1. The Psychophysical Matching Argument

Phenomenal invariantism holds that color constancy consists in the stability of color appearance across changes in illumination. As will be familiar, however, changes in lighting often make an appreciable difference to the visual appearance of objects within the scene. Familiar examples include the appearance of shadows falling across a surface and the comparatively cool cast of colors viewed under fluorescent bulbs.

The variance intuition need not necessarily pose a problem for invariantism. The question is, do these illumination-dependent variations in appearance consist in changes in color appearance? And if so, are these variations in color appearance significant enough to undermine the invariantist’s proposed phenomenal explanation of color constancy?

Variantists provide positive answers to both of these questions. In paradigmatic instances of color constancy, they claim, color appearance exhibits a high degree of illumination-dependent variation:

Variant Color Appearance implies that color appearances typically are not remotely stable under lighting changes. If this is right, then our commonplace intuitions of color constancy will not be explicable via any phenomenal stability across changes in viewing context:

Taken together, these two claims spell trouble for phenomenal invariantism.

The strongest grounds for Variant Color Appearance and Nonphenomenal Color Constancy derive from matching arguments, which come in two forms: intuitive and psychophysical. Noë (Reference Noë2004) presents an intuitive matching argument. Consider a variably illuminated object such as a white wall partly in shadow. According to Noë, we have a robust constancy intuition regarding the color of the wall: it seems to us that we perceive the wall, in some sense, as uniform in color. Now suppose you are presented with a range of color samples and asked to select the samples that best match (a) the directly illuminated region of the wall and (b) the shaded region of the wall. Noë (128) argues that different color samples would be selected in each case and that this implies a difference in color appearance between the two regions. The inference is that if these regions are matched by different color samples, then the difference in phenomenal character caused by the difference in illumination must itself be a difference in color appearance, as per Variant Color Appearance.

The psychophysical matching argument brings some experimental rigor to these claims. The argument first appeared in the philosophical literature in Thompson (Reference Thompson1995, 197) and is developed by Cohen (Reference Cohen2008).Footnote ² It centers on some famous experiments by Arend and Reeves (Reference Arend and Reeves1986) employing an asymmetric matching paradigm. In this paradigm, subjects are presented with two stimuli: the ‘standard field’, with a uniform reflectance R presented under illuminant I ₁, and the ‘test field’, with the same reflectance R presented under a different illuminant I ₂. The subject is instructed to adjust the chromaticity of the test field until she achieves a match between the test field and the standard field. The chromaticity of a stimulus signifies its coordinates in the CIE (Comission Internationale de l'Eclairage) chromaticity diagram.Footnote ³ The degree of color constancy exhibited can be represented using a color constancy index (CCI), with values ranging from 1 (idealized or perfect constancy) to 0 (absence of constancy; see Arend et al. Reference Arend, Reeves, Schirillo and Goldstein1991).

Intuitively, the CCI value represents the degree to which the difference in illumination between the two fields affects the response of the subject’s color perception system to these stimuli. The higher the CCI, the smaller the implied effect of the illumination change on her perceptual state and, hence, the better her implied color constancy.

The crucial twist in Arend and Reeves’s experiments is that before making any matches, subjects received one of two possible task instructions. The first was to “match the hue and saturation of the test field to that of the standard field” (Arend and Reeves Reference Arend and Reeves1986, 1745). The labels ‘hue’ and ‘saturation’ are taken to refer to dimensions of the hue, saturation, and lightness color appearance space. Call this the appearance match condition (AMC). The second was to “make the test field look as though it is cut from the same piece of paper” (1745). Call this the surface match condition (SMC). Subjects in the two conditions performed significantly differently on the matching task. Subjects in the AMC achieved fairly low CCIs, averaging 0.2. In contrast, subjects in the SMC achieved much higher CCIs, averaging 0.52. In a replication of these results, Bäuml (Reference Bäuml1999, 1537–41) found average CCIs of 0.23 in the AMC and 0.79 in the SMC.Footnote ⁴

Arend and Reeves’s results provide satisfying confirmation of the competing intuitions of constancy and variance, familiar to us all when viewing an object under different illuminants. A plausible interpretation of the differing CCIs is that subjects in the AMC are attending to some relatively variant aspect of their color perception system’s overall response to the stimuli, whereas subjects in the SMC are attending to some reasonably invariant aspect of their perceptual response. Given that subjects in the AMC had been instructed to attend to the hue and saturation of the stimuli, a natural inference is that these appearance dimensions underwent significant illumination-dependent variation, as per Variant Color Appearance. Cohen (Reference Cohen2008, 67–68) argues as follows,

To summarize, the positive conclusion of the argument is captured by Variant Color Appearance: when viewing stimuli of equivalent reflectance under different illuminants, the phenomenal character of subjects’ color experience exhibits significant illumination-dependent variation. The associated negative conclusion is captured by Nonphenomenal Color Constancy: our color constancy intuitions therefore cannot be explained by an invariance in the qualitative dimensions of color appearance. What does explain our constancy intuitions on this view? This is all up for grabs: variantists differ as to how they ultimately explain our capacity for color constancy. The force of the argument is simply to leave phenomenal invariantism moribund, with some or other form of variantism our best remaining option.

2. What Is the Scope of the Psychophysical Matching Argument?

The psychophysical matching argument has been taken by its philosophical advocates to warrant quite sweeping conclusions about the nature of color constancy. I read Cohen (Reference Cohen2008), for example, as arguing for variantism about color constancy simpliciter, across the board and without qualification. This fits a clear pattern within the philosophy of perception, in tacitly assuming that color constancy is a unified phenomenon, admitting of a single theoretical treatment. On broader inspection of the empirical literature, however, this uniqueness assumption seems frankly untenable.

As an example, one basic distinction in the study of color constancy is between simultaneous and successive constancy. Simultaneous color constancy reflects our ability to judge accurately, within a scene at a time t, that two objects under different illuminants have the same surface color. Successive constancy reflects our ability to judge accurately that a single object under varying illumination conditions at times t and t + n remains the same color. The focal study by Arend and Reeves concerns simultaneous color constancy. Arend and Reeves’s stated aim (Reference Arend and Reeves1986, 1743) was to isolate the contribution of ‘simultaneous mechanisms’ of constancy. They accordingly presented the standard and test fields concurrently, side by side on a monitor. Cohen (Reference Cohen2008, 63) nonetheless thinks that a similar pattern of results is to be found in successive constancy: “In cases of successive color constancy we find the same pair of perceptual reactions that occur in cases of simultaneous color 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 color. 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 color.” It seems clear, then, that Variant Color Appearance is taken to apply to both simultaneous and successive forms of color constancy.

Cohen is surely right that in many cases, successive illumination changes will produce strong variance intuitions. This fits our experience, for example, of a lamp being flicked on and off or a cloud’s shadow passing over a green field. In other cases, however, things are less clear-cut. While rapid changes in illumination caused by moving shadows and the like are extremely common, an even more regular feature of our environment is the gradual change in natural light that occurs over the course of the day. Now crucially, it is well established that changes in illumination that occur over longer durations allow greater scope for adaptation by the visual system, and adaptation to the illuminant is known to have a significant normalizing effect on color appearance (Cornelissen and Brenner Reference Cornelissen, Brenner and Blum1991).Footnote ⁵ Indeed Arend and Reeves (Reference Arend and Reeves1986, 1743) raised precisely this point, noting that “there are extensive data showing that adaptation, alone or in combination with simultaneous mechanisms, can produce large hue and saturation shifts.” This gives us reason to doubt that successive color matches involving longer timescales will follow the pattern of Arend and Reeves’s results. This is confirmed by Kuriki and Uchikawa (Reference Kuriki and Uchikawa1996), who administered a dichoptic successive matching task in which subjects were preadapted to the illuminant for 15 minutes. They found CCIs of 0.72 in the AMC and 0.77 in the SMC. This all but eliminates any difference in performance between these two task conditions, with subjects displaying comparably high CCIs in both conditions. These data do not fit the pattern of Variant Color Appearance. In fact, in these viewing conditions, the data are consistent with, and adequately explained by, phenomenal invariantism.Footnote ⁶

The conclusions of the psychophysical matching argument therefore need to be hedged appropriately. Properly qualified, the positive conclusion should be that color appearance exhibits a significant degree of illumination-dependent variation under some conditions, such as conditions of low adaptation. Similarly, the negative conclusion should be that in such conditions, our color constancy intuitions are not explained by an invariance in the qualitative dimensions of color appearance. This suggests a more complex picture of color constancy than is typically assumed in the philosophical literature. In summary,

The idea behind Pluralism is that our naive intuitions of color constancy—our judgments that things in some sense look the same color across changes in illumination—will be explained by different underlying perceptual capacities in different contexts. These explanations will differ in whether they appeal primarily to phenomenological or nonphenomenological factors, for example, or whether they fit invariantist or variantist specifications. A moderate pluralism was in fact proposed by Arend and Reeves (Reference Arend and Reeves1986, 1743, 1749) and later reiterated by Reeves, Amano, and Foster (Reference Reeves, Amano and Foster2008, 220). In a detailed investigation of this literature, Wright (Reference Wright2013) endorses a very similar view. In what follows, I will be developing and expanding on this pluralist theme in several ways, yielding an even more complex and heterogeneous picture.

3. Viewing Strategies and the Unfixed Nature of Phenomenology across Task Conditions

The psychophysical matching argument has both a positive and a negative conclusion. The purported evidence for the positive conclusion, Variant Color Appearance, is fairly well understood: subjects in the AMC are asked to match stimuli in respect to the appearance dimensions of hue and saturation, and they achieve very low CCIs. The purported evidence for the negative conclusion, in contrast, is far less clear. What exactly is the basis for Nonphenomenal Color Constancy?

Let us start by considering subjects’ performance in the SMC. In this condition, subjects are instructed to make the stimuli look as though they are cut from the same piece of paper. Subjects here achieve comparably much higher CCIs than in the AMC. As such, we can infer that whatever aspect of their perceptual response subjects are attending to in the SMC, this aspect is apt to explain color constancy, such as it is, in such conditions. This invites the question as to what this constancy-grounding perceptual aspect is exactly. As noted above, variantists differ in their views on this matter. The key negative claim is simply that, whatever else it might be, this aspect does not include any invariance in respect to color appearance. How does this follow? The variantist’s reasoning, it seems, is that we know from the AMC data that subjects have highly illumination-variant color experiences when attempting appearance matches with exactly the same stimuli. Assuming that subjects undergo similarly illumination-variant experiences of these stimuli when in the SMC, it is reasonable to expect that their color experiences similarly exhibit insufficient invariance to explain their higher CCIs. In summary, the phenomenology implied by the matching data from the AMC is assumed to be fixed across task conditions, in the following sense. For subject X who achieves a CCI of, say, 0.25 with respect to stimuli A and B in the AMC, her color experience of A and B in the SMC will exhibit a sufficiently similar degree of illumination-dependent variation to that in the AMC, such that any increase in CCI in the SMC is not attributable to an increase in appearance invariance in the SMC. Let us call this the fixed phenomenology assumption.

I want to apply some moderate pressure to this assumption. I argue that subjects’ color experiences in the SMC might in fact undergo a partial change from the AMC, as a result of the change in task conditions. Although changes of this particular sort would be insufficient to explain the entire difference in CCIs, a relatively more invariant color appearance in the SMC might provide part of the explanation of the higher CCIs recorded in this condition. The proposed mechanism is that the change in task instructions influences subjects’ viewing strategies, which in turn influences the degree of illumination invariance in their color experiences. By a ‘viewing strategy’, I mean a combination of factors including the direction and distribution of gaze across the stimuli, the amount of attention assigned to various parts or features of the stimuli, and the amount of time spent viewing parts of the stimuli. My argument draws on a study by Cornelissen and Brenner (Reference Blum1995). Their hypothesis is that the differing task instructions could alter the amount of time that subjects spend looking at certain parts of the stimuli, with the consequence that subjects in the SMC are more adapted to the illuminant than in the AMC. Such differences in adaptation in turn could alter the character of subjects’ color experiences, which might partly explain the differences in their CCIs.

Cornelissen and Brenner’s findings require careful interpretation. They did observe a significant change in subjects’ viewing strategies between the two task conditions. In particular, subjects spent longer looking at the stimulus surround before making a match in the SMC than in the AMC (Cornelissen and Brenner Reference Blum1995, 2437). They then estimated the likely state of adaptation for each subject, given the amount of time exposed to the stimulus surround, and calculated the expected influence of this adaptational state on their color experience. This predicted adaptational effect was then compared against the size of the difference in CCIs between the two task conditions. The results differed significantly from subject to subject. Two subjects exhibited much larger differences in CCI than predicted by their likely difference in adaptation. These subjects happened to have the most marked difference in CCI between the two conditions. It was predicted that differences in color experience explained at best between 10% and 15% of this difference in constancy performance. For three further subjects, the effects of instruction were consistent with an explanation largely due to eye movements and adaptation. Complicating these results, however, is the fact that these subjects did not produce marked differences in matches across the AMC and SMC (2435).

What are we to conclude from these data? For subjects exhibiting a marked difference in CCIs between task conditions, changes in viewing strategy and subsequent adaptation clearly do not explain all of this difference. Nonetheless, as Cornelissen and Brenner (Reference Blum1995, 2439) note, such changes “probably do contribute to some small extent to color constancy [in the SMC].” Contrary to the fixed phenomenology assumption, then, it is a mistake to assimilate wholesale the implied appearance data from the AMC with matching data from the SMC. The AMC data tell us about the degree of illumination-dependent variance exhibited by subjects’ color experiences when asked to match stimuli for hue and saturation but need not accurately reflect the degree of variance encountered by subjects even in closely related task conditions.Footnote ⁷

Contrary to Nonphenomenal Color Constancy, it is thus premature to dismiss appearance invariance as completely irrelevant to subjects’ improved CCIs in the SMC. Subjects in the SMC are likely to undergo color experiences with slightly higher degrees of invariance than in the AMC. Whereas variantists would like to attribute subjects’ color constant surface matches entirely to some nonphenomenal process, the evidence suggests that moderate improvements in appearance invariance could in fact play some role. The moral to draw is that the seemingly binary distinction between phenomenal and nonphenomenal color constancy presents a false dichotomy. While Pluralism claimed that color constancy can be sometimes phenomenal, sometimes nonphenomenal, it is perhaps more accurate to say that constancy can be more or less phenomenal, with appearance invariance explaining subjects’ color constant matches to a greater or lesser extent, depending on context. In summary,

4. The Nature of Color Appearance

Following a widely accepted standard in color science, Arend and Reeves (Reference Arend and Reeves1986) and those following them have assumed a three-dimensional hue, saturation, and lightness model of color appearance. Three-dimensional models of color date back at least to the eighteenth century. Significant theoretical advances were made by figures such as Munsell at the turn of the twentieth century. The three-dimensional Munsell Color System of hue, value (i.e., lightness), and chroma (or ‘purity’, related to saturation) remains one of the most common tools for representing color appearance.Footnote ⁸ From the 1950s, more rigorous studies of color appearance were enabled by multidimensional scaling (MDS) techniques, in which subjects are asked to compare color stimuli for pairwise (dis)similarity, and the results were analyzed in order to extract dimensionality and distances between stimuli in a metric space. MDS studies have been taken to provide some of the strongest confirmations of the three-dimensional nature of color appearance. For example, in a seminal work, Indow (Reference Indow1988) performed 19 MDS experiments, which recovered a very close approximation of Munsell’s original three-dimensional space.

Given this history, it is predictable and to some extent reasonable that color appearance is so routinely assumed to have three dimensions. In the present context, however, this assumption is highly questionable. It is an underappreciated fact that the aforementioned models of color appearance were generated using color stimuli presented under neutral and homogenous illumination. The same applies to Indow’s key MDS studies. This invites the question as to whether three dimensions of color appearance are adequate to represent stimuli viewed under varying illuminants. As we will now see, if this assumption fails, the invariantist is presented with a number of additional responses to the psychophysical matching argument.

One such response is due to Hilbert (Reference Hilbert2005, 152). Hilbert endorses the idea that when viewing variably illuminated stimuli, color appearance has additional dimensions that represent the way that an object is illuminated. While Hilbert does not recommend any specific model, he cites as an example the five dimensions proposed by Fairchild (Reference Fairchild2005, 91ff.): brightness, lightness, colorfulness, chroma, and hue. Hilbert’s strategy is to appeal to such additional dimensions to defuse Variant Color Appearance. He concedes that subjects’ matching performance in the AMC is explained by illumination-dependent variations in color appearance but argues that these variations occur in dimensions such as brightness and colorfulness, rather than hue and saturation/chroma. Hilbert thus retains the core invariantist view that constancy consists in the stability of hue and saturation, which he takes to represent objects’ surface spectral reflectance properties.

Hilbert’s response faces a number of problems. As Wright (Reference Wright2013, 449) has argued, whatever the merits of supplementing the traditional three dimensions of color appearance, it is unmotivated to claim that subjects in the AMC are attending to anything other than hue and saturation. This is because these subjects were explicitly instructed to attend to these dimensions. One could argue that subjects might have been inaccurate or fallible in following these task instructions. Perhaps subjects simply misunderstood or made systematic errors in assessing and reporting their own phenomenology. While clearly possible, such skepticism is largely muted by the fact that subjects in Reeves and colleagues’ (Reference Reeves, Amano and Foster2008) replication study were given significant training in performing hue and saturation matches. These subjects performed the task with confidence and consistency, making the suggestion of misunderstanding or systematic error seem ad hoc.

I propose an alternative strategy. Whereas Hilbert sought to explain away Variant Color Appearance, let us grant that subjects in the AMC are following task instructions and performing hue and saturation matches. As in the previous section, I want to focus attention on Nonphenomenal Color Constancy. Another assumption that drives the inference from Variant Color Appearance to Nonphenomenal Color Constancy is that single dimensions of hue and saturation (and lightness) exhaust the possible dimensions of color appearance to which subjects could attend in either task condition:

The introduction of additional dimensions of color appearance allows us scope to deny Exhaustiveness. I argue that subjects in the SMC are also tracking phenomenal dimensions of hue and saturation, albeit hue/saturation dimensions of a different kind from those tracked in the AMC. This requires distinguishing two different types of hue and saturation: material or surface hue and saturation, on the one hand, and lighting or illumination hue and saturation, on the other. Let us call this the duplicate dimensions gambit. This gambit allows for a phenomenal explanation of both the appearance matching and surface matching data. The view ultimately will be that subjects in the SMC are matching stimuli by attending to material dimensions of color appearance, while subjects in the AMC are matching via lighting dimensions of color appearance.

The duplicate dimensions gambit has a long history within color science, although as Mausfeld (Reference Mausfeld, Mausfeld and Heyer2003, 386) notes, the approach has remained well outside the mainstream. In important recent work on this theme, Tokunaga and Logvinenko (Reference Tokunaga and Logvinenko2010b, Reference Tokunaga and Logvinenko2010c) sought to reassess the dimensionality of color appearance using MDS methods but allowing variations in illumination across the color stimuli. Tokunaga and Logvinenko found that in these conditions, a minimum of six appearance dimensions were required to model subjects’ dissimilarity judgments. This is broadly in keeping with previous duplicate dimension views, on which our experience of a uniform surface under colored light involves two distinct phenomenal attributes: a material color and a lighting color. Total color appearance is specified by two independent triples of hue, saturation, and lightness.Footnote ⁹ In a break from such views, however, Tokunaga and Logvinenko argue that their six color dimensions are not best modeled as two independent attributes. They claim that “both triplets constituting these six numbers are determined by a pair object/light, not object separately and light separately” (Reference Tokunaga and Logvinenko2010a, 2556; see Tokunaga and Logvinenko Reference Tokunaga and Logvinenko2010b, 1744). On their analysis, then, the dimensions of material and lighting color are modeled as constituents of a single, complex, object color attribute. Our visual experience of object hue, for example, is thus “essentially 2D” (Tokunaga and Logvinenko Reference Tokunaga and Logvinenko2010a, 2556): we do not experience material blue or lighting yellow simpliciter, for example, but rather material blue under a yellowish illuminant.Footnote ¹⁰

Relating back to our central puzzle, this view yields a second-generation invariantism, on which color constancy consists in the approximate invariance of material color appearance, while allowing for significant variation in lighting color appearance. Let us call this complex invariantism, as distinguished from traditional invariantist models incorporating just three color dimensions.Footnote ¹¹ The conjecture is that subjects’ responses in the AMC are driven either primarily by lighting hue and saturation or some complex function of lighting color and material color, whereas subjects in the SMC are attending primarily to material hue and saturation. Complex invariantism thereby grants a version of Variant Color Appearance while resisting Nonphenomenal Color Constancy, providing a satisfying synthesis of traditional invariantist and variantist views.

5. The Limits of Complex Invariantism

Complex invariantism is not intended as a decisive response to the psychophysical matching argument. My aim was to cast doubt on the move from Variant Color Appearance to Nonphenomenal Color Constancy, by questioning the assumption of Exhaustiveness. Exhaustiveness is far from secure, given recent evidence that color appearance has multiple dimensions of hue and saturation in conditions of multiple or varying illuminants. Given that Arend and Reeves’s experiments involve simultaneously viewing two stimuli of equivalent reflectance under differing illuminants, we have reason to think that these conditions would involve such complementary dimensions. If that is right, then complex invariantism should provide a good alternative explanation of the matching data. This conjecture is tentative, however, and must await empirical confirmation. In keeping with Pluralism, moreover, we should note that in scenes with single or constant illumination, the traditional three dimensions of color appearance might suffice to model subjects’ dissimilarity judgments (Logvinenko and Tokunaga Reference Logvinenko and Tokunaga2011, 444). Traditional forms of invariantism and variantism may therefore still be required to explain our constancy intuitions in such contexts, such as they may be.

A further qualification is that the mere presence of dimensions of material and lighting color in a context does not guarantee that color constancy will be best explained by invariant material color appearance. We should allow that in some contexts, both lighting color and material color appearance could exhibit significant illumination-dependent variation. These dual color spaces therefore open the door to complex forms of variantism, as well as complex invariantism. Traditional variantists hold that subjects ‘infer’ an object’s surface color from patterns of illumination-dependent variation in hue, saturation, and lightness. A complex variantist, in contrast, could hold that subjects appeal to variations in dimensions of both lighting color and material color, in inferring a stable surface color. Development of this idea must await another occasion.

A third issue concerns our interpretation of Arend and Reeves’s task instructions in the AMC. In this condition, subjects are instructed to “match stimuli in respect of hue and saturation” (Arend and Reeves Reference Arend and Reeves1986, 1745). One interpretation of complex invariantism noted above is that subjects subsequently match stimuli in respect to lighting hue and saturation. This would raise the question, however, as to why subjects disambiguate the task instructions this way. Why default to matching lighting hue and saturation, rather than material hue and saturation? One explanation is that subjects are cued to adopt this reading by those administering the task. In the training regime of Reeves and colleagues (Reference Reeves, Amano and Foster2008), for example, perhaps subjects were taught that ‘hue and saturation’ matches should be performed by equating stimuli for lighting hue and saturation. The nagging follow-up question, of course, is why those administering the tasks default to this understanding of ‘hue’ and ‘saturation’. I do not know the answer to this question but speculate that the history of these technical terms is so closely bound up with colorimetric studies of the colors of lights that those inculcated into existing scientific practice acquire recognitional concepts of ‘hue’ and ‘saturation’ that denote lighting dimensions of color appearance. This issue is clearly contentious, however, and requires more detailed consideration than I can provide here.

A fourth issue concerns the interpretation of subjects’ dissimilarity judgments in Tokunaga and Logvinenko’s studies. Subjects were presented with two colored papers, each under different lighting, and instructed to “evaluate dissimilarities between papers.” Tokunaga and Logvinenko deliberately avoided using terms such as ‘color appearance’ and ‘color stimulus’ in their instructions. Moreover they “did not specify explicitly the color dimensions between which the dissimilarity was supposed to be measured. The intention was to ascertain the dimensions which will emerge from the multidimensional analysis of dissimilarities rather than to impose some dimensions on observers” (Reference Tokunaga and Logvinenko2010b, 1741). Given that the aim of any such MDS study is to generate a model of subjects’ color appearance space, then, Tokunaga and Logvinenko reasonably judge that they should not presuppose a specific view of appearance in their task instructions.Footnote ¹²

While such neutrality is therefore required by the nature of the MDS study, it presents a fundamental problem. Given the indeterminacy in the instruction to “evaluate dissimilarities between papers,” how can we be sure that subjects are specifically and exclusively assessing features of color appearance? Can we rule out, for instance, that subjects were assessing overall dissimilarity in part by appeal to color appearance but also in part by appeal to the output of some nonphenomenal or quasi-cognitive process? Variantists may well object that it is question-begging to rule out such alternative explanations of the data. After all, the very issue at hand concerns the appropriate interpretation of subjects’ competing intuitions of similarity and dissimilarity when viewing colored stimuli under differing illuminants. The variantist’s proposal is that our intuitions of dissimilarity reflect the illumination-dependent nature of color appearance, whereas our intuitions of similarity reflect the outputs of some nonphenomenal process. And perhaps this variantist model could explain why six dimensions are required to model subjects’ dissimilarity judgments: three dimensions to model variant color appearance, as standard, and a further three dimensions to model the content of the variantist’s putative nonphenomenal process.

This issue threatens a serious deadlock. On the one hand, complex invariantism appeals to the MDS data to vindicate an appearance-based explanation of color constancy. On the other hand, variantists may seek to fit the data to their own preferred nonphenomenal account of constancy. It is not altogether clear who has the upper hand here. One point that tells against the variantist response, however, is that it requires some selectiveness in interpreting MDS studies. As with almost everyone, variantists are happy to adopt the three-dimensional models of color appearance generated by previous MDS studies, in which illumination conditions were kept uniform. Given that Tokunaga and Logvinenko’s studies adopt the same general approach, it seems unprincipled to explain away half of their data as irrelevant to color appearance. Indeed the variantist seems even guiltier of begging the question here. Variantists seek to explain half of the dissimilarity data by appealing to their preferred nonphenomenal account of color constancy. But as argued above, Nonphenomenal Color Constancy is only motivated given the assumption of Exhaustiveness, which in turn presupposes that color appearance has only three dimensions. Given that the argument for Nonphenomenal Color Constancy contains this presupposition, it is most definitely question-begging to appeal to the argument’s conclusion to fend off challenges to the three-dimensional model of color appearance. Of course, there may well be other, more independent, routes to blocking these challenges. But as things stand, the onus is on the variantist to provide such independent grounds.

6. Discriminatory and Relational Color Constancy

Let us take stock. Color constancy is a highly heterogeneous and complex phenomenon. The phenomenological basis for color constancy should be assessed on a case-by-case basis, with appearance invariance—either in the traditional three appearance dimensions or in material color appearance—playing more or less of an explanatory role, depending on context. The psychophysical matching argument therefore misses its mark: there is no straightforward dialectical route from asymmetric matching to a generic variantism about color constancy. The evidence suggests a far more nuanced and diverse picture.

I now want to complicate matters more by introducing two further concepts of color constancy: discriminatory color constancy (DCC) and relational color constancy (RCC). The seminal presentation of these notions is due to Craven and Foster (Reference Craven and Foster1992). While this work has received a fair amount of attention in vision science, it has been largely neglected in philosophy. This is unfortunate, for Craven and Foster (1359) are motivated by the very puzzle under discussion here, concerning the appropriate response to Arend and Reeves’s famous results. After noting the difficulties posed by these results for “the traditional definition of color constancy,” that is, phenomenal invariantism, they present

This passage introduces two related capacities. The first is a discriminatory capacity: the ability accurately to distinguish changes in surface spectral reflectance from changes in illumination. I refer to this capacity as DCC. The second is a relational capacity, on which colors are somehow ‘perceived to stand’ in constant relations of similarity and difference across changes in illumination. This capacity is RCC, on which constancy consists not in the stability of monadic color appearance but in the (approximate) invariance of perceived color relations across changes in context. My questions are as follows. What exactly is the connection between DCC and RCC? And what is the relationship between these notions and the views of color constancy discussed earlier?

In the remainder of the article, I argue for two claims. First, although Craven and Foster originally presented DCC as an operationalization of RCC, RCC is not the only possible basis for DCC. I suggest that these discriminatory capacities are better explained in some contexts by the subject’s awareness of changes in the complementary dimensions of material or lighting color appearance. Second, I propose that DCC provides a dimension of classification for our color constancy capacities that is orthogonal to the invariantist-variantist characterizations discussed above. The concept is strictly neutral as to whether the phenomenology of color constancy is traditional invariantist, traditional variantist, or complex invariantist. As such, DCC provides a useful unifying characterization of color constancy, a kind of lowest common denominator view of the constancy-related abilities involved across widely differing viewing contexts.

DCC was presented by Craven and Foster as an alternative to phenomenal invariantism, jettisoning the requirement that color appearance should be stable across changes in illumination. DCC requires merely that subjects are able to discriminate changes in illumination from changes in surface material properties. What explains our capacity to make these discriminations? What perceptual phenomena are involved? According to Craven and Foster, “all that is needed” to perform such discriminations is for surfaces viewed under differing illuminants to be perceived, in some sense, as standing in the same relations of similarity and dissimilarity. In other words, the proposed perceptual basis for DCC is RCC. As later explained by Foster and colleagues (Reference Foster, Nascimento, Craven, Linnell, Corenelissen and Brenner1997, 1342), “discriminating illuminant changes from material changes … corresponds to discriminating whether the relations between surface colours are unchanged.” Perceptual awareness of these color relations thus “underlie[s] the ability of observers to discriminate, reliably and effortlessly, illuminant changes from material changes in scenes” (1341).

How exactly does RCC explain DCC? The idea seems to be as follows. RCC with respect to stimuli A and B involves the perceptual awareness of the invariant color relations between A and B across changes in illumination. By the same token, it is assumed that subjects will be aware of some variance in the color relations between A and B if the surface color of either stimulus is changed. DCC is grounded in (a) the subject’s capacity to discriminate between changes in color appearance that preserve color relations and those that do not and (b) the ability to judge as follows: given some change in distal conditions C, and subsequent transformation T in the color appearance of A and B, if T preserves the color relations between A and B, then C is likely to have been an illuminant change; if not, C is more likely to have been a surface material change.

I do not have the space here to assess whether this explanation of DCC is plausible. I note, however, that RCC remains an extremely underdeveloped notion and would benefit greatly from more sustained philosophical attention. In particular, it is unclear in what sense objects are “perceived to stand” in invariant or variant color relations. Craven and Foster never adequately explained this claim, and their brief attempts at pinpointing the phenomenology of RCC are quite confusing (see esp. Craven and Foster Reference Craven and Foster1992, 1364; Foster, Amano, and Nascimento Reference Foster, Amano and Nascimento2001, 287–88). I discuss these issues in more detail in future work. In any event, RCC does not provide the only possible explanation of DCC. Indeed in contexts of multiple or varying illuminants, it may not even provide the best explanation. Drawing on the model developed in section 4, a much simpler and clearer explanation of DCC in such contexts appeals to the phenomenal dimensions of material and lighting color appearance. The proposal is satisfyingly straightforward: our ability to discriminate a material change from a lighting change reflects our ability to distinguish a change in material color appearance from a change in lighting color appearance. In such contexts, DCC is explained by the subject’s sensitivity to the phenomenological difference between changes in material color appearance, as contrasted with changes in lighting color appearance.

It is interesting to contrast this proposal with Craven and Foster’s view. On their view, DCC provides an operationalization of RCC. DCC is grounded in the subject’s capacity to perceptually discriminate whether a transformation in (three-dimensional) color appearance preserves or violates the color relations between objects in the scene. Subjects then judge on this basis whether the transformation is likely to have been caused by an illuminant change or a material change. On their view, then, subjects do not strictly perceptually discriminate changes in material or lighting properties. Such changes are merely “attributed” (Craven and Foster Reference Craven and Foster1992, 1360) on the basis of the perceived color relations in the scene. On my view, in contrast, our ability to discriminate illuminant changes from material changes is grounded in the subject’s capacity to perceptually discriminate changes in material properties and lighting properties themselves, via awareness of changes in material and lighting color appearance. These two explanations have quite different implications for the perceptual representations involved in DCC. On my view, DCC is explained by perceptual capacities that function to represent monadic properties of both surface material and lighting in the scene. On Craven and Foster’s view, DCC is explained by appeal to the subject’s perceptual awareness of color relations. As noted above, it remains unclear how we should characterize this putative relational awareness and what kinds of perceptual representation it might involve. As Craven and Foster intended it, however, it seems fairly clear that RCC does not involve representations of surface material and lighting properties.

To recap, I have argued that in some contexts, DCC will be well explained by the six-dimensional color appearance model developed in section 4. In keeping with the spirit of Pluralism and Complexity, however, I suggest that DCC will receive different explanations in different viewing contexts. Assuming the details can be worked out, for instance, Craven and Foster’s explanation of DCC in terms of RCC may prove the most plausible in contexts in which color experience has the traditional three dimensions of variation. As a general concept of color constancy, however, DCC is satisfyingly broad: it can be applied in widely differing viewing contexts, in which the phenomenology of color constancy can vary significantly. Indeed I will now argue that DCC is strictly neutral as to whether the phenomenology of color constancy fits the specifications of traditional invariantism, traditional variantism, or complex invariantism.Footnote ¹³

From the preceding paragraph, let us assume that DCC can be explained in a context either by RCC or by the subject’s awareness of changes in the phenomenological dimensions of material and lighting color. From the latter case, DCC is clearly consistent with a complex invariantist account of the phenomenology of color constancy. What about the former case? I argue that when DCC is explained by RCC, it is consistent with either a traditional invariantist or traditional variantist view of color constancy. Consider two colored stimuli A and B presented under illuminant L ₁, where A appears red and B appears orange. Grant that A appears redder and darker than B. Let A and B viewed under L ₁ be mapped to locations (w, x) and (y, z) in the chromaticity diagram. Now suppose that A and B are presented under a different illuminant L ₂. Let the subsequent change in the appearance of A and B be modeled by the transformation of chromaticity coordinates from (w, x) to (w′, x′) and (y, z) to (y′, z′). The idea behind RCC is that color constancy is consistent with any such change in appearance, so long as the illumination transformation preserves all color relations between A and B. For example, the location (w′, x′) should represent a color that is both redder and darker than that represented by (y′, z′). We should note, however, that this constraint is trivially satisfied in the null case in which the transformation maps (w, x) and (y, z) onto themselves. That is to say, it is trivial that if A and B appear exactly the same color across the illumination change, then A and B will appear to stand in the same color relations.Footnote ¹⁴ Formally speaking, then, RCC is consistent with both traditional invariantist and variantist accounts of the color appearance of A and B across changes in illumination. As such, insofar as DCC is to be explained by RCC, DCC is consistent with both traditional invariantist and variantist accounts of color constancy. Combining these results, DCC is consistent with traditional invariantist, traditional variantist, and complex invariantist accounts of constancy. As a concept of color constancy, then, DCC does not imply any one view of the phenomenology of color constancy: DCC, let us say, is phenomenologically neutral.

One might object that where the color appearance of A and B is completely invariant constant across changes in illumination, our explanation of DCC need not appeal to RCC. In such cases, subjects could judge that there has been no change in surface material—and hence that there must have been a change in illumination—simply by introspecting the invariant monadic color appearance of A and B. My view is that it is an empirical question as to what explains subjects’ discriminatory capacities in such contexts. My prediction would be that, as elsewhere, subjects’ judgments probably will be explained by multiple factors: in this case, perhaps appearance invariance, in part, and RCC, in part. In any event, the objection does not undermine the point that insofar as RCC explains DCC, DCC is strictly speaking neutral as between traditional invariantism and variantism.

DCC’s phenomenological neutrality makes it extremely appealing in the present context. In sections 2 and 3, I argued that the extant matching data do not decisively favor traditional variantism over traditional invariantism. The principles of Pluralism and Complexity suggest a far messier and context-bound view of the phenomenological bases for color constancy. This picture was muddied further by the introduction of complex invariantism in section 4. This heterogeneity is at once both illuminating and frustrating. On the one hand, our taxonomic powers with respect to subjects’ constancy abilities hopefully have been expanded and refined. On the other hand, it is natural to despair at the fragmentation of color constancy into such a ragbag of phenomenological types. Would it be too much to hope for a disambiguation of ‘color constancy’ that picks out some more general, fundamental, psychological kind?Footnote ¹⁵ DCC’s phenomenological neutrality presents us with a unifying opportunity here. Where there is color constancy of any type, I propose, there will be DCC. One thing that even the most extreme invariantist and variantist types of constancy will have in common, I suggest, is that the perceptual capacities involved will support a high degree of DCC. This proposal will not satisfy those who have set their lofty sights on theorizing the phenomenology of color constancy. But if the foregoing view is right, there is no such unique thing.

7. Conclusion

In closing, I want to address an issue that has been kept firmly in the background, concerning the relationship between color constancy and color ontology. For a time, there was hope that color constancy could provide clues as to the nature of the colors. In its traditional invariantist guise, color constancy was taken by some to support color physicalism, the view that colors are surface spectral reflectances (Byrne and Hilbert Reference Byrne and Hilbert2003). The underlying assumption was that if color appearances are largely illumination independent, then so must be the colors. As Cohen (Reference Cohen2008) has argued, if phenomenal invariantism is an inaccurate characterization of color constancy, then this undercuts the claimed support for color physicalism. By the same token, if traditional variantism is true, this seemingly favors the view that colors are constituted by illumination-dependent properties. This approach appears fundamentally misguided, however, in light of the extreme heterogeneity and complexity of color constancy. There is no straightforward, context-free answer as to whether color appearance is illumination invariant. Indeed the very interpretation of ‘color appearance’ likely differs from one context to another. A proper understanding of color constancy therefore will not help settle these long-standing debates about ontology. In emphasizing color constancy’s pluralist and complex nature, however, the foregoing discussion may help reroute color ontology into less doggedly sectarian territory.