Can Colour Be Reduced To Anything?
Department of Philosophy and Trinity College
University of Toronto
C. L. Hardin has argued that the colour opponency of the vision system leads to chromatic subjectivism: chromatic sensory states reduce to neurophysiological states. Much of the force of Hardin's argument derives from a critique of chromatic objectivism. On this view chromatic sensory states are held to reduce to an external property. While I agree with Hardin's critique of objectivism it is far from clear that the problems which beset objectivism do not apply to the subjectivist position as well. I develop a critique of subjectivism that parallels Hardin's anti-objectivist argument.
1. Introduction. For philosophers who write about colour, opponent colours theory is all the rage. On the assumption that philosophical discussions of colour should be empirically responsible, this is as it should be: the opponent theory is, as the vision scientists Dorthea Jameson and Leo Hurvich and have put it, "universally accepted." (1989, 2)
C. L. Hardin (1988) has argued that, when properly understood, opponency leads us to an ontological position he calls chromatic subjectivism. On this view colours are not in the world. They are in the mindas chromatic sensory statesbut each of these mental states reduces to a neurophysiological state. Much of the force of Hardin's argument derives from an initial critique of chromatic objectivism. On this ontological position, colours are in the world and chromatic sensory states are held to be reducible to some or other external property: surface spectral reflectance is the usual candidate. While I agree with Hardin's critique of chromatic objectivism, as do most philosophers who write about colour, it is far from clear that the problems which beset objectivism do not apply to the subjectivist position as well. I shall develop a critique of subjectivism that parallels Hardin's anti-objectivist argument and consider the implications of that critique.
2. A problem for objectivism and subjectivism. Let us begin with a brief recapitulation of Hardin's argument against the objectivist. On the most plausible objectivist view, colour is a property of objects, namely, their surface spectral reflectance (SSR). The reason for preferring this property is straightforward: the ratio of absorbed to reflected light across the spectrumthe "reflectance profile" of an objectis a stable property which does not vary in relation to incident illumination and other conditions of view. We thus have a physical property which is relevant to human colour perception. Does this mean that objects are coloured and that their colours are identical with their SSRs?
One of the basic principles of colourimetry is colourimetrical identity . "If two [such] objects have identical spectrophotometric curves ... for given angular conditions of illumination and view, we may be sure that under these conditions they will be perceived to have the same colors, no matter what light is used to see them by and no matter which observer looks at them. "(Judd and Wyszecki 1963, 103-104)
In so far as we recognize this claim to be qualified we can take it to support the reflectance theory, i.e., the claim that colour is to be identified with SSR. The problem comes with the introduction of another notion basic to colourimetry, metameric identity :
if the two curves [i.e., the spectral reflectance curves for two objects] differ in a complicated way, such as with three or more crossing points... it may not be possible to tell by mere inspection in what way the colors of the specimens differ. Indeed, under some lights and judged by some observers the two will be seen to have the same color. Such specimens give rise to metameric stimuli , that is, the radiant fluxes reflected from the two specimens have different spectral compositions but match in colour. (Judd and Wyszecki 1963, 103-104)
As a consequence of metamerism, which is a pervasive phenomenon, there is no identity of SSR and perceived colour to be had. As Hardin puts it:
We may, of course, decide to settle for such properties as relative spectral reflectance, illuminance, etc. as constituting 'physical color', and drop the requirement that objects that match metamerically over a wide range of illuminants are to be denominated as having the same colour. However attractive this strategy may seem on other grounds, one must realize that the concept of 'color' it yields is one in which two matching yellow spots will usually not have the same color. (Hardin, 63-4)
Let's call this the argument from metamers. It concludes that the absence of any principled correlation between SSRs and chromatic sensory states is sufficient to defeat chromatic objectivism. The objectivist must answer the question: What is it that two qualitatively identical yellow spots have in common? But the answer cannot be couched in terms of reflectance for, often, reflectances for matching samples will differ radically. So objectivismor one version of itis implausible. That brings us to chromatic subjectivism and to opponent colours theory.
On the opponent colours theory, in its functional version, receptoral outputs from the three cone types in the retina are processed through two colour channels. The so-called "red-green channel" produces either a red response or a green response. If the red value is 3 and the green value 7, the output is green 4. Because of the opponent nature of this channel there is no composite red-green response (the same goes for the yellow-blue channel). If both the red-green and yellow-blue channels are active, composite responses result: mixtures like orange and turquoise. One consequence of this theory should be noted: for an indefinite number of response patterns the outputs of the opponent channels will be identical. To simplify this point: suppose that red=6; green=10. Then the output is, as before, green 4.
This simplified account of opponency brings out many salient features of the theory: its ability to account for unique hues (red, green, yellow, blue); for certain binary hues (orange, turquoise); for colour exclusions (no red-green, no yellow-blue). It also provides a partial account of how it is that metamerism happens: an indefinite number of response patterns may be causally responsible for token distinct, but type-identical, chromatic sensory states.
The plausibility of chromatic subjectivism derives, in part, from its seeming ability to answer the question that objectivism cannot: What is it that two qualitatively identical yellow spots have in common? The answer is that for any such spots the opponent processor is in the same state. But what sort of a state is this? As we have seen, type-identical chromatic sensory states may have distinct causal structures: the processes which bring them about need not be type-identical since an indefinite number of response types are compatible with type-identical sensory states. Further, assuming that the response patterns are neurophysiological states (an essential element in the subjectivist's reduction of colour to neural states) we must conclude that there are sensory states which are type-identical at the perceptual level (the matching spots) but not type-identical at the neurophysiological level. An indefinite number of neurophysiological tokens (and an indefinitely large disjunction of neurophysiological type-states) may be correlated with any chromatic sensory state type.
One way to put the objectivist's difficulty is as follows: she says colour is an objective propertySSRbut she can't type-identify colours in terms of SSR. But the subjectivist has, on the argument developed here, the same problem: he can't type-identify colours in terms of neural state.
3. The circularity of content ascription. In what way are objectivism and subjectivism alike? It is proposed that there is for both positions an absence of unique correspondences between reducing states and the states to be reduced. This absence is non-problematic for some views about the mind and for some views about colour. It is a problem for views that are reductive. For now let us note that the argument, as stated, asserts the existence of many to one mappings from (a) reflectances to colours, and (b) neural states to colours. We can characterize this problem in terms of content. Given psychophysical methods for determining identity of chromatic sensory contentand taking such methods as definitive of sensory content , we cannot identify content with either reflectances or neural states. Unless, that is, we are willing to accept an account of content that is disjunctive. Whatever the merits of this approach, it is beset by a difficulty. Any specification of the appropriate disjunction of states (reflectances or neural states) will have to take the sensory definition as criterial. And this is prima facie circular. Suppose that we identify content with reflectance. But different reflectances produce psychophysically identical samples. Thus we identify content with the disjunction of reflectances that produce the identical samples. But, in doing so, we use the samples to determine identity of content. Thus we have no non-circular answer to the question: What is it that two qualitatively identical yellow spots must have in common? We can't say "same reflectance," for that is false, and to assert a disjunction of reflectances at this point is logically equivalent to asserting that the thing that they have in common is their qualitative identity.
This argument as to the circularity of content ascription is, to my mind, the hard core of the argument against reductive viewsbe they objectivist or subjectivist.
4. Objectivism and content ascription. Let us consider an objectivist response to this argument first. Contemporary objectivism, of the sorts proposed by Matthen (1988) and Hilbert (1992), involves a theory of error. (I shall only consider Matthen's view here though I take it that Hilbert's argument falls prey to the same general problem described below.) Matthen proposed, in 1988, that we should not expect perceived colour to reduce without remainder to SSR. Our colour vision system might make many errors in detecting SSR; errors that are the consequence of a system that is not perfect at the execution of its task but is, nonetheless, of evolutionary value to us. To imagine strict veridicality in a perceptual system is, as Matthen put it, "to show a touching, but quite unbiological devotion to truth." (1988, 13) That said, Matthen remains devoted to truth: once we factor out different types of misperceptionMatthen coined the term "normal misperception" to account for systemic error in the detection of SSRwe may retain the notion that the biological function of colour vision is to detect SSR. The system reaches for veridicality, but its reach exceeds its grasp. The notion that chromatic sensory content is properly characterized in terms of the biological function of the colour vision system provides a way of dealing with the failures of fit. As Matthen has recently said, "The functional view of content is not committed to [any] smooth mapping from experience to distal property space.... Phenomenal space might contain structure that totally fails to correlate with anything in the structure of content..."(1992, 46)
The disarticulation of distal property space from "experience"the phenomenal quality spaceis essential to the revised objectivist position. Yet as the preceding quotation from Matthen implies, there may well be a gap between experience and the distal world. Larry Hardin and Evan Thompson have argued that the gap is a chasm. Hardin has argued that the structure of the colour spaceMatthen's "phenomenal space"is replete with structure. The four opponent colours and the perceptual space they circumscribe cannot be characterized, not at all, in terms of a distal property like SSR. The circularity that I have noted with respect to objectivism is nothing compared to the silence of the objectivist who is faced with a body of literature that shows all colours to be describable in terms of the four unique hues of opponent theory; these four hues to be salient psychologically; these four hues to be the ones young babies most readily attend to, these four hues to have, as my brief description of opponent theory suggests, a neurophysiological rationale: not only is there a phenomenal structure that pervades "experience," there is, it seems, a lot of neural structure from which that experience arises (Hardin, 1988).
It is one thing to note that content-space and phenomenal-space might not correspond to one another. That is just another way of stating that biological systems may fail to execute their representational tasks. But once the detection of SSR is specified as the task to be executed, and given the essentially physical nature of SSR, one can find no room for the structure of phenomenal space in that specification. Such structure must be viewed as irrelevantor negatively relevant to the vision system's biological function.
What is the overall plausibility of SSR detection as a specification of the colour vision system's biological function? Evan Thompson has pointed out that, from a comparative perspective, there seems to be no one distal property that it is the function of colour vision to detect, for the range of species that possess it. Thompson provides a list of animals that appear to have specific as well as general purposes for colour vision: to heighten contrasts in water, to detect silhouettes against a background of sky; to monitor changing illumination conditions; to facilitate the segmentation of the visual scene, and so forth. He concludes that "there is no single type of distal property that it is the biological function of colour vision to detect." (Thompson 1995, 6) What counts as a case of normal misperception, from Matthen's perspective, may be precisely what is of adaptive value to an organism.
The point is not that SSR detection is unimportant but that it has no empirical preeminence when it comes to characterizing the biological function of colour vision. Once we see this, we have a motivation for examining the structure of the phenomenal colour space: what is its point, vis-a-vis adaptation, if any? Thompson, and also Dedrick, have argued that the nature of the perceptual space may, in itself, be adaptively advantageous. One thing that an opponent structured vision system accomplishes is a kind of regimentation of the various distal properties it registers. As Dedrick says, "rather than being errors relative to SSR recovery, metamersgroups of stimuli which differ in physical composition but not in perceived colourmay be the consequence of a system "designed" to simplify, for perceptual and ecological purposes, a complex stimulus space." (1995, 42)
Matthen disarticulates the sensory and distal space in order to account for certain types of error within a distinctly representational paradigm. For Thompson and Dedrick, the disarticulation is a consequence of a system that has another, non-representational purpose. Thompson writes that "rather than providing constant perceptual indicators of surface reflectance, the primary role of colour vision is probably to generate a relatively stable set of perceptual categories that can facilitate object identification and then guide behaviour accordingly." (1995, 23)
Objectivismsophisticated objectivismdeals with the problem of error by proposing a biological function for the colour vision system. The essential problem for this view is that once this particular function is postulated, we must focus not on the aspect of colour vision that is physically tractable but on colours as they present themselves phenomenally. Such concentration requires us to ask the following question: what is the ecological value that attaches to seeing colours in the way that we see them? What I will suggest but not argue herethough I've mentioned some reasons for thinking it's trueis that the answer will lead us away from objective properties and away from a concern with representation and error.
5. Subjectivism and content ascription. Since subjectivism is, at bottom, a neurophysiological theoryand since we have some good reason for believing that it is neurophysiology that is responsible for sensory qualitiesit would seem that we are in the right ballpark when it comes to explaining why we see colours in the way that we do. What are the prospects for a successful neurophysiological reduction given my argument as to the circularity of content ascription? The subjectivist should, in the first place, distinguish between relatively global neurophysiological processes, and relatively local ones. Colour processing occurs across a long and complex neural highway that runs from the retina, to the Lateral Geniculate Nucleus, to the Striate Cortex (V1) and into more specific locations in the cortex. To see a colour, in the global sense, requires a great deal of neural activity, proceeding in parallel, through a number of streams. If we treat the "neural state" responsible for colour in this global manner, then it will almost certainly turn out that we will not be able to type identify colours in terms of such states. For one thing, chromatic information processed in the visual streams is bound up with information concerning motion, orientation, edges, shape, and texture. This has led some vision scientists to contend that there is, in neurophysiological fact, no colour vision system but, rather, a more global vision system of which colour processing forms a part. (Davidoff, 1991) At some level of analysis this is surely true. On the other hand, there seem to be many neural structures and arrays that perform more-or-less specific and localized functions.
We can distinguish between "small-f" functionsthe functions of specific organsand "large-F" functions; functions that involve the activity of distinct organs. This distinction can be applied to neural processing. The large-F function of the vision system is to produce an integrated visual scene. This function is subserved by small-f functions which are relatively local and relatively simple. Can we discover small-f functions that are responsible for the various properties of sensed colour?
Austen Clark (1993) has developed the most explicit version of a subjectivist reduction. He argues that we should proceed in the following way: First, construct a psychophysical map of the colour quality space. This is a difficult practical problem, for it involves constructing, by extremely painstaking means, the ways in which colours are sensed to resemble and differ from one another. (Estimates of the number of colour discriminations humans can make range as high as 10 million.) What we are after, in any case, is something likebut more accurate thanthe Munsell Colour Solid. This is a three dimensional colour order where the three dimensions specify hue, chroma, and value"hue", "saturation", and "lightness" (or "brightness") in the more standard, non-Munsell jargon. The basic idea of the Munsell order is to represent the colour quality space in terms of its essential dimensionsthe properties in terms of which any colour may be scaled and, hence, ordered relative to any other colour. Let's assume, though this is in general problematic, that the visual scientists Judd and Wyszeki are correct when they say that "An object colour perceived as a part of any observers' visual field may vary in lightness, saturation, and hue, but in no other way describable in terms of combinations of these." (Judd and Wyszecki 1963, 34)
So: colours may differ only in hue, saturation, and lightness. And any such difference in sensed colour is available to subjects. Since such differences are available to subjects, they have been preserved throughout the stages and streams of visual processing. What we want, then, is to discover differentiative processes which correspond to the dimensions in terms of which colour is qualitatively scaled. An interpretation which will specify such processes will, as Clark says, "stand in just the same pattern of relations as those obtaining among points in the quality space. One thereby gives a neurophysiological explanation for the structure of qualitative differences." (1993, 148) Further, "Examples of differentiative properties are the hue, saturation, and brightness of colours.... Sensory states can differ in each such attribute independently of the others. A differentiative property is a respect in which encodings can differ that renders the stimuli discriminable." (1993, 71)
Let us concentrate upon hue. A salient feature of hue is that it forms a closed circuit. Take the visible spectruman essentially one-dimensional array which runs from red to blue. In terms of the elecromagnetic spectrum this will be from approximately 400nm to 700nm. Below 400nm there is the infra-red; above 700nm the ultra-violet. Both of these regions are largely invisible to the naked eye. If, however, one takes the 400nm end of the visible spectrum and "bends" it around to touch the 700nm end one has formed the closed hue-circle of sensory colourwith a region we call "purple" in between the reds and the blues. As Ralph Evans of the Kodak corporation has said: "The circuit of hues can thus be considered as completely continuous and as having four unitary hues, visible in mixtures only, between them in the circuit." (1974, 67)
The notion of a unitary or "unique" hue is well established. This has got to do, partly, with the phenomenology of colouropponent colours theory was originally formulated qualitatively, long before there was any physiological evidence for opponency. But there is physiological evidence. Output from the three different receptor types in the retinathe coneswill produce different activation patterns depending on the types of cells they are connected to. One class of cells, the so-called red-green opponent cells, will be inhibited by medium wavelength light (green light, lets say) and excited by short wavelength ("red") light. If there is no input to such a cell, or if the input falls below some response threshold, the cell fires at its base rate. If the cell is, overall, inhibited, it slows down and fires below its base rate. When this happens then, as Hardin says, it "codes" (1988, 35) for green. If the cell is, overall, excited, then its firing rate increases and it "codes" for red. Similar cells are said to code for yellow and bluethe so-called yellow-blue opponentsand, in a similar way, for black and white.
Clark argues that
Each opponent system provides an interpretable axis for the colour solid. The red-green process provides the axis that runs through the hue circle from red to green. The yellow-blue process yields an independent axis running from yellow to blue. The white-black process sums all these cone processes and thereby tracks the overall intensity of light. it gives the lightness axis [of the colour space], which stacks hue circles of different lightnesses on top of one another. (1993, 150)
One of the advantages of this interpretation is that it gives us a neurophysiological rationale for many of the properties of the colour space. A unique green, for example, will be sensed when the red-green cells (or some aggregate of them) code for green, and the yellow-blue cells fire at their base rate and code for what is called "brain grey." Mixtures of the unique hues, like orange and turquoise, result from activity in the two independent processes combining their outputs.
Let us come back to the distinction which launched my discussion of the subjectivist program: a distinction between small-f functions and large-F functions. Have we identified the appropriate small-f functions? Does it matter?
To simplify things lets concentrate upon a hue ordera hue circle at a given level of lightness and saturation. For each distingishible item in this order there will be (i) a distinct H coordinate for each location in the order and (ii) that coordinate, according to Clark, will map onto a neurophysiological coordinate which differentiates the hue of the equivalence class of sensory states at that location. Does it follow from this that any difference in hue is a neurophysiological difference? Yes, if opponent neural processes are discriminative: to say two colours differ in hue is just to say that there is a distinct neural coordinate for each colour. The more interesting question is whether or not any two sensory qualities collected by the equivalence class at a certain location in this colour order indicate the same neural state. This is a version of the circularity argument.
Consider a segment of the hue orderinga segment of a larger hue circle in quality space. A, B, and C each have distinct hue coordinates. There is, however, overlap between A, B, and C. By this I mean that any stimulus that presents A, and any stimulus which presents B will be locally indiscriminable, but globally discriminable. Locally indiscriminable because, on a pairwise discrimination task, one cannot tell them apart. They are globally discriminable because there is some further task that allows them to be discriminated. Imagine that, under some set of conditions, a subject cannot tell the difference between a colour chip which presents A and one which presents B. Nor can he tell the difference between B and C. Yet he can tell the difference between A and Cthe stimuli which present A and C are discriminable. On the view we have been canvassing, A, B, and C all have different hue valuesdespite the pairwise matchingbecause there must be differentiative attributes at the neurophysiological level. Indeed, by referring to this level we can make the compelling claim that it is two differences below sensory threshold the difference in the stimulus that presents A and the difference in the stimulus that presents B which add up to a difference above threshold: the fact that we can discriminate the stimulus that presents A from that which presents C. Note that this is not a case of the neurophysiological account driving the sensory account. It is, rather, a neurophysiological explanation of a phenomenon that reveals itself at the sensory level in terms of discrimination tasks more complex than pairwise matching. I am going to suppose that the difference between A and B is a minimum qualitative difference. This is not an untoward assumption since the point of our ultimate mapping of the colour space is to identify such differences and construct an order from them. At some point, and I am supposing that we are at it, there will be no stimulus which presents a quality between A and B. Any such candidate will be qualitatively identical with A or qualitatively identical with B.
If the distance between A and B is a minimum qualitative difference, we can ask the following question: is the difference between the neurophysiological coordinate for Aindicated by its hue valueand the neurophysiological coordinate for Bindicated by its hue valuethe smallest neurophysiological difference? If so, the hue values will pick out unique neural states. If not, we may suppose that two chromatic sensory states that are qualitatively identical pick out different neurophysiological states. Qualitative identity will collect the sensory states, but on what principle are the neurophysiological states collected? I claim that the circularity objection returns here: a range of neurophysiological states is compatible with two qualitatively identical yellow spots, and the criterion for identity of the range is qualitative: neurophysiological states are collected just because they cause qualitatively identical sensory states, and Clark's version of subjectivismthe only clearly stated version that I am aware offalls prey to my argument as to the circularity of content ascription. 
6. Conclusion. There are various, more or less tasty bullets-to-bite for both the objectivist and the subjectivist. The sophisticated objectivist can argue that the content of chromatic sensory states is not sensed colour but something else (obvious candidate: reflectance). But as I have noted, this is an extremely odd view for a philosopher committed to the ecological value of colour vision. Perhaps objectivism can be formulated without reference to biological function. I would note, however, that both Matthen and Hilbert introduced the notion of biological function in order to deal with the circularity argument. As for the subjectivist, there are a few more options. It is possible, in the first place, that the grain of neurophysiology corresponds to that of sensation: that there are no neurophysiological differences that do not correspond to sensory differences. I think that this is unlikely. Following Clark's strategy, we are already below sensory threshold (with respect to pairwise matching) when we admit a qualitative overlap between A and B. To say that we have reached a limit point with respect to neurophysiological differences is nothing but philosophical prejudice. Of course, it may be the case that the subjectivist gets lucky. Whether she does or not is an empirical matter, and I don't propose to beg that question. On the other hand we should ask: what general evidence do we have for believing that every relevant neurophysiological difference (relevant to sensation) presents itself in sensation? Another subjectivist response might appeal to the distinction between processes and states. On this view, requiring state-state identities is a lost cause and places an empirically irresponsible burden upon legitimate neuropsychology. Perhaps this is true. But if it is, the process reductionist owes us an account of why the reduction of sensory states to neurophysiological processes is not just as well described in non-reductive functional terms.
1. We need to know more than the fact that two stimuli match in order to determine identity of content, since matching is non-transitive: if A matches B and B matches C it may still be the case that A does not match C. This cannot be the case for qualitative identity. We can define qualitative identity as follows: A matches B and there is no third stimulus which matches either A or B but not both. This is essentially Goodman's criterion for the identity of qualia (1977). Austen Clark develops this notion of qualitative identity (1993).
2. It is often supposed that the opponency exhibited by cells at the LGN makes the LGN the locus for chromatic reduction. This supposition is reflected in Clark's account. Recent work in neurophysiology and psychophysics (e.g. Abromov and Gordon, 1994) argues that this cannot be correct. Considerations of space prevent discussion of this work.
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