Abstract
Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability: it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting putative cases of non-transitivity, fallibilists would have to claim that there can’t be any perceptual limitations of any kind on human chromatic discrimination. But there are good reasons to think such limitations exist.
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Notes
Note the difference in quantification between (ntl) and (tran): the former is all one needs to falsify the latter. Note also the existential quantification over subjects in both (ntl) and (tran). The prime reason for this is that (tran) could be too easily false—and (ntl) too easily true—if their respective formulations quantified universally over subjects: surely, there could be some unusual perceivers for whom the antecedent of (tran) is true, but not its consequent. On the other hand, against the formulation of (tran) used in the text, one could object (as an anonymous referee did) that (1) it renders the truth of (tran) dependent on the existence of perceivers, and that (2) (tran) could turn out to be trivially true, if there is a subject for whom nothing ever looks the same—perhaps, because her eyes are closed. Both worries seem misguided. Regarding (1): if, as most (including looks-fallibilists) seem to assume, visual appearances depend to some extent on certain features of our experiences and/or our visual system, then one should expect that the truth of claims like (tran) or (ntl) depends, amongst other things, on the existence of perceivers without whom there wouldn’t be experiences and/or visual systems. As for (2), its importance shouldn’t be exaggerated. If one assumes a classical semantics (i.e., the semantics of the horseshoe) for conditionals like (tran), then such conditionals can always be trivially true (and rather easily so) just in case their antecedent is false. Thus, even if (tran) quantified universally over subjects, one could still imagine various scenarios where its antecedent is false, and the whole conditional true. For instance, substitute any invisible property for ‘F’; or consider (tran) during a solar eclipse. Surely, however, the substantive issue between proponents of (tran) and (ntl) is in no way undermined by such possibilities. For the real question is: when we have three (or more) overlapping pairs of adjacent patches that really look chromatically the same, do the end patches look the same too, or not?
If they seem discriminable to you, imagine a series with many more patches, much thinner in width, so that adjacent patches really are chromatically indiscriminable. That is, don’t confuse the limitations of the illustration for a significant aspect of the case.
I shall treat anyone who (i) attempts to deflect putative counterexamples to (tran) by (ii) essentially denying (pils) on the ground that (iii) we have only fallible access to appearances, as committed to some form of fallibilism about looks. This seems to include, to different extents, Fara (2001), Mills (2002), and Williamson (1990, 1994). This isn’t to say that these authors don’t make use of any other strategy and argument in their attempt to defend (tran), as Fara (2001) clearly does, for instance. (For discussion of some such arguments and strategies, see, for instance, De Clercq and Horsten (2004), as well as Chuard and Corry (2006).) But I lack the space to discuss all their arguments and strategies here: I’m only concerned with the denial of (pils) and how it can serve to resist certain intuitive motivations for (ntl). However, in n. 34, I explain how some of these arguments do not apply here. Finally, though there is a large terminological and theoretical overlap between proponents of fallibilism about looks, there are complex and subtle differences between their respective versions of looks-fallibilism, some of which I’ll discuss below. I should also insist that I do not take looks-fallibilists to present an argument for their position, as an anonymous referee suggested I did: the fallibilist strategy, as I understand it, simply comes down to undermining certain examples—and the assumptions informing such examples—which intuitively falsify (tran). (Though, of course, insofar as the considerations looks-fallibilists advance in so doing can be reconstructed in argument-form, as indeed they can, one could say that such considerations do, strictly speaking, amount to an argument.)
To be contrasted with an epistemic notion of “looks”—as in “it looks as though the democrats will win”—which can be construed, either as reporting evidence one has for a given proposition, or as making a statement one is uncertain of. It’s not entirely clear what’s the best way to draw the distinction between the phenomenal and the epistemic conceptions of “looks”, let alone whether there is a precise way to draw such a distinction. For a recent survey of ways to carve out the differences, see Maund (2003, chap. 7).
One complication worth noting: the notion of an ‘observational predicate’ can be cashed out differently. Compare:
Colour predicates […] are in the following sense purely observational: if one can tell at all what colour something is, one can tell just by looking at it. The look of an object decides its colour, as the feel of an object decides its texture or the sound of a note its pitch… (Wright 1975, p. 338).
On the account of observationality which figures in Dummett […], a predicate is observational if whether it applies to an object can invariably be determined just by (unaided) observation of that object (Wright 1987/1997, p. 223).
A predicate is observational just in case its applicability to an object (given a fixed context of evaluation) depends only on the way that object appears (Fara 2001, p. 907).
Depending on how “decides”, “determines”, and other cognate notions are interpreted, we can extract at least three different conceptions of observational predicates from these passages. The first (see the quotes by Wright) is epistemic: observational predicates are those predicates denoting properties to which our only epistemic access is via observation—so that the only epistemic justification we have for their true application is grounded in observation. The second conception is metaphysical, and involves a different reading of the same two passages: a predicate is observational in the sense that observation determines or fixes the actual extension of the predicate. This second conception is stronger than the first because, unlike the first, it does not allow that one falsely (though warrantedly) applies an observational predicate on an observational basis. A third reading seems to be at play in Fara’s explanation of the notion: there, she seems to be concerned with the ‘correct’ application (“applicability”) of an observational predicate, where correctness might be thought to be primarily pragmatic. In this sense, one might correctly use a predicate “is F” even if one fails to express an epistemically justified or true belief with such an assertion—making this third conception weaker than the other two.
Though distinct, they may be related. One could hold, for instance, that the look of an object on a given occasion is partly determined by the subject’s experience, its phenomenal character, or by some features of the subject’s visual system—‘partly’, because how an object visually appears to a perceiver is also determined by certain properties of the surface of the object (and of other objects around it), as well as various features of the external conditions in which such an object is experienced (e.g., the lighting conditions, the spatial relations between the object and the perceiver, etc.). Perhaps, this is why Fara, even though she recognises the difference between the appearances of objects and the qualia of experiences, suggests that one of Goodman’s (1951) criteria for matching qualia is extensionally equivalent to a notion of “looking the same” (2001, p. 911).
There seems to be some divergence amongst looks-fallibilists regarding our epistemic access to looks. Whilst Fara (2001, p. 910) seems to deny (i) a thesis of revelation about looks (i.e., she denies that, when having perceptual access to the look of an object, one is in a position to know everything about that look), as well as (ii) the claim that we cannot have false beliefs about looks, Mills allows that we have some degree of infallibility regarding determinable looks (like “looks red”), to the extent that, if S believes that o looks w (where w is determinable), then o looks w (2002, p. 385). Hence, there are some looks which, contra Fara (2001, p. 910), we cannot have false beliefs about (see Mills 2002, p. 406, n. 11 for some complications). Note that Mills (2002, p. 391) doesn’t think such infallibility carries over to maximally specific chromatic appearances. Nor, importantly, does it carry over to whether or not two objects share such maximally specific looks (Mills 2002, pp. 391–392, 394).
Especially if looks are picked out by observational predicates in any of the three senses specified in note 6.
Indeed, if one assumes that the representational content of experience is closely connected with its phenomenal character—such that, for instance, the latter supervenes on the former, as Intentionalists (like Byrne 2001; Dretske 1995; and Tye 1995, 2000) have it, or vice versa—then, visual appearances may be determined by both, though perhaps not quite in the same way.
For an interesting account of the differences between these two readings, see Yablo (2002, pp. 465–466). One interesting question is whether the two interpretations of (D) are, pace Yablo, compatible—so that experiences both constitute and represent appearances. In any case, it’s important to note that, under either interpretation, (D) is perfectly compatible with the claim that looks are objective, in the sense that they are not response-dependent, and that we can have false beliefs—or simply lack belief—about them. As a tracking thesis, (D) only says that veridical experiences can accurately represent differences in appearances, not that our beliefs do. Similarly, even if the looks of things are constituted (entirely, or only in part) by our experiences, this is compatible with the requirement that looks aren’t dependent on the subjects’ beliefs or verbal reports. Perceptual and doxastic responses aren’t the same thing, and it’s compatible with (D) that subjects can make mistakes—or lack belief—about their own perceptual responses.
Note that (ls1) ought to be kept distinct from a third interpretation of “looking the same as …” in terms of strict identity, which quantifies over colours (rather than appearances) and analyses the relation of looking the same as … in terms of “looking to have the same colour” where there is a colour both objects look to have (Fara 2001, p. 914; Jackson 1977, p. 114). Of course, this third reading will be equivalent to (ls1), under the assumption that two objects have the same chromatic appearance if and only if there is one colour they both look to have.
For the distinction, see Williamson (1990, p. 93), who develops it for “feels” rather than “looks”; and Fara (2001, p. 915), who adds that she finds it “barely coherent” (2001, p. 916). It is interesting that, when complaining against the second conception of “looking the same as …”, Fara comes awfully close to sounding infallibilist:
The opponent of transitivity is [..] committed to the possibility that A and B might be perceptually indistinguishable yet have different looks. But what I have difficulty understanding is, if it is really the look of the two which is different, why cannot this come across, so to speak, by looking just at them? […] Moreover, it becomes impossible, […], to tell by looking whether two things have identical looks—it becomes impossible for the identity of their looks to visually come across. […] Thus, there is a heavy burden on the opponent of transitivity to persuade us that the look of a thing is, […], still a phenomenal quality. (Fara 2001, pp. 915–916).
What is interesting is that, as we shall see (Sect. 2.3), Fara advocates a similar claim against (pils)—that differences in looks may not come across visually, just by looking at them (see n. 28). And yet, she nowhere attempts to meet her own challenge and explain how visually inaccessible differences in looks still count as phenomenal—as De Clercq and Horsten (2004, pp. 443–444) have noted. If the challenge can be met, then, presumably, her opponents can meet it too. It’s also worth noting (as did an anonymous referee) that, if Fara is right, advocates of non-transitivity are also committed to some form of fallibilism. What is crucial to the kind of looks-fallibilism at issue in this paper, however, is the use of claims like (a) and (b) to preserve (tran) from intuitive counterexamples (see n. 4).
Note the reason why Fara takes (p) to be a truism: it’s supposed to follow from the observational nature of “looks red”. Depending on which conception of observationality one has in mind (see note 6), however, it’s unclear whether that’s quite right. Indeed, nothing short of the stronger conception I called ‘metaphysical’—where observation fixes the true extension of such observational predicates—can ensure the truth of (p). In particular, the fact that “looks red” is correctly used only on the basis of observation (what I called the ‘pragmatic’ conception) may ensure that the use of such predicates in (p) is correct, but not necessarily that (p) is true—likewise for the epistemic conception. For Williamson, in contrast, (p) follows from (ls1)—where ‘looking the same as …’ is a matter of the strict numerical identity of chromatic appearances—coupled with Leibniz’s Law (indiscernibility of identicals): if x and y have the same look, then any property had by the look of x (including being a red appearance) is shared by the look of y. It’s also worth noting that there are readings of (p) where it is false—and hence, not a truism. Following Mills (2002, p. 390), suppose that x looks red whilst y looks orange: still, there is a highly determinable chromatic appearance, encompassing red and orange appearances, which x and y share so that they look the same in this sense (they have the same highly determinable chromatic look). But if they look the same in such a way, the fact that x looks red does not entail that y looks red too (since it looks orange).
Here, I essentially follow Fara’s presentation; Mills’ is somewhat different. For one thing, he seems more focused on solving the phenomenal sorites than just resisting (ntl): he does insist that if adjacent patches look chromatically the same in the sense that they share the same determinate chromatic appearance à la (ls1), then there is no paradox, since strict identity of determinate appearances is transitive (2002, p. 393). For another, Mills claims to be denying the “induction premise” (2002, p. 384), but characterises (ibid.) it differently, in terms of the consequent of (p), not (p) itself. But both agree that there is no reason to accept the antecedent of (p) as applied to adjacent patches on a phenomenal sorites series. For some further differences between their accounts, see Sect. 2.3.
Where the premises she seems concerned with (see the version of the phenomenal sorites on p. 934) are those stating that adjacent patches look the same. Two things worth pointing out here. First, it’s a mistake to think that phenomenal sorites arguments are arguments against the transitivity of looking the same as … (as an anonymous referee seemed to suggest). Phenomenal sorites arguments merely rely on the assumption that (ntl) is true about the phenomenal sorites series. In itself, such an assumption hardly constitutes an argument against (tran). It’s just that if (tran) is true, there is no phenomenal sorites argument (and hence no paradox) to solve. Second, and more importantly, there are reasons to be sceptical of this motivation for denying (ntl). True, phenomenal sorites arguments presuppose that (ntl) is true of the phenomenal sorites series. However, it’s unclear that the solution advocated by looks-fallibilists is actually incompatible with (ntl)—it’s only incompatible with the claim that the whole phenomenal sorites series instantiates (ntl), not with the claim that (ntl) is instantiated by at least some triple of objects on the series. For all it takes to block the phenomenal sorites argument along the lines just sketched by Mills and Fara is to deny of at least one pair of adjacent patches that they look chromatically the same, which leaves it open that many other pairs of adjacent patches look chromatically the same (at the same time), so that there can still be a succession of such pairs (a subset of the series) which instantiates (ntl)—Mills (2002, p. 394), who is explicit about this point, also makes the stronger claim that no adjacent patches look the same insofar as their maximally specific appearances are concerned. Hence, it’s a mistake to think (as Fara suggests in the above passage) that such a solution must be grounded in the transitivity of looking the same as …. For more on this, see Chuard (2008b).
Which some are indeed prepared to deny (thanks to Graham Priest and Mark Colyvan).
To say that two objets x and y are perceptually indiscriminable to a subject S in a given respect F is to say that S cannot detect any difference between x and y pertaining to their F-ness simply on the basis of looking at them (and only on that basis). The kind of discriminability (or indiscriminability) at issue is based entirely on S’s current perceptual experience(s) of x and y, and hence (i) cannot involve any other source of information, nor (ii) can it involve inferences based on other sources of information. In this sense, perceptual indiscriminability is supposed to be “direct” rather than “indirect”—where x and y are indirectly indiscriminable if and only if any z that’s indiscriminable from x is indiscriminable from y and vice versa (see Williamson 1990, pp. 13–14; and also Fara 2001, p. 910; Mills 2002, p. 392). Second, if x and y are perceptually indiscriminable to S, this need not mean that S actually judges that they are the same in the relevant respect. Rather, it means that S is in no position to judge that they are different. Third, what is the connection between perceptual indiscriminability with respect to colour and chromatic appearances? Note that it is the colours of objects which are supposed to be perceptually indiscriminable in the first place. But if objects have chromatic appearances distinct from—though likely dependent upon, at least in part—their chromatic properties (see Sect. 2.1.ii), it seems likely that we perceive the latter by perceiving the former. Hence, it may be that the colours of two objects are discriminable (or indiscriminable) because their chromatic appearances are discriminable (or indiscriminable). In which case, a failure to discriminate colours reveals a failure to discriminate chromatic appearances.
Looks-fallibilists need not deny the converse of (pils), though: they can agree that if two objects look the same in some respect, they are therefore perceptually indiscriminable in that respect (see Williamson 1994, p. 179).
A third type of explanation, which seems less easily applicable to the case of colour and simultaneous pairwise presentations of adjacent patches—which is why I shall ignore it here—has to do with memory and its limitations: see Williamson (1990, pp. 59, 99) for discussion.
Where noticing is meant as a ‘cognitive’ notion. For Fara (2001, p. 928), when S notices x, it seems that the following (at least) must hold: (i) x exists, (ii) x is “apparent” (presumably, in the sense that S consciously perceives x), and (iii) S believes that x exists and is apparent. It would be reasonable to assume that the belief in (iii) cannot be based on just anything (such as testimony, say), but must be caused by S’s perceptual experience. Presumably, the reason why we fail to notice small differences in appearance, according to fallibilists, has to do with (iii) rather than (i) or (ii).
I should say that what Fara targets in this passage (and others cited below) is a premise—which she dubs the ‘homogeneity thesis’—in an argument for the non-transitivity of looking the same as … based on the existence of phenomenal continua. The premise says that small enough regions of a phenomenal continuum—for instance, a series of coloured patches organised in such a way that the series appears to change in colour continuously—look homogeneous (Fara 2001, pp. 924–925). I shall not be concerned here with such an argument, or the homogeneity thesis itself (for discussion, see Chuard and Corry 2006). The crucial point is that the explanation on offer—which is designed to undermine certain motivations for the homogeneity thesis—also works against (ntl) in the sense that it is designed to undermine (pils). The idea is that adjacent parts of the relevant series—in this particular passage, spatio-temporal phases of the hour-hand of a clock—do not in fact look the same. And yet, they are perceptually indiscriminable because we cannot notice the difference in appearance.
Which suggests that, for Fara, looks may be constituted, at least in part, by the phenomenal character of perceptual experiences, so that:
- (D*):
-
x and y look different to S with respect to F ↔ S’s experience of x has phenomenal property P & S’s experience of y has phenomenal property P’ & P ≠ P’.
where phenomenal properties P and P’ are the properties of an experience constitutive of its phenomenal character, at least in relation to the perceptual representation of property F. Note that (D*) is also compatible with the claim that looks are objective, in the sense that they are not determined by the subject’s doxastic or verbal responses (see Sect. 2.1.iii). Perhaps, if Fara endorses (d*), this could explain why she seems prepared (2001, p. 911) to treat the identity of looks as equivalent with the matching of qualia.
A caveat: the suggestion need not be, of course, that one consciously infers a belief about how things are, or look, on the basis of introspection of one’s experiences. Rather, the latter may be partly constitutive of (or accompany) the automatic process by which one forms beliefs about the perceived environment. For discussion and defence of this sort of ‘introspective fallibilism’, see Williamson (1990, chap. 6; 2000, pp. 97–98), as well as Fantl and Howell (2003).
In both quotes, however, the examples show at most that the relevant difference is not discriminated on a given occasion. They do not show that such a difference is truly indiscriminable, since the subject is able, later, to discriminate it. Hence, such examples fail to support the rejection of (pils), for (pils) is not so strong as to say that, if x and y are not discriminated in a certain respect, they look the same in that respect. On the other hand, if different looks truly are indiscriminable, there is the question as to how we can know they are different (Mills 2002, p. 391). Though Mills (2002, p. 392) insists that adjacent patches on a series are pairwise indiscriminable—it’s impossible to notice the difference between their maximally specific chromatic appearances in a context where they are presented side-by-side, as on a phenomenal sorites series—he grants that such distinct chromatic appearances must be discriminable, if only indirectly (Mills 2002, p. 392). In contrast, Fara insists that “looks” are observational predicates, and as such accessible on the basis of observation (Fara 2001, pp. 915–916), yet some of her examples (see 2.3.i) do suggest that differences between looks may not be accessible: see also De Clercq and Horsten (2004, pp. 443–444).
Is this sufficient to solve phenomenal sorites arguments? One reason for scepticism is that, even if two adjacent patches have at least one chromatic appearance by which they differ (presumably, their maximally specific appearance) and which the subject cannot notice, there can still be extensive overlap between the patches, insofar as their more determinable chromatic appearances are concerned. Hence, there can be at least some chromatic appearances that both patches share, which is enough to make it true that they “look the same” (in this sense), in such a way that if one looks red, the other does too (provided that the chromatic appearances they share are at least as determinate, if not a little more, than what is required to make it the case that they both look red). But then, there are at least some versions of the phenomenal sorites which could still go through. Indeed, if coloured patches have more than one look, the mere fact that there are some chromatic appearances by which two adjacent patches differ does not show that they don’t look the same in some sense (compare Mills 2002, p. 390).
Three comments. Notice, first, how the point made here seems to motivate Fara’s final answer to the phenomenal sorites: see Fara (2001, p. 934), quoted in Sect. 2.2 above. Second, note that Fara’s approach here seems strikingly contextualist: she seems to be suggesting that, in different perceptual contexts (contexts generated by the subject’s shifts of her visual attention), the chromatic appearance of the relevant objects changes—for such context-shift approach, see for instance Raffman (2000) and Jackson (1977, p. 113); and for discussion and criticism, see Mills (2002, pp. 387–389) and Chuard (2008a). What’s surprising is that Fara explicitly does not endorse such an approach (2001, pp. 913–915). Finally, there is a problem with the motivation offered in this passage. Fara (2001, pp. 926, 934) rightly insists that the fact that (i) two objects sometimes look the same in some respect does not entail that (ii) they always look the same in that respect. However, to support this claim, Fara appeals to a particular example of ‘spreading effect’. The problem is that the mere fact that (i) attention-shifts sometimes induce changes in the appearance of objects need not entail that (ii) they always do. Hence, there is no good reason to think that in the relevant examples (i.e., phenomenal sorites series), something like a ‘spreading effect’ always occurs.
But, of course, no reason to think that they look different either. Thus, unless looks-fallibilists come up with evidence that the relevant patches do in fact look chromatically different (and not just that they can), it seems as if we’ve reached a stalemate, rather than a resolution in favour of (tran). At best, the strategy used by looks-fallibilists merely raises doubts about the intuitive reasons one might have to think that, in the examples under consideration, adjacent patches look the same.
By “veridical”, I have in mind at the very least a contrastive notion: if an experience is veridical, it is not a case of illusion or hallucination. For more on this, see (Sect. 5.2).
However, it’s important to note that δ should not be characterised in terms of differences in hue, saturation, or lightness, as given by appearance-based models of phenomenal colours such as the Munsell colour system (or any other similar system of phenomenal colour categories: for a survey, see Brainard 2003). The reason is simple: since such systems only categorise discriminable colours (i.e., discriminable by normal human subjects, in fixed optimal conditions), they necessarily leave no room for the possibility of limitations on colour discrimination (except for those limitations due to sub-optimal conditions). In this respect, such colour systems don’t even allow for the possibility of unnoticeable (and hence, indiscriminable) differences in chromatic appearance, let alone unnoticeable chromatic differences (whether they look the same or not). That’s why fallibilists about looks are unlikely to dispute the assumption made here: not only do such systems collapse the distinction between colours and their appearances (see Sect. 2.1.ii), but they characterise both in terms of their discriminability (or indiscriminability), thus removing the possibility of a gap between colours and/or appearances, and our epistemic access to them. My attention to this point was drawn by Byrne and Hilbert (2003, p. 11). See also (Sect. 5.2).
Also, (lcp) ought to be distinguished from two other conceptions of perceptual limitations discussed by Fara (2001, p. 917):
-
(A)
For some sufficiently slight amount of change (in colour, sound, position, etc.), 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.
-
(B)
For some sufficiently slight amount of change (in colour, sound, position, etc.), we cannot perceive an object as having changed by less than that amount unless we perceive it as not having changed at all.
Fara (2001, p. 918) argues that, though (A) can serve to entail (ntl), it also has the implausible consequence that we are perfect perceivers of chromatic identity, since (A) entails that when there is no chromatic difference between two objects—zero difference, being below the threshold specified in (A)—normal subjects must perceive the objects as being chromatically the same, hence ruling out the possibility of illusions misrepresenting one of the objects’ colour. Against (B), Fara (2001, p. 919) claims that it can entail (ntl) only under the further assumption that there are phenomenal continua—i.e., differences in appearances which appear continuous, rather than discrete—the existence of which she questions (Fara 2001, pp. 923, 927).
Regardless of whether Fara’s arguments are sound (for scepticism, see Chuard and Corry 2006; as well as De Clercq and Horsten 2004), it’s important to see that they do not apply to (lcp). For one thing, unlike (A) or (B), (lcp) is explicitly restricted to veridical perceptual representation of non-zero chromatic differences. For another, the argument below derives (ntl) from (lcp) without appealing to phenomenal continua—if anything, the argument might be thought to rely on chromatic continua (if the spectrum of chromatic variations involves continuous variation), but even that would be a mistake: chromatic differences between the three objects mentioned below can be as discrete as you like, provided they are small enough to fall below the threshold. Also, note that, whereas (A) and (B) are explicitly diachronic (assuming change takes time), (lcp) isn’t.
-
(A)
See Pokorny and Smith (2003, p. 133; 2004, p. 912). We have to assume, it goes without saying, that, in the example under consideration, all three objects are seen in exactly the same optimal conditions: in particular, each pair of objects is seen for the same amount of time in exactly the same conditions of illumination. For details on the relevant conditions: see, e.g., Pokorny and Smith (2003, p. 133).
To be more specific: the first two conjuncts of (6) follow from the consequents of (3) and (4), respectively, by modus tollens on the left-to-right reading of (2); whereas the last conjunct of (6) follows from the consequent of (5) by modus ponens on the right-to-left reading of (2).
Indeed, if looks-fallibilists were to reject (D), their epistemic claim (b) about what cannot be noticed in experience would become redundant. In this respect, note that the argument in (Sect. 3.1) goes through whether or not subjects notice that (i) o 1 and o 2 look the same, that (ii) o 2 and o 3 look the same, or that (iii) o 1 and o 3 do not look the same. The reason is that the argument does not rely on perceptual indiscriminability.
Compare Fara (2001, pp. 915–916) and Mills (2002, p. 392). Here, I’m assuming that it does make sense to say, along with (unl), that something can look a certain way to S even if it is impossible for S to notice it. But (unl) seems to make sense provided we interpret looks as represented, or even constituted, by perceptual experiences—depending on which interpretation of (D) one favours. Fara (2001, p. 927), for instance, may think of looks as determined by the phenomenal character of experiences (see n. 26): this is compatible with saying that some differences in looks are unnoticeable because the corresponding differences in the phenomenal character of experience are unnoticeable. In contrast, it’s much more difficult to make sense of the suggestion that o could look F to S (or that x and y could look different to S with respect to F), even if S doesn’t experience o as F (or S doesn’t experience the difference between x and y with respect to F), especially if looks are supposed to be determined by the phenomenal character of experience. Likewise, if looks are in some sense observational (see n. 6), and observationality is a matter of what can be perceived, (upl) entails that some looks aren’t observational after all. Similarly, note that if, by observational, one means not just what can be perceived, but also what can be accessed and believed on the basis of perception, the same problem arises for (unl).
Admittedly, there are differences between this version of the sorites and the one discussed earlier in Sect. 2.2. For one thing, the one just considered raises a paradox about the coherence of the representational content of experience, rather than about an objective property of objects such as their chromatic appearance. And you might think that it’s quite alright if some experiences have an incoherent content. Still, the conclusion of the above sorites is just as absurd as the conclusion of the phenomenal sorites we started with. And since the argument seems valid and sound, it is as much in demand of a solution as the original phenomenal sorites argument.
See in particular Pokorny and Smith (2003, 2004) for helpful introductory reviews of the empirical literature. Please, do not say that the evidence reviewed below is controversial (as one referee did): it isn’t (as another referee insisted)! If unsure, check Gegenfurtner (2003) for a recent helpful survey of what is by now widely accepted, and what is still speculative, in physiological explanations of colour vision. Though there is still some speculation about the exact role the mechanisms and phenomena described below play in the overall visual system—with different theories ascribing a more or less central role to such mechanisms—there is no disagreement at all about their existence and importance. See also Palmer (1999, pp. 107–121) and Hardin (1998).
These results are based on a comparison of Pokorny and Smith’s own research in 1970 with several other studies from 1934 to 1970. Though the results aren’t precisely identical, they strongly converge. See Pokorny and Smith (2003, p. 133; 2004, pp. 913–915). The values specified for the example used in (Sect. 3.1) are based on these results.
The three types of cones are sensitive to different ranges of wavelengths which span many hues and overlap. Cones of type S are sensitive to wavelengths between 400 and 500 nm (with a peak of sensitivity at 440 nm), including hues between purple and blue. Cones of type M react to wavelengths in the order of 460–600 nm (with a peak at 530 nm), going from blue to green. Finally, cones of type L cover a range from 470 nm to 650 nm (peak at 560 nm), from green to red including yellow and orange (Palmer 1999, p. 112; Hardin 1998, pp. 27–28, 31).
It’s important to note that, in fact, adaptation is pretty much constant in the ganglion cells in the retina, and that it is factored in models of chromatic discrimination as a crucial element in the explanation of chromatic discriminatory thresholds (Pokorny and Smith 2003, p. 138; 2004, pp. 918–919). Hence, it’s not as if we could differentiate two stages of discrimination: one without adaptation where discriminatory abilities are at their best, followed by another phase where adaptation hinders discriminability. Indeed, adaptation may play a crucial role (at least at an early stage of processing) in enhancing sensitivity and discriminability, rather than hindering it: simplifying greatly, adaptation allows cells in the retina to be more sensitive to chromatic differences after adaptation than they were before (see, e.g., Carrasco et al. 2007, pp. 2–3, and references therein; Carrasco and Ling 2006; Pokorny and Smith 2003, p. 138; 2004, p. 918).
See Palmer (1999, p. 128) for an even more striking example of this illusion, and for its explanation.
This representational condition may be just one necessary condition amongst others for the analysis of perceptual veridicality. Others may include, for instance, restrictions on the relations—whether such relations are causal or not—between a given experience and what it represents. See, e.g., Lewis (1980). Indeed, we can distinguish ‘thick’ from ‘thin’ notions of veridicality, depending on whether they only include conditions for correct representation (thin), or also include further relational constraints (thick)—whereas the former allow for the possibility of veridical hallucinations, the latter may not.
Which isn’t to say that our visual experiences represent such colours as determinable. Nor do experiences need to represent them as determinate, by the way: otherwise, they might misrepresent them to some extent. Visual experiences may not represent colours as determinable or determinate: it’s just that we naturally assume (perhaps mistakenly) that our experiences represent highly specific and determinate colours (or the most determinate colours). Thanks to Doug Ehring for pressing me on this.
Here, one might try to argue that, if it’s true that such an experience does not represent the F 1 – F 2 difference between o 1 and o 2, it need not represent the objects in the same way either. The non-representation of a difference is not the same thing as the representation of sameness. True. But, in this case, if an experience doesn’t represent a difference between two objects, it seems safe to say that such an experience does represent them in the same way—in the sense that, with regard to all the relevant properties the experience represents as properties of the relevant objects, it represents the same properties for both objects.
It’s possible, of course, to distinguish stronger and weaker versions of both (rv) and (av). For instance, different specifications of the relevant perceptual context will give rise to different versions of (rv). If the perceptual context involves only reference to optimal or ‘normal’ lighting conditions, say, it may be that an experience of a white wall at sunset isn’t veridical, because the wall looks orange, not white (though visual experiences can correctly represent white walls as white in optimal conditions). On the other hand, if the context is restricted to the actual lighting conditions in a particular situation, the experience will be veridical (white walls look orange at sunset). As a result, the latter conception will generate less illusions than the former.
Thanks to Doug Ehring and Brad Thompson for discussion of this section.
For a physicalist conception of colours as highly specific reflectance properties of the surfaces of objects (specific to the extent that any difference in wavelength corresponds to a chromatic difference, even if such differences aren’t perceivable by normal human subjects), see, e.g., Hilbert (1987). For a version of physicalism where colours are types of spectral reflectance properties individuated in terms of (but not identical with) the complex perceptual responses they give rise to in certain types of perceivers in certain types of conditions, see Byrne and Hilbert (1997, 2003).
As an anonymous referee suggested.
Note that the combined assumption of (i) and (ii) is widespread: for instance, many colour categorisation systems of so-called ‘phenomenal’ colours—like the Munsell colour system, for example—categorise colours in terms of their discriminability and indiscriminability by normal human perceivers in more or less optimal conditions (see n. 33). On such views, judgements of chromatic discriminability and indiscriminability—supposed to track chromatic appearances perfectly—carve out the colour world at its joints.
Worse, if perceptual indiscriminability is non-transitive, as looks-fallibilists seem to grant, such a conception of colour is incoherent. Indeed, if perceptual indiscriminability is sufficient for chromatic identity, it follows that chromatic identity violates the transitivity of identity. Not a welcome result from the perspective of defenders of (tran), I take it.
The same problem arises for an alternative interpretation of what an anonymous referee might have meant with the second worry. Suppose (i′) colours are to be individuated solely in terms of certain features of our visual system (such as responses in our opponent colour processing system, say), so that, again, perceptual limitations on wavelength discrimination are built into the definition of colours, and suppose that (ii′) appearances are entirely determined by those very same features. It should follow, again, that (iii) colours and chromatic appearances perfectly match (the referee only mentioned (i′), but, it seems to me, we don’t get perfect match (iii) without also assuming something like (ii′)). On such a view, I take it, chromatic indiscriminability need not be sufficient for chromatic identity. Colours and appearances aren’t determined by our cognitive abilities (or inabilities) for discrimination. Both are determined by certain features of our visual system. One problem with this response is that it misconstrues the point of the argument in (Sect. 3.1). The consequence that colours and chromatic appearances correspond perfectly is implausible only if one is driven to such a consequence by denying that there are perceptual limitations on colour and/or wavelength discrimination. The suggested view doesn’t deny that there are such limitations, at least not for wavelength discriminations (they are, again, factored in the definition of colour). But this doesn’t help looks-fallibilists. I claimed that fallibilists are committed to the denial of perceptual limitations of any kind in order to resist premise (1). Yet, if the suggested view grants premise (1), as it appears to, then it cannot serve to resist the main argument of this paper. Sure, there is a way to make sense of perfect correspondence between colours and chromatic appearances, but that’s entirely irrelevant to the argument.
Such a conception of colour also has the consequence that colours, and not just chromatic appearances, have inconsistent conditions of individuation. Since the view grants that there are limitations on wavelength discrimination, the main argument goes through and (ntl) seems to be true. But if differences in chromatic appearance perfectly coincide with chromatic differences, then, given (ntl), “being the same colour as” must be non-transitive.
A similar problem faces an alternative route to the same conclusion that chromatic appearances and colours match perfectly. Here, the idea is that (i*) there could be ideal observers for whom colours perfectly match chromatic appearances, and (ii*) the existence of perceptual limitations for normal perceivers like you and me doesn’t entail that such ideal observers are similarly limited—they are ideal after all (thanks to Aaron James for the suggestion). However, even if there really were such visual appearances ‘sub-ideal-observers’, as it were (and we have no reason to think so), it need not follow that these are the only visual appearances there are. There may also be visual appearances as determined by properties of our visual system, and a host of other possible appearances (including, in particular, a variety of species-specific looks). Admittedly, the argument in this paper might fail for those visual appearances only ideal observers have access to. But it can still work for the visual appearances we perceive—which is what I took the issue to be about in the first place. The notion of looking the same as … at play in the dispute between advocates of (tran) and (ntl), which figures in all the arguments considered so far, including the argument in (Sect. 3.1), as well as principle (pils), is relational and includes a relation to a subject: x and y look the same (or not) to S with respect to F, where S is the very subject for whom x and y are perceptually F-indiscriminable—subjects like you and me, that is. Whether there is another relation such that x and y look the same to S* with respect to F, where S* is an hypothetical ideal observer, but where x and y are F-indiscriminable to S (a normal subject), is entirely irrelevant.
Different appearances which are indiscriminable. Otherwise, if the different chromatic appearances of the same colour are themselves discriminable, it should follow by (iii) that instances of that colour are discriminable. In which case, (i) should entail that we don’t have a unique colour after all.
In other words, without assuming that:
the chromatic appearance of x is indiscriminable from the chromatic appearance of y ↔ the chromatic appearance of x = the chromatic appearance of y.
The combination of (i) and (ii):
-
(i)
the colour of x is perceptually indiscriminable from the colour of y ↔ the colour of x = the colour of y.
-
(ii)
the colour of x is perceptually indiscriminable from the colour of y ↔ the chromatic appearance of x is indiscriminable from the chromatic appearance of y.
does not entail the desired correspondence between colours and chromatic appearances:
-
(iii)
the colour of x = the colour of y ↔ the chromatic appearance of x = the chromatic appearance of y.
Yet, against the first assumption, it seems that looks-fallibilism is committed to the possibility that:
The chromatic appearance of x ≠ the chromatic appearance of y & the chromatic appearance of x is indiscriminable from the chromatic appearance of y.
-
(i)
As an anonymous referee did.
Of course, perceptual indiscriminability with respect to colour is about colours and their differences, and our ability to detect them. But that’s not what the issue between advocates of (tran) and (ntl) is about—especially if looks-fallibilists are right, and there is no straightforward inference from chromatic indiscriminability to looking the same as ….
That’s why, in order to resist the argument, fallibilists about looks have to make a rather strong claim. They must claim, against the evidence presented in the last sections, not just that we are perfect perceivers of colour and colour differences, but, more importantly, that we are perfect perceivers of spectral reflectance and differences in wavelengths—so that any difference in wavelength can be veridically represented in perceptual experience. Otherwise, the argument suggests, we can have instances of (ntl). Such a strong claim, however, flies in the face of the empirical evidence reviewed in (Sect. 4).
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Acknowledgements
Writing this paper was prompted by an as-always-helpful discussion with Daniel Friedrich. For comments on previous versions of this paper, thanks also to Daniel, to the members of the work-in-progress seminar at SMU, as well as two anonymous referees. A shorter version of this material was presented at the University of Sydney, UC Irvine, and at the Joint Session in Bristol: many thanks to those attending for their questions.
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Chuard, P. Non-transitive looks & fallibilism. Philos Stud 149, 161–200 (2010). https://doi.org/10.1007/s11098-008-9326-x
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DOI: https://doi.org/10.1007/s11098-008-9326-x