A Subjectivist Reply to Spectrum Inversion

American Philosophical Association, Pacific Division Meeting, March 1993, San Francisco

Austen Clark
Department of Philosophy U-54
University of Connecticut
Storrs, CT 06269-2054

Subjectivists hold that you cannot specify color kinds without implicitly or explicitly referring to the dispositions of observers. Even though "yellow" is ascribed to physical items, and presumably there is something physical in each such item causing it to be so characterized, the only physical similarity between all such items is that they all affect an observer in the same way. So the principles organizing the colors are all found within the skin.

I shall argue that a functionalist analysis of color terms which hews to subjectivism yields a new answer to the problem of spectrum inversion. Classically the problem of spectrum inversion is that (a) it strains credulity to deny that inversion is logically possible, but (b) admitting the mere logical possibility seems to defeat any functionalist analysis of color terms. While much energy has been focused on (a), the new reply I will sketch concedes the logical possibility of spectrum inversion and focuses instead on (b). We will deny that the logical possibility is inconsistent with the analysis.


To begin, we need to re-visit the birthplace of qualia. I recommend that for the nonce we all become Carnapian methodological solipsists. Endnote 1. Consider just your own experiences of color, and make no presumptions about the experiences of others, or about whether anything corresponds or fails to correspond to your experiences. A particular quale--a particular shade of bluish-green, say--is repeated in various of your experiences. It is presented by multiple items. How could you go about identifying it?

Inevitably, you would find yourself following Carnap's footsteps, using some variant of a similarity relation: recollection of similarity, matching, or indiscriminability. Two items that are discriminable clearly do not present the same qualia, so immediately we know that qualitative identity implies the indiscriminability of the respective items. Unfortunately, indiscriminability is not sufficient to assure qualitative identity, because of the pesky problem of non-transitivity. You may find items A and B indiscriminable, and find items B and C indiscriminable, yet somehow manage to discriminate between A and C. A and B then cannot present you with the same qualia (even though you find them indiscriminable) since A can be discriminated from something that B cannot. So to assure qualitative identity, we need something even stronger than indiscriminability, namely global indiscriminability. For items A and B to be qualitatively identical, there must be no item C discriminable from one but not the other. That other methodological solipsists in the classic tradition arrived at similar formulations can only be reassuring. Endnote 2.

Whatever similarity relation you choose, its non-transitivity has one delightful bonus: it allows you to place your qualia in an order. You can construct a map whose guiding principle is that qualia that are more similar to one another are to be placed closer to one another that are those that are less similar. With our three items A, B, C, we can deduce immediately that the qualia presented by B must be placed between those of A and C, since B is indiscriminable from both A and C, but those two are discriminable from one another. In Carnapian terms, the overlapping of similarity circles yields an ordering relation. Or perhaps you are willing to plonk immediately for a triadic predicate of relative similarity: x is more similar to y than to z. As Quine has shown, such a triadic predicate can be reduced to our simpler two-place notions (using stimulus generalization tests), so we can be confident that the three-place predicate smuggles nothing illicit into the analysis. Endnote 3. With it we can briskly generate an ordering of qualities. That x is more similar to y than to z immediately places x closer to y than x is to z. A few such judgements (eg, is y also more similar to x than to z?) and the ordering of qualities is soon constrained to a unique solution.

The notions employed so far--discriminability, matching, and relative similarity--are generally conceded to functionalists. Endnote 4. After all, they have behavioral consequences. Whether Jack finds x and y indiscriminable can be assessed in relatively straightforward fashion. We can put him to the test. Notions of similarity and relative similarity are also fair game. They can be assessed even among non-verbal species, in sensory modalities we do not share, using standard techniques of conditioning, stimulus generalization, and extinction. Endnote 5. But they suffice to order the qualities. With sufficient patience, we can construct a complete quality space for colors. Stimuli sensed as relatively similar will be assigned locations that are relatively close to one another in such a space.

For example, orange is somewhat reddish and somewhat yellowish, and it is relatively more similar to red or to yellow than it is to turquoise. If we model relative similarities by distances, we are obliged to place orange somewhere between red and yellow. The structure of relations provides an intrinsic spacing of the qualities. Orange cannot be placed next to turquoise, since the two are so dissimilar, and each is relatively more similar to many other colors.

When you are finished constructing the quality space for colors, you will find your task as a methodological solipsist has also been completed. We employ criteria for the individuation of colors of varying degrees of precision. At the most precise, pushed to the minimal discriminable units, a particular color will correspond to a point in the quality space for colors. More commonly, "a" color comprises many discriminable shades. In that more common usage, a color quality is identified as a region or volume in this space. Endnote 6.


The notion of a quality space yields a more potent formulation of subjectivism. We find a structure of relative similarities ordering color qualia. In it orange is between red and green. Various of the relations in this order have special names. Green is the complement of red. There is a unitary green--a green that is not at all yellowish and not at all bluish--but not a unitary orange. And so on. Now the subjectivist can state a second pre-requisite for any objectivist theory of color. Not only must you specify in extra-dermal terms the physical kinds making up all the instances of (say) orange, red, and yellow: more importantly, you must also find some physical relation between the kinds so identified sufficient to place orange between red and yellow. That is, you must specify in extra-dermal and non-dispositional terms some physical model for the full structure of relative similarities among the colors. The subjectivist position: this cannot be done. The colors have a structure of qualitative similarities and relations to which nothing extra-dermal corresponds.

In the headlines subjectivism is sometimes construed as the view that colors are purely internal phantasms. In fact it is this structure of relative similarities among colors that is "generated" internally. That is, if nothing outside the skin can account for the structure of relative similarities that we perceive among the colors, then that structure must be produced from within. We happily turn to neurophysiology for details. Distal stimuli of course impinge upon us, but the eventual patterns of qualitative similarity in which they fall can only be explained by reference to sensory mechanisms within the observers.


The contentious and amusing part of the story comes when two methodological solipsists compare notes. Take the paradigmatic 90's couple, choosing wallpaper for the bathroom. "It's too blue" says she. "You're wrong," he says, "it has the exact mix of blue and green needed to match our aqua telephone". While the scene descends into bathos and recrimination, the subjectivist can only chuckle: both of them may be correct! Color discriminations in the blue-green portion of the spectrum are notoriously variable. She may see more blue in the very same paper that he sees as blue-green. He perceives the paper to match the telephone in hue, while she does not.

Differences in color perception, even among those with "normal" color vision, can be demonstrated in various ways. The simplest is to pick monochromatic primaries and have observers attempt to match some intermediate stimulus by mixing the primaries in different proportions. The proportions may differ vividly. Endnote 7. A mixture that matches the target for Jack may not for Jill. So if we are attempting to define the name of the hue presented by that intermediate stimulus, we cannot name what matches for Jack or for Jill.

More dramatic demonstrations are available once percipients know some hue names. Given an array of greenish Munsell chips, and the instruction "pick the chip that to you presents a unitary green--not at all yellowish and not at all bluish", an individual will manage to pick one chip, and will reliably pick that same chip again on repeated occasions. But different individuals will (reliably) pick different chips. Endnote 8. The differences are readily perceptible to anyone involved in the test: Jack's chip will look noticeably bluish to Jill, while hers will be seen as yellowish by Jack.


These differences present a problem. Suppose we wish to present an analysis of color terms consistent with the possibility of applying the same term to the experiences of two (or more) methodological solipsists. Given the variations in normal color vision, we cannot identify color kinds with classes of stimuli. The class that presents aqua to Jack may not do for Jill.

What then generalizes? Why do we even think that two different people are sometimes presented with the same aqua quale? What we find is that while the exact stimuli needed to make a match vary somewhat from person to person, there is an identifiable pattern of relations that generalizes from person to person. The structure of relations generalizes, even if the particular relata do not.

The point can be put in simple logical terms. One might expect to generalize across people with the form:

There is a stimulus x perceived by every person y as a green that is not at all yellowish and not at all bluish.

but this hope is dashed, even among those with "normal" discriminations. Instead we need to say something of the form:

For every person y there is a stimulus x perceived by y as a green that is not at all yellowish and not at all bluish.

Once we identify such "unitary" hues we can state a great deal about the color perceptions of an individual in terms of that individual's unitary hues. For example, suppose we find that for some person y, l1 is the wavelength mixture that presents unique blue, and l2 presents unique yellow. Endnote 9. Then for person y some combination of l1 and l2 will yield achromatic white. But that pair may not be complementary for another person x. To x, l1 may be a slightly greenish blue, and l2 may be a slightly greenish yellow, and their combination will always appear somewhat greenish to x, no matter how their relative intensities are adjusted. So we cannot say

l1 and l2 are such that, for any person x, l1 combined with l2 yields an achromatic white for x.

Instead, we must say

For any person x there are wavelength mixtures l1 and l2 such that l1 combined with l2 yields an achromatic white for x.

The structure generalizes, but the particular stimuli occupying a particular place in the structure vary somewhat from person to person.


A simple conclusion follows: if we are to define a qualitative term, we cannot mention any stimuli. We can mention only the structural properties that give the quale its place in the quality space. "Orange" cannot be defined as "the color of ripe oranges" or in any similar way, no matter how sophisticated. Endnote 10. It can only be defined as something like "the color midway between red and yellow, and more similar to either than to turquoise." The terms "red", "yellow" and "turquoise" would all receive similar analyses.

For any particular methodological solipsist, "orange" refers to a place in the color quality space, which can be identified by picking out a class of stimuli. As soon as we change observers (or the viewing conditions, or the state of adaptation of the observer), the stimulus specifications fail. The color quality spaces of different people also vary somewhat because of their differing abilities to discriminate. We must somehow identify corresponding places in the color quality spaces of other individuals, but this cannot be done by listing stimuli. Only a structure description will do. The problem is analogous to identifying, in the skeleton or anatomy of different people, which parts are the femur or the nose. These parts are rarely shaped identically in any two people, so one could not identify the femur or the nose with any specific configuration of bone or tissue. Fortunately, the pattern of relations that they bear to other parts of the person generalizes in a rough (homologous) fashion. We pick the corresponding place in a homologous (not identical) pattern of relations.

The same works for color qualia. Technically, we would first describe the structure constituted by the similarity relations among the colors, and then define each color term with a structural description. "Landmarks" in the structure can be identified relationally, and other terms individuated by reference to those landmarks. The structural descriptions can then be replaced by structural definite descriptions. "Orange" is "the color standing in such and such relations to landmarks x, y, z", where the landmarks x, y, z are identified uniquely by the relations in which they stand. A color quale is a place in the psychological color space, and it could be identified uniquely by the relations in which it stands to other such places.


Now we have the wherewithal to give a new answer to the problem of spectrum inversion. Consider the possibility that Jack sees as red what Jill sees as green. The usual conclusion is that "functional definitions" for qualitative terms must fail. The basic idea of a "functional definition" is to define a psychological term by the relations in which it stands to other psychological terms, to inputs, and to outputs. Endnote 11. The terms are construed as theoretical terms, defined by describing the place of the term within the theory. We first describe a pure relational structure, and then define each psychological term with a structural definite description, identifying its place in that structure.

Now for the first new idea. Functionalists propose that psychological terms be defined by the relations in which they stand to one another, to stimulus inputs, and to behavioral outputs. There is no requirement that every functional definition mention all such relations. Perhaps some terms are not attached definitionally to any stimulus inputs. Perhaps the analysis of other terms makes no reference to behavioral outputs. Perhaps some terms, naming internal psychological processes, will be defined only by their relations to other internal processes. I suggest that qualitative terms fall precisely in this latter category.

Of course any term in the structure described by the theory will be connected relationally to other such terms, so eventually all the terms in the structure are tacked down to observables. But it simply does not follow that each analysis must mention all those relations, no matter how remote.

The point can be made by noting two different senses of the term "functional role". In any complex system the functional role of a part can be described in terms that are either relatively proximal or relatively distal. If one describes only the parts that are next to the given part, its immediate inputs, and the effects it has on its immediate neighbors, then one describes what can be called the "proximal" functional role of the part. If however the system works in a consistent fashion, one can trace the more remote antecedents and consequences of that proximal role, perhaps all the way to peripheral stimulus inputs and behavioral outputs. If so, one describes the "distal" functional role of the part: its particular contribution to the input-output regularities of the system as a whole.

Qualitative terms can only be defined by their proximal functional roles: the relations of qualitative similarity and relative similarity that they bear to one another. Their distal roles--their connections to particular stimuli--are simply too variable and contingent. The job descriptions we give them cannot reach so far.

It is easy to imagine cases in which the distal functional role of a part changes dramatically, even though its proximal role is undisturbed. Suppose you live in a house with a forced air heating system and an attic fan. One day the fan motor in the heating system burns out, and you replace it with the motor of your attic fan. The brushes and contacts in that motor have the same proximal roles they always had. (Otherwise the motor would not work correctly.) But distally--traced out to more remote antecedents and consequences--they now play a totally different role in your household. They serve as part of a heating system and not a cooling system. The "stimuli" that turn on the motor are totally new, as are its effects on the temperature of the house.

In a recent article Ned Block recognizes the possibility of describing functional roles in these two different ways. He describes what he calls "long-arm" functional roles as ones that "reach out into the world of things" and "short-arm" functional roles as ones that are "purely internal" (Block 1990, p. 70). He goes on to ask:

Why can't the functionalist identify intentional contents with long-arm functional states and qualitative content with short-arm functional states? The result would be a find of "dualist" or "two factor" version of functionalism. My response: perhaps such a two factor theory is workable, but the burden of proof is on the functionalist to tell us what the short-arm functional states might be. (Block 1990, p. 70)

Subjectivists embrace short-arm roles and eschew long ones. The short-arm roles that define qualitative contents are all and only those that define the place of a quale in its quality space. They are the purely structural relations of relative similarity that define the intrinsic spacing of qualities.


Consider how this analysis can cope with spectrum inversion. The typical description is that in Jack and Jill we find two states that serve the same functional role but are qualitatively distinct. But now we know that "functional role" is ambiguous. Are we talking about distal functional roles or proximal ones?

In all the standard varieties of spectrum inversion we imagine changes in the distal functions of sensory states. You look at a ripe orange and experience the color quale orange. In cases of inversion, that quale comes to be associated with new stimuli, either in other people, or in you at other times. Looking at oranges would no longer generate the quale orange. But this would be nothing but a change in distal roles. The place of orange in the quality space is unchanged. Orange is still somewhat reddish and somewhat yellowish, and it is still the complement of blue-green. We have new stimuli causing the same old qualia.

One can imagine the quality space for surface colors as a three-dimensional solid. Its shape and the placement of all the qualia in it are defined by the relations of relative similarity and discriminability. In spectrum inversion that structure--the pattern of relations among qualia--does not change. The only change is that new stimuli become associated with points in that structure. Subjectivists in particular can readily acknowledge this possibility. That structure of relative similarities is generated from within. Some parts of sensory systems are presumably responsible: they create the patterns of discrimination and relative similarity. In typical cases of spectrum inversion, they carry out the same job, but for new customers--new distal stimuli.

It is instructive to consider what sort of inversion would be required to defeat the analysis of qualia in terms of their proximal roles. One would need to imagine that the same qualitative state could come to serve different proximal roles, or that different qualitative states could be found to have identical proximal roles. This is very different from the standard sorts of spectrum inversion. One would need to imagine that orange--that very same quale--would no longer resemble its current neighbors. The parts of the system that create the patterns of discriminability and relative similarity must start working in a radically new way, but without altering any qualia. Orange--not the experience caused by looking at oranges, but orange itself--would for example have to cease to be somewhat reddish and somewhat yellowish. It must continue to be the quale it is, though it could no longer resemble the qualia it does. Perhaps the quale orange comes most closely to resemble blue. In a series of hues ordered by relative similarities, that very same quale would now be placed over there, among the blues and greens. Or perhaps the quale orange becomes unitary, so that Jill can pick out a pure orange--one that is not at all reddish and not at all yellowish.

These latter inversions seem to me to be incoherent. Orange, whatever it is, is somewhat reddish and somewhat yellowish, no matter what stimuli in turn present red or yellow. The relations among the qualitative terms define them. In spectrum inversion, we imagine the same psychological color space--the same structure of qualitative relations--but associated with new stimuli. It is simply transplanted into new surroundings, like our attic fan moved to the furnace. Its distal roles change, while the proximal ones are undisturbed.

We propose to define qualitative identity in terms of location in a quality space, which requires identity of proximal--not distal--functional roles. Such a functionalism has nothing to fear from standard varieties of spectrum inversion. Endnote 12.


1. In the sense of Carnap's Aufbau. See Carnap 1967, pp. 101-102.

2. See Goodman 1977, p. 196; Russell, 1940, ch. 6.

3. See Quine 1974, pp. 16-19.

4. That discriminability is a functional notion is argued in Shoemaker 1975a, 1975b.

5. As Quine puts it:

Without some such prior spacing of qualities, we could never acquire a habit; all stimuli would be equally alike and equally different. These spacings of qualities, on the part of men and other animals, can be explored and mapped in the laboratory by experiments in conditioning and extinction. Needed as they are for all learning, these distinctive spacings cannot themselves all be learned; some must be innate.... it can be said equally of other animals that they have an innate standard of similarity too. It is part of our animal birthright. (Quine 1969, p. 123)

6. See Westphal 1987, p. 98.

7. The "Nagel anomaloscope" presents observers with a split field, in one half of which is a stimulus of 589 nm. In the other is a mixture of 535 nm and 670 nm light, whose relative intensities are adjusted by the observer until they match the 589 nm stimulus. That ratio is commonly used to assess various color vision anomalies. But even in the range of ratios considered "normal", some observers will completely reject matches made by others. See Hurvich 1981, pp. 227, 230.

8. See Hurvich 1981, p. 223.

9. This generalization and those that follow are true only for those with "normal" color discriminations--eg, the non-anomalous trichromats.

10. This moral is bolstered by purely logical considerations. It seems to make sense to suppose that oranges might not have been orange, but it makes no sense to suppose that orange might not have been orange. The color is only contingently attached to any stimulus paradigm one cares to mention. Furthermore, with a few accidental twists along the evolutionary path, oranges might never have existed. The definition of the color hence should not commit one to the existence of the fruit. (These arguments were put forth (in a different context) in Jackson 1977.)

11. The "Ramsey-Lewis" technique underlying functional definitions is described in Carnap 1966, Lewis 1970, Block 1980. By "functionalism" I mean nothing more than the proposal that theoretical terms can be defined by such a technique. Functionalism is Carnap resuscitated: "Science deals only with the description of structural properties of objects" (Carnap 1967, p. 19) and "Structure descriptions...form the highest level of formalization and dematerialization.... Scientific statements speak only of forms without stating what the elements and the relations of these forms are." (Carnap 1967, p. 23)

12. There are of course other varieties of inversion that need separate treatment. One sort employs the contrary-to-fact logical possibility that we be endowed with a relationally symmetric color quality space, so that qualitative terms could not be provided with structural definite descriptions, but only with structural descriptions. Another sort invokes a concept of qualia under which there is no good evidence to believe that two people are ever presented with the same quale, allowing various oddball interpersonal inversions. The problems raised by these varieties can be answered, but not in twenty minutes.


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Westphal, Jonathan. (1987). Color: Some Philosophical Problems from Wittgenstein. Oxford: Basil Blackwell.

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