3.1. The Context Sensitivity of Color Perception

When performing experiments on color perception, the usual setup involves a test light and three primary lights.Footnote ³ The subject's visual field is divided, with the test light on one side and the primaries mixing on the other; the subject manipulates the intensities of the primary lights until their mixture appears subjectively identical to the test light. Symmetric matching experiments such as this can be used to identify the class of metamers for a given subject. Demonstrably, this class of metamers is invariant with respect to context so long as the context remains symmetric. In other words, suppose that A and B are two metameric spectral power distributions, β₁ and β₂ are two contexts (i.e., colored environments within which the test lights occur), and β _i (X) is the value in phenomenological color space induced by spectral power distribution X in context β _i . Then, since A and B are metamers, it will be the case that $\beta _{1}( A) =\beta _{1}( B) $ and $\beta _{2}( A) =\beta _{2}( B) ,$ but it will not in general be the case that $\beta _{1}( A) =\beta _{2}( B) ,$ or vice versa (or even that $\beta _{1}( A) =\beta _{2}( A) ) .$ The crucial point is that context affects the phenomenological color value assigned to a particular spectral power distribution.

For example, Jameson and Hurvich (Reference Jameson and Hurvich1959) compare two equations for describing the coding of spectral power distributions in three variables. One such equation includes an additional factor (I, $I^{\prime },$ etc.) for capturing the influence of context on neural processing, while the other does not. They remark:

A similar point is made by Suppes et al. (Reference Suppes, Krantz, Luce and Tversky1989):

So the subjective appearance of a colored light depends on the context, or the spectral power distribution of nearby colored light. Now, since Churchland has taken the theory of metamers for spectral power distributions of light and applied it, mutatis mutandis, to surface reflectance properties of objects, it seems fair to bring along as well the inherent context sensitivity of subjective color assessments. In other words, even if we presume that standard lighting conditions have been stipulated, in terms of “broad daylight,” say, the same reflectance profile will produce different subjective color assessments depending upon the reflectance profiles of nearby surfaces. In fact, this is empirically the case as we can see from the Munker illusion, the watercolor illusion, and the neon color spreading illusion, to name just a few.Footnote ⁴

Of course, color illusions involving reflectance properties of surfaces usually involve distinct surface reflectance profiles occurring in very close proximity. Churchland may therefore attempt to argue that such contextual effects are purely “local,” that is, occur only when the two surfaces subtend a sufficiently small angle in the visual field. One could therefore avoid the phenomenon by stating that the (homogeneous) surface in question must subtend some substantially large angle in the visual field. No matter how recalcitrant, any contextually induced effects on subjective color assessment should disappear if the contextual factors are removed to a sufficient distance from the focal viewing area. Nevertheless, if one adds such a specification to the requirements of standard viewing conditions, one reintroduces the subject into the equation. One can only specify the visual angle the stimulus will occupy in terms of the subject's position with respect to the stimulus, and thus its distance from the stimulus will become a factor in the characterization of standard viewing conditions. At first blush, introducing such a fix to the context sensitivity problem removes the objectivity of the characterization of reflectance profiles.

There is a further wrinkle, however: the assumption that we can fix the standard viewing conditions by specifying the subject's position with respect to the stimulus depends upon the homogeneity of surface reflectance properties. Yet such surface properties are not in general homogeneous. A consequence is that some objects will fit the standard viewing conditions multiple ways and will thus be multiple colors simultaneously. Consider, for example, a cloth of finely woven blue and yellow threads. If viewed from a very close distance, such that individual threads subtend a large enough angle of visual space to conform to the standard viewing conditions, the object will be striped blue and yellow. If viewed from a further distance, however, such that the cloth as a whole subtends the appropriate angle, it will be a homogeneous shade of green. Depending, in other words, on the size of the patch of heterogeneous surface one chooses to average over, the surface reflectance profile and thus the “objective” color may be significantly different.

3.2. The Inferential Character of Color Perception

Ironically, it is the context sensitivity of color vision that produces our subjective sense of color constancy. It is only because “color appearance depends more on the local contrast of the cone absorptions than on the absolute level of cone absorptions” (Wandell Reference Wandell1995, 289) that an object (say, an apple) will appear the same color in vastly different viewing conditions (say, high noon and twilight). Since Helmholtz, many vision scientists have found it useful to interpret the computations of the visual system that result in judgments such as color constancy as inferential in character. Although the process by which conclusions about color are derived is unconscious, and thus may be qualitatively different from that of conscious inference, the epistemological status of these “unconscious conclusions” is the same as those produced by conscious reasoning.

If we accept (as many perceptual scientists do) Helmholtz's analysis, then phenomenological color space is a kind of theory about the world. The problem of determining the reality of colors, then, may be analogous to the problem of determining the reality of a scientific theory. In particular, even the most robust scientific theories (say, Newton's gravitational theory) bear only a statistical relationship to the data that support them, leaving perpetually open the possibility that a better theory may come along and prove them “false.” Likewise, color judgments bear only a statistical relationship to surface reflectance properties. Churchland's argument can only go through if he can eliminate the probabilistic character of this relationship by specifying standard viewing conditions. As discussed above, however, there exist objects for which even the best subject-independent notion of standard viewing conditions makes no sense.

Perhaps it would be useful here to consider an analogy with a perceptual domain that is commonly taken to be objective: size. Size judgments exhibit the same context sensitivity as color judgments for precisely the same purpose, namely, to induce a constancy over perceptions of size. The effects of context on size judgment can easily be seen in the Ames room illusion. Consider another optical illusion, however, the changing size of the moon. Subjectively, the moon appears significantly larger when it is close to the horizon, yet the moon always subtends the same angle of visual space, as its distance from any observer remains (approximately) constant. Something about the contextual cues when the moon is close to the horizon induces the visual system to infer that the moon is larger than it infers it to be when it is higher in the sky (although several explanations for the phenomenon have been proposed, there is no consensus on the correct explanation). Now, since it is quite easy to operationalize our notion of size in a manner that is invariant with respect to viewing conditions (say, by measuring with a ruler), we have an objective notion of the size of the moon. But suppose that we had no recourse but to specify the size of the moon with respect to standard viewing conditions. What standard viewing conditions would allow us to make an appropriate judgment about the size of the moon? The problem here is that any of the candidates for standard viewing conditions that might work for everyday objects (middle-sized dry goods, etc.) cannot be adapted to viewing conditions for planetary bodies: planets are simply too big for the perceptual system's techniques for inferring size to apply.

Returning to color, I can now state the problem for Churchland more succinctly: so long as the only test available for the “objective” partition of the space of surface reflectance properties is that it matches phenomenological color space, the very properties of color perception that produce color constancy for everyday objects like oranges and apples will defeat the uniqueness of color values for atypical objects. Yet, if color is objective, then these atypical objects should have unique, determinate colors associated with them.

4.1. A Program for Naturalizing Representational Content

Model theoretic semantics assigns primitive terms and predicates “meaning” by providing them an interpretation in a set theoretical structure. Can we make sense of an analogous project for nonlinguistic domains such as, say, the space of percepts for a given sense modality? Since perceptions can vary continuously with respect to certain features (e.g., sourness, heat, loudness, redness), an account of the meaning of these perceptual “qualia” might, analogously, be given via an interpretation of the axes that define the space of variation with respect to the axes of variation of some model (potentially, though not necessarily, characterized in set theoretic terms). If, furthermore, the “model” of a given perceptual space is a structure external to the brain and well defined by natural science, we might claim to have provided a “naturalistic semantics” for the perceptual space. Churchland motivates a project along these lines with a “just so” story about the evolutionary development of contentful cognitive structures:

This account suggests a bipartite program for providing a naturalistic semantics for representational mental states. One goal is to provide a mapping between some well-defined domain of variance in the environment (whether it be surface reflectance profiles, spectral power distributions, or what have you) and a cognitive representational space (e.g., say, the phenomenological color space). The second goal is to provide a detailed causal story for how such a mapping is induced; such a causal story will, necessarily, incorporate the causal structure of the perceptual system's “inferential” computations.

Churchland only explicitly acknowledges the first of these goals, claiming that by providing a mapping between cognitive domain and external feature domain, one has provided a semantics for the cognitive domain:

However, he seems to explicitly acknowledge the importance of the second goal when referring to “the nature and ground of our internal map” (Churchland Reference Churchland2007, 125). If I interpret Churchland correctly here, by “nature” he means the well-developed (empirically confirmed, axiomatizable, etc.) theory of phenomenological color space, and by “ground” he means the physiological story about how this space is neurally coded (partially understood, though many questions remain concerning the exact connection between the physiological and the phenomenological here).

Churchland himself has attempted to engage in the second goal in Churchland Reference Churchland2005, where he argues for a correspondence between idealized models of the neural wiring for opponent color vision (as offered in, e.g., Hurvich Reference Hurvich1981, Chapter 11) and phenomenological color space. Yet neural network models such as Churchland considers (those in which the three types of cone cells are wired into three types of opponent color cells: red-green, blue-yellow, and white-black) are hand tuned, as it were, to correspond to the phenomenological color spindle. A perhaps more critical step for the program outlined here is a detailed account of the relationship between such idealized models of neural wiring and the actual wiring of the visual system as discovered via experimentation. For example, Derrington, Krauskopf, and Lennie (Reference Derrington, Krauskopf and Lennie1984) found neurons in the macaque LGN that respond as if receiving a red-green opponent color signal yet that “do not meet the specification of the canonical R-G opponent cell” (264). Wandell notes:

4.2. The Role of “Reductions.”

Churchland (Reference Churchland2005, 554) concludes with some remarks on the import of the “reduction”:

I hope that the above discussion has demonstrated, however, that we are still far from providing a detailed enough account of the relationship between phenomenological color space and reflectance properties (or even between idealized neural network models and empirical measurements of neural activity) for there to be any serious candidate for a reduction of color qualia on the table. In fact, if such a “reduction” is ultimately provided, it may be so convoluted and qualified that our intuitions concerning its ontological import could well be defeated.

Suppes (Reference Suppes2002, 52) observes:

These general considerations aside, if we do manage to succeed in providing a convincing naturalistic semantics for a particular perceptual domain along the lines outlined above, will we have then provided a “reduction” of that domain?

Here is precisely where the nonnaturalist's eyes begin to glaze over; her resistance to “reduction” in any form will make her skeptical of the entire project. Yet, the strategy for providing naturalistic semantics outlined above is minimal in just this sense: it is neutral with respect to the ontological import of such an account. Consider, for example, Mary's question, namely, “Will the complete scientific account of color vision tell one (ideally one who has never seen it) what it is like to experience the color red?” To oversimplify, here, briefly, are three potential answers:

1. 1. [Metaphysical naturalist] Yes, because we have reduced color “qualia” to X (= reflectance properties, or whatever).

2. 2. [Methodological naturalist] No, because the question is ill posed; science is not in the business of explaining what subjective experiences are “like.” Insofar as the question can be recast in operational terms, then yes.

3. 3. [Nonnaturalist] No, there will always be an additional phenomenon (the “qualia”) in need of (philosophical) investigation that cannot be explained via the scientific account.

Yet, as stated above, the project of providing a naturalistic semantics for color is neutral between these answers. Even if it succeeds as an account of “meaning” for color percepts, the implications of this semantics for ontological questions, or questions of explanatory power, will remain open. In fact, even the nonnaturalist should benefit from such a proposed semantics: surely one can better critique the view that color qualia can be reduced to physical phenomena if one is informed by the exact proposal? As we have seen in the quote from Wandell that concludes the previous section, ammunition for the antireductive view may come from science itself.

A minimal naturalistic semantics will provide the best available candidate for a reduction of any perceptual domain to physical phenomena, yet an argument that such a reduction has been provided will be needed in addition to the minimal account. Furthermore, even philosophers resolutely opposed to reductive programs may benefit from such an account. Finally, the resolute naturalist himself would do well to clearly distinguish between those aspects of his argument that carry ontological weight and those of a more minimal character, the better to communicate with those whose too hasty dismissals depend upon the former and blind them to the general value of the latter.