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Colour Constancy as Counterfactual
Jonathan Cohen
There is nothing in this world constant, but inconstancy. — Jonathan Swift, “A Critical Essay upon the Faculties of the Mind”.
Abstract In this paper I argue that two standard characterizations of colour constancy are inadequate to the phenomenon. This inadequacy matters, since, I contend, philosophical appeals to colour constancy as a way of motivating illumination-independent conceptions of colour turn crucially on the shortcomings of these characterizations. After critically reviewing the standard characterizations, I provide a novel counterfactualist under- standing of colour constancy, argue that it avoids difficulties of its tradi- tional rivals, and defend it from objections. Finally, I show why, on this improved understanding, colour constancy does not have the philosophical consequences that have been claimed for it in the literature. In recent years, vision scientists and philosophers of perception have de- voted considerable attention to questions about colour constancy. Among the most important issues surrounding colour constancy are those about how we should understand the phenomenon and those about what the phenomenon shows about the nature of colour. Many writers explicitly link these two sets of questions: they have enlisted certain kinds of answers to the former set as a way of arguing for certain kinds of answers to the latter set. In particular, many have appealed to a certain understanding of the empirical phenomenon as evidence for the view that colours are illumination-independent: viz., many have taken constancy as support for the widely-held position that colours are subject-independent, physical properties of objects.^1 All the vocal proponents of this view (e.g., [Hilbert, 1987], [Byrne and Hilbert, 1997a], and [Tye, 2000]) have taken colour constancy as a central pillar of support, and even those who reject the view typically allow that colour constancy is something they need to discount or play down in order to meet their opposition (e.g., [Hardin, 1988], 46ff; [Hurvich, 1981], 199; [Jameson and Hurvich, 1989]). I believe that the phenomenon of colour constancy has been misunderstood, and that correcting this misunderstanding will have the effect of undercut- ting the apparent support the phenomenon provides to accounts of colour as
(^1) Among such views (which have sometimes gone by the names ‘physicalist’, ‘primary qual- ity’, or ‘objectivist’ theories of colour), the most currently influential position holds that (surface) colours are identical to (classes of) surface spectral reflectance distributions.
illumination-independent properties.^2 Aside from its independent interest, the exercise of correcting these faults will also provide a methodological moral about the way in which arguments over colour ontology should proceed: it will remind us to remain on guard against characterizing phenomena in ways that tacitly beg disputed metaphysical questions. In §§1–2 I’ll examine critically some attempts to characterize the phenome- non of colour constancy. Next, in §3, I’ll consider the ontological lessons some have attempted to draw from the phenomenon. Finally, in §§4–5, I’ll offer my own characterization of colour constancy, argue that it does not suffer from the problems that plague other characterizations, defend it from objections, and show why, on this improved understanding, colour constancy does not have the philosophical consequences that have been claimed for it in the literature.
1 Constancy as Invariance
Since colour constancy is easier to recognize than to define, I’ll begin with the example depicted in figure 1 — a coffee cup on a table, partially in direct sunlight and partially in shadow.^3 Consider the region of the coffee cup (and the region of the table) in direct sunlight, and compare it against a similar-sized, adjacent region of the coffee cup (and a region of the table) that are in shadow. If you are like most normally sighted subjects, you will find that these two regions are, in some sense to be explained, alike in apparent colour.^4 On the other hand, again
(^2) I suspect that one source of misunderstanding has been the tendency by philosophers writ- ing about colour and colour constancy to focus on a limited portion of the relevant empirical literatures. This is true not only of the psychophysical literature on colour constancy to which I’ll advert below, but also of computational accounts of colour constancy. For example, the discussions of computational theories in [Hilbert, 1987] and [Byrne and Hilbert, 2003] empha- size only theories that model the recovery of (illumination-independent) spectral reflectance distributions from the energy falling on the retina (e.g., [Maloney, 1986], [Wandell, 1989]). But this overlooks other computational models of colour constancy that attempt to determine whether two regions are relevantly alike (though different in illumination) without extract- ing an illumination-independent representation of the regions (e.g., [Craven and Foster, 1992], [Zaidi, 2001]). (^3) The case I have in mind is one in which the subject is visually perceiving a coffee cup, not a photograph of the coffee cup (notwithstanding the arguments of [Walton, 1984], I take it that when a subject sees a photograph of x, she does not ordinarily see x as well [Cohen and Meskin, 2004]). Hence, I am using figure 1 to depict the stimulus – I am not using it as the stimulus. This will matter, since it is plausible that there is a variation in the illumination under which the coffee cup is perceived, whereas it is doubtful that there is a significant variation in the illumination under which figure 1 is perceived. For ease of expression, I’ll be pretending that the reader can perceive the depicted coffee cup in what follows. (Mutatis mutandis for depicted objects in other photographs throughout.) (^4) In talking of apparent colours of objects, I mean the colours that objects are represented by subjects (/visual systems of subjects) as having. I see no reason to regard the recognition of apparent colours (as properties over and above the colours that objects have) as ontologically profligate. It is a banal fact about objects that they exemplify colours, sizes, shapes, smells, and many other properties. It is a banal fact about us that we represent objects as exemplifying colours, sizes, shapes, smells, and many other properties. But the properties we represent objects as having can’t be identified with the properties objects have, since we sometimes misrepresent the properties of objects.
of them. Although the effect is less obvious here (perhaps partly because com- parison between non-simultaneous presentations introduces confounding consid- erations about perceptual memory), in cases of successive colour constancy we find the same pair of perceptual reactions that occur in cases of simultaneous colour constancy. On the one hand, normally sighted subjects find that the two (successively presented) regions of interest are, in some sense to be explained, alike in apparent colour. And on the other hand, normally sighted subjects find that the two (successively presented) regions of interest are, in some sense to be explained, easily, obviously, and quickly visually discriminable in apparent colour. Many writers who have considered the phenomenon of colour constancy have emphasized two facts: first, that subjects classify the two patches under com- parison as (in some sense to be explained) alike in apparent colour — this is the first reaction mentioned above; and second, that the two regions differ in the illumination falling on them. And this has led to a more or less standard understanding of colour constancy as a kind of invariance. In particular, on this view (henceforth, invariantism), colour constancy is an invariance of ap- parent colour across changes in illumination. Invariantism has become the de facto standard understanding of colour constancy in both philosophical and scientific work on colour; for example, versions of this characterization can be found in many recent textbooks and anthologies on colour and vision (often in glossary entries for ‘colour constancy’) including ([Byrne and Hilbert, 1997b], 445), ([Zaidi, 1999], 339), ([Goldstein, 1999], 567), ([Stoerig, 1998], 141), and ([Brainard et al., 2003], 308–309). While these formulations differ slightly in their details,^7 they share the core idea that colour constancy should be regarded as an invariance in our perceptual reaction to members of a pair of stimuli de- spite differences in the illumination under which each member of the pair is viewed. Moreover, as I’ve said, the invariantist understanding of colour constancy has played an important role in arguing for views according to which colours are illumination-independent properties of surfaces. To a first approximation, the argument is that, if apparent colour is indeed invariant across differences in illumination, then the theory that best explains that fact is one that takes colours to be illumination-independent properties.^8 (I’ll return to consider this
(^7) In particular, they disagree about whether what is invariant across changes in illumination in cases of colour constancy is “perceived color” (Byrne and Hilbert) “the color percepts assigned to individual objects” (Zaidi), “the perception of an object’s hue” (Goldstein), and so on; needless to say, a more thorough search of the literature would turn up yet other formulations. For expository convenience I’ll be concentrating on the idea of invariance of apparent colour across changes in illumination. As far as I can see, nothing of significance hangs on this particular choice: the points I’ll be making can be extended easily to the other formulations of invariantism. (^8) That the phenomenon plays this role in motivating illumination-independent accounts of colour also explains why it is in the interest of the invariantist to describe the phenomenon as an invariance of apparent colour rather than an invariance of colour. Namely, since the assumption that the two regions of interest in figure 1 share a colour is tantamount to the (dis- puted) conclusion that colours are illumination-independent, building that conclusion into the description of the phenomenon would deprive the latter of any capacity to provide indepen-
Figure 2: Common objects under different daylight illuminants.
of the illumination difference.^10 How can asymmetric colour matching help us to assess invariantism about colour constancy? According to invariantism, colour constancy is a kind of invariance across illumination differences; hence, on this view, colour constancy will be exhibited to the extent that the effects of illumination differences (as measured by chromaticity/lightness differences in such experiments) are small. So what do the results of asymmetric colour matching experiments show about colour constancy? Unsurprisingly, asymmetric colour matching brings out the very same points considered above, and does so more precisely than the qualitative measure dis- cussed. Roughly, it seems that (most) subjects can respond in two different modes — one mode that assimilates surface pairs like that in figures 1–2, and one that distinguishes such pairs. Moreover, it seems that (most) subjects can be made to switch between these two modes of response as a result of experi- mental instructions: instructions to “adjust the test patch to match its hue and saturation to those of the standard patch” lead subjects to distinguish members of such pairs, while instructions to “adjust the test patch to look as if it were ‘cut from the same piece of paper’ as the standard, i.e., to match its surface color” ([Arend and Reeves, 1986], 1744) lead subjects to assimilate members of such pairs.^11 (I’ll follow [B¨auml, 1999] in talking about the first sort of matches — those that distinguish the two surfaces — as appearance matches, and the second sort of matches — those that assimilate the two surfaces — as surface matches. Obviously, no substantive conclusions should be inferred from the choice of these labels.)
(^10) Two methodological remarks are in order. First, until recently, most psychophysicists using asymmetric colour matching to study colour constancy have in fact used colour contrast as a proxy for changes in illumination. That is, the typical experimental display consists of a test and a standard patch set against circular surrounds of differing chromaticity, but with the whole scene under uniform illumi- nation (indeed, usually surface illumination is negligible, as such displays are produced on luminous computer monitors). Subjects are then asked to change the chromaticity of the test patch against its surround until it perceptually matches the standard patch against its surround. On its face, this task seems to use chromaticity changes to measure the effect of a difference in surround, rather than the effect of a difference in illumination. Fortunately, a number of investigators (led by David Brainard and his colleagues), have begun to measure the effects of illumination differences more directly (see, for example, [Brainard et al., 2003]). In correspondence, Brainard has indicated to me that the patterns of results that I’ll be present- ing below are sustained in the more direct experiments he employs. As such, I’ll be ignoring this complication in what follows. Second, for obvious reasons, the techniques under discussion here are not applicable to the study of colour constancy in non-human and infant human subjects (see §4.2), so investigators have had to rely on other methods in these contexts. (^11) These results have been confirmed by a number of studies. See [Evans, 1948], 163–164 and [Beck, 1972], 66–67 for an overview of some of the earlier work; more recent findings to the same effect (typically restricted to simultaneous colour con- stancy) are reported in [Arend and Reeves, 1986], [Blackwell and Buchsbaum, 1988], [Valberg and Lange-Malecki, 1990], [Arend et al., 1991], [Troost and deWeert, 1991], [Cornelissen and Brenner, 1995], and [B¨auml, 1999]. While there has been far less sys- tematic investigation of this effect with respect to cases of successive colour constancy, the bimodal pattern of results depending on instructions has been found for successive colour constancy as well ([Delahunt, 2001], 114–117; [Delahunt and Brainard, 2004], 71–74).
So, once again, the problem is that, while the invariantist characterization of colour constancy is consistent with one reaction that subjects have to canonical cases (as measured by qualitative and quantitative methods), it is inconsistent with another, equally good reaction that subjects have to the very same cases (as measured by qualitative and quantitative methods). Invariantism predicts the invariance/surface match reaction, but not the variance/appearance match reaction. What should the invariantist say about this situation?
1.1 Invariantist Responses
First, the invariantist might attempt to discount the problematic variance re- actions by insisting that, when subjects have both variance and invariance re- actions to a pair of surfaces, the case is not an instance of colour constancy. But this alternative strategy seems inadvisable. After all, insofar as the pair of conflicting responses seems to be a hallmark of paradigm cases of colour constancy, the strategy in question amounts to emptying the phenomenon of instances merely to save a favored theory. Presumably this is unacceptable.^12 A more promising invariantist strategy would be to find an alternative char- acterization of the troublesome variance reaction as a discrimination along some dimension other than that of apparent colour. If the invariantist can do this, there would be no need to take the variance reaction as contravening the core invariantist idea that colour constancy involves an invariance in perceptual re- action despite differences in illumination. In particular, an obvious alternative characterization would be that the visual system is here discriminating a dif- ference in the illumination falling on the surface regions (a difference that must exist, given the setup of the case) rather than a difference in apparent colour.^13 Now, in order for this suggestion to constitute a genuine alternative to the claim that the variance reaction reveals a difference in apparent colour, the in- variantist must be thinking of illumination as something that is not merely a dimension of apparent colour.^14 But there is reason for doubting that illumina-
(^12) Similarly, an interlocutor might object that visual discriminations are unreliable in cases where there is a difference in the illumination falling on the two samples; therefore, she might say, the cases I’ve appealed to fall outside the realm within which visual discriminability is an adequate test of difference in apparent colour, and so should be put aside. But once again, this line of response seems unwise in the present setting; for if we are debarred from considering discriminations between regions that differ in illumination, then we can never decide whether regions are invariant in apparent colour across variations in illumination. But variations in illumination are precisely the variations that we must consider in assessing whether or not there is colour constancy, as that phenomenon is understood by an invariantist; therefore, the proposed strategy of setting aside subjects’ visual discriminations in such cases would mean that these cases — paradigmatic cases, and therefore precisely the cases that an adequate understanding of colour constancy ought to capture — could never be regarded as instances of colour constancy (on an invariantist account). (^13) I’m putting aside obvious dimensions of visual discriminability such as size, form, or texture as possible explanations; for, even if there are salient differences along these dimensions in figures 1–2 in particular, there are other paradigm cases of colour constancy (which we can produce in the psychophysics laboratory as needed) in which these possible confounding sources of discriminability are eliminated. (^14) Besides constraining the interpretation of the invariantist proposal on the table, this con-
regions at issue differ in apparent colour), illumination is not a dimension of apparent colour, it is hard to see why a modification in the apparent colour of a region should also change its illumination. Moreover, it is simply untrue that two regions will cease to be discriminable when they are different in their apparent colour (hue, saturation, and lightness) and alike in the illumination falling on them; on the contrary, subjects have no difficulty discriminating regions under those conditions. Perhaps the invariantist will attempt to account for the post-manipulation discriminability of the regions by suggesting that the two are, at the end of the manipulation, discriminable along some dimension other than that of illumi- nation (which, on the present story, accounts for the variance reaction). That is, she might suggest that the regions are discriminable along the dimension of illumination before the manipulation, but discriminable along some differ- ent dimension after the manipulation — indeed, the obvious suggestion is that the post-manipulation discrimination is a discrimination in apparent colour. But this, too, is hard to accept. For one thing, there is no phenomenological or psychophysical evidence for thinking that visual systems are responding to a different dimension of difference before and after the manipulation, as the invariantist suggests. Moreover, what the invariantist proposes about the post- manipulation situation is implausible on its face. The reason the manipulation comes to an end is that the regions are no longer discriminable tout court, not that the regions are no longer discriminable along the dimension of illumination albeit discriminable along some other dimension. If the invariantist offers a de- scription of the situation that makes the regions come out post-manipulation as discriminable (as we are imagining), then we have reason to reject that descrip- tion no matter how she proposes to analyze the discrimination. Pending answers to these concerns, I take it that the invariantist response we have been considering is unsatisfactory.^16
(^16) A quite different objection to the line I’m pressing concerns the relationship between colour constancy and other forms of perceptual constancy. As it happens, colour constancy is just one among many perceptual constancy phenomena standardly explained in invariantist terms — e.g., size constancy is characterized as an invariance of perceived size across changes in the distance between the subject and the test object, shape constancy as an invariance of perceived shape across changes in the position from which the subject views the stationary test object, etc. If the considerations adduced so far against invariantism about colour constancy are persuasive, one might think, they should be equally telling against these other forms of perceptual constancy as well. But that sort of revision might seem too radical. There are a number of things to say about this worry. First, before we generalize too quickly, it should be emphasized that the problem we’re considering for invariantism about colour constancy arises from the conflict between the commitment of the view and the empirical facts about apparent colour. As such, the applicability of the present worry to size and other constancy phenomena is an entirely empirical matter: there is such an analogous problem for invariantism about (say) size constancy just in case, as a matter of empirical fact, invariantism about apparent size conflicts with the data about apparent size. Assume, however, as seems not implausible, that the empirical facts about apparent size are relevantly analogous to those about apparent colour: suppose that we can get subjects to treat two disks of the same diameter, viewed at different depths, as unlike in apparent size. In this case, I think we would be justified in concluding that there’s a good sense in which the two disks are unlike in apparent size, hence that the size-invariantist’s claim that the two disks
1.2 Summing Up
Here’s where we are. We’ve seen that invariantists claim that, in the cases under consideration, the regions of interest are treated by visual systems as being alike in apparent colour. On the other hand, we’ve seen that, while there is a sense in which visual systems treat the members of the pair as alike in apparent colour, there is another sense in which they treat the members of the pair as unlike in apparent colour. Or, in still other words, while there is a sense in which the pair of surfaces share a common apparent colour, there is another sense in which the pair of surfaces vary in apparent colour. So the situation cannot be quite as the invariantist describes it. In the face of these data, an invariantist could reasonably cling to her char- acterization of the phenomenon if she could provide some reason for taking the half of the data that accords with invariantism (viz., invariance reaction/surface match data) seriously while ignoring the half of the data that does not (viz., variance reaction/appearance match data). But I don’t see what that reason would be, and I certainly don’t see that one has been given; on the contrary, for all that has been said, both sets of matches have an equal claim to reflect the vi- sual system’s representations about whether there is a single apparent colour or not.^17 Thus, pending some independent reason for siding with surface matches, and against appearance matches, the most we can say is that the existence of the invariance in terms of which invariantism characterizes colour constancy is supported by at most half of the data. On the other hand, while the data don’t appear to provide a direct con- firmation of invariantism, it should be admitted that the results can no more obviously be claimed as a direct refutation of the view. After all, it seems significant that the data show two distinct patterns of response, rather than a continuous range. Moreover, it is suggestive that most subjects can be made to switch between the two patterns of response by modifying the experimental
are alike in apparent size (despite a difference in depth) is inadequate as a characterization of the phenomenon. (Likewise for other perceptual constancies.) However, I want to suggest, this conclusion lacks the ontological significance for size that it has in the case of colour, and so is far less pressing. This is because we don’t need the phe- nomenon of size constancy to serve as evidence for the conclusion that size is independent of viewing depth. In particular, we have agreed upon standards for size that are constituted in- dependently of viewing depth (these standards are called ‘rulers’), and that give us reasons for believing that size is independent of viewing depth. Thus, while rejecting invariantism about size constancy might require a more careful characterization of the phenomenon, it would not undercut our reasons for taking size to be independent of viewing depth. In contrast, invari- antism about colour constancy is the main reason for thinking that colours are independent of illumination (and is presented as such by proponents of that view); as I have argued elsewhere [Cohen, 2004], there are no standards for the colour of x that are constituted independently of the illumination under which x is viewed. Thus, undercutting invariantism about colour constancy leaves the claim that colours are illumination-independent wholly unsupported. (^17) Of course, there is a difference in the instructions that elicit each set of matches — “adjust the test patch to match its hue and saturation to those of the standard patch” versus “adjust the test patch to look as if it were “cut from the same piece of paper’ as the standard patch.” But it is hard to find in this instructional difference (or, as noted, in the different labels chosen by the experimenters) any good reason for favoring the surface match data over the appearance match data.
Although a surface with a reflectance distribution R may reflect one way under illuminant I 1 and a different way under illuminant I 2 (and consequently may be thought to change its apparent colour under varying illumination), it will con- tinue to have reflectance distribution R despite the change in illuminant. This result is unsurprising, insofar as reflectance distributions are dispositional prop- erties — they are dispositions of surfaces to affect light of certain wavelengths in certain ways. Generally speaking, dispositions remain in place whether or not their activation conditions are satisfied: objects exemplify their dispositions before their activation conditions are satisfied, while their activation conditions are satisfied, and after their activation conditions are no longer satisfied. Table salt, for example, is soluble whether or not it is in fact immersed in water: it exemplifies the disposition to go into solution when immersed in water before it is ever immersed in water, at the moment that it is immersed in water, and after it is no longer immersed in water (say, by being precipitated out of water). Similarly, a surface that has the disposition to reflect 45% of the incident light of wavelength λ will (unless it is changed in some finkish way that would de- mand independent explanation, as in the case of photographic paper) exemplify that disposition before it is illuminated by light of wavelength λ, while it is illuminated by light of wavelength λ, and after it is no longer illuminated by light of wavelength λ. That is to say, the reflectance distribution of a surface is (exceptions aside) invariant across changes in the illumination under which the surface is presented. Given that reflectance distributions are (exceptions aside) invariant across changes in illumination, and given that the trouble with invariantism is that, in one good sense, apparent colour is not invariant in this way, it is natural to turn to the reflectance account as a way of saving what is right about invariantism. Formulations of colour constancy along these lines are advocated by a num- ber of authors (although they are less prevalent than invariantist formulations):
Color constancy is the ability to perceive the reflectance spectrum of surfaces despite changes in illumination and other viewing condi- tions” ([Palmer, 1999], 705).^19
The ability of a vision system to diminish, or in the ideal case, re- move, the effect of the illumination, and therefore “see” the physical
dispositions that disappear when their manifestation conditions occur [Martin, 1994]. For obvious reasons, the reflectance perception account cannot be extended straightforwardly to these cases. I shall put aside this potential objection to the account, since I believe it faces more serious problems. (However, I’ll return to the topic of finkish dispositions in defending my own account of colour constancy in §4.3.) (^19) Note that Palmer’s mention of “other viewing conditions” suggests that he thinks varia- tions other than those of illumination are relevant. Since this won’t matter for our purposes, I’ll put this matter aside. Also notice that Palmer’s formulation describes constancy as in- volving our abilities to perceive something despite changes in the illuminant; this is worrisome insofar as constancy is sometimes revealed not despite changes in the illuminant, but because of changes in the illuminant. For example, if two patches are discriminable for me in some viewing condition, I might not know whether I have a case of colour constancy on my hands until I see how the visual appearances of the two change with respect to each other as the illumination changes uniformly on both of them.
scene more precisely, is called colour constancy ([Barnard, 1998], 1).^20
Because reflectance perception accounts are formulated in terms of reflec- tance distributions, and because the latter (again, exceptions aside) have the right sort of invariance, these accounts are not vulnerable to falsification by empirical data in the way that invariantist accounts are (see §1). That said, reflectance perception accounts are subject to their own sets of worries. In the rest of this section, I want to raise two kinds of worries for re- flectance perception accounts. The first, which I take to be potentially solvable, is an undergeneration worry — a worry that reflectance perception accounts fail to count as instances of colour constancy cases that might reasonably be thought to be instances. The second, to which I don’t see any solution, and which I consequently regard as much more serious, is that such accounts over- generate instances of colour constancy — that they count as instances cases that should not be so treated.^21 The undergeneration worry I have in mind is that the reflectance perception account of constancy is, on its face, inapplicable to instances of colour con- stancy involving transparent volumes, luminous sources, and films, insofar as the apparent colours (and colours) of these objects are not well accounted for in terms of spectral reflectance distributions. But it seems inappropriate to rule out these cases preemptively: some cases involving transparent volumes, lumi- nous sources, and films seem to be (pending reasons to believe the contrary) bona fide examples of colour constancy.^22 A prima facie example involving a transparent volume can be generated by replacing the coffee cup in figure 1 with a transparent volume of beer (suppose the volume of beer is contained within a transparent glass). One example involving a luminous source — one that is standardly used in empirical investigations of colour constancy — involves adjacent CRT regions that fall under varying amounts of illumination by dif- fuse room lighting; another example is the firefly whose bio-luminescent body is partly illuminated and partly unilluminated by a flashlight. Finally, we can consider the case of a soap film that, like the coffee cup in figure 1, is partly in direct sunlight and partly in shadow. Each of these cases, I suggest, has a strong
(^20) The difference between Barnard’s and Palmer’s formulations is less significant than it might seem, for the rest of Barnard’s essay makes it clear that what he has in mind by “see[ing] the physical scene” is the extraction of surface spectral reflectance distributions. (^21) A third, more philosophically motivated worry about reflectance perception accounts arises from arguments to the effect that dispositional properties cannot be perceived (see, for example, [McGinn, 1996] and [Jackson, 1996]). Since reflectance distributions are dispo- sitional properties, reflectance perception accounts threaten to entail the (presumably un- wanted) consequence that colour constancy is (necessarily) never instantiated. On the other hand, for reasons I’ve discussed in [Cohen, 2003], I am not convinced by the worry that dis- positional properties are imperceptible, so I don’t take this objection to be decisive. (^22) I do not believe that such cases must be counted as instances of colour constancy. Rather, I am suggesting that they have a good prima facie claim to be so counted, and that this prima facie claim is something that should not be preempted stipulatively at the beginning of the day. This is intended to leave open the possibility that we might decide to revise our initial assessments at the end of the day.
Figure 3: Adding a well-placed border to figure 1 substantially weakens the impression that the two regions of the depicted coffee cup are alike in apparent colour.
sunlit region of the coffee cup. But this small change has the interesting effect of substantially weakening the impression that the two regions of the depicted coffee cup are alike in apparent colour. That is, figure 3 is unlike figure 1 in this crucial respect: most subjects have the reaction (regardless of whether they are asked to make appearance matches or surface matches; see §1) that the surface depicted in the left half of figure 3 (the shadowed region) is different in apparent colour from the surface depicted in the right half of the figure (the sunlit region). Presumably, then, this case should not come out as a case of colour constancy. But suppose we understand colour constancy as the percep- tion of spectral reflectance distributions, as per a reflectance perception account. And suppose that (waiving the worries mentioned in note 21) we can and do perceive reflectance distributions. Then presumably we perceive reflectance dis- tributions when we visually attend to the adjacent regions depicted in figure 3. (At least, there is no less reason for thinking that we perceive reflectance dis- tributions when we attend to the adjacent regions depicted in figure 3 than there is for thinking that we perceive reflectance distributions when we attend to the corresponding regions depicted in figure 1.) If we do succeed in perceiv- ing reflectance distributions in this case, then nothing has prevented us from perceiving reflectance distributions; a fortiori the change in illumination under which the coffee cup is viewed in the two halves of figure 3 has not prevented us from perceiving reflectance distributions when we look at the regions of the coffee cup. Thus, when visually attending to the coffee cup depicted in figure 3,
we perceive reflectance distributions despite changes in illumination. Conse- quently, on reflectance perception accounts of colour constancy, we experience an instance of colour constancy when we visually attend to the regions depicted in figure 3 — an outcome at odds with our initial assessment of the case as a paradigm failure of colour constancy.^24 Now, a likely response to this objection is that it turns on an uncharitable reading of its target. Reflectance perception accounts, on this response, must not hold (despite the formulations in the sources quoted above) that colour constancy would involve any instance of the ability to perceive reflectance dis- tributions despite changes in illumination. Rather, perhaps such accounts are intended to say something more like the following: a visual system exhibits colour constancy just in case it co-classifies samples that share a common spec- tral reflectance distribution, despite variations in the illumination. This modifi- cation does, in my view, manage to evade the difficulty pressed above: namely, it correctly classifies the failure of colour constancy involving figure 3 as a failure of colour constancy. However, the modified version of the proposal suffers from the problems brought out in our earlier discussion of invariantism (§1). For, as we have seen, subjects often fail to co-classify samples that share a common reflectance distribution when those samples are presented under different illumi- nations (namely, when they make appearance matches among those samples). Thus, proponents of the reflectance perception account appear to be faced with a dilemma: either they adopt the proposed modification, in which case they are susceptible to the difficulties that plague invariantism, or they reject the pro- posed modification, in which case they are stuck with an excessively permissive treatment of colour constancy. Neither option seems attractive.
3 Colour Constancy and Colour Ontology
We have seen two possible understandings of colour constancy, and noted that there are serious troubles for each of them — that there are reasons for worrying that neither of them provides an adequate characterization of the phenomenon of colour constancy. I now want to suggest that this has serious repercussions for certain prominent arguments about the nature of colour that turn on these
(^24) Once again, I’m interested in the case where what is perceived is the coffee cup, not the photograph of the coffee cup (see note 3). Here, however, one might reasonably object that the border that distinguishes figure 3 from figure 1 is not part of the scene depicted, but only part of the representational vehicle. That is, one might worry that the crucial aspect of figure 3 on which the current objection depends cannot arise in any ecologically valid stimulus. I’ll answer this worry by describing what seems to me to be an ecologically valid case that has the structure I need. Suppose, then, that a subject views the partially lit coffee cup (the very coffee cup depicted in figures 1 and 3) through a clear glass panel upon which an opaque black quadrilateral has been painted. The subject views the coffee cup through the panel at an angle and distance so that the quadrilateral surrounds the entire region of the coffee cup that is under direct sunlight and visible. In short, the subject’s view of the scene is much like your view of figure 3. The subject is perceiving the coffee cup, not the figure. But the opaque black border is also perceived and thereby has a perceptual effect on the subject that is equivalent to the effect that the black border in figure 3 has on you.
Of course, (1′) will not, by itself, give us any reason to believe the intended conclusion (3) unless we take (1′) to tell us something about colour, as opposed to apparent colour. The thought, then, must be that (1′) is a (defeasible) reason for believing this:
(1∗) The colour of a surface is invariant across changes in illumination.
The objectivist’s inference, on this reading, comes out as a pair of inferences to the best explanation. It moves first from the empirical premise (1′) to the ef- fect that apparent colours are illumination-independent to the allegedly best ex- planatory conclusion (1∗) to the effect that colours are illumination-independent; and from (1∗) and the definitionally true premise (2) to the effect that reflectance distributions are illumination-independent, to the allegedly best explanatory conclusion (3), that colours are identical to reflectance distributions. Understood in this way, the objectivist’s inference invites a number of wor- ries. First, there is a concern that, in the context of a debate about what the empirical results about apparent colour tell us about colour, the inference from (1′) to (1∗) will strike many as too hasty (cf. note 8). Although I am sym- pathetic to this criticism, I’ll put it aside in order to focus on what seem to me more fundamental problems with the inference that concern premise (1′) in particular. One fundamental problem is that the results discussed in §1 provide reasons for suspecting that (1′), the key empirical premise of the argument, is false. Unless and until these suspicions can be allayed, we should reject the inference. A second fundamental problem is that, even putting aside the variance/ap- pearance match reactions discussed in §1 entirely, there are many uncontrover- sial cases — cases that even Hilbert and Tye would accept — where the alleged invariance cited in (1′) fails; perhaps the case involving the stimulus depicted in figure 3 is one of them (although nothing I say will turn on the assessment of this particular case). I take it that this much would conceded by all sides; cer- tainly it is uncontroversial for colour scientists, who frequently take such cases to show the limitations on human colour constancy (thus, in an entirely typical passage, Peter Lennie writes that “Formal accounts of color constancy char- acterize mechanisms that perform better than human observers: Human color constancy is imperfect” ([Lennie, 1999], 245–246)).^25 Indeed, I take it that the parenthetical qualification in the quotation above from ([Tye, 2000], 147–148) is intended to concede that the claimed invariance fails in at least some cases. But if the invariance fails in many cases, then we are justified in wondering why it is properly thought of as an invariance at all (rather than a variance). And given that Tye, Hilbert, and others are prepared to take the invariance of apparent colour across changes in illumination as evidence that (apparent colours, and therefore) colours are illumination-independent, why should we
(^25) For more on the gap between invariance characterizations of colour constancy and the performance of human visual systems, see also [Mausfeld, 1998] and [Troost, 1998]. For a more extreme view, see [Foster, 2003], who argues that it is inappropriate to think of the human visual system as exhibiting colour constancy at all, insofar as that is taken to require recovering an invariant (i.e., illumination-independent) characterization of perceived surfaces.
not take the failures of invariance as showing that (apparent colours, and there- fore) colours are illumination-dependent properties of objects? Or, to put the point in terms of the inference form outlined above, our question is why, on an invariantist account of colour constancy, the empirical premise (1′) in the objec- tivist’s inference is not refuted by the empirical evidence: why is the empirical claim that apparent colours are illumination-independent not disconfirmed by the (uncontroverted) cases where invariance fails? Tye and Hilbert are aware of this worry, and their attempts to answer it are instructive. They propose to regard the violations of invariance as exceptional cases to the general rule (viz., the rule of invariance) on the grounds that these cases are cases of colour misperception (cf. [Hilbert, 1987], 71–72, [Tye, 2000], 153ff). Unfortunately, it is not clear to me that there are reasons for endorsing this view that are independent of the intended conclusion that colours are il- lumination-independent. Of course, if colours are assumed to be illumination- independent properties, then cases in which apparent colour is shown not to be illumination-independent are plausibly described as cases where the apparent colour fails to reveal the true colour of objects — as cases of colour mispercep- tion. But this result, of course, turns on assuming that colours are illumination- independent, and presumably this is not a supposition that we should make in our characterization of colour constancy if we hope to appeal to colour con- stancy to motivate the view that colours are illumination-independent. Nor, as far as I can see, is there any other reason in the offing for treating the uncontro- verted violations of invariance as ignorable exceptions. Thus, short of begging the ontological question that colour constancy is being enlisted to answer (via the objectivist’s inference), it is not clear why the acknowledged failures of in- variance should not be regarded (pace Hilbert and Tye) as evidence for the illumination-dependence of (apparent colour, and therefore) colour.
3.2 Reflectance Accounts and Colour Ontology
If the invariantist understanding of colour constancy does not support the ob- jectivist’s inference, we should ask whether that inference can be saved by re- liance on a reflectance perception account of colour constancy. On this reading, premise (1) in the inference is to be understood as this empirical claim:
(1′′) We have the ability to perceive surface reflectance distributions (/produc- tances).
The question I now wish to consider is how, even granting the truth of premises (1′′) and (2), the conclusion (3) is supposed to follow.^26
(^26) For the moment I’ll put aside the further issue about how we should read ‘we’ in (1′′). As I shall discuss in §4, there is evidence of colour constancy at work in the visual systems of infant humans and many non-human animals, inter alia. It is not clear whether the proponent of the current version of the objectivist’s inference would want to apply the inference to these visual systems as well, although if not more would need to be said about why.
