration of two adjacent members of a sorites

series affects this contextual feature as the result of a kind of pressure or tendency to

apply the same predicate to both members of the series, given how similar they are. A

consequence of these two ideas is that when we consider any two adjacent collections

of grains of sand, the semantics of the vague term 'heap' interacts with the context to

make the relevant conditional ('If thatn is a heap, then thatn+1 is also') true. This results in a subtle equivocation as we consider distinct conditionals in a long sorites

argument, and this subtle equivocation?so says the contextualist?saves us from

having to say that a valid argument leads from truth to falsity.2 Stanley's worry about this kind of solution to the sorites paradox depends

essentially on the following 'fact about indexical expressions': they have invariant

interpretations in Verb Phrase ellipsis.3 Consider the sentence: 'John likes this room, and Bill does too'. Here the Verb Phrase in the second clause is elided. It corresponds to the explicit Verb Phrase 'likes this room' in the first clause. Now, suppose that I utter the first part of the sentence in the dining room, and Victoria (overhearing what I've said and shouting from the kitchen) adds the second part. Victoria's addition

would not indicate that Bill likes the kitchen, as it would have had she not elided the Verb Phrase. Rather, because of the ellipsis, Victoria's addition indicates that Bill also likes the room that / referred to: the dining room. The elided indexical phrase 'this room' has the same content in the elided Verb Phrase as it had in the unelided

Verb Phrase. The problem for the contextualist can then be made vivid with a one sentence version of the paradox of the heap: 'If thati is a heap then so is that2, and if

that2 is, so is that3, and if that3 is, so is that4...'. For if Stanley's 'fact about indexical

expressions' is really a fact, then all the occurrences of 'so is' in this long sentence

should have the same content: 'is a heap', where 'heap' has the content of its first actual (i.e. non-elliptical) occurrence. That is, Stanley's 'fact' precludes the shifting content strategy from being applicable, since it is, in essence, a stipulation that content does not shift. And, since Stanley is surely right that the one-sentence version of this sorites paradox does not differ in the source of its plausibility or puzzlingness from the more common many-sentence version, the contextualist seems not to offer a

solution to the many-sentence version either.

One might worry about Stanley's quick move from the contextualist's central

idea, which is that vague terms are context-sensitive, to the idea that the contextualist is committed to taking vague terms to be indexicals. Indeed,

Raffman?whom Stanley includes in his list of targets, and whose account formed

1 For present purposes we need not distinguish content from referent.

2 This contextualist solution borrows heavily from Raffman (1996), although it omits many details and

probably distorts others. Raffman no longer counts herself as a contextualist about vagueness. See

Raffman (2005). The present sketch is not meant to be an improvement on Raffman's, but is only meant

to supply a clear sample target for Stanley's general criticism. 3

Stanley (2003) p. 271.

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Vague terms, indexicals, and vague indexicals 439

the basis of the sample contextualist account presented above?denies that her

(1996) contextualist solution made vagueness a matter of indexicality.4 Rather, she

claims that on her account the referent of a vague term depended on context in a way

analogous to the way in which the referent of 'big' depends on whether we are

talking about buildings or fleas. I myself am slightly suspicious of taking this analogy (which Raffman uses very effectively to explain and motivate her account) as more

than an analogy. There is a way in which the sense of 'big' in 'That flea is big' can

really be understood as the same as the sense of the relational predicate 'big-for-a

flea'. But the 'orange' in 'That car is orange' seems much less plausibly to have the

linguistic disposition of the speaker (or anything else that Raffman would count as

the relevant aspect of context) as part of its sense. Rather, Raffman's account seems

most plausible if we take the disposition of the speaker to be an aspect of content that

merely determines reference, much as we take the intentions of the speaker to do in

the case of more paradigmatic indexicals such as 'that'. Of course much more would

need to be said here to settle this issue. Happily, we can leave this worry about

Raffman aside, since we can take Stanley's target to be an explicitly indexical

version of Raffman's account. Moreover, and more importantly, even if we grant

Stanley his claim that the contextualist holds vague predicates to be indexicals, his

argument still fails. At least, this is what the present papers aims to show.

Jonathan Ellis (2004) has offered one response on behalf of the contextualist. His

suggestion is that even such paradigmatic indexicals as 'here' do not really have

invariant interpretations in Verb Phrase ellipsis. Let me briefly describe the situation

that Ellis takes to provide a counterexample to Stanley's claim. A number of people, as part of a game, are to stand in various locations. The first person, Jill, takes her

position and says 'I'm going to stand here'. 'Here', as used by Jill on this occasion,

presumably has a certain reference?perhaps vague?that excludes, for example, a

point six feet away from her. The second person, Tom, as a sort of joke, takes his

position very close to Jill, whereupon Jill says 'And so is Tom!' The third person,

Sally, then continues the joke, standing as close to Jill as possible, and Jill says 'And

I guess Sally is too!' About 30 people later, Jonathan takes his position, as close to

Jill as possible, and Jill says 'And so, of course, is Jonathan!' But Jonathan is now

six feet from Jill, at the periphery of a small dense crowd. Had Tom?the second

person to take a position?stood where Jonathan now stands, Jill would have been

speaking falsely had she said 'Tom is standing here too'. But, according to Ellis, Jill

speaks truly in making her claim about Jonathan. Thus Ellis takes his example to

falsify Stanley's claim about invariance, since the elided 'here' seems to change in content as the game progresses. Stanley (2005) has disputed this, but his grounds for

dispute seem to rest on a misunderstanding of the point of Ellis' story. In particular, Stanley takes Ellis to be offering a story in which a sorites series leads us from a true

statement ('So is Tom') to dubious or false one ('Jonathan is too').5 But contrary to

4 Raffman (2005) p. 245.

5 Stanley (2005) pp. 165-166. It is unclear why Stanley thinks that the sentence 'Jonathan is too' is not

true, and I side with Ellis in thinking that it is plausibly true. One possible explanation is that Stanley was

thinking that Ellis was somehow trying to tie the vagueness of 'here' to its obvious indexicality. Although this would be an extremely uncharitable reading of Ellis, it would explain why, in discussing Ellis'

example, Stanley writes (166) 'vagueness remains even when indexicality goes away'.

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440 J. Gert

this understanding, it seems clear that Ellis intends his readers to take the latter

claim to be simply and unambiguously true: when Jill says, at the end of the

game, 'And so, of course, is Jonathan', she is speaking truly, and clearly truly. Ellis' point is that the claim about Jonathan is rendered true in part by the

presence of the small dense crowd and the history of its formation, while that

same claim would have been unambiguously false had Jonathan taken his same

position immediately after Jill. That is, a contextual feature (the presence of the

dense crowd) alters the content of the final elided indexical (the implicit 'here' in

'so is Jonathan') from what it originally was, showing that the content of that

indexical is not invariant in the way Stanley claims. Below I will explain the

important way in which Ellis is correct. But I will also explain why Ellis'

presentation of the example ignores a truth to which Stanley's position is an

(oversimplified) response. Here is my initial worry about Stanley's objection to contextualism: he offers

absolutely no reason to think that all indexicals behave in the same way. It may well

be true that some indexicals have invariant interpretations in Verb Phrase ellipsis. But why can we not simply say that vague terms are indexicals that do not have

invariant interpretations in Verb Phrase ellipsis? There is absolutely no theoretical

pressure to elevate the feature of indexicals that Stanley mentions in offering his 'fact

about indexicals'?a feature that may well be instantiated in the indexicals with

which Stanley chooses to illustrate it?into an essential feature of all indexicals. On

the contrary, there is theoretical pressure to deny this, and to hold that not all

indexicals share this feature. For the whole force of Stanley's objection to the

contextualist's proposal rests on the undefended assumption that vague terms, if they are a special sort of indexical, must function in the same way that more paradigmatic indexicals do. To the degree, then, that we find the contextualist proposal

independently plausible, we can take Stanley's argument to place pressure on the

undefended assumption on which it rests. That is, Stanley's argument provides theoretical pressure to say that what differentiates vague terms from non-vague indexicals is precisely the fact that vague terms are indexicals that do vary in content

in Verb Phrase ellipsis.

Stanley asserts that any response that the contextualist gives to his argument 'must be consistent with the fact that switching interpretations under [Verb Phrase]

ellipsis is not possible with other indexicals'.6 By 'other indexicals', Stanley means

'indexicals other than vague terms, which the contextualist it trying to treat as a

special kind of indexical'. And by using 'other' in this way, he reveals his

assumption that, on any contextualist account that explains vagueness as a kind of

indexicality, indexical terms will fall into two mutually exclusive classes: (1) those that are not vague terms, and that therefore have invariant reference in Verb Phrase

ellipsis, and (2) those that are vague terms, the vagueness of which is a distinct

species of indexicality that does allow variation in reference in Verb Phrase ellipsis. An example from class (1) might be T, while an example from class (2) might be

6 Stanley (2003) p. 273.

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'orange'.7 But reflection on these two examples quickly reveals that a large and

important class of terms has been omitted: terms such as 'here'. 'Here' is clearly an

indexical in the way T is indexical, and is also clearly vague in the way 'orange' is

vague. But if its vagueness is to be explained in the same way in which the

contextualist explains the vagueness of 'orange', then the indexicality that will

figure in that explanation will not be the obvious indexicality that 'here' shares

with T.

What the preceding remarks highlight is that if vagueness is a species of

indexicality, then it is a subtle form of indexicality. Bearing this in mind, let us

return for a moment to Ellis' suggested counterexample to Stanley. During the

playing of the game, the following phrases have, plausibly, the same reference:

'here', as uttered by Jill, and 'where Jill is standing', as uttered by an observer.

Now, if the vagueness of 'where Jill is standing' is to be accounted for by appeal to

a subtle form of indexicality, then 'here' will have this same form of indexicality, in

addition to the obvious and paradigmatic indexicality that it shares with T. 'Here',

therefore, along with other such obviously vague and paradigmatically indexical

terms as 'recently', will be doubly indexical: its reference will be a function of more than one feature of the context. The idea of such double-indexicality may

initially seem odd, but a little reflection should reveal that it is not at all problematic. For example, it is easy to imagine an indexical that combines both 'here' and 'now', so that its content, on an occasion of use, is a function of more than one feature of

the context. The imagined indexical, 'here-and-now', would contribute a content

that was a function not merely of spatial location (as 'here' is), or of time (as 'now'

is), but of both. This example is sufficient to show that it is easy to imagine indexical terms that have their content determined by two (or more) distinct features

of the context. What this paper is suggesting is that vague indexicals such as 'here'

might be a special subclass of such complex indexicals. The additional twist, in the case of vague indexicals, is that their associated content-determining function would not treat each of their arguments in the same way. In yielding content on an

occasion of use (in particular, on an elided occasion), one relevant feature of the context might be treated as invariant, while another feature might not be.

It will be useful to put the current proposal in terms of a simplified and modified

version of David Kaplan's account of indexicals, although the current proposal by no means implies any commitment to such an account.8 Let us define a context (for the moment) as an ordered quadruple <w, a, p, t>, which specifies a world and,

within that world, an agent, place, and time; we can assume that the agent of a

context exists at the time and place of the context in the world of the context.

7 Of course it is to some degree contentious that T is not vague. But the possible vagueness of T does

not present any problems for the argument of the paper here. For it is Stanley who assumes that words can

only be indexical in one way. That is, it is Stanley who is here assuming that since T is clearly indexical

in a way that is not associated with the contextualist account of vagueness, it cannot also be vague in a

way that is associated with the contextualist account of vagueness. It is one point of this paper that this is

false, so there is no problem if paradigmatic indexicals such as T should turn out to be vague as well. 8

For more details, see Kaplan (1989). As presented, the modified account has problems that will be fairly obvious for anyone familiar with the literature that has grown up around Kaplan's logic. But none of these

problems are relevant to current purposes.

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442 J. Gert

Linguistic expressions, such as 'he', or 'Jonathan', or 'here' will have what we can

call contents in contexts. For 'he' and 'Jonathan' the content will be a person, while for 'here' it will be a location. Sentences will also have contents in contexts, but for

present purposes we need say no more about them than that they will depend fairly directly on the contents of their constituent expressions in those contexts, and that

they can be evaluated as true or false with respect to any given world. For Kaplan, linguistic expressions have what is called a character, which is a function from contexts to contents. It is the character of an expression that determines its content

in a context. For non-indexical expressions, this function will be a constant function,

always yielding the same content in any context. For example, 'George Washing ton' has George Washington as its content in all contexts. But indexical expressions have non-constant functions as their character; when I use the expression T, for

example, its content is me, but when you use it, its content is you. When a character is a non-constant function of a context, different features of the context will be relevant to the determination of the value of that function. For example, for the function that gives the character of T, the only relevant feature is the agent of the context, and the value of the function simply is that agent. In the case of 'now', it is the time of the context.

Now let us move on to the question of the variability of the content of an

expression within a sentence. Consider the sentence 'If it is now exactly 3:00, then it is not now even one second after 3:00'. There are obvious reasons to regard this sentence as necessarily true.9 But in order to so regard it, we will need to take the content of both occurrences of 'now' as having the same content; that is, they will both have to refer to the same time. And that means that we will associate only one context with the sentence when evaluating its truth on an occasion of use, and we

will understand the content of 'now' in that sentence as given by its character evaluated at that single context. In language that should seem familiar, the content

of 'now' will be invariant within the sentence. So far, so good. But consider the sentence 'If he [pointing to one person] is five-foot-ten, then he [pointing to another, taller person] must be well over six feet'. If we think of the character of 'he' as a

function that yields (to put it sloppily) the male demonstratum (a newly introduced fifth element) of a context, and if we treat the sentence as having only one context relevant to its truth on an occasion of use?as our consideration of 'now'

suggested?then this sentence will turn out to be false whenever the male demonstratum is in fact five-foot-ten. For no one is both five-foot-ten and also well over six feet. The obvious need to have each occurrence of 'he' have a distinct content might suggest that each occurrence of 'he' has its own distinct context. But this goes against the conclusion we arrived at earlier, in considering 'now'. We can

deal with this by having each context contain not merely one male demonstratum,

but an ordered series of them. Then the first occurrence of 'he' will have the first demonstratum as its content, and the second occurrence will have the second

demonstratum, and so on. Again, in language that will be familiar, the content of

'he' will be variable over multiple occurrences in the same sentence.

9 Even those willing to regard this sentence as ambiguous should grant the existence of a plausible

interpretation on which it could not be false.

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So far our account says nothing about ellipsis. But it does already allow some

expressions to have invariant content within a sentence, and others to have variable

content. And it allows all of this while associating only one context with a given sentence. Let us call 'now' an invariant indexical, and 'he' a variable one. What

happens to a variable indexical in Verb Phrase ellipsis? Consider the sentence

'Marilyn hates him, and so do I'. Here the elided Verb Phrase is 'hate him'. It is

clear that the elided indexical, even though it is one we have classified as variable, will have the same content as the non-elided occurrence of 'him': no second male

demonstratum could even be relevant to the content of this sentence. This may

seem to support Stanley's point. But we have already granted that the invariance of

'now' over multiple non-elided occurrences does not imply a similar invariance for

'he'. Similarly, when we consider the invariance of 'he' (and other obvious

indexicals) in elided Verb Phrases?an invariance that Stanley takes to support a

thesis about indexicality quite generally?we need not take it to imply anything about the invariance of non-obvious indexicals such as vague terms in elided Verb

Phrases. According to the contextualist, the behavior of 'he' across non-elided

occurrences provides a model on which we can understand the behavior of vague terms across elided occurrences. That is, just as the character of 'he', as used in

non-elided contexts, makes use of an ordered series of male demonstrata, the

character of vague terms, as used in elided contexts, will make use of an ordered

series of dispositions of the speaker of the context, so that repeated occurrences

will have distinct contents. What about vague indexicals? Nothing in our simple version of Kaplan's account prohibits more than one feature of a context from

being relevant to the character of an indexical expression. Vague indexicals will

then have two features of the context relevant to their character. One feature may make its contribution in the way in which the location of the context does for

'here', but another feature may make its contribution in the way in which the

ordered series of male demonstrata does in non-elided occurrences of 'he'. And,

importantly, this second relevant feature?an ordered series of dispositions of the

agent of the context?will make its contribution in this way even in Verb Phrase

ellipsis. Let us make use of our modified version of Kaplan's account to describe what is

going on in a slight variant of Ellis' story. One initial worry that we can dismiss

is that since Ellis' example involves multiple sentences, our account will not help in

understanding it. But just as an argument is a set of sentences all of which may need to be interpreted in the same context in order to avoid equivocation (think of

arguments that make use of the expression 'now' in distinct premises), so too can

we regard all of the sentences that Jill utters as ?valuable with respect to the same

context. Now, when Jill says 'I'm going to stand here', 'here' has its content

determined by its character. That character, on the contextualist proposal as

interpreted via our modified version of Kaplan's account, makes two features of the

context relevant: the location (Jill's location when she first speaks), and an ordered

series of dispositions to apply the predicate (Jill's dispositions at the various points at which she utters the word 'here', or a phrase that includes an elided occurrence of

'here'). Let us call this first item of the context 'p', and the second 'd'. Keep in mind

that d is an ordered series, so that we can speak of its members: di, d2, and so on.

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444 J. Gert

Since the occurrence of 'here' in 'I'm going to stand here' is the first one in the

relevant set of sentences, its content is determined by p and di. When Jill says 'And

so is Tom!' the elided occurrence of 'here' has its content determined by p and d2. Now let us suppose that Jill's back begins to hurt, so that after her report of Tom's

location she walks over to a bench and sits down. At the same time Sally continues

the game by taking up a position near Tom. When Jill?speaking from her sitting

position on the bench?says 'And I guess Sally is too', the elided occurrence of

'here' has its content determined by p and d3. That is, the behavior of 'here' with

respect to p exhibits the kind of invariance that Stanley takes to be characteristic of

all indexicals in Verb Phrase ellipsis. But its behavior with respect to the ordered

series d exhibits the kind of variability Ellis points out: a variability that we also saw

in imelided uses of 'he'. Appeal to double-indexicality therefore allows the

contextualist to respect something that Stanley may well be right about, in a way that Ellis' simple denial of invariance does not.

Keeping in mind the possibility of double-indexicality, and also the fact that the

contextualist will view vagueness as a non-obvious form of indexicality, it seems

that Stanley's 'fact about indexical expressions' ought really to be interpreted only as a fact about expressions insofar as they possess the obvious kind of indexicality found in phrases such as T, 'here' and 'an hour ago'. Certainly all of Stanley's

examples involve this sort of indexicality. But an expression can be characterized by this sort of indexicality and also another sort of indexicality: one that involves

change of content across elided occurrences.

Talk of double-indexicality is of course trickier than talk of simple indexicality. Because of this, the contextualist account of vagueness is most clearly presented by

making use of vague expressions that are not also indexicals in the traditional sense.

But if the proposal is unproblematic for terms like 'red' or 'heap', it does not

become problematic when one applies it to traditional indexical expressions such as

'here' and 'now' that are also vague. Rather, we need only draw attention to the

fact that an expression can be indexical in more than one way. I myself am

committed to no particular view of vagueness, and I do not pretend to have

presented any arguments in favor of the indexical view in this paper. But I do claim that Stanley's claims about invariance in Verb Phrase ellipsis provide no reason to

reject that view.

It is no response to this paper to claim that it gives a disjunctive account of

indexicality, and that we should be suspicious of such accounts. I agree with

Stanley, for example, that we should prefer a unified treatment of the sorites

paradox, whether that paradox takes a one-sentence form or a many-sentence form,

and whether it concerns verbs such as 'shout', nouns such as 'heap', or adjectives such as 'bald'. Partly this is because the paradox seems to have common source in

all these versions, and partly it is because unified treatments really are to be

preferred, other things being equal. But my argument against Stanley does not

depend on giving a disjunctive account of indexicality. I myself favor a unified treatment of indexicality, but take this only to involve the following claim: what counts as indexicality in one case is the same non-disjunctive property that counts as

indexicality in another. Here is one suggestion as to what that property might be: a

primitive linguistic expression counts as indexical if and only if its content depends

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on context in a rule-governed way.10 But even if this suggestion should turn out to

be false or incomplete, it would not undermine my confidence that indexicality is a

univocal notion. For this extremely plausible hypothesis does not imply that all

forms of indexicality have the same implications for elided contexts.

Acknowledgements Many thanks to Diana Raffman, Jason Stanley, Jonathan Ellis, and an anonymous referee.

References

Ellis, J. (2004). Context, indexicals and the sorites. Analysis, 64, 362-364.

Kaplan, D. (1989). Demonstratives. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan. New York: Oxford University Press.

Raffman, D. (1996). Vagueness and context relativity. Philosophical Studies, 81, 175-192.

Raffman, D. (2005). How to understand contextualism about vagueness: Reply to Stanley. Analysis, 65, 244-248.

Soames, S. (2002). Replies. Philosophy and Phenomenological Research, 62, 429-452.

Stanley, J. (2000). Context and logical form. Linguistics and Philosophy, 23, 391-434.

Stanley, J. (2003). Context, interest relativity and the sorites. Analysis, 63, 269-280.

Stanley, J. (2005). Knowledge and practical interests. UK: Oxford University Press.

10 See Soames (2002) p. 445. Compare Stanley (2000), p. 400.

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Vague Terms, Indexicals, and Vague Indexicals