Phenomenal sorites paradoxes and looking the same
ROSANNA KEEFE
DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF SHEFFIELD, EMAIL: [email protected]
ABSTRACT
Taking a series of colour patches, starting with one that clearly looks red, and making each so
similar in colour to the previous one that it looks the same as it, we appear to be able to show that
a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a
unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they
do not need such a solution, nor do they succumb to one. In particular, I reject the claim made by
Fara and Raffman that looks the same is a transitive relation, which would allow us to solve
phenomenal sorites paradoxes by denying the possibility of the required kind of sorites series.
Take a large vat of bright red paint and use it to paint a patch of colour on a white
wall: that patch will, of course, look red. Then, add to the vat of red paint small
drops of yellow one at a time, mixing well, and paint a new patch on the wall
each time. Each patch will look the same as the previous one, for we are unable to
detect the minute change in the composition of the paint. Consider now the
compelling principle that if x looks red and x and y look the same colour, then y
looks red. Using this principle, we could run through our patches of colour and
reach the absurd conclusion that the final patch looks red even if we have added
five times more yellow paint than the original red. We can call this a phenomenal
sorites paradox: it is a sorites paradox based on an observational predicate whose
applicability depends on how things look and it involves a principle about when
two things appear the same in the relevant way. Other phenomenal sorites will
involve predicates such as ‘sounds loud’ and ‘smells sweet’, based on relations of
sounding the same or smelling the same that hold between members of the series.
This paper will consider and reject a proposed solution to this important class
of paradoxes. According to this solution (see, e.g., Fara 2001), relations such as
1.
looks the same as are transitive, and this means that there could never be the kind
of series needed for the phenomenal sorites.
1. PHENOMENAL SORITES
One general form for a sorites for the predicate F starts with the two premises:
(1) Fa1
(2) If Ryx then if Fx, Fy
and a series a1 … an such that Rai+1ai for all i. Both premises appear true, but, for
some suitably large n, the putative conclusion
(3) Fan
seems false. For example, if F is ‘is tall’ then R could be ‘is one-hundredth of an
inch shorter than’, with the series starting with a 7-foot man and ending with a 4foot one. Or if F is ‘looks red’ then R can be ‘looks the same colour as’ and the
series can be one such as that described at the beginning of the paper.
Phenomenal sorites fit nicely into this form. Fara gives the following two
defining features of phenomenal sorites (2001, p.907): ‘(i) the occurrence of ‘looks
the same as’ (or ‘smells the same as’ etc.) in the antecedent of the inductive
premiss; and (ii) the occurrence of an observational predicate ... in the other
constituents of the argument [i.e. as ‘F’ in the above formulation]’, where ‘a
predicate is observational just in case its applicability to an object ... depends only
on the way that object appears’. ‘Looks red’ is, then, observational, but ‘is tall’
probably isn’t (for someone can be tall but not look tall). Regarding the first
condition, we will not limit ourselves to paradoxes involving the looks the same
relation (or the equivalent for the other sensory modalities), but will be
interested, for example, in series where each member counts as ‘indiscriminable
2.
from’, or ‘indiscernible from’ the next. I will talk of ‘matching relations’ to refer to
all such relations, whose applicability to a pair of things depends on how those
things look.
Do phenomenal sorites and non-phenomenal sorites call for distinct types of
solution? On most theories of vagueness, the solution to the sorites paradox
involves denying that the inductive premise is true. So, for example, according to
epistemicism and supervaluationism, it is false that ‘if x is tall and y is onehundredth of an inch shorter, then y is also tall’, either because it has an
unknowable false instance (as according to epistemicism) or because it comes out
false on every way of making ‘tall’ precise (as according to supervaluationism).
The denial of such a compelling principle for ‘tall’ is a prima facie implausible
feature of a theory, and one that needs explanation: this is a task that the
epistemic view and supervaluationist tackle in different ways. 1 But is it even less
acceptable to deny the parallel inductive premise of a phenomenal sorites?
Let us see what Fara (2001) says about this, considering the following
principle:
(I)
For all x and y, if x and y look the same and x looks red, then y looks
red.
Fara has described it as a truism that if two things look the same in respect of
colour then if one looks red so does the other, and she defends the contrast with
the corresponding non-phenomenal principles. She writes,
1 For defences of epistemicism and supervaluationism see Williamson 1994 and Keefe 2000
respectively. Williamson’s solution to the sorites paradox involves a detailed account of why we
are ignorant of the boundary of a vague predicate (i.e. ignorant of the false instance of the sorites
premise). We cannot distinguish between our actual situation and a possible situation with a
different false instance, he argues. The supervaluationist’s theory of vagueness declares a vague
sentence true iff it is true on all ways of making it precise – an account that preserves the truth of
compelling ‘penumbral connections’ such as ‘this blob is red or pink’, said of a borderline red–
pink blob. Every way of making ‘tall’ precise renders some instance of the sorites paradox
inductive premise false. So, since that generalized premise is false on all ways of making the
language precise, it comes out false simpliciter without commitment to a unique false instance.
3.
If two men differ in height by even one-hundredth of an inch, then they differ in
a respect that is relevant for the applicability of ‘tall’. But if two colour patches
look the same (not just similar, but the same) in respect of colour, then they do not
differ, on the face of it at least, in any respect relevant for the applicability of
‘looks red’. (2001, p.908).
I would deny the second half of the claim: the physical constitution of something
is certainly relevant to the application of ‘looks red’ and this may vary slightly for
a pair of things that nonetheless look the same. This may not seem enough of a
difference to affect the applicability of ‘looks red’, but nor does one-hundredth of
an inch seem enough to affect the applicability of ‘is tall’: that is the force of the
sorites paradox.
Next, take a second quotation from Fara: ‘someone who sincerely claimed
that two colour patches looked the same and yet that one looked red and the
other not ... would not merely seem to be plainly mistaken, but also to be in a
state of confusion’ (2001, p.909). Now, even if true, this does not threaten either
supervaluationists or epistemicists – the two major theories of vagueness that
deny the truth of the inductive premise of sorites paradoxes. For they can both
maintain that even if (I) is false, we could never be in a position to locate a false
instance, either because there is no such unique instance (as according to
supervaluationism) or because such an instance is unknowable (as according to
the epistemic view). Both theories can acknowledge that anyone who claimed to
identify a sharp boundary to ‘looks red’ that fell between two things that look the
same to them would not count as a competent user of that phrase. There need be
no contrast here with predicates such as ‘is bald’ or ‘is a tadpole’ that are, we are
assuming, not observational: if anyone claimed to identify a specific instance
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falsifying the inductive premise, they would generally appear to be either
misunderstanding the expression or perhaps stipulating a boundary for present
purposes.2
Finally, can we show (I) to be true purely in virtue of the logical features of
‘looks the same’? Suppose ‘looks the same’ amounts to ‘has the same look’, where
this commits us to something which is ‘the look’ of the thing, which is the same
for any two things that look the same and which may or may not be red. Then,
the antecedent of (I) implies that there is something which is the look of x and the
same thing is the look of y, in which case the consequent of (I) follows trivially,
amounting to the claim that if the look of x (=the look of y) is red then that same
thing is red.
So, there appears to be an interpretation of (I) on which it is guaranteed to be
true. But that interpretation may be problematic in various ways and may, for
example, commit us to an incoherent notion of ‘the look’.3 Additionally, it might
not be a reading which is appropriate for a sorites paradox, if, for example, it
relies on a notion of ‘the same look’ for which there are no non-trivial instances
(i.e. more than just cases where x has the same look as y because x=y).
On the reading in question here, then, ‘look’ functions as a noun in the scope
of ‘the same’ – as ‘has the same look’ – and logical properties of ‘looks the same’
follow from logical properties of ‘the same’. On the alternative, more natural,
reading, ‘the same’ is in the scope of ‘look’, so that ‘looking the same’ is a matter
2 Consider also Dummett’s objection (1975, p.264) that if a looks red and b looks the same as a, b
cannot fail to look red, because I could not determine by looking that it does not look red, if it
looks the same as a (based on the observationality of ‘looks red’). At best this shows that (I) cannot
have a false instance. If, as the supervaluationist maintains, (I) is false but there is no false
instance, then nothing will defy the principle that we can tell by looking whether the predicate
applies.
3 See, e.g., Peacocke 1981, p.131 on the incoherence of a notion of ‘the look’, sometimes described
as ‘the observational shade’. I am not committing myself to the claim that there is no coherent
notion of ‘the look’. Rather, we cannot assume that the notion required for this interpretation of (I)
is a coherent one. See §7 for further discussion and see Martin 2010 for a recent detailed
discussion of ‘What’s in a Look?’.
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of appearance of sameness (with ‘look’ functioning as a verb). Saying that A looks
square does not mean that there is a thing – the look of A – which is square;
similarly, saying that A and B look the same needn’t mean that A and B have
looks that are the same.
I will return, in §7, to interpretations of ‘looks the same’ that commit us to
something which is ‘the look’ of the thing. First, I note that even if we have
concerns about talk of ‘the look’, we can still talk freely about ‘how a thing looks’.
‘How a thing looks’ can be a matter of whether it looks red or looks square or
whatever. ‘Judging how something looks’ is short-hand for judging that it looks F
(for some F). We may want to distinguish between the way something looks and
the way it is, but we can do this by distinguishing apparent properties – ones it
seems to have – from real properties of the thing. So we do not need to see these
as properties of two different subjects – the thing and the look. Talk of how
something looks is talk of apparent properties of that thing.
Having asked whether we are obliged to regard (I) as true, I turn, in the next
section, to responses to the phenomenal sorites paradoxes that do accept the truth
of (I).
2. A NEW SOLUTION TO PHENOMENAL SORITES?
Fara argues that there is an alternative response to the sorites paradox, which is
available in the case of phenomenal sorites, though not in other cases (2001,
p.908-9). This response is to deny that there could be a series of items that would
allow the phenomenal sorites argument to yield its absurd conclusion. Now, in
the case on which we have focused, such a series would consist of patches where
each adjacent pair matches, but the endpoints don’t, and this will mean that
matches, (or looks the same as etc.) would have to be non-transitive. If we could
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show that such relations are, in fact, transitive, we could then deny that any such
series is possible. This is Fara’s strategy in her 2001. 4 Such a position implies a
significant difference between the treatment of phenomenal sorites and the
treatment of other sorites: there is no option of denying that there could be a
series of men each one-hundredth of an inch shorter than the previous one, for
example. My aim is to question Fara’s case for the transitivity of matching
relations with a view to showing that the attempted distinctive treatment of
phenomenal sorites cannot be maintained: we should not expect a different
solution from that of other sorites.
First, note one respect in which the range of sorites paradoxes that could
possibly be solved by the suggested maneuver is narrow. As things are set up, it
is only directed at sorites built on observational predicates like ‘looks F’ (or
‘sounds F’ etc.), rather than ‘is F’ (e.g. ‘is red’ ‘is sour’, let alone ‘is tall’ or ‘is
bald’). But, the strategy in question will not even help with all sorites involving
these observational predicates.
Take our original example of the vat of red paint to which yellow drops of
paint are added one at a time. We formulated the sorites premise above by
appealing to the presumed fact that each patch will look the same as the previous
one. But the sorites argument need not be formulated in this way: we can simply
say, when looking at the series of patches, that if one patch looks red, then so will
the next, or ‘if ai looks red then ai+1 looks red’, where the ai are the series of
patches in question. This inductive premise is highly plausible in its own right,
without explicitly invoking the looks the same as relation. It might be claimed that
actually the plausibility of this premise rests on the assumption that the
4 I focus, in what follows, on questions of whether patches look the same as each other. That may
seem to ignore the disjunctive nature of Fara’s solution which leaves space for a response to a
putative non-transitive series on which we deny that the patches are each homogeneous. Since
homogeneity is a matter of parts of the patch looking the same as each other, we can, without loss,
focus on features and behaviour of ‘looking the same’ and not explicitly discuss homogeneity.
7.
consecutive pairs always look the same. But I deny this. We might say of a pair ‘I
don’t know whether they look (exactly) the same, but they are so similar that it is
certainly the case that if one looks red, so does the other’. We would accept the
successive conditionals corresponding to instances of the premise without first
confirming that the relevant pairs look the same. It may be claimed that in such a
series, some pair (or pairs) of patches may seem to look the same, but in fact do
not; but this would not shake the conviction that the conditional ‘if ai looks red
then ai+1 looks red’ holds of each pair. Denying the non-transitivity of looks the
same as will thus not help to solve this compelling sorites paradox on ‘looks red’,
and the option of denying the possibility of the series is clearly unavailable since
we have described how the series in constructed in terms of an unproblematic
physical set-up.
This is just the first kind of case that cannot be solved by the suggested
maneuver. As the paper progresses, we will see that it also fails for more and
more paradoxes seemingly of the right sort.
3. TYPES OF MATCHING RELATION
The alleged solution to the phenomenal sorites relies on a formulation of the
paradox involving a particular kind of relation that holds between consecutive
members of the relevant series. Let’s consider further what that relation must be
like. As remarked above, various such relations give rise to a highly compelling
inductive premise. For example, the premise may talk of ‘matching’, ‘looking the
same as’, ‘being indiscernible from’, ‘being indiscriminable from’ or ‘having the
same look as’ (interpreted in such a way as to commit us to something, perhaps a
quale, that is the look of something). In this section, I explore some features these
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relations may or may not have, with a view to clarifying which are suitable for a
phenomenal sorites paradox and which, if any, are susceptible to Fara’s response.
Matching notions may be relativised to a person, amounting to ‘looks the
same to me’, or ‘is indiscriminable by Bob’, and use of this sort of relation might
be encouraged given that, intuitively, what looks the same to one person may not
look the same to another (perhaps even assuming something which is the look of a
thing, we could acknowledge a different look for different people).5
We will also need to specify the respect in which the things do (or don’t) look
the same, e.g. in respect of colour. For simplicity, we will focus on the example of
series of colour patches of the same size and shape, so that there is no issue about
looking the same or different in other respects. Other aspects of context may also
need to be fixed; clearly, if something changes colour over time, we may want to
say that it is indiscriminable from another thing at one time but not at another. The
role of fixing context will be crucial to §6 below.
One way in which different matching relations may differ is in relation to the
answers to questions such as the following. If it seems to S that Rab (e.g., that a
and b are indiscriminable), does it follow that Rab? And if it seems that not-Rab,
does it follow that not-Rab? There is a very natural notion of ‘looks the same as’
for which the answer to both these questions is ‘yes’: there is no gap between
how things look to someone and how they seem to look to them, so two things
look the same to someone iff they seem to look the same to that person. As we
will see, this type of notion is particularly important for phenomenal sorites
paradoxes.
5 Many philosophers have assumed (or argued) that ‘o looks F to S’ is semantically prior to ‘o
looks F’; see, e.g. Jackson 1977 and Tye 2002. Martin 2010, by contrast, offers an account which
reverses this order of priority. I need not take a stance on this debate about the semantics of
‘looks’: both sides accept the coherence of both the relativised and unrelativised notions, though
they differ on their account of the understanding of each and the relation between them. Either
assumption about the order of priority is compatible with my discussion.
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Some matching relations, on the other hand, may invalidate the first form of
reasoning. For example, if the look of something can outstrip what we know about
how it looks, then perhaps it can seem to me that two things have the same look,
when in fact they don’t. We’ll explore the idea of ‘the look’ further in §7.
With ‘is indiscriminable from’, the answer to our second question must be
‘no’, for sometimes we make incorrect discriminations between physically
identical things. If they are identical in all physical properties that ground colour,
at most it could merely seem as if I can discriminate between their colours. So, it
doesn’t follow from the fact that it seems that a and b are discriminable that they
are actually discriminable.
Are all matching relations equally effective in a phenomenal sorites paradox?
There are good reasons, I suggest, to require a relation that validates at least the
first of our inferences, from seeming to look the same to looking the same. For,
the idea with the phenomenal sorites paradox is that on the basis of how the
subject judges a pair from the series, he/she is driven to classify the next item the
same way as the previous one and is thereby driven through the series. If we
can’t typically tell whether the matching relation involved in the principle
actually applies to the pairs – it can seem to apply when in fact the pair doesn’t
match – then we will not be in a position to apply the principle and move
through the series. The phenomenal sorites paradox is compelling because it
seems that we would be driven through the relevant series on the basis of how
the items seem to us – the pairs seeming the same will warrant the application of
the premise – so a matching relation reflecting this idea is particularly important.
In §5, we will consider how this kind of thought undermines the alleged solution
to phenomenal sorites paradoxes under consideration. First, I appeal to
differences between different matching relations sketched in this section in
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asking how far other considerations about perception rule out the transitivity of
matching relations.
4. THE LIMITATIONS ON OUR POWERS OF DISCRIMINATION
Many philosophers have assumed that there clearly are, or at least could be,
phenomenal continua, and this is incompatible with the solution to the
phenomenal sorites under consideration. For example, Wright says it is ‘familiar
that we may construct a series of suitable, homogeneously colored patches, in
such a way as to give the impression of a smooth transition from red to orange,
where each patch is indiscriminable in colour from those immediately next to it; it
is the non-transitivity of indiscriminability which generates this possibility’ (1975,
pp. 338–9). Similarly, with something that changes very gradually over time, it
may well be that it looks the same at some time as at a second earlier, but that
several seconds later it does not look the same as at the original time.
Fara considers the suggestion that non-transitivity might follow from
considerations about the limitations on our powers of discrimination – the
thought that ‘physics is finer than the eye’ (Travis 1985, p.350). She uncovers
some arguments to this effect and rejects them. She offers two formulations of the
claim about the limitations on our powers of discrimination, rejects one, (a), as
unacceptable and shows that the other, (b), does not yield the non-transitivity of
matching. I will argue that her two formulations do not exhaust the possibilities,
and that an alternative principle that does yield the non-transitivity of various
matching relations is not subject to her objections. Her formulations are as
follows (they govern change through time rather than differences between two
things, but they could be easily adapted for the latter role):
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(a) For some sufficiently slight amount of change [in colour, or in the
physical basis of colour], when we perceive an object for the entirety of an
interval during which it changes by less than that amount, we perceive it as
not having changed at all during that interval.
(b) For some sufficiently slight amount of change [in colour], we cannot
perceive an object as having changed by less than that amount unless we
perceive it as not having changed at all (as having changed by zero
amount). (2001, p.917)
The intended difference between these principles is that with (a) the
limitation is on the level of difference needed for us to perceive a difference –
below a certain level of change we will perceive no change. With (b), the claim is
that we can’t have experiences of a change of certain tiny amounts – amounts
below the limit. So in (a) the threshold concerns physical differences between
things (the threshold below which no difference is perceived), whereas in (b) the
threshold is on how small a difference we can represent or experience the
difference between things as being.
(b) does not yield non-transitivity in the way that (a) does. But (b) is anyway
an odd principle, appealing, as it does, to the amount of perceived difference.
(The idea of a scale of quantity of apparent difference does not seem relevant:
surely it is only significant whether or not there is perceived to be a difference,
not the degree to which things are perceived as different.) The reason (a) is
rejected, however, does not give us reason to move from considering thresholds
concerning the difference in things to a threshold concerning represented
differences. Fara rejects (a) because it implies that if two things are physically the
same, then we will perceive them as such, when in fact, we can mistakenly judge
that two things are the same colour. As Fara summarises, (a) is incompatible with
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‘the fact that we have certain very mild hallucinations’ (p.932). But Fara’s
objection leaves open the possibility that we replace (a) with a related principle
that avoids Fara’s problem, yet still supports the inference to non-transitivity.
We need to adapt the principle so that it allows for things not looking the
same even when they are the same. By contrast, it is reasonable to say we can
never discriminate between them when they are the same. This suggests that by
using a notion with the logical properties of ‘indiscriminable‘ rather than those of
‘looks the same’, we may be able to preserve the inference to non-transitivity
while not succumbing to Fara’s objection.6 The following principle is better
placed for the task:
(a*) For some sufficiently slight amount of change in colour, or in the
physical basis of colour, when we perceive an object for the entirety of an
interval during which it changes by less than that amount, we cannot
successfully discriminate between the way it is before the change and the way it is
afterwards.
This principle still guarantees the non-transitivity of its central relation. For we
can mirror Fara’s argument (p.918) showing that (a) would support nontransitivity:
(A) Suppose, for example, that whenever we perceive an object that has
grown in height by some amount less than e, we cannot discriminate with
respect to height at the end of the growth as at the start. As long as an object
can grow by an amount less than e, and as long as we can eventually discern
a change in height after repeated growths of amounts less than e, the non-
6
In fact, it is more than the logical properties of ‘indiscriminable’ that are needed, since (a*) also
rules out discrimination when the difference between x and y is below the threshold. This is
accountable for by the fact that ‘discriminable’ is a success term – below the threshold any
difference cannot be detected.
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transitivity of indiscriminable with respect to height clearly follows. (Directly
based on Fara 2001, p.918, with ‘cannot discriminate’ replacing ‘looks to us
the same’)
At the least, then, this argument shows that the transitive matching relations
cannot include ‘indiscriminable’, which further restricts the class of sorites that
can be solved by Fara’s maneuver. But, can we also argue from the nontransitivity of indiscriminable to the non-transitivity of looks the same? Now,
typically when two things are indiscriminable for S, they do look the same to S.
So, when the difference between two things is below the crucial threshold of
discrimination, they will typically look the same. We can thereby chain together
pairs that look the same and get end points that do not look the same. So, a nontransitive sequence for indiscriminable will often also be a non-transitive sequence
for looks the same. We can acknowledge that in some cases S is unable to
discriminate between two things although they do not look the same to S, so
some non-transitive sequences for indiscriminable will not demonstrate the nontransitivity of looks the same; but as long as some sequences serve both purposes,
we reach the desired conclusion for looks the same.
This, however, still leaves open the possibility that there are no such
sequences for looks the same as. There may be no a priori guarantee that successive
stages of our series look the same, because there are no circumstances under
which we can guarantee that two things look the same. But, first, this should
make us suspicious about whether there can be an argument for transitivity
either. And, second, if we can know by looking that pairs in a series do in fact
look the same, as you might expect, then we will be home and dry. The defender
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of transitivity will have to deny that we can know this: this feature of the
required notion of looks the same will feature prominently in what follows.
In this section I have argued that appealing to limitations on our powers of
discrimination can show the non-transitivity of certain matching relations and
gives us good reasons to expect the non-transitivity of others.7 Fara’s response to
phenomenal sorites paradoxes won’t work for the former, and I will go on to
argue that maintaining, against the above arguments, that ‘looks the same’ is
transitive comes at too high a price.
5. MAINTAINING TRANSITIVITY
It seems to us as if there are series of things that demonstrate the nontransitivity of matching relations and, indeed, that the series involved in
phenomenal sorites are among such series. Take the example from the beginning
of this paper in which patches are painted from a vat of paint as drops of yellow
paint are added one at a time. The patches start out looking red and finish off
looking a yellowy orange, and each patch looks the same as the previous one.
What can the defender of transitivity say about these apparently non-transitive
series?8 In §6, I will consider responses that appeal to a change of context for the
different comparisons. In this section I focus on options that do not rely on claims
of context change.
The most obvious response to restore transitivity would be to say that in
every apparently non-transitive series there is, in fact, a non-matching
consecutive pair. This saddles us with considerable error in our judgment of how
things look to us: I think that consecutive pairs look the same to me, but in fact
7
Hellie 2005 offered a detailed account of perceptual indiscriminability that accommodates its
non-transitivity by appeal to the ‘unavoidable presence of noise in perception’ (p.489), which
ensures inexactness in our colour perception.
8 The argument that follows depends on the assumption that there are series that at least appear to
demonstrate non-transitivity. I cannot show this a priori, but my claim is none the worse for that.
15.
not all of them do. It drives a wedge between what seems to look the same to me
and what in fact does look the same. And there will be a non-matching pair that I
judge to match whenever there is apparent non-transitivity, which will occur very
frequently along the sorites series. So, it is not simply that each sorites series from
something looking F to something looking not-F commits us to a pair about
which we are wrong (as the epistemicist is committed to a single false instance of
the sorites premise). Transitivity fails over and over again through small sections
of the series, so on this view there will be many pairs about which we are wrong
and we will not even count as generally reliable when it comes to our judgments
of when two things look the same to us.9 I return in §7 to this widespread
fallibility about our judgments of when things look the same.
The matching relation most crucial to phenomenal sorites and the most
natural interpretation of ‘looks the same’ is one for which looking the same
cannot come apart from seeming to look the same. But could someone object that
there is in fact no such coherent notion? I think this line is implausible, but
anyway the problem would surface again if we appealed, instead, to the idea of
‘seems to look the same’: when we judge of each consecutive pair of the series
that they look the same as each other, they surely at least seem to look the same.
But if we allow that consecutive members of the series seem to look the same,
then we can simply run the phenomenal sorites with ‘seems to look the same’
9 Fara says that she is focusing on ‘a sense of “looks” that carries no explicit epistemological
implications, so that to hold that a person does or could know everything about the way things
look to her, or even to hold that a person could have no false beliefs about the way things look to
her, is to hold a substantive thesis’ (p.910). Resisting the wedge between looking the same and
seeming to look the same does not amount to such a substantive thesis in full generality. It may
be, for example, that we are not altogether reliable informants on whether something looks the
same to us as it did an hour ago: our memory of how things looked to us is far from infallible. So,
Fara’s case – pp.927–28, where she only notices that her friend’s hair is lighter than the previous
day after it is pointed out to her – is significantly different from the kind of judgment involved in
the sorites series. We can, of course, present the members of a sorites series so that consecutive
members are adjacent and seen together. The proponent of the described view is committed to
rampant error over our judgments about whether things look the same to us even when things
are presented in ideal conditions.
16.
instead of ‘looks the same’. The reformulated phenomenal sorites premise may
then read (S) if x seems to look red and x seems to look the same as y, then y
seems to look red. Clearly this premise is highly plausible. Again, it appears that
you can have series which, given this premise, lead us through from the
indubitable to the absurd. Taking the line described above would require saying
that there are pairs that apparently seem to look the same but actually don’t. But
this does not seem to be taking seriously the intended notion of seeming to look
the same.
Of course, standard solutions to the sorites paradox will, as in other cases,
have to deny the truth of (S). But, take the supervaluationist solution: there is no
instance that is a counter-example to this principle. There is no a and b of which it
is true that a seems to look red, a seems to look the same as b, but b does not seem
to look red. Rather, the vagueness of ‘seems to look red’ accounts for the falsity of
the premise: there is no unique point at which it suddenly becomes true that the
patch seems to look red and so we have to consider all the possible patches
corresponding to ways of making that notion precise.
We are left with an even narrower range of matching notions that may be
transitive. Correspondingly, at best, denying the existence of the appropriate
sorites series has provided a reply to a smaller class of sorites arguments and not
the paradoxes it was particularly important to solve (as we saw at the end of §3).
In §7, I will ask just how narrow the category of solved paradoxes is. But first I
will consider another option for the defender of transitivity – an appeal to
changes in context that occur between different judgments that different pairs
look the same.
6. TRANSITIVITY AND CONTEXT
17.
‘Taller than’ is a transitive relation. But Arnie can be taller than Barney in 1990,
Barney taller than Carlie in 2000, while Arnie is not taller than Carlie in 2000.
Intuitively, this fails to show that ‘taller than’ isn’t transitive, because the three
comparisons do not all take place in the same context. Similarly, Raffman
considers the case where ‘A is indiscriminable from B in infrared light, B is
indiscriminable from C in incandescent light, and A is discriminable from C in
the noonday sun.’ (2001, p.161) and claims, plausibly, that this won’t work as a
counter-example to the transitivity of indiscriminability.
A counter-example to the transitivity of R will be of the form
(C) Rab & Rbc & ¬Rac
The above cases suggest that there must be a single context in which all three
of these conjuncts hold together.
Now, the way that something looks to us with respect to colour can change if
its surroundings change. There are striking cases where the background against
which a coloured square is set can make the square look darker or lighter or
perhaps more green or more blue (see e.g. Hardin 1988, plate 2). Apparent colour
may even change as the subject focuses on something different within a scene.
So, even if we find a triplet of things where the subject judges the first and
second to look the same, the second and third to look the same, but the first and
third to look different, this does not serve to establish that looks the same is nontransitive unless we can be confident that context hasn’t changed between the
comparisons.
This point could then be used in response to the phenomenal sorites as
follows. Imagine going through the sorites series for ‘looks red’, and judging each
consecutive pair to look the same. Transitivity and the phenomenal sorites
inductive premise would compel you to say that everything looks red given that
18.
the first thing does. But, suppose you judge c to look the same as b, when b, after
its comparison with a, has been judged to look red. This need not force you to say
that b and c both look red; you can say that neither of them does. This isn’t to
contradict your assertion that b looked red when compared with a, for the look of
b can change with the context - change induced by comparing it with something
different. This is the basic idea of Raffman’s defense of transitivity, and is also
central to Fara’s defence (see, e.g., 2001 p.934). It can be traced back to Jackson
and Pinkerton (1973), who sought to defend ‘sensory items’ (i.e. visual qualia)
against attacks via non-transitivity.
Is the simple fact that the middle term, b, is compared with different things in
the two comparisons enough to yield a different context? If so, this would mean
that there could never be a single context in which Rab & Rbc & ¬Rac. But then,
nor could there be a context obeying transitivity in which Rab & Rbc & Rac but a≠c
(for, when a≠c, Rab and Rbc will always hold in different contexts) and this
renders transitivity a trivial matter. This cannot be the intended interpretation.
What matters for putative counterexamples to transitivity is not what we call
different contexts, but whether there is a relevant difference between the contexts
in which the two comparisons occur. So the putative counterexamples are only
met if the contexts in which Rab and Rbc are relevantly different. If the middle
term, b, looks the same in the two comparisons, then why think that the change in
what it is compared to is significant?10
And I suggest that b will frequently seem to look the same, even though it is
compared with two different (though very similar) things; that, for one, is my
experience. Suppose the subject does judge that b looks the same when being
10 Raffman says, p.162, ‘If the argument for nontransitivity is to succeed … each patch must look
the same in both of its comparisons.’ In Fara’s terms, if b looks the same in the two comparisons,
we have ‘license to carry over the “middle term”’, (2001, p.913). These quotes both strongly
suggest that there is a coherent possibility of b looking the same in the two contexts of
comparison.
19.
compared with the patch on the left as it looks when it is compared with that on
the right. Can’t we trust them on this? Raffman leaves the burden of proof with
the defender of non-transitivity, pointing out the problems with guaranteeing that
the patches look the same throughout (p.163). But, as long as the subject thinks
they look the same throughout, this, again, would mean that their judgment of
whether two things look the same was not a reliable guide to whether they do
look the same to that subject. That this is an unacceptable consequence for
Raffman should be apparent from the following quote: ‘discriminatory judgment
and phenomenology go hand in hand: stimuli look the same (different) to a
subject in a context just in case the subject would make a judgment of sameness
(difference) were he to compare the stimuli in that context’ (p.158).11
Might Raffman reply that the fallibility I have diagnosed involves looking the
same across contexts, not within a single context? Maybe such fallibility is easier
to swallow. But is that distinction sustainable? If you can compare two things (or
one thing in two different circumstances), then there must be a context in which
you are comparing them. (For example, for the cases where one stage is after the
other, you will be comparing them in the context of the later stage.) And that
comparison is the one that is problematic for Raffman. She may then say that this
is a new context, so it does not amount to comparing across contexts, so nor can it
serve to challenge transitivity. But this is then to return to the trivial version of
denying non-transitivity, by ruling that anything of the required form is
impossible regardless of how the things look in the various contexts.12
11
Mills 2002 also argues that ‘perceptual inconstancy does not lie at the heart of the paradox’
(p.388).
12 Fara 2000 and Raffman 1994 both, more generally, defend theories of vagueness that could
broadly be called ‘contextualist’ and that seek to accommodate vagueness by appeal to changes in
context between different judgments (see, e.g. Fara 2000 and Raffman 1994). For some objections
to such accounts, see e.g. Stanley 2003 and Keefe 2007.
20.
Certain substantial changes in environment can change how something
looks, and we can notice that change, but if the small change made by comparing
b with c rather than the (barely different) a has any effect on the colour of the
patch, we can (often) honestly say that it is an effect that we cannot see. Thus, as
with the non-contextualist way of maintaining transitivity discussed in the
previous section, the contextualist response commits us to widespread fallibility
about our own judgments of whether things look the same, or are
indiscriminable, to us.
7. WHAT A TRANSITIVE MATCHING RELATION WOULD HAVE TO BE
LIKE
We have reached some conclusions about what a transitive matching relation
must be like. First, it cannot be a notion of indiscriminability according to which
two things can never be discriminated when they are the same in the relevant
respects; otherwise we could show that the relation must be non-transitive (see
§4, above). Second, the fact that someone, in ideal conditions and after careful
consideration always judges that a looks the same as b does not imply that a and b
do look the same to her. Whether things look the same to me can be (and often is)
beyond my grasp. This feature was needed to ensure that series in which we
make judgments that appear to commit us to non-transitivity do not show that
there is non-transitivity. Let us consider this last feature in a little more detail.13
Fara’s ‘phenomenal sense of looks’ is supposed to be the sense used in
observational reports (Fara 2001 p.910); but if two things seem to look the same,
that will be the content of our observational report, leaving no room for those two
things in fact to fail to look the same. If there is a gap between how things look
13 See also Mills 2002 on the fallibility required in relation to the notions involved in a
phenomenal sorites.
21.
and how they seem to look, observational reports will line up with the latter and
so the required notion of matching would need to line up with it too. The
fallibilist notion needed for the view in question is thus not what Fara meant. It
is, as I argued earlier, also not the notion that best draws us down the sorites
series, since our judgments of consecutive pairs looking the same does not ensure
the applicability of the sorites premise or its corresponding inference about the
next item in the series. Moreover, the assumption that we cannot be wrong about
how things look to us made particularly striking the contrast between nonphenomenal sorites and other sorites. For example, you may allow surprising
ignorance regarding an expression such as ‘is tall’ – we are not quite the masters
of such expressions that we thought – but deny it for expressions of which we
cannot fail to be master since their applicability depends entirely on our
judgement. If we turn out to be ignorant about applicability of the phenomenal
notions in question, then the standard solutions may be just as viable as in the
non-phenomenal cases.
Returning to the notion required for transitivity: when do two things look the
same to me on this understanding, given that it is not simply when they seem to
look the same? Perhaps, the answer is that whether they look the same depends
on the look of those things. Looking the same can amount to having the same look,
where we needn’t assume that all aspects of the look of something are accessible to
us. But what does having the same look amount to? Is there a coherent notion of
‘the look’ to play the required role?
Recall that there is no guarantee that two things have the same look just
because they are the same in the relevant physical respects: Fara used this in her
rejection of a proposed argument for non-transitivity. So, for Fara at least, it
22.
cannot be that the look of a thing is entirely determined by its physical properties
and its surroundings (e.g. viewing conditions).
Could the look be an apprehended qualitative property, i.e. the quale
perceived? On this understanding, two things present the same qualia iff they
look the same. Fara and Raffman both cite a particular argument against qualia or
sense-data as another reason why we should be interested in whether matching
relations are non-transitive. The argument appeals to the alleged non-transitivity
of matching relations as follows (see e.g. Armstrong 1968). Suppose a, b and c
constitute a counter-example to the transitivity of looks the same. Then if a and b
look the same, they present the same qualia, and if b also looks the same as c then
all three of a, b and c must present the same qualia, which is incompatible with a
and c not looking the same.
Some have thought that the above argument demonstrates that there can be
no qualia. Fara and Raffman can respond that no such non-transitive triple of a, b
and c is in fact possible because looks the same is transitive. They appeal to the
above argument as a reason to place the burden of proof on those arguing against
transitivity. But, with a clearer idea of what a transitive matching relation must
be like, we can see that it is not the kind of relation to which the typical defender
of qualia is likely to appeal.
For example, typical characterizations of qualia have it that we are generally
right in our beliefs about our own qualia. This is in tension with our fallibility
about how things look to us to which, I have argued, the defender of transitivity
is committed. On the other hand, there are physicalist and/or functionalist
characterizations
that
are
compatible
with
the
non-transitivity
of
indiscriminability (see e.g. Clark 1985), so those will not help our defender of
transitivity.
23.
One way to explain what it is to have the same look would be to adopt
something like Goodman’s criterion of sameness of phenomenal shade: a and b
have the same phenomenal shade/look iff they match all the same things
(Goodman 1951). This would explain why you cannot always tell whether a and b
have the same look just by looking at a and b, for it may be that they appear to
match, but that only one of them matches a third thing, c. For Goodman, then,
looking the same (‘matching’ in his terminology) is not the same as having the
same look (or presenting the same quale). Although having the same look implies
looking the same, it is not implied by it. So, we could consider a sorites premise
involving a Goodmanian notion of ‘having the same look’ and then deny the
existence of the corresponding series. But this is, at best, not the most natural
formulation of phenomenal sorites paradox. A phenomenal sorites paradox will
not generally appeal to this notion but rather to the notion of matching on which
this notion is built; no response has been given to that central case. And it cannot
be maintained that the non-transitive notion of matching is not coherent, for that
is exactly the notion required to comprehend Goodman’s transitive notion (which
is a matter of matching all the same things).
In short, if there is a coherent notion of the look or qualia, it may indeed
support the transitive notion of ‘having the same look’. But, it is not the relation
central to phenomenal sorites paradoxes. Fara herself, however, rejects
Goodman’s distinction between ‘looks the same’ and ‘has the same look’,
claiming to find it ‘barely coherent’. But we should doubt whether there is any
coherent notion of ‘the look’ that plays all the roles she needs.
Denying non-transitivity and so the availability of a sorites series does not
provide a satisfactory solution to phenomenal sorites paradoxes. It is, I suggest,
24.
like solving the paradox of the heap by considering a formulation of the inductive
premise such as ‘if we take one grain away from a heap without altering the
arrangement of grains, then we are left with a heap’. This principle is highly
compelling, and is true because we cannot remove a grain without changing the
arrangement of grains. No series can be constructed that chains together
instances of the premise and results in absurdity. But how significant is this when
we still get a paradox of the heap using the highly compelling premise ‘if we take
one grain away from a heap (with minimal alteration of the arrangement of
grains), then we are left with a heap’?
The transitivity solution to phenomenal sorites paradoxes that we have
discussed here implies that our proper response to a phenomenal sorites paradox
would be to refuse to acknowledge that pairs exemplify the premise: ‘ah, they
don’t actually look the same even though they seem to (or even though I judge
that they do, or some such), so it may be that one looks red and the other doesn’t’.
Can that really be an adequate response to the force of the argument that pulls
you down the series? You may feel as compelled to carry on down the series even
after acknowledging that some pairs do not literally fulfill some such demanding
relation. That suggests that the problem has to be pinned on the vagueness of
‘looks red’ and that one of the standard solutions to the paradox is required to get
to the heart of the matter.14
The category of phenomenal sorites paradoxes is of particular interest
because of the observationality of the terms involved. But, I have argued, there is
14 Such a solution will not be the end of the story in relation to the paradox for ‘looks red’, as
further explanation may be needed of the vagueness of such a term. But that gap could be filled in
a variety of ways. For example, suppose you adopt Martin’s account according to which ‘looks
statements are made true just by properties of objects that we need to appeal to in order to explain
the truth of sentences that are not explicitly looks sentences’ (2010, p. 197) and such statements are
to be understood in terms of comparisons with other things that we take to be paradigm
examples. Vagueness in ‘looks red’ can then naturally be attributed to vagueness in the level of
similarity required or the choice of paradigms; and, for example, someone seeking to treat
vagueness as a species of ignorance can locate our ignorance in such matters without denying our
authoritative knowledge of our own psychological states.
25.
no conclusive reason to think that phenomenal sorites and non-phenomenal
sorites call for different solutions.∗
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∗
I’m very grateful to several anonymous referees for helpful comments and suggestions and to
Dominic Gregory for discussion of a draft of the paper. I am also very grateful to the AHRC, who
funded a period of leave in which I worked on material for this paper and I acknowledge the
‘Borderlineness and Tolerance’ project, of which I am a part (ref. FFI2010-16984, MICINN, funded
by the Government of Spain).
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27.