Vagueness and Non-Indexical Contextualism
April 2009
.
Jonas Åkerman and Patrick Greenough
1. Preamble.
Contextualism concerning vagueness (hereafter ‘CV’) is a popular response to the puzzle of
vagueness.1 The purpose of this paper is to highlight some of the most basic components of CV, and
to show that it is crucial to distinguish between two types of context-sensitivity in order to evaluate
CV properly. In §2, we sketch a generic form of CV. In §3, we distinguish between Indexical and
Non-indexical context-sensitivity and two corresponding versions of CV.2 In §4, we discuss the
extent to which various forms of “blindness” are problematic for these two versions of CV. Nonindexical CV is found to fare better than Indexical CV in this respect. In §5 we address a challenge
posed by Keefe (2007) to the effect that CV entails that any speech report of what has been said by
a particular vague utterance, where the context of utterance and the reporting context are relevantly
different, will almost always be inaccurate. While this challenge is prima facie effective against
Indexical CV it proves to be less effective against Non-Indexical CV.3
1
CV is defended by Kamp (1981), Raffman (1994, 1996), Soames (1999, 2002), Fara (2000), and Shapiro (2003,
2006); see also Lewis (1979). For criticism of certain forms of CV, see Williamson (1994, 2002), Stanley (2003), Heck
(2003), Greenough (2005), and Keefe (2007).
2
The label ‘Non-Indexical Contextualism’ is due to MacFarlane (2007, 2009). For a non-indexical model of ‘knows’
see Kompa (2002) and Brogaard (2008). For a non-indexical model of predicates of taste see Lasersohn (2005). For an
extensive defence of the general framework, see Recanati (2007).
3
Stanley (2003) has argued that CV is flawed because (i) The sorites paradox can be run using verb-phrase ellipsis, (ii)
indexical expressions are invariant under verb-phrase ellipsis, and (iii) any solution to a verb-phase ellipsis version of
the sorites should be on all fours with a solution to the standard formulation of the paradox. Even if Stanley’s argument
is cogent it is only directed at indexical forms of CV and so might be thought to provide a further reason to prefer NonIndexical over Indexical CV. However, as it turns out, matters are somewhat more complicated. We hope to address this
issue in future work.
1
2. Generic Contextualism Concerning Vagueness.
Generic Contextualism concerning vagueness (hereafter ‘GCV’) is characterized via four key
theses. Firstly, we have:
(GCV1): Vagueness consists in a certain kind of context-sensitivity.
GCV1 is not simply the claim that all vague expressions are context-sensitive since it is perfectly
consistent to follow Travis (1985, 2008) or Searle (1978, 1980) and accept ‘Radical
Contextualism’—the thesis that all expressions (and so all vague expressions) are contextsensitive—and yet deny that vagueness is a species of context-sensitivity. What is needed is the
claim that vagueness is constituted by a particular species of context-sensitivity.4
Say that a sentence type S is generically context-sensitive with respect to contextual factors
c1,…,cn if and only if there is a context of utterance C and a context C' differing only with respect to
c1,…,cn such that either S is true relative to C but false relative to C' or the proposition expressed by
S in C differs from the proposition expressed by S in C' (relative to a fixed subject-matter for S).5
So, while a shift in truth-value is sufficient for (sentential) context-sensitivity, it is not necessary. 6
The sentence ‘I am here’ cannot take different truth-values in different contexts of utterance. When
uttered, this sentence is always true.7 Yet it can be used to express different propositions in different
contexts, which is sufficient (though not necessary) for context-sensitivity.
Which features of the context are relevant to vagueness? Any sensible form of CV ought to
represent many of the context-sensitive features of vague expressions as having nothing per se to do
Williamson (1994, p. 214) says ‘the lack of natural boundaries for vague words makes context-dependence hard to
avoid, but that is an empirical correlation not an a priori law’. According to GCV, there is such a law.
5
Even if the weights of everything remain fixed, the predicate ‘is heavy’ can nonetheless change in extension (or
property expressed) across different context of utterance. Hence, the qualification ‘relative to a fixed subject matter for
the sentence in question’.
6
A context of utterance (hereafter ‘a context’) is taken to be a sequence of parameters: world, speaker, time, location,
orientation, etc.
7
We are ignoring the ‘answering-machine’ data discussed by Sidelle (1991), Predelli (1998). However, there seems to
be examples which are not threatened by such data, like ‘Today is today’. (We owe this example to Martin Montminy.)
4
2
with vagueness. The expression ‘here’ is vague, but its vagueness need have nothing to do with the
fact that its reference can shift depending on the place of use.8 Equally, the application of the
predicate ‘is tall’ can vary as a function of the operative comparison class and/or what is taken to be
typically tall. But such shiftiness in the extension of ‘is tall’ need have nothing as such to do with
vagueness.9
But then just what kind of contextual parameters are responsible for the shiftiness in truth-value
or proposition expressed which is constitutive of vagueness? We will not try to answer this question
in what follows. Rather, we will use the term v-standards as a neutral placeholder for whatever
contextual parameters are taken to be responsible for the shifts. However, the v-standards cannot be
just any kind of contextual parameters, so the following two qualifications are needed.
Firstly, shifts in comparison class can effect shifts in standards. To borrow an example from Fara
(2000), the sentence ‘John is rich’ might be used to express the proposition that John is rich for a
philosopher on one occasion and used on another to express the proposition that John is rich for an
executive at Microsoft. Here what counts as rich depends upon which comparison class is being
invoked. But not all shifts in standards are due to such shifts. When the comparison class is made
explicit in the syntax of the predicate then the standards for when the predicate counts as applying
can typically still shift—at least if vagueness remains in play. For example, take the predicate ‘is
tall for a Ugandan pygmy’. In the context of writing an academic paper, this predicate may fail to
apply to Ugandan pygmies of a certain height, yet in the context of a discussion which takes place
in the pub, the predicate may apply. Indeed, the application of many predicates does not involve an
implicit comparison class at all, but rather a relativisation to a (contextually fixed) paradigm case. 10
Given this, the v-standards must remain in play even after the relevant comparison class and/or
paradigm case has been fixed.
8
See Williamson (1994, p. 215).
For this reason, in speaking of the vagueness of ‘is tall’ it is better to speak of the vagueness of the predicate ‘is tall
with respect to the operative comparison class’, e.g. ‘is tall for a Ugandan Pygmy’. For convenience, we shall usually
omit such relativisation in what follows.
10
Many standards-sensitive terms involve no relativisation to either a paradigm case or comparison class, e.g., ‘The
Earth’s atmosphere’, ‘now’, ‘nearby’, ‘roughly 10,000’, ‘looks somewhat triangular’, ‘is browner than’.
9
3
Secondly, the v-standards cannot quite be Lewis’s standards of precision (see Lewis 1979). For
many vague expressions it does not even make sense to talk about a standard of precision. Paradigm
examples of vague predicates like ‘is bald’, ‘is a heap’, or ‘is red’ are not such that their correct
application depends on standards of precision. So it seems better to think of the v-standards as
something like standards of application rather than standards of precision. The idea would be that in
some contexts a higher amount of the relevant property is required for an object to fall in the
extension. For instance, in some contexts a yellowish-orange surface might count as yellow, but in
other contexts where the standards of application are higher, it might not count as yellow. However,
raising the standards for one predicate may entail that we lower it for another predicate, if those
predicates are contraries like ‘is red’ and ‘is yellow’, or contradictories like ‘is red’ and ‘is not red’.
For instance, if I go through a sorites series of patches ranging from yellow to red, and keep judging
increasingly more reddish patches as yellow, I will simultaneously lower the standards of
application for yellow, and raise the standards of application for red. Thus it makes no sense to say
that the v-standards, in the case in hand, have become more or less strict simpliciter. Rather they
have become more liberal for ‘is red’ and less liberal for ‘is not red’.11
With these qualifications in place, and given the definition of generic context-sensitivity, we can
now state the second key principle of GCV thus:
(GCV2): A sentence type S is vague if and only if S is generically context-sensitive with
respect to the v-standards.12
The context-sensitivity which is constitutive of vagueness is not unconstrained. In particular:
(GCV3): The context-sensitivity which is due to vagueness must respect polar case
constraints.
11
Cf. Keefe (2000, p. 173).
We don’t propose GCV2 as a reductive analysis since a full account of the right hand-side may itself, at some point,
deploy the concept of vagueness.
12
4
For instance, when we have a sorites series like the one just described, positive polar case
constraints mandate that ‘is red’ express a property that determines (together with the relevant nonlinguistic facts) that positive polar cases, like the first couple of clearly red patches in the series,
belong to its extension. The same holds, mutatis mutandis, for negative polar case constraints. In
general, across a typical sorites series for F-ness there is a zone of variation (‘the borderline area’)
in the middle of the series, whereby whether ‘is F’ applies to an object in this zone depends on the
v-factors. Outside the zone of variation, polar case constraints mandate that the predicate applies (or
does not apply) regardless of the v-factors.
A further key thesis (with respect to predicate vagueness) is:
(GCV4) If x and x' are adjacent objects in the sorites series running from F to not-F, it is not
the case that there is a context C such that x and x' are considered together as a pair in C and
‘is F’ (as used in C) is true of x and ‘is F’ (as used in C) is false of x'. 13
GCV4 is classically equivalent to:
(GCV4)* If x and x' are adjacent objects in the sorites series running from F to not-F, then for
all contexts C, if x and x' are considered together as a pair in C then if ‘is F’ (as used in C) is
true of x then ‘is F’ (as used in C) is true of x'.
GCV4 is cognate to both Raffman’s principle IP* which says that ‘for any n, if patch x is F then patch x' is F, relative
to a pairwise presentational context (1994, p. 68), and Fara’s salient-similarity constraint which says that ‘if two things
are saliently similar, then it cannot be that one is in the extension of the predicate, or in its anti-extension, while the
other is not’ (Fara 2000, p. 57). Cf. Soames (1999, pp. 214-6) and Shapiro (2003, pp. 42-3).
13
5
Roughly, GCV4 says that, when considered pairwise, adjacent members of the series are never
category different. GCV4 is a principle of weak tolerance since it permits that (a) there is a context
C and a context C' such that ‘is F’ (as used in C) is true of x and ‘is F’ (as used in C') is false of x',
and that (b) there can be a sharp boundary within C if x and x' are not considered together as a pair
in C.
One symptom of vagueness is that vague predicates draw no known boundary across their
dimension of comparison.14 GCV4 provides us with a way to explain how this symptom of
vagueness arises: as we inspect each pair of adjacent items in the series, GCV4 ensures that the
members of each adjacent pair cannot be category different. Given the factivity of knowledge, there
is no context C such that there are two adjacent items x and x', which are considered together in C,
such that a subject knows that ‘x is F and x' is not-F’ (as used in C) is true. Roughly, no (context in
which there is a) boundary between saliently similar objects in the series entails no (context in
which there is a) known boundary between those objects. Moreover, we can also draw on GCV4 to
explain the appeal of the induction step of the sorites paradox: It is plausible because we confuse
the weak and valid principle of tolerance GCV4* with the following strong and invalid principle of
tolerance:
(ST) If x and x' are adjacent objects in the sorites series running from F to not-F, then for all
contexts C, if ‘is F’ (as used in C) is true of x then ‘is F’ (as used in C) is true of x'.
Roughly, we easily confuse the (true and plausible) claim that there is never a boundary between
any adjacent items considered together as a pair with the stronger claim of ST that there is no
boundary. Such a ready confusion confers plausibility onto the stronger claim—explaining why we
14
Greenough (2003) dubs this symptom ‘epistemic tolerance’.
6
believe ST despite its falsity. However, while GCV4* is valid, ST is invalid since it can be used as
the major premise in a standard sorites paradox.15
3. Indexical CV and Non-indexical CV
We have seen that a sentence type is (generically) context-sensitive just in case in different contexts
tokens of this sentence type can take different truth-values or express different propositions or both
(relative to a fixed subject-matter). Given this disjunctive characterization, we can make the
following distinction:
Content Context-Sensitivity: A sentence type S is content context-sensitive with respect to
contextual factors c1,…,cn if and only if there is a context of utterance C and a context C'
differing only with respect to c1,…,cn such that the proposition expressed by a use of S in C
differs from the proposition expressed by a use of S in C'.
Truth Context-Sensitivity: A sentence type S is truth context-sensitive with respect to
contextual factors c1,…,cn if and only if there is a context of utterance C and a context C'
differing only with respect to c1,…,cn such that S as used in C is true while S as used in C' is
false (where the subject matter for S does not vary between C and C').
ST entails that the predicate ‘is F’ is tolerant in all contexts. So, in the present context, for all x, if x is F then x' is F.
That is, the major premise of the standard sorites paradox follows from ST. Given classical logic, and the fact that the
first member of the series is F and the last member is not-F, then the major premise is false and so ST is false.
Arguably, not all forms of CV should take the major premise to be false. See Greenough (2005) and Åkerman and
Greenough (2009) for relevant discussion.
15
7
Restricting ourselves to sentences which are ‘utterance-contingent’ (i.e. not always true/false when
uttered) then Content Context-Sensitivity entails Truth Context-Sensitivity, though not vice versa.16
Given this distinction, we can draw a further distinction between two forms of CV as follows:17
Content CV: A sentence type S is vague if and only if S is content context-sensitive with
respect to the v-standards.
Truth CV: A sentence type S is vague if and only if S is truth context-sensitive with respect to
the v-standards.18
There are two important forms of Content CV:19
Surprise Indexical CV: the context-sensitivity which is constitutive of the vagueness of a term
is indexical context-sensitivity.
On such a view, vague terms would be indexical in much the same way that ‘I’, ‘now’, and so on,
are indexical. The only difference between the indexicality which is constitutive of vagueness and
the familiar indexicality of such terms is that vagueness-related indexicality is not obvious
indexicality—it is what Cappelen and LePore (2005, p.12) call ‘surprise indexicality’. Soames
seems to be the only extant contextualist who sponsors this view:
16
Lewis (1979, p. 345) does not think that context-sensitivity is exhausted by content context-sensitivity when he says
that ‘[T]he constituents of an uttered sentence […] may depend on the score for their intension or extension’ (our
italics).
17
This distinction was drawn in Greenough (2005, p. 172) before the present authors encountered MacFarlane on NonIndexical Contextualism (MacFarlane 2007, 2009). In Greenough (2005) and in Åkerman and Greenough (2009), we
also distinguish between ‘Boundary-Shifting CV’ and ‘Extension-Shifting CV’.
18
An immediate consequence of Truth CV is that, insofar as one thinks that the sentence ‘I am here now’ is always true
relative to a context, then this sentence is not extensionally vague (even though it may remain vague what has been said
by an utterance of this sentence since we do not know the exact extension of ‘here’ as used in any context).
19
A further form of Content CV entails that vagueness-related context-sensitivity is to be modelled using an
‘unarticulated constituent’ strategy. For reasons of space, we shall not dwell on the form that such a strategy may take.
8
To say that vague predicates are context-sensitive is to say that they are indexical. While the
semantic content of an indexical varies from one context of utterance to another, its meaning
does not (2002, p. 445).20
On a broadly Kaplanian model, this means that vague terms have two levels of meaning: a
character (a function from contexts to content) and a content (a function from circumstances of
evaluation to extensions/truth-values) (see Kaplan 1989).
Another form of Content CV is as follows:
Hidden Indexical CV: Vague terms contain a typographically (and phonetically) unrealized
argument place at the level of logical form—a so-called “hidden variable”.21
For example, a vague sentence ‘Tube 50 contains red paint’ has something like the logical form
Tube 50 contains red paint relative to standards X, where context fills in the relevant parameters for
X. Roughly, on both forms of Content CV, the proposition expressed by an utterance, made in paint
shop A, of the sentence ‘Tube 50 contains red paint’ is Tube 50 contains red paint by the standards
of paint shop A. This proposition is true in the world of A and so the utterance is true simpliciter. If
this sentence is uttered in paint shop B then it expresses the proposition Tube 50 contains red paint
by the standards of paint shop B. This proposition is false in the world of B and so the utterance is
false simpliciter. So, as the proposition expressed shifts as a function of shifting standards, so can
the truth-value of the sentence.
Though truth context-sensitivity may come in a variety of forms, the most developed exemplar
of the view is what MacFarlane (2007, 2009) calls Non-Indexical Contextualism. MacFarlane
20
21
Though in his 1999 and 2003 Soames merely speaks of extensions shifting as the context shifts.
The term ‘hidden indexical’ is due to Cappelen and LePore (2005, pp. 8-9).
9
develops a non-indexical model within a Kaplan-style semantics, whereby the following schema
fixes the conditions under which a sentence, relativised to a context of use, is true:
(T) A sentence type S, as used in context C, is true simpliciter just in case the proposition
expressed by S in C is true at the circumstances of evaluation determined by C.22
Here the context of utterance plays two roles with respect to the determination of sentential truth:
firstly, the context of use (plus the conventional linguistic meaning of S) determines which
proposition is expressed; secondly, the context of use fixes the circumstance of evaluation against
which this expressed proposition is evaluated for truth. MacFarlane (2009) usefully calls these the
‘content-determinative role’ and the ‘circumstance-determinative role’, respectively. Content
context-sensitivity involves the former role, while truth context-sensitivity involves the latter. Given
this, we thus have:
Non-Indexical Context-sensitivity: A sentence S is non-indexically context-sensitive with
respect to contextual factors c1,…,cn if and only if there is a context of utterance C and a
context C' differing only with respect to c1,…,cn, and a proposition P, such that a use of the
sentence S in C expresses P and P is true relative to the circumstances of evaluation as
determined in C, while a use of the sentence S in C' expresses P and P is false relative to the
circumstances of evaluation as determined in C' (where the subject matter for S does not vary
between C and C').
All those who accept the (standard) model theoretic notion of a proposition which can be true
relative to some worlds and false relative to others are committed to a minimal form of NonIndexical Contextualism. Temporalism—the view that a proposition can be true at one time and
22
Cf. Kaplan (1989, p. 522), Lewis (1980).
10
false at another—is also a form of Non-Indexical Contextualism whereby the circumstances of
evaluation contain a time parameter (in addition to a world parameter). Given the definition above,
the form of Non-Indexical Contextualism we are going to be concerned with here can be defined as
follows:
Non-Indexical CV: A sentence type S is vague if and only if S is non-indexically contextsensitive with respect to the v-standards.
Whatever the context, the proposition expressed by a use of the vague sentence ‘Tube 50 contains
red paint’ is always the (v-standards-neutral) proposition Tube 50 contains red paint. This content
may be true relative to the v-standards of C and false relative to the v-standards of C'. Given that
‘Tube 50 contains red paint’, as uttered in C, is true simpliciter if and only if the proposition
expressed by this sentence in C is true relative to the circumstances of evaluation determined by C,
then we can explain why the sentence, relative to C, is true simpliciter and, relative to the context of
use in C', is false simpliciter. So, while propositional truth is v-standards relative, utterance truth,
i.e. truth for sentence tokens (sentence-context pairs) is absolute.23
In what follows, we will only be concerned with Surprise Indexical CV (henceforth
‘Indexical CV’) and Non-indexical CV, and we will argue that the latter is a better alternative, at
least with respect to the issues we will be concerned with. Could extant proponents of CV accept
Non-indexical CV or are they committed to other forms of context-sensitivity? Well, in fact, many
of them are somewhat unclear about what kind of context-sensitivity they are committed to. Soames
is an exception; as shown in the quote above, he explicitly endorses Indexical CV. However, since
his account of vagueness is only concerned with extension shifts, and does not rely on Indexical CV
in any crucial way, he too could reject Indexical CV without having to make any substantial
revisions of his theory. We will not attempt to uncover whether or not any of these forms of
23
Sentence-context pairs cannot shift in truth-value and yet such pairs seem to be vague. But if vagueness consists in
context-sensitivity then CV seems to be in trouble. Call that the simple objection to CV. See Åkerman and Greenough
(2009) for two ways out of the problem.
11
context-sensitivity could reasonably be ascribed to other proponents of CV, like Raffman, Shapiro,
and Fara. For present purposes it suffices to observe that all of them could adopt Non-indexical CV
without distorting any essential elements of their theories.
5. Blindness
A general worry about CV is that it seems to entail that speakers are blind to certain features of their
own language. The extent to which such blindness is problematic depends on what form it takes, so
let us first distinguish between some varieties of blindness:
Strong Content Blindness (SCB): Speakers are blind to the fact that what content
is expressed by an utterance of a vague sentence is (partly) determined by the
context.
Weak Content Blindness (WCB): Speakers are ignorant of what content is
expressed by an utterance of a vague sentence.
Strong Truth Blindness (STB): Speakers are blind to the fact that the truth-value of
what is expressed by an utterance of a vague sentence is (partly) determined by
the context.
Weak Truth Blindness (WTB): Speakers are ignorant of the truth-value of what is
expressed by an utterance of a vague sentence.
12
It seems obvious that speakers do not take vague expressions to be context-sensitive in the way that
CV claims, since otherwise, CV would hardly be controversial at all.24 If this is right, then,
Indexical CV entails (SCB) and Non-indexical CV entails (STB). Is this a problem?
What would we say if we were confronted with a speaker who was blind to the context
sensitivity of an overt indexical? For instance, consider a speaker who does not readily recognise
that the content of ‘here’ depends on features of the context. Would such a speaker count as fully
understanding ‘here’? It seems not. Such blindness would lead us to think that the speaker does not
have an adequate grasp of ‘here’. Indeed, if you are not aware that the truth-value or content of
sentences containing this expression depends on the context of utterance in a certain way, you are
unlikely to be very successful in communicating with it. Now, speakers of vague languages
arguably have an adequate grasp of vague predicates in this sense, but they do not readily recognise
them to be context dependent in the way that CV claims. So, if the point just made about ‘here’
were to hold in the case of vague expressions, there would be at least prima facie evidence against
CV. However, it is far from clear that we can generalise from the case of ‘here’ and other overtly
context sensitive expressions. After all, vague expressions as conceived by CV differ from overt
indexicals in that their context sensitivity is less obvious, so it seems more likely that ordinary
speakers might be ignorant of it without compromising their grasp of these expressions. Moreover,
everyday communication with vague predicates does not require that speakers recognise this special
kind of context sensitivity in the same way as in the case of overt indexicals. So, it is not at all clear
that SCB and STB pose any significant problem in this respect.
Let us turn to the other forms of blindness. According to CV, ordinary speakers are typically
unaware of the shifts that occur in the relevant contextual factors, and they are also ignorant of what
context they are in.25 In other words, CV ascribes a form of context blindness to ordinary speakers.
Now, since context blindness entails that speakers do not know what context they are in at a given
24
Note that we are talking about the special context-sensitivity that CV claims to be constitutive of vagueness, not
humdrum forms of context-sensitivity, which are irrelevant to the problems of vagueness, but are nevertheless exhibited
by vague expressions. See §2 above.
25
See Raffman 1996: 188.
13
moment, and that contexts may shift in a way that alters the content/truth-value without their
noticing, Indexical CV will entail WCB and Non-indexical CV will entail WTB. In fact, that the
truth-value depends on context in this way is entailed by both forms of CV, so both of them will be
committed to WTB.26 However, only Indexical CV entails WCB.
WTB is more local than WCB in two respects. Firstly, WTB holds only for the borderline area,
since when it comes to the polar cases, there is no shiftiness or ignorance of truth-value.27 No matter
what the extension of the vague predicate used is, the boundary will always be inside the zone of
variation. However, WCB holds outside the borderline area as well. If the property ascribed to the
polar cases depends upon unknown contextual factors, which can shift at any moment and thus
effect a change in the property expressed by the vague predicate, the speaker will not know which
property she ascribes to the polar cases, even though she can know that her ascriptions are correct.
Secondly, according to most versions of CV, the judgements that competent speakers make in
the borderline area are bound to be correct, either because the judgement itself determines that the
judgement is true, or because the same facts that determine the judgements also determine that the
judgement is true.28 On either of these alternatives, the speaker reliably makes correct judgments
within her own context. Thus, there is scope for claiming that speakers (at least implicitly) know the
truth-values of her own (present) uses of vague sentences, and that WTB is restricted to judgements
made outside one’s own context.
Are WCB and WTB problematic? When it comes to overt indexicals, corresponding forms of
blindness are not problematic in general. For instance, we can be ignorant of the content expressed
by a sentence like ‘It is quiet here’, because we are ignorant of the values of the relevant contextual
factors, viz. the place of the utterance. Patrick might be locked up in the trunk of a car, and have no
idea of where he is. He could still utter the sentence, and refer to the place where he happens to be,
26
As noted in §3 above, Content-Context Sensitivity entails Truth Context-Sensitivity.
See GVC3 above.
28
The former would be a form of judgement dependence, while the latter could be called co-determination. Shapiro
(2003, 2006) defends a version of judgement dependence, while Raffman (1994) seems to defend a version of codetermination. In Raffman’s account, it is somewhat unclear whether or not there is a genuine determination relation
between the judgements and the truth-values or whether they are co-determined by psychological states of the speaker,
but that is not of great importance here. Soames (1999: 209) claims that speakers have a discretion to include object in
the borderline area in the extension or anti-extension of the vague predicate.
27
14
but he will be ignorant of what proposition he expresses by this utterance (Cf. Kaplan 1989, p. 536).
Instances of (weak) content blindness that result from such ignorance of what the context is should
not lead us to question the speaker’s linguistic competence. What about ignorance of truth-value?
Such ignorance is equally harmless, at least when the reason that we are ignorant of the truth-value
of what we say is that we are ignorant of the (non-linguistic) facts that determine the truth-value.
So, blindness due to ignorance of the (non-linguistic) factors that determine content or truthvalue need not compromise a speaker’s grasp of the expression in question. Does that mean that
WTB and WTC are equally unproblematic with respect to this? That depends. The reason that
Patrick can be ignorant of the content of ‘It is quiet here’ and still count as having an adequate grasp
of ‘here’ is that he would have known what the content was had he had the required access to the
relevant contextual factors. In other words, Patrick knows the character (in Kaplan’s sense) of
‘here’, and that is what constitutes his grasp of this expression. The reason that ignorance of truthvalue is not problematic in general is that we often have a grasp of the proposition expressed, so
that if we had access to the relevant (non-linguistic) truth-determining factors, we would know the
truth-value. So, ignorance of content need not compromise the speaker’s grasp of an indexical given
that she knows the character, and ignorance of truth-value need no compromise a speaker’s grasp of
a sentence in general given that she knows the proposition expressed. Are these strategies available
to CV? Well, given that WTB is restricted to judgements outside one’s own context (for the reasons
given above), it could be claimed that speakers actually display knowledge of the Non-indexicalist’s
v-standards neutral proposition (conceived of as a function from circumstances to truth values),
since when the speaker is in a given context, she will make judgements that are true at the
circumstance determined by that context. So, the Non-indexicalist can maintain that speakers have
an implicit grasp of the proposition expressed. Could the Indexicalist claim that speakers display
implicit knowledge of the character in a similar way? No. Since WCB is not restricted to
judgements outside one’s own context, they will be ignorant even of the propositions expressed by
15
their own (present) utterances.29 This leaves the proponent of Indexical CV with the problem of
explicating what the speakers’ grasp of vague expressions consist in. If vague expressions are
indexicals, and they do not know the character, in virtue of what do they know their meaning?
6. Speech reports
We take ourselves to be able to use indirect speech to report what other people have said in different
contexts. However, if the contents of vague expressions are in constant flux due to contextual
variation, how is this possible? This is the gist of Rosanna Keefe’s recent objection to CV:
‘S said that a is F’ will almost never be strictly true. For the context of this report will be different
from that in which S made the utterance, due to the [difference in v-standards]; correspondingly,
‘a is F’ will express a different proposition in those two contexts. We will generally be lacking a
way to report speech, and the indirect speech reports that we do make will almost always be
inaccurate. (Keefe 2007: 286.)
It seems that this challenge is only effective against Indexical CV. According to Non-Indexical CV,
the content does not vary between the context of the original utterance and the context of the report,
so there is no problem with indirect speech reports. In an intuitively correct report, the same
propositional content is expressed in the report and the original utterance, despite the context
change, so the report is not rendered false by Non-indexical CV. The linguistic vehicle used in
29
It is worth noting that if WCB were restricted in the same way as WTB, speakers would be able to know what
property their use of a vague predicate expressed, and since property determines extension (according to Indexical CV)
and they can know all the relevant facts about the objects in the sorites series, this would mean that they could know the
location of the boundary. But this would conflict with epistemic tolerance (see §2 above).
16
making the utterance can also be used to report the utterance.30 Thus, Non-Indexical CV—but not
Indexical CV—can easily allow for correct and reliable indirect speech reports.31
But why take the v-standards neutral proposition to be the content expressed rather than the vstandards neutral proposition together with the v-standards determined by the context? After all,
only the latter is truth-conditionally complete. Well, in fact, the Non-Indexicalist can acknowledge
that there are two different levels of content: the relativised content and the complete content, where
the former is just the v-standards neutral proposition p, while the latter consists of both p and the vstandards determined by the context. Following Recanati (2007), we can then go on to claim that
the relativised content is the explicit content, and this is what needs to be preserved in a correct
speech report. In other words, when we ask about what the speaker said, all we need to care about is
what proposition the speaker expressed. In that case, the relativised content is enough. However,
when we want to evaluate the utterance, we need the complete content.32
So, according to Non-indexical CV, a speech report may leave out important aspects of the
utterance, namely the v-standards determined by the context, without omitting anything that is
crucial for fulfilling the purpose of reporting, which is just to convey the explicit content of the
utterance, i.e., the v-standards neutral proposition that the speaker expressed. This means that there
is a sense in which the report is incomplete, but this incompleteness does not lead to any problems
as regards the correctness of the report.
While Keefe’s objection does not work against Non-Indexical CV, the challenge for Indexical
CV remains, and it is unclear how it can be met. However, the Non-indexicalist framework seems
to generate some counterintuitive consequences, which must be dealt with before we can conlude
that Non-indexical CV is superior when it comes to handling speech reports. The remainder of this
section will be devoted to this task.
30
Modulo the required substitutions of indexical expressions.
For the same resons, Non-indexicalists can also ascribe disquotational knowledge of meaning and content to ordinary
speakers, contrary to what Keefe claims.
32
Recanati (2007, pp. 82-86) invokes this distinction to rebut Mark Richard’s famous objection against Temporalism
(see Richard 1981). The basic idea is that belief reports are ambiguous between one interpretation which requires the
complete content, and another one which requires the relativised content. The most obvious similarity with the present
application is that it is when we are interested in the truth-conditional properties of the belief that we need the complete
content. Similarly, it is when we focus on the truth of someone’s utterance that we need the complete content.
31
17
Suppose Julia utters the following: ‘Sebastian said that Charles is tall, but it is false that Charles
is tall, so Sebastian said something false’.33 Suppose further that Sebastian uttered ‘Charles is tall’
in C, and thereby expressed the v-standards neutral proposition p, and that Julia’s reporting context
is C'. Moreover, let C and C' differ only with respect to the v-standards, and let p be true in C but
false in C'. According to Non-indexical CV, both Julia’s report and her claim that it is false that
Charles is tall are correct. Intuitively, her reasoning is fine, so she should be in a position to
conclude that Sebastian said something false. However, according to Non-Indexical CV,
Sebastian’s utterance was true when he made it, so Julia should not be able to (correctly) draw this
conclusion.
In order to solve this puzzle, we need to distinguish between the truth-value of what Sebastian
said and the truth-value of his utterance. In other words, we should distinguish utterance truth from
propositional truth.34 ‘Sebastian said something false’ should be taken as a claim about the
complete content of his utterance, while ‘It is false that Charles is tall’ should be interpreted as a
claim about the proposition he expressed, i.e., the explicit content.35 Given this distinction, the
falsity of the proposition that Sebastian expressed in the reporting context does not entail that
Sebastian’s utterance was false, so Sebastian’s utterance can be true, and Julia’s reasoning thus
turns out to be flawed. But now a different problem emerges: according to the account just given,
Julia could correctly say ‘Sebastian said that Charles is tall, but it is false that Charles is tall;
however Sebastian said something true’. Since most ordinary speakers would arguably find this
utterance self-contradictory, this example provides yet another challenge for Non-Indexical CV.36
In order to cope with this objection, we should simply deny that the utterance is inconsistent. It
only seems inconsistent as long as we fail to make the crucial distinction between utterance truth
and propositional truth. Moreover, Julia’s utterance is misleading in that it fails to make explicit that
there is a significant difference between the original context and her own. If Julia had said
33
This example is due to Peter Pagin.
As was done in §3 above.
35
The relation between utterance truth (i.e. truth of sentence-context pairs) and propositional truth is captured in
principle T (see §3 above).
36
Thanks to Martin Montminy for pointing out this problem.
34
18
‘Sebastian said something true in that context’ or something to the same effect, it would have
seemed less contradictory. Once we take the contextual variation into account, and distinguish
between utterance truth and propositional truth, the appearance of inconsistency vanishes. Finally,
we should not be worried or surprised if ordinary speakers do not notice the contextual variation or
fail to make the crucial distinctions, and thus have a hard time seeing that there really is no
inconsistency, since such theoretical knowledge is rarely needed in everyday communication with
vague language.
8. Conclusion.
We have argued that there is an important distinction between two different kinds of CV: Indexical
CV and Non-indexical CV. We have also argued that non-indexical CV is far less problematic than
indexical CV, at least with respect to the issues we have considered here. Of course, this is not
sufficient to settle the score between Indexical CV and Non-indexical CV, or to vindicate any form
of CV. Many outstanding issues remain: What should CV say about higher-order vagueness? Is a
relativistic theory of vagueness superior to Non-Indexical Contextualism? Does CV allow us to
keep classical logic in its entirety? Is CV at bottom of a form of epistemicism? But these remain
issues for another day.37
37
Parts of this paper were presented at the Seventh Arché Vagueness Workshop, November 2006, The Arché Audit, June
2007, a workshop on vagueness at the University of Navarre, Spain, June 2007, in Sydney, August 2008, and in
Stockholm, September 2008. For valuable feedback thanks to Elizabeth Barnes, Herman Cappelen, Maria Cerezo, Mark
Colvyn, Richard Dietz, Mikael Janvid, Dan López de Sa, John MacFarlane, Teresa Marquez, Martin Montminy, Aidan
McGlynn, Paula Milne, Sebastiano Moruzzi, Kathrin Glüer-Pagin, Peter Pagin, Diana Raffman, Sven Rosenkranz,
Mark Sainsbury, Stewart Shapiro, Levi Spectre, Åsa Wikforss, Crispin Wright, and Elia Zardini. This paper was
completed while one of the authors (Greenough) was a Postdoctoral Research Fellow in the Epistemic Warrant Project
at ANU 2007-8 and a Visiting Fellow at the Centre for Time, Sydney, August 2008. Thanks to all the philosophers at
both ANU and Sydney for their immense (philosophical) hospitality.
19
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