VAGUENESS, I NDISCERNIBILITY, AND PRAGMATICSCOMMENTS ON BURNS
Achille C. Varzi
Istituto per la Ricerca Scientifica e Tecnologica (IRST)
I-38050 Povo (Trento), Italy(Published in The Southern Journal of Philosophy 33, Suppl. (1995), 49-62.)

I am sympathetic with Ms. Burns’ general philosophy of vagueness as a pervasive,
multidimensional phenomenon with a variety of sources. I am not, however, all that
comfortable with some of the specific arguments she offers in support of this view. In
particular, I am uneasy with Burns’ central arguments to the effect that the borderline
case variety of vagueness—that which produces the sorites paradoxes and puzzles
concerning the possibility of higher-order vagueness—is in fact less extraordinary(and less disastrous) than people in the tradition of Michael Dummett and Crispin
Wright have alleged. The point is crucial, of course, because it provides necessary
grounds for resisting the objection that this type of vagueness is irremediably more“inquiry resistant” than mere informational vagueness. All the same, it seems to me
that the proposed treatment involves presuppositions that cannot be taken for granted.
My purpose here is to take a closer look at some of these presuppositions, to weighthem against the arguments, and to show that they may—when left ungrounded—
undermine much of Burns’ general program.

I
Let me try to summarize the basic structure of Burns’ treatment of the sorites paradox,
which she, of course, takes as paradigmatic of the purported earmark of borderlinecase vagueness. As I understand it, it involves three main steps. First, the principle oftolerance and observational match originally indicated by Dummett [5] and Wright [13]as the source of all difficulties is slightly amended to do justice to the apparent multidimensionality of natural language predicates. Whether something is a heap does not depend on just one property, say the number of grains it contains; it also depends on its
shape, on its composition, and perhaps on something else as well. Likewise, two people may differ by one single hair and yet instantiate clear cases of the predicates ‘bald’and ‘hairy’ respectively, due to the actual distribution of the hairs on their scalps.

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Thus, in general, the sort of tolerance principle needed to construct a sorites argument
should require a series to be continuously varying with respect, not to a single determining property, but to a complete group of interdependent determining properties:[M] Where Φ is the set of determining properties for a predicate F, and a and b
are indiscernible with respect to every member of Φ, then if F applies to
one of the pair it applies to the other also.
This step of the argument is, of course, only hinted at in Burns’ paper [4], but we find
it fully developed in other works of hers [2, 3]. On this basis, the next step is to
reduce every candidate sorites series to what I call an Armstrong triad (after [1]), that
is, a triple of items a, b, and c such that the following hold for the relevant property φ:
(i)
(ii)
(iii)

a is indiscernible from b with respect to φ;b is indiscernible from c with respect to φ;c is just discernibly different from a with respect to φ.

(It is understood that the relevant notion of indiscernibility should be relativized to a
specific observer in a specific context, but for the time being we may assume these parameters to be uniformly fixed.) Finally, the third step establishes that every such triad
is sure to involve some relevant discernible difference between adjacent members(even if we keep everything as constant as possible): for, given any property φ, indiscernibility with respect to φ is always sure to be a determining property relevant to theapplication of any predicate F for which φ is a determining property. Thus, given a, b,
c as above, there is a relevant difference between a and b in that one but not the otheris indiscernible from c; and there is a relevant difference between b and c in that one
but not the other is indiscernible from a. It would therefore be a mistake to treat a, b,
and c as uniformly indiscernible in the sense required by the amended version of theprinciple of observational match [M], and it would therefore be illegitimate to extend
the application of a predicate F from a to b or from b to c on the grounds of such a
principle. By generalization, it follows that no Armstrong triad—and consequently nofull-blown sorites series—can ever satisfy the principle. We can thus conclude that theparadox is harmless: there simply is no way one can come across a sorites series, justas there is no way one can come across, say, a Russellian barber. Such entities cannot
exist.
I think the overall structure of this argument is intriguing, and I am ready to gowith it. In particular, the first step seems to me to be perfectly fair. Perhaps one could
argue that the amendment of the tolerance rules calls for more grounding. A while ago,
for instance, Stephen Schwartz [9] objected that if we construe our series as involving
a single person gradually losing hair, rather than a sequence of distinct people eachwith one less hair (or if we traffic in clones rather than different people, to follow a
recent suggestion by Roy Sorensen [10]), any hidden complexity of the predicate
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VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS‘bald’ becomes irrelevant. Sorensen [11] also objected that the appeal to multidimensionality is unsupported. For even if we grant that every predicate has various dimensions (by subscribing to some form of “conceptual holism”, for instance), it does notfollow that every dimension is relevant or determining in the sense required by [M]. I
am not impressed by this line of criticism, though. For as far as we are concerned, thereply lies already in Step 3: the argument only relies on all predicates being at least
two-dimensional, and this can be viewed as a matter of necessity if we agree with
Burns’ ingenious point, that is, if we agree that if a property φ is found to be determining for the application of a given predicate, then so is indiscernibility with respect
to φ.
One thing, however, worries me with this maneuver (Step 3). For consider atypical Armstrong triad consisting of, say, three color patches a, b, c, and suppose
you remove one of the two end members, say c. Then a and b are perfectly
indiscernible with respect to color. Suppose further that we applied our predicate, say‘red’ (a specific shade of red), to a. Shall we still withhold it from b on account of thefact that it is possible for us to find (or for there to be) a third element c that is not red
and such that a, b and c form an Armstrong triad with respect to color? This would bea suspicious step into the territory of modal discourse. For that would mean that, ingeneral, there can be properties distinguishing a from b which are not actually present
and which can in no way be established by observation, but which are neverthelessrelevant to the application of a predicate like ‘red’. Apart from conflicting with the notion of ‘red’ as an observational predicate, this would put Burns’ account under acloud of suspicion, since it suggests that one never really knows whether two given
items that look the same (in the relevant respect φ) do in fact deserve the same observational predicate (for which φ is determining): possible comparisons with possible third
items would also matter. Moreover, this appears to conflict with the general programof Burns’ paper. For she talks of the indeterminacy of b as being describable in termsof equivocation: “the information available to the observer leaves it open which exact
shade b is” ([4], p. 15). This is what allows her to draw a crucial analogy between informational and borderline case vagueness. But how is the amount of available information to be determined, if all sorts of possible situations also matter? How do weknow whether the information that is actually available is enough for an observer toapply a predicate like ‘red’?
This is an old story, and I suppose Burns would reject these worries simply byemphasizing the context-sensitivity of vagueness phenomena. In the absence of a third
element there is no relevant difference between a and b? Very well, then, there is no
relevant difference between a and b, hence b is red after all—so one could argue. It is
all a matter of context. In one context (where c is absent) we are entitled to call b red;in a different context (where c is present) we may refuse to do so. There is nothing
special with this, just as there is nothing special with the fact that people may not be
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VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS

consistent in their decisions to apply or refuse to apply the same predicate to the sameunchanged object over time ([4], p. 17). As Burns put it in her 1991 book, we are justfacing “an inevitable consequence of the looseness of fit of observational predicates tothe world” ([3], p. 148). The important thing is that when the context involves asmoothly varying sorites series (or an Armstrong triad), the observer is not forced toapply the predicate inconsistently, for in such a context an observer would find therelevant differences.
If we are ready to accept this, then I think we are ready to go a long way with
Burns’ program. Vagueness is no semantic mystery; it is the pragmatics of vague
terms and predicates that may involve inconsistent changes in applications. We may
also see in a new light the connection between the two varieties of vagueness. But
there is some cost too: for a lot of weight is now on the observer’s always finding therelevant differences. And this opens the way to what seems to me a deeper line ofobjection, to which I now turn.

II
The line of objection I have in mind concerns the assumption that the relation of indiscernibility be perfectly sharp. This assumption plays a crucial role in the second stepof Burns’ argument, since to claim that every potential sorites series is reducible to an
Armstrong triad is to claim that there must always be a first item of the series which isdiscernibly different from an end member, and this is to assume that there must always
be a sharp break in terms of the items’ indiscernibility from the end members. It ishere that I have reservations.
I know Burns is aware of the problem, for she discussed it at length in her otherworks. Her point seems to be that indiscernibility must possess sharp boundaries
insofar as it behaves non-transitively. For instance, in Vagueness she makes the claim
quite clear:
we may rely upon the commonsense argument that an observer who sees that the end
members of a series look different from one another in some respect and judges the first few
members to be indiscernible from the initial member cannot go on judging all the succeeding
members to be indiscernible from that initial member. They must start noticing a difference
from an end member somewhere. ([3], p. 132f)

It is, however, difficult for me to find satisfaction in this explanation, consideringthat the commonsense argument at issue is precisely what gives a paradoxical flavor toa standard sorites argument in the first place. Why can’t indiscernibility yield a similarparadox? What is it that protects it from being tolerant to marginal change just likeheaphood or baldness?
Some grounds for answering these questions may be located in an argument of4

VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS

Dummett’s (in [6], pp. 9ff) to the effect that indiscernibility is an observational
relation, and one cannot make sense of tolerance for relations. In general, that would
presuppose finding some means for establishing that if pj is a pair of things that standin a relation R, and pj+1 is a neighbor pair that is indiscernible from pj , then the things
composing pj+1 are also related by R. But how can we characterize the relevant notionof indiscernibility between pairs? Dummett says that we cannot, for “we lack any
notion of a perception of a relevant difference between two pairs of objects” (p. 10).
Hence, we cannot find any analogue of the tolerance rule for observational relations,and that in turn implies that the relation of indiscernibility (between objects) cannot betolerant.
This argument is not as strong as it looks, however. For, on the one hand, theclaim that we lack any notion of indiscernibility between pairs of objects is not
generally obvious. There is a perfectly clear sense in which, for instance, the two pairson the left (a) of the following picture can be said to be indiscernible (although inreality they may not be exactly alike), whereas the two pairs in the middle (b) and thetwo pairs on the right (c) involve relevant perceptual differences (in one case withrespect to the size of the constituent objects, in the other case with respect to theirrelative distance).

(a)

(b)

(c)

On the other hand, in some cases it does not even seem hard to provide a characterization of such a relation of indiscernibility between pairs in terms of qualities of theconstituent objects. For instance, suppose R is the relation ‘close to’, and consider the
relation I that holds between two pairs pj and pk when the distance between the twoconstituents of pj looks the same as the distance between the two constituents of pk .
Then I qualifies as a suitable relation of indiscernibility between pairs with respect tothe relative distance of their constituent objects. (Thus, the two pairs in figures (a) and(b) above would be indIscernible in this sense, while the pair in (c) would not.) Thisis the primary determining property for the application of R. And, in fact, we can immediately construct a sorites series taking us from a pair of objects that are definitely
close to each other to a pair of objects that are definitely not close. The observational
relation ‘close to’ is tolerant to marginal change.
So, in general, it is not true that one cannot make sense of a relation ofindiscernibility between pairs (or n-tuples, for that matter) of objects. The point thatreally interests us, though, is whether anything like this can be done when the relation
R that may or may not hold between the objects is itself a relation of indiscernibility (in5

VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS

some relevant respect φ). Can we make sense of an “external” relation of indiscernibility between pairs with respect to an “internal” relation of indiscernibility
between their constituents with respect to a given property φ? I see two cases,
depending on whether we follow Burns in assuming the existence of an Armstrong
triad relative to φ.
If we do not make the assumption, then again I see no difficulty in providing anindirect characterization of the external relation between pairs in terms of qualities of
the constituent objects, as we did above. The obvious candidate is to certify two pairs
indiscernible just in case their respective constituents are indiscernible with respect to φ
(φ-indiscernible for short), i.e., just in case each constituent of the first pair is φ-indiscernible from the corresponding constituent of the second pair. Of course, this would
eventually clash against the intuition that φ-indiscernibility should in general not betransitive. For given any triple a, b, and c such that a is φ-indiscernible from b and bfrom c, the pairs 〈a, b〉 and 〈a, c〉 will come out indiscernible by the above construction;and if φ-indiscernibility is to be tolerant, this means that a and c will come out φ-indiscernible as well. On the present assumption, however, this cannot be an argument
against the proposed characterization. Surely we do not want φ-indiscernibility to
behave transitively. But the reason why we do not want it to behave transitively is thesame reason why we do not want a man with a million hairs to qualify as bald. We
have to explain where the transitivity goes wrong, just as we have to explain where thetolerance of ‘bald’ gets us into trouble.
To put it in other terms, of course φ-indiscernibility is globally non-transitive; but
locally it may very well behave transitively unless we assume it to be sharp, which iswhat one does when one argues that every potential sorites series is reducible to an
Armstrong triad. (We may recognize here a general source of trouble. Think of a Moebius strip: each portion is two-sided, hence perfectly standard; it is the global topologythat is peculiar.) Now this feature (global non-transitivity versus local transitivity) is
the relational analogue of the sorites feature of vague predicates (gobal discriminability
versus local tolerance to marginal change). And, in fact, if we keep one of the two
relata fixed so as to shift from a binary relation to a monadic predicate, we can reduce
the former to the latter case. To illustrate, let h be a small heap of sand (consisting of,say, a thousand grains), and construct an apparently continuous sequence h0, …,
h1,000,000 as follows:
(i)
(ii)

h0=h
for all j ≥ 0, hj+1 is obtained from hj by adding one grain of sand.

(It is not necessary that the grain addition be made in such a way as to preserve
heaphood, so we need not bother about the fact that ‘heap’ is vague. In fact, theexample can easily be adapted to arbitrary objects.) Then we can construct the following familiar-looking argument:
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VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS

h0 is indiscernible from h.
For all j ≥ 0, if hj is indiscernible from h, then so is hj+1 .
Ergo, h1,000,000 is indiscernible from h.
This is, of course, where Burns and Dummett would say that the induction must
eventually come to a halt. But why? Why then not just argue in the first place that wemust eventually come to a halt in applying ‘heap’ or ‘bald’ in a standard sorites
argument?
We are thus left with the need to assume the existence of an Armstrong triad for φ.
(Indeed, Burns’ position in this regard involves quite strong empirical assumptions.
For she needs to assume that there is such a triad for every property φ that can be adetermining property for some observational predicate F. That is, one needs an Armstrong triad for things matching in color, one for things matching in baldness, one forthings matching in height, in age, in length, and so on.) Now, if we follow her inmaking such assumptions, then the construction of external indiscernibility considered
above will not do. However, this need not imply that we cannot make any sense of therelation. In fact, precisely our assumptions force us to admit that there is a sense inwhich two pairs can be said to be discernible or indiscernible from each other. For if
a, b, c is an Armstrong triad, the very fact that a is φ-indiscernible from b but not fromc should guarantee that the pairs 〈a, b〉 and 〈a, c〉 are not indiscernible, and we could
likewise agree that the pairs 〈a, b〉 and 〈b, c〉 are indiscernible. This, of course, does
not by itself justify the objection that φ-indiscernibility may be tolerant. The example isalready assuming everything there is to be known about a, b, and c with regard to φindiscernibility, and there would be no point in arguing, for instance, that since a andb are φ-indiscernible and 〈a, b〉 and 〈b, c〉 are indiscernible in the relevant respect, thenb and c are also φ-indiscernible. However, all we need to point out is that in general
we could argue this way. We are relying here on the internal relation of φ-indiscernibility to make sense of the notion of external indiscernibility; but once this is clear, we
may then generally rely on the latter to reason about the former. This involves noquestion begging.
So even in this case I find the tolerance of φ-indiscernibility to be all but
impossible. Perhaps one can still try to force things in the direction of a negative
answer. One may argue that the sorites argument itself relies on the possibility ofmaking determinate discriminability judgments. If an observer has to be able to seethat every member of a series is indiscernible from its predecessor for the paradox tobe set up, then—one could argue—there can be nothing wrong with assuming thatsome member will eventually be seen as discernibly different from the initial member(see [2], p. 505). There is an important and correct intuition here. Yet, again, I do notthink this can close the issue. For this account puts the disposition to treat two things

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as indiscernible in some respect φ (on the one hand) and the capacity to discern a
difference between things with respect to φ (on the other) at the same level. This mightwell be the case for some non-vague predicates. But in general I find the difference
relevant. If φ is a determining property for, say, the predicate ‘red’, seeing theindiscernibility of adjacent colored strips in a sorites series does not require drawing
any boundary. It just so happens that physics knows finer distinctions than the eye, asCharles Travis put it ([12], p. 348). By contrast, finding a first element in the series
that is just discernibly different from an end element x (given that its predecessor is
indiscernible from x) involves an active perceptual shift, the drawing of a sharpboundary. And that is the issue.

III
So is indiscernibility tolerant? I have objected to the a priori arguments against this,but there are still two loose ends to be tied up.
The first is whether indiscernibility actually admits of borderline cases, which is,of course, a necessary condition for tolerance. Here I have more like a methodologicalanswer to offer. There is, I think, something ironic in trying to resolve such issues bymeans of simple armchair speculations. For instance, I understand actual experimental
psychology attempts to match or discriminate items that are phenomenally quite similar
do not behave very consistently. Particularly if the experimental set-up does not proceed by showing the items in the right sequence, it is all but impossible for a subject todiscriminate items that are physically very close while matching items that are muchfurther apart. (C. L. Hardin, for one, takes this very seriously in [7]). So it is not clear
why the “plain fact of human behavior” relied upon by Burns—the fact that people doeventually start noticing a difference somewhere—should be given much credit.
Moreover, even if we content ourselves with armchair arguments, it is hard toresist the temptation to produce examples revealing the difficulty of the question.
Imagine, for instance, that I ask you to compare the relative lengths of the following
lines:

I know you are going to smile at this: “You won’t fool us—we are all aware of theillusion”. But of course, the Müller-Lyer illusion applies when the line on the top
looks shorter than the line at the bottom where in fact they are exactly the same. That is
the illusion. By contrast here I am not telling you anything about the actual length ofthe lines. I might not even know it, for all you know, and I just want you to tell me
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how they look to you. Can all of you make sharp discriminations? To make things
more entertaining, imagine a sorites series based on a gradual change of length of the
top line (from very short to very long), keeping the bottom line fixed. Where do you
make the discriminations? Where do you stop seeing the line above as shorter than the
one below?

M

This takes us to the second loose end. Does the presence of borderline cases forindiscernibility actually revive the paradox? In other words, can they be made to fadeaway gradually, thereby introducing tolerance to marginal change? The question is
also considered and eventually dismissed by Burns in [2] and [3]. She does so on the
grounds of the following discrimination principle (cp. [3], p. 145):[D]

Wherever a determining property for a predicate extends to one thing and it
is an indeterminate matter whether or not it extends to a second thing, there
is a difference between the two in a respect relevant to the application of thatpredicate.

Thus, if z is an intermediate item inserted between the first two members of a typical
Armstrong triad a, b, c, and if it is indeterminate whether z is indiscernible from thethird member c with respect to the relevant property φ, then z will differ significantly
both from a and b (even if all three of them are indiscernible with respect to φ). For
neither a nor b shares with z the property of being indeterminate with respect to φ-discernibility from c. Accordingly, higher-order differences between a and b in terms of
their φ-indiscernibility from c cannot be made to fade away in the same fashion as
lower-order differences, for any intermediate item z introduces a significant difference.
This principle is important, because it supplements the principle of tolerance andobservational match [M] in imposing a clear constraint on the conditions under which
two items should be said to differ significantly with respect to a determining property
for a given observational predicate. However, what grounds do we have to accept
such a constraint?
I can only think of the following line of argument, at least when the property inquestion is, as in the case we are interested in, the relational property of being
indiscernible from other members with respect to a determining property φ. Let ‘ψ’stand for the relational property in question, and let ‘Iγ’ indicate the relation of being
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VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS

indiscernible (for a fixed observer in a fixed context) with respect to a given property
γ. Then the following should generally hold:(1)Iψ (b, z) → ∀x(Iφ (b, x) ↔ Iφ (z, x)).

From this, by universal instantiation we derive:(2)Iψ (b, z) → (Iφ (b, c) ↔ Iφ (z, c))

Now let ‘∇’ stand for the operator ‘indefinitely’, or ‘it is indefinite whether’. Then(the argument goes), the following must also hold:(3)

Iφ (b,c) ∧ ∇(Iφ (z, c)) → ¬(Iφ (b,c) ↔ Iφ (z, c)).

But the following are true by hypothesis:(4)(5)

Iφ (b,c)∇(Iφ (z, c)).

Thus, by conjunction and modus ponens from (3) we obtain(6)¬(Iφ (b,c) ↔ Iφ (z, c)).

And from this, by modus tollens from (2) we conclude(7)¬Iψ (b, z).

(A similar reasoning will establish a corresponding conclusion with a in place of b).
By showing that (7) follows from (4) and (5), this argument would provide
grounds for accepting the discrimination principle [D], at least relative to the example
in question. However, the reasoning is fallacious. The crucial step is the use of (3) inthe derivation of (6). For (3) is a conditional with true antecedent and can therefore betrue only if one of the following holds: either the consequent (i.e., (6)) is true, or theconsequent is not true and we endorse a semantics for ‘→’ which certifies true a
conditional with true antecedent and non-true consequent. The latter option is in myview utterly untenable. In any case, since we want to detach the consequent by modus
ponens, it cannot serve our purposes, unless we are ready to undertake a radical
revision of our entire logical machinery. So we must go with the truth of (6). But (6)is the negation of a biconditional involving a true sentence, I φ (b,c), and an indefinite
one, Iφ (z, c). So (6) is true only if one of the following conditions holds: either weassume a semantics for ‘↔’ that treats such a biconditional as false, or we certify the
biconditional indefinite, i.e., neither true nor false, and we assume a semantics for ‘¬’that certifies as true the negation of an indefinite sentence. Again, the first option is in
my view untenable, and contrasts with all familiar three-valued or supervaluational semantics. So I suspect we must endorse the second option, which effectively amounts
to taking ‘¬’ as a connective of external negation. Now this is feasable, though prima
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facie unexpected. But then the conclusion (7) obtained from (6) and (2) by modus
tollens must also owe its truth to an interpretation of ‘¬’ as external negation. This too
is legitimate, of course. But it leaves open the possibility that Iψ (b, z) be undefined intruth value (as opposed to false). And this conflicts plainly with the intended use of[D].
As I see it, the moral to be drawn is that the discrimination principle [D] is toostrong to be justified on the sole basis of (1); all we can accept is the following variant:[D'] Wherever a determining property for a predicate extends to one thing and it
is an indeterminate matter whether or not it extends to a second thing, it isan indeterminate matter whether or not there is a difference between the twoin a respect relevant to the application of that predicate.
The difference is not of lesser importance. Were [D] true, the derivation of (7)would simply prevent the observer from applying the principle of observational match[M], and there would be uncertainty as to whether z should be ascribed the relevant
predicate. In short, z would be a borderline case. But if we only have [D'], then thequestion of whether or not [M] applies is itself indeterminate, thereby making z aborderline case of a borderline case. And this of course opens the door to all sorts ofhigher-order vagueness problems.
So I think Burns should face the issue very carefully. For unless we are given
good reasons to endorse [D] instead of [D'], the sharpness of indiscernibility is notestablished, with serious consequences for the main argument.

IV
Let me now try to bring all of this back to Burns’ general program. I have pointed outthat the program puts considerable weight on an observer’s ability to recognize
relevant differences in every context that is prone to the sorites paradox. And I haveargued that this involves presuppositions which undermine Burns’ ingenious treatmentof the paradox. Now, I imagine this result does not by itself affect the general claimthat vagueness is essentially a pragmatic phenomenon. It does, however, seem to me
to have important consequences for the specific pragmatic perspective on vaguenessthat Burns advocates in her paper.
For, on the one hand, Burns’ appeal to the contextual nature of vaguenessbecomes rather flimsy. Her basic strategy is to show that within a single context nodramatic problem arises: within each context the boundaries of application of vague
predicates can be drawn—they are de facto drawn by people with an understanding of
their meaning, although there is no truth of the matter as to where the boundaries
should be drawn. It is rather the intercontextual business, so to speak, that is in11

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coherent, thereby yielding vagueness: different people (or the same person on different
occasions) draw different boundaries, and there is no way to say who does it better.
Thus, vagueness ceases to be a matter of semantics and becomes the concern ofpragmatics. The problem is now that the starting point of this whole account isquestionable. For I have tried to show that such troubles as the sorites paradox stillthreaten even within individual contexts. To put it differently, Burns says that thesources of sorites problems “are to be found in the use of alternative precise languages
and resulting conflicts” (p. 20), in the spirit of David Lewis’s philosophy of language[8]. This presupposes that such precise languages are available, and Burns’
explanation of the sorites paradox is to provide grounds for such a presupposition. If
the explanation is found faulty, the entire account is in jeopardy.
On the other hand, it seems to me that Burns’ account of the connection between
the two varieties of vagueness is also weakened. We are told that vagueness—any
type of vagueness in language—is in the end a matter of informational failure. Of
course there is a difference between the information provided by our sensory sources
and the information involved in a communicative exchange. But—so the accountgoes—in both cases vagueness arises because the amount of information made available is faulty, indefinite, or otherwise insufficient relative to a contextually determined
purpose (applying an observational predicate or evaluating a conversational contribution). In particular, an observer confronted with a sorites series is in a position of
uncertainty as to where a line should be drawn separating the positive instances of apredicate from its negative instances. According to Burns, and if we are ready tofollow her account of observational predicates as involving ceteris paribus conditions,the line is eventually drawn. This aligns human observers with people confronted withinformational vagueness. But then, again, this is precisely where the argument isleaky. And if this argument is leaky, the analogy with informational vaguenessbecomes unsteady.
With all this, I would like to suggest that the distinction between the two varieties
of vagueness is still worth keeping, at least as a working hypothesis. Maybe Burns isright in her conclusion that it all boils down to communicative fault. But for the time
being I find her arguments a bit too optimistic. Old fashioned vagueness—that which
she wants to deport into language use—still threatens.

REFERENCES[1] David M. Armstrong, A Materialist Theory of Mind, London: Routledge and Kegan Paul, 1961.
[2] Linda C. Burns, ‘Vagueness and Coherence’, Synthese 68 (1986), 487–513.
[3] Linda C. Burns, Vagueness. An Investigation into Natural Languages and the Sorites Paradox,
Dordrecht/Boston/London: Kluwer Academic Publishers, 1991.
[4] Linda C. Burns, ‘Something to Do with Vagueness’, this issue.
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VAGUENESS, INDISCERNIBILITY, AND PRAGMATICS[5] Michael Dummett, ‘Wang’s Paradox’, Synthese 30 (1975), 301–324.
[6] Michael Dummett, ‘Common Sense and Physics’, in G. F. Macdonald (ed.), Perception and
Identity. Essays Presented to A. J. Ayer with His Replies to Them, London: Macmillan, 1979,
pp. 1–40.
[7] C. L. Hardin, ‘Phenomenal Colors and sorites’, Noûs 22 (1988), 213–234.
[8] David K. Lewis, ‘Language and Languages’, in K. Gunderson (ed.), Minnesota Studies in the
Philosophy of Science, Volume VII, Minneapolis: University of Minnesota Press, 1975, pp. 3–
35.
[9] Stephen P. Schwartz, ‘Vagueness and Incoherence: A Reply to Burns’, Synthese 80 (1989),
395–406.
[10] Roy A. Sorensen, ‘A Thousand Clones’, Mind 103 (1994), 47–54.
[11] Roy A. Sorensen, Review of [3], Philosophy and Phenomenological Research 54 (1994), 483–
486.
[12] Charles Travis, ‘Vagueness, Observation, and sorites’, Mind 94 (1985), 343–366.
[13] Crispin Wright, ‘On the Coherence of Vague Predicates’, Synthese 30 (1975), 325–364.

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