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In this target article I discuss the relations among mind,brain, behavior, and science in the particular domain ofcolor perception. My reasons for approaching these diffi-cult issues from the perspective of color experience aretwofold. First, there is a long philosophical tradition of de-

bating the nature of internal experiences of color, datingfrom John Lockes (1690/1987) discussion of the so-calledinverted spectrum argument. This intuitively compellingargument will be an important historical backdrop for muchof this target article. Second, from a scientific standpoint,color is perhaps the most tractable, best understood aspectof mental life. It demonstrates better than any other topichow a mental phenomenon can be more fully understoodby integrating knowledge from many different disciplines(Kay & McDaniel 1978; Palmer 1999; Thompson 1995). Inthis target article I turn once more to color for new insightsinto how conscious experience can be studied and under-stood scientifically.

I begin with a brief description of the inverted spectrum

problem as posed in classical philosophical terms and thendiscuss how empirical constraints on the answer can bebrought to bear in terms of the structure of human color ex-perience as it is currently understood scientifically. Thisdiscussion ultimately leads to a principled distinction,called theisomorphism constraint, between what can andcannot be determined about the nature of experience byobjective behavioral means. Finally, I consider theprospects for achieving a biologically based explanation ofcolor experience, ending with some speculation about lim-itations on what science can achieve with respect to under-standing color experience and other forms of conscious-ness.

1. Detecting transformations of color experience

The basic intuition that underlies Lockes (1690/1987) in-verted spectrum argument is that other people might havethe same overall set of color experiences you do but theymight be differently connected to objects in the external

world. When you and I look at the same red apple underthe same lighting conditions, for example, do we have thesame internal experience of redness, or might I have the ex-perience you call greenness, or yellowness, or some othercolor? The issue is perhaps most clearly captured by the sit-uation of looking at a rainbow. You perceive a particular or-dering of chromatic experiences from red at the top to vio-let at the bottom, but I might perceive exactly the reverseof your experiences, with violet at the top and red at the bot-tom. We would both name the color at the top red and theone at the bottom violet, of course, because that is what

BEHAVIORAL AND BRAIN SCIENCES (1999) 22, 923989Printed in the United States of America

1999 Cambridge University Press 0140-525X/99 $12.50 923

Color, consciousness, and theisomorphism constraint

Stephen E. PalmerDepartment of Psychology, University of California, Berkeley,

Berkeley, CA 94720-1650

[email protected] socrates.berkeley.edu/~plab

Abstract: The relations among consciousness, brain, behavior, and scientific explanation are explored in the domain of color perception.Current scientific knowledge about color similarity, color composition, dimensional structure, unique colors, and color categories is usedto assess Lockes inverted spectrum argument about the undetectability of color transformations. A symmetry analysis of color spaceshows that the literal interpretation of this argument reversing the experience of a rainbow would not work. Three other color-to-color transformations might work, however, depending on the relevance of certain color categories. The approach is then generalized toexamine behavioral detection of arbitrary differences in color experiences, leading to the formulation of a principled distinction, calledthe isomorphism constraint, between what can and cannot be determined about the nature of color experience by objective behavioralmeans. Finally, the prospects for achieving a biologically based explanation of color experience below the level of isomorphism are con-sidered in light of the limitations of behavioral methods. Within-subject designs using biological interventions hold the greatest promisefor scientific progress on consciousness, but objective knowledge of another persons experience appears impossible. The implicationsof these arguments for functionalism are discussed.

Keywords: basic color terms; color; consciousness; functionalism; inverted spectrum; isomorphism; qualia; subjectivity; symmetry

Stephen E. Palmeris Professor of Psychology, Di-rector of the Institute of Cognitive Studies, and Direc-

tor of the undergraduate major in Cognitive Science atthe University of California at Berkeley. He is the au-thor of over 60 scientific publications in the area of vi-sual perception, including his new textbook Vision sci-ence: Photons to phenomenology (1999, MIT Press),

which provides an introduction to all aspects of visionfrom an interdisciplinary perspective. He is a memberof the Society of Experimental Psychologists, a Fellowof both the American Psychological Association and theAmerican Psychological Society, and a member of theGoverning Board of the Psychonomic Society.


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we have all been taught. Color naming is presumably me-diated by internal color experiences, but it is only the soci-olinguistically sanctioned stimulus-response associationsthat matter in our ability to communicate about colors. Thefact that we name the same objects and lights with the samecolor terms is hence insufficient to determine whether ourinternal chromatic experiences are the same.

The rainbow-reversal interpretation of the inverted spec-trum argument is quite literal in the sense that we have sup-posed that my experiences of the spectrally pure (mono-chromatic) colors are simply the inverse of yours aboutthe spectral midpoint. Notice that the inverted spectrumargument is actually something of a misnomer: It is not thespectrum that is inverted that is, nothing has happened tothe rainbow itself but the inner experiences in responseto the spectrum. It would therefore be more accurate to callthis the inverted color argument. And because Lockes es-sential point is not limited to literal inversion, but could ap-ply equally well to any possible mapping of color experi-ences in one observer (e.g., you) to the same set of colorexperiences in another observer (e.g., me), we will call it thetransformed color argument. The problem it poses is

whether any such color-to-color transformation (excluding

the identity mapping) could accurately describe the rela-tion between our color experiences without the differencesbeing objectively detectable. Because we do not have directaccess to each others internal experiences, the questionboils down to whether any such color-to-color transforma-tion could exist without being detectable through system-atic differences in our behavior.

Notice that the transformed color argument as formu-lated above presupposes two important conditions: (1) thatthe two observers (canonically referred to as you andme) have experiences in response to different spectraof electromagnetic energy, and (2) that their overall sets ofcolor experiences are the same. Dropping one or both ofthese assumptions leads to different versions of the more

general color problem. Relaxing condition (2) suggeststhe possibility that you and I both have experiences in re-sponse to different light spectra but that one or both of ushas at least some experiences the other does not. Our ex-periences might overlap to some degree, or they might evenbe completely disjoint, so that all my chromatic experiencesin response to light spectra are qualitatively different fromall of yours. Relaxing condition (1) suggests that I mighthave no experiences of color whatsoever in response to dif-ferent light spectra and yet behave as you do with respectto them. I would be a color zombie, able to name colorsproperly and produce standard data in various color dis-crimination and matching experiments, but without havingany corresponding experiences at all. These possibilities

will come to the fore later in this target article, but for nowwe will concentrate on the standard form of the problem inwhich it is assumed that both you and I have the same setof color experiences, whatever those might be, and ask

whether they can be shown to be differently arranged, soto speak.

The first problem is how to get a scientific handle on thisphilosophical problem of whether transformed color expe-riences could be detected in publicly observable behavior.Locke presumed that we could not, but there are many sci-entifically documented aspects of color-related behaviorthat bear critically on the answer. I will argue that whetherthere exist any undetectable color-to-color transformations

can be recast into the simple question of whether an em-pirically accurate model of human color experience con-tains any symmetries.

1.1. Color similarities. In scientific discussions, color expe-rience is usually described in terms of spatial models. Per-haps the simplest and best known is the color circle devisedby Newton (1704), by now familiar to artists and much ofthe general public (see Fig. 1). It is an example of a colorspace: a multidimensional spatial representation (or model)in which different color experiences correspond to differ-ent points in the model. The locations of points represent-ing colors are chosen so that the degree of psychologicalsimilarity between pairs of colors corresponds to the dis-tance between the corresponding points in the model. Inthe color circle, thespectral colors of the rainbow are posi-tioned in order along most of the circles perimeter, and thenonspectral colors, including many reds, all magentas, andmost purples, are located along the perimeter between theblue-violet and orange-red limits of the visible spectrum, asindicated in Figure 1 by the location of the color names out-side the circle.

The color circle is a useful model of many aspects of color

experience because it is easy to comprehend yet managesto capture an immense number of facts about the relationsamong color experiences in a highly economical fashion.The fact that red is perceived as more similar to orange thanto green, for example, is reflected in the fact that the pointrepresenting red is closer to the point representing orangethan it is to the point representing green. Corresponding

Palmer: Color and consciousness

924 BEHAVIORAL AND BRAIN SCIENCES (1999) 22:6

Figure 1. Newtons color circle and spectral inversion. Colors arearranged along the perimeter of a color circle, as indicated by thenames on the outside of the circle. Open circles correspond tounique colors (red, green, blue, and yellow), which look subjec-tively pure. The dashed diameter indicates the axis of reflectioncorresponding to literal spectral inversion, and the dashed arrowsindicate corresponding experiences under this transformation.Letters in parentheses inside the circle indicate the color experi-ences a spectrally inverted individual would have to the same phys-ical stimuli a normal individual would experience as the colors in-dicated on the outside of the circle.


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similarity relations among triples of color experiences thatblue is more similar to purple than to yellow, and so on are thus faithfully preserved in the distance relations amongtriples of points in the color circle. This correspondence be-tween psychological similarity relations and spatial proxim-ity relations lies at the heart of Shepards (1962a; 1962b) el-egant nonmetric method of multidimensional scaling, andrecovering the color circle from similarity data was one ofhis first demonstrations of its use.

We will now employ Newtons (admittedly simplistic)color space to illustrate how such models relate to the in-

verted spectrum argument and why Lockes intuition seemsinitially so compelling. Consider once again the case of lit-eral spectral inversion, which we will henceforth call rain-bow reversal to be perfectly clear. The hypothesis that mycolor experiences are rainbow-reversed relative to yours

would mean that my color circle is the reflection of yoursabout the dashed line shown in Figure 1. The abbreviationsinside the circle indicate the color experiences I have in re-sponse to the same lights that you experience as indicatedon the outside of the circle. Thus, your red corresponds tomy violet (and vice versa), your orange to my blue (and vice

versa), your yellow to my cyan (and vice versa), and your

chartreuse to my green (and vice versa), as indicated by thedashed arrows perpendicular to the axis of reflection. Thequestion is whether this color-to-color transformation couldbe detected by behavioral means.

It might seem at first blush that similarity judgmentsamong colors would reveal rainbow reversal, but, in fact, they

would not. You would say that orange is more similar to redthan to green, but so would I, even though this would corre-spond internally to my experiencing blue as more similar to

violet than to chartreuse. Indeed, we would make all thesame relative similarity judgments about rainbow colors de-spite the enormous differences in our internal experiences ofthem. With respect to color similarity judgments among rain-bow experiences, then, Locke was right: Rainbow reversal

cannot be detected behaviorally from such data.The reason rainbow reversal is not behaviorally de-tectable from such color similarity judgments is that theempirical model they specify (i.e, the basic color circle) issymmetric about the axis of reflection that corresponds toreversing the rainbow. A symmetry in a spatial model is atransformation that maps the model onto itself so that it isthe same before and after the transformation. Rainbow re-

versal is thus a symmetry of the color circle but so is anycentral reflection or rotation. Indeed, the only thing thatmakes any pair of such reflected or rotated color circles dif-ferent is the nature of the internal experiences themselves.Because these are private events, any differences between

yours and mine can be assessed only indirectly through our

publicly observable behavior, as Wittgenstein (1953) ar-gued so forcefully. The general claim is that any symmetryin a behaviorally constrained color space necessarily speci-fies a color-to-color transformation that cannot be detectedby the behaviors that constrain the spatial model.

1.2. Color composition. There is much more that we knowabout color experience from behavioral observations, how-ever, and these facts must also constrain the color space

whose symmetries we seek to understand. One importantfactor is the composition relations among colors: how somecolor experiences can be analyzed into combinations ofother, more basic color experiences. Most colors of the rain-

bow are binary in the sense that they appear to be com-posed of (or are analyzable into) two of the four primarychromatic colors: red, green, blue, and yellow.1 Oranges,for example, seem to contain both redness and yellowness,purples seem to contain both blueness and redness, and soforth. In contrast, there are particular shades of red, green,blue, and yellow that do not appear to be composed of anyother colors.2 For example, there is a particular red, calledunique red, that appears purely red, with no traces of yel-lowness, blueness, or greenness in it. There are similarly de-fined unique colors for green, blue, and yellow, each of

which is pure in the same sense of having no traces of theother primary colors. Moreover, pairs of these primaries arerelated to each other as polar opposites: red versus green,and blue versus yellow. These important hypotheses aboutcompositional relations among color experiences werepointed out by Ewald Hering (1878/1964), who used themas the basis of his opponent process theory of color vision.

Relations of color composition are not the same as or re-ducible to the relations of color similarity discussed above.As the color circle shows, the similarity relations among red,blue, and purple are essentially the same as those among or-ange, red, and purple (see Fig. 1). Even so, purple looks like

it is composed of red and blue, whereas red does not looklike it is composed of orange and purple. A complete modelof color experience therefore requires that the uniquenessof the four chromatic primaries be represented within colorspace. It also requires a representation of the compositionof colors in terms of how they are perceived to be analyzedinto the four primaries.

Unique red, green, blue, and yellow can be representedby singular points at diametrically opposed locations in thecolor circle, and color composition relations of binary col-ors by their projections onto its orthogonal red green andblue yellow axes. Notice that this elaboration of the colorcircle now breaks many of the symmetries that were previ-ously candidates for undetectable color-to-color transfor-

mations based only on color similarity relations. Only sevenremain: the four central reflections about the dimensionalaxes and their angular bisectors and the three central rota-tions of 90, 180, and 270. Rainbow reflection has beeneliminated because, if my color experiences were related to

yours by this transformation, I would judge purple, char-treuse, orange, and cyan to be unique colors rather thanred, green, blue, and yellow. All other transformations thatmap unique colors to binary colors are likewise eliminated.

It is now clear how one might proceed in a scientific eval-uation of the transformed color argument: Document evi-dence of the existence of asymmetries in a behaviorallyconstrained model of human color experience. If all sym-metries can be shown to be broken, then Locke was wrong;

my internal color experiences cannot be a transformation of yours without the difference being detectable in my be-havior relative to yours. The focus must be on finding asym-metries rather than finding symmetries because the natureof scientific hypothesis testing requires ruling out null hy-potheses (i.e., finding that differences are present) ratherthan accepting them (i.e., failing to find such differences).In the context of symmetries, this amounts to detectingasymmetries where there are differences rather than de-tecting symmetries where there are no differences.

1.3. Asymmetries in lightness. The color circle we havebeen using as a model of human color experience is inade-


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quate, however, primarily because it leaves out the vast ma-jority of color experiences, including white, black, all theirmixtures with each other (grays), and all their mixtures withthe chromatic colors along the perimeter of the color circle.These color experiences are missing because the color cir-cle is only two-dimensional, whereas the full set of color ex-periences is three-dimensional. Figure 2 shows a morecomplete spatial model of human color experiences that re-flects color similarity relations in all three dimensions ofperceived surface color and the full set of six compositionalprimary colors: red, green, blue, and yellow (as before) plusblack and white.3

The experiences of surface colors represented in Figure2 are classically defined by three dimensions, which we willcall hue, saturation, and lightness.4 (For lights, thethird dimension is usually designated as brightness ratherthan lightness.) The dimension we normally associate

with the basic color of a surface or light is called its hue.In color space, hue corresponds to the angular direction inthe horizontal plane from the central axis of color space tothe location of the point representing that color. The sec-ond dimension of color space, called saturation, repre-sents the vividness of color experiences. It corresponds to

the perpendicular distance from the central axis to the po-sition of the color experience in color space. For example,the vivid colors of the rainbow lie along the outside edge be-cause they have maximum saturation. All the grays lie alongthe central axis because they have zero saturation. Themuted, muddy, and pastel colors in between have in-termediate levels of saturation. The third dimension of sur-face color is called lightness. In the coordinates of colorspace, lightness refers to the height of a colors position asit is drawn in Figure 2. All surface colors have some valueon the lightness dimension, although it is perhaps most ob-

vious for the achromatic grays that lie along the central axis,with white at the top and black at the bottom. In particular,it is worth noting that browns are represented as dark yel-

lows and oranges (i.e., ones low in lightness), as indicatedin Figure 2.

The color circle corresponds to the perimeter of anoblique section through this color solid. This section isoblique because the most saturated yellows are quite light(and therefore higher in color space), whereas the most sat-urated blues and purples are quite dark (and thereforelower in color space), with the most saturated reds andgreens at intermediate lightness values. This variation inlightness of maximum saturation colors breaks further sym-metries in color space. A rotation of 180 about the verticalaxis, for example, would map yellow to blue and blue to yel-low. This color transformation could be detected behav-iorally, however, because you would judge unique yellow tobe lighter than unique blue, whereas I would judge the re-

verse. Because the color solid has no rotational symmetries,any simple rotation of color space about its lightness axiscan be ruled out as a behaviorally undetectable color-to-color transformation. That is, rotations of three-dimen-sional color space can be detected and cannot be used tosupport the color-transformation argument.

There are still three approximate reflectional symme-tries of the three-dimensional color spindle shown in Fig-

ure 3 that are likely to escape behavioral detection exceptin the most precise psychophysical tasks. One is reflectionof red and green in the blue-yellow-black-white plane(Fig. 3A). This works because, at least to a first approxi-mation, red and green are the same in lightness, and blueand yellow are mapped to themselves. A second symme-try is reversing both the blue-yellow and black-white axes(Fig. 3B). This solves the lightness problem with revers-ing blue and yellow because it also reverses the lightness(black-white) dimension. The third symmetry is the com-position of the other two: namely, reversing all three axes,red for green, blue for yellow, and black for white (Fig.3C).

Although all three of these transformations are logically

possible, by far the most plausible is reflecting just the red-green dimension. Indeed, a persuasive argument can bemade that such red-green-reversed perceivers may actu-ally exist in the population of so-called normal trichro-mats (see Nida-Rmelin 1996). The argument goes likethis: Normal trichromats have three different pigments intheir three cone types. Some people, called protanopes,are red-green color blind because they have a gene thatcauses their long-wavelength (L) cones to have the samepigment as their medium-wavelength (M) cones. Otherpeople, called deuteranopes, have a different form of red-green color blindness because they have a different genethat causes their M-cones to have the same pigment astheir L-cones. In both cases, people with these genetic de-

fects lose the ability to experience the red-green dimen-sion of color space because the visual system codes this di-mension by taking the difference between the outputs ofthe M- and L-cones. Now, suppose that someone had thegenes forboth forms of red-green color blindness simulta-neously. Their L-cones would have the M-pigment, andtheir M-cones would have the L-pigment. Such people

would, therefore, not be red-green color blind at all, butsimply red-green-reversed trichromats.5 They should ex-ist. Assuming they do, they are proof that this color trans-formation is either undetectable or very difficult to detectby purely behavioral means, because no one has ever man-aged to identify such a person.



Figure 2. Three-dimensional color space. Colors are repre-sented as points in a three-dimensional space according to the di-mensions of hue, saturation, and lightness. The positions of the sixunique colors (or Hering primaries) within this space are shownby circles.


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1.4. Basic color categories. Harrison (1973) and Hardin(1997) have argued that there are further hurdles for trans-formed-color arguments to clear concerning the implica-tions of color categories. Although it is not entirely clearthat such categories reflect basic facts about color experi-ence rather than some later cognitive stage of processing,but if they do, they have important consequences for thebehavioral detectability of color transformations. To explaintheir import on color transformation arguments, we willhave to review briefly some background claims about colornaming and categorization.6

In their ground-breaking studies of cross-cultural colornaming, Berlin and Kay (1969) found that there are a verysmall number ofbasic color terms (BCTs) across all the lan-guages they studied. These BCTs refer to a correspondingset ofbasic color categories (BCCs) into which color expe-rience can be partitioned. (We will assume the obvious one-to-one mapping between BCTs and BCCs in the discussionthat follows.) Further research and analysis have postulatedthree different types of BCTs:primary, derived, and com-posite (Kay & McDaniel 1978). The most basic are the sixprimary categories: RED, GREEN, BLUE, YELLOW,BLACK, and WHITE. From these, six more categories are

derived by the fuzzy-logical AND-ing (via fuzzy-set in-tersection; see Zadeh 1975) of two primary color categories:GRAY WHITE AND BLACK,ORANGE RED AND YELLOW,PURPLE RED AND BLUE,BROWN BLACK AND YELLOW,PINKWHITE AND RED,GOLUBOI (a Russian word) WHITE AND BLUE.7

Notice that this set does not include all possible combina-tions of primary BCCs. Some are ruled out by the structureof color space itself, such as red-green and blue-yellow,

which cannot exist because they simply do not overlap andtherefore have no exemplars in their fuzzy-logical intersec-

tion. Other combinations could exist as BCTs, such as blue-green, but do not for reasons that are as yet unknown.

The four composite color categories are formed by thefuzzy-logical OR-ing of two or more primary color cate-gories:

WARM RED OR YELLOW,COOL GREEN OR BLUE,LIGHT-WARM WHITE OR WARM WHITE OR

RED OR YELLOW,DARK-COOL BLACK OR COOL BLACK OR

GREEN OR BLUE.Again, not all possible combinations of primary BCCs existas composite BCTs. It seems reasonable that they be re-stricted to combinations of nearby primary BCCs in colorspace, ruling out RED OR GREEN and BLUE OR YEL-LOW. However, it is not clear why there are either no orfew composite BCTs in known languages for RED ORBLUE, GREEN OR YELLOW, WHITE OR COOL, orBLACK OR WARM. These and other mysteries remain tobe solved.

It is important to realize that these facts about BCTs arerelevant to the present discussion only if they reveal im-portant asymmetries in the structure of human color expe-

riences. For example, if for some reason there are morejust-noticeable-differences ( jnds) between unique red andunique yellow than there are between unique green andunique blue, the wider psychophysical gap might explain

why there are BCTs for ORANGE in many languages, butnot for CYAN (blue-green). The fact that there are strong(possibly even universal) constraints on the BCTs that havebeen discovered in a large number of natural languages sug-gests that some basic neural mechanisms of human color vi-sion are likely to be responsible. The most plausible alter-native explanations are that the constraints on BCTs reflectstructure in the nature of the environment (e.g., perhapsthere are more salient orange-colored objects than cyan-



Figure 3. Approximate symmetries of color space. The color space depicted in Figure 2 has three approximate symmetries: reversal ofthe red-green dimension only (A), reversal of the blue-yellow and black-white dimensions (B), and reversal of all three dimensions (C).


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colored objects), the nature of an organisms fit to its eco-logical niche (e.g., perhaps distinctions between differentshades around orange are more important to the organismthan those around cyan), or the patterns of contact and in-fluence between languages.

If the empirical constraints on BCTs do, in fact, reflectunderlying nonhomogeneities in the structure of color ex-perience, they can be used to break further symmetries ofcolor space. Primary BCTs, for which the evidence of uni-

versality is strongest, actually do not break any of the sym-metries illustrated in Figure 3. This is because they corre-spond to the six Hering primaries (red, green, blue, yellow,black, and white) described above, which have already beentaken into account by the unique points and axes of thecolor space.

Adding the derived and composite BCTs, however,breaks all further symmetries. Consider first derived BCTs.Red-green reversal (Fig. 3A) is ruled out, for example, bythe asymmetry between the frequency of derived BCTs forORANGE and PURPLE (frequently found) versus CYANand CHARTREUSE (infrequently or never found). If I

were red-green reversed and if derived BCTs reflect in-trinsic nonhomogeneities in my color experience I should

find it strange that BCTs were distributed in this way ratherthan in the opposite way. I should also find it odd that thereis a BCT for PINK rather than light green. These facts poseno problem for blue-yellow and black-white reversal (Fig.3B), however, because ORANGE maps to PURPLE (and

vice versa) and PINK maps to itself.Table 1 shows how different BCTs break the three can-

didate symmetries illustrated in Figure 3. The entries inthis table were generated from Kay and McDaniels (1978)analysis as follows. First, the transformation indicated at thetop of each column dictates the remapping of primaryBCCs as shown in the first six rows. Red-green reversal (col-umn 1), for example, only requires changing RED toGREEN and GREEN to RED, where the first term indi-

cates the original system of BCCs and the second desig-nates the transformed system of BCCs. Next, the appropri-ate substitutions are made in Kay and McDaniels formulas(see above) for the derived and composite BCCs. If the re-sulting formula for a new BCC corresponds to one for anold BCC, then a is placed in the column for that trans-formation and the row of the original BCT. If not, then an is entered there. To illustrate, consider the row forPURPLE. After red-green reversal (column 1 of Table 1),PURPLE RED AND BLUE becomes PURPLE GREEN AND BLUE. Because GREEN AND BLUE isnot the formula for a BCT in Kay and McDaniels theory,an is indicated in the PURPLE row of the first column,meaning that this transformation maps this BCC into a non-

BCC. After blue-yellow and black-white reversal (column2 of Table 1), however, PURPLE RED AND BLUE be-comes PURPLE RED AND YELLOW. Because REDAND YELLOW is the formula for a BCT (namely, OR-ANGE), a is entered in the table, indicating that thistransformation maps a BCC into another BCC. For com-plete reversal (column 3), PURPLE RED AND BLUEbecomes PURPLE GREEN AND YELLOW, which isnot a BCT; hence the in column 3.

The validity of this analysis rests on the validity of Kayand McDaniels original theory, of course, including the setof BCTs they enumerate and their definitions in terms offuzzy-logical operations. If new BCTs have been discovered

in the meantime or if new formulas have been proposed,the analysis of Table 1 will be correspondingly wrong in de-tail. However, the general nature of the reasoning is sound

within this qualitative theoretical framework, and a morecomplete or accurate theory can be substituted for Kay andMcDaniels original one. Notice also that the analysis inTable 1 involves only approximate, qualitative evaluationsof asymmetries, not metric evaluations. As long as there isa BCT in the general neighborhood of the transformedBCT, the relation is counted as symmetrical () in Table 1.As it turns out, metric precision is unnecessary because thesymmetries are broken qualitatively.

The analysis in Table 1 shows that no color-to-color trans-formations survive a thorough BCT analysis intact, indicat-ing that all symmetries are broken by the behavioral con-straints implied by BCTs. I am not aware, however, of anybehavioral data that directly support these asymmetries forderived and composite color categories in color experience.In many cases, the difference between derived or compos-ite BCTs and non-BCTs is subtle enough that direct intro-spections are too blunt an instrument with which to decide.I myself would be hard-pressed to claim, for example, thatit seems better or more natural to me that there is a

BCT for light reds (PINK) than for light greens, indepen-dent of the fact that my language actually has a BCT forlight reds and not for light greens. The case for ORANGEand PURPLE over blue-green and yellow-green seemssomewhat more compelling. Even so, it would be hard totell how much of such preferences for derived and com-posite BCCs over non-BCCs is the product of sociolinguis-tic training and how much the asymmetries in my underly-ing color experiences.

The existing evidence most relevant to these asymme-tries comes from Roschs (Heiders) studies of learningcolor terms in the Dani tribe of New Guinea (Heider 1972).In a classic cross-cultural experiment, Rosch found that theDani, who have BCTs only for LIGHT-WARM and DARK-

COOL, were able to learn new categories for RED, BLUE,GREEN, and YELLOW more easily than new categoriesfor ORANGE, PURPLE, CYAN, and CHARTREUSE.This result shows that primary BCCs appear to be preferredover other color categories for the Dani and presumablyother cultures with composite BCTs even though thesecategories are not overtly expressed in the BCTs of theirlanguage.

It is not yet clear whether this distinction would also besupported for derived or composite BCTs which are theonly ones that break the symmetries in Figure 3 becauseRoschs studies with the Dani examined the learnabilityonly of primary BCTs. Some derived BCTs were used in thestudy (ORANGE and PURPLE), but they were actually

employed in the contrasting non-BCT control categories.Moreover, her results, which have traditionally been inter-preted in terms of the learnability of primary BCTs, can beexplained equally well by color composition relations basedon the four chromatic Hering primaries. The latter expla-nation has the advantage of a clearer basis in phenomenol-ogy and physiology than is available for BCTs in general.

The main question is whether the derived and compos-ite BCTs are grounded firmly enough in color experiencefor the asymmetries they imply to be detected. Perhaps anew category for light green would be just as easy to learnas PINK for people whose language has neither BCT, andperhaps a new BCT for blue-green or yellow-green would




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be just as easy to learn as ORANGE or PURPLE. Thestrongest argument for a phenomenologically privilegedstatus of a derived BCC can be made for BROWN, insofaras it seems qualitatively different from the yellow and or-ange hue families of which it is part (Hardin 1997).

The crucial question at the center of this issue is whetherthe structure associated with BCCs is caused by nonhomo-

geneities of color experience. The most obvious way to doc-ument such effects of categories on perceptual experienceis to look for so-called categorical perception phenomena.Categorical perception refers to a phenomenon in whichsmall changes in certain stimulus continua across a cate-gorical boundary produce large changes in perceptual ex-perience, whereas corresponding changeswithin categoryboundaries produce much smaller changes in experience.The classic case is the effect of continuous acoustical vari-ables on categorical perception of phonemes (e.g., Liber-man et al. 1957).

In the color domain, the evidence is mixed. On the onehand, categorical effects in color perception have been re-ported by several researchers, even in infants (e.g., Born-

stein et al. 1976) and monkeys (e.g., Sandell et al. 1979), forwhom linguistic labels cannot be the mediators of such ef-fects. On the other hand, these categorical effects areseldom as sharply defined as for categories of speech per-ception, and the fuzziness and ineffability of categoryboundaries is well documented in many other studies (e.g.,Berlin & Kay 1969; Rosch 1973). Moreover, the categoricaleffects that have been reported are typically restricted tothe primary BCTs of red, green, blue, and yellow, leavingus, once again, with an open question about the status of de-rived BCTs.

One phenomenon of normal experience that can beviewed as supporting categorical structure in color experi-

ence is the banded appearance of the rainbow (Hardin1997). The physical continuum of photon wavelength thatunderlies the rainbow is purely quantitative and unidimen-sional, with no physical divisions that would producebands of any sort. Why, then, does a wavelength rainbowappear banded? One possibility is that qualitative distinc-tions between color categories are directly represented in

perceptual experience, as Hardin (1997) has argued, andthat these produce qualitatively distinct bands in the ap-pearance of the rainbow.

There is an alternative to the categorical explanation thatmust be considered, however. Because all chromatic colors(except the four unique ones) are experienced as mixturesof different amounts of red, green, blue, and yellow, thebanded appearance of the rainbow might arise simply fromthe gradual transitions between these qualitatively differentcolors. In this case, the bands are attributable to color com-position rather than to color categories. The most obvious

way to discriminate between these two possibilities is to askwhether orange is perceived as a distinct band, qualitativelydifferent from the adjacent reds and yellows, whether it is

perceived merely as a transition between them, or whetherit is something in between. The BCC view predicts a sepa-rate orange band because of the existence of the derivedcolor category for orange, whereas the compositional viewpredicts no such band. If people do experience a separateorange band, there is the further question of whether thisband is present only in the perceptions of people who speaklanguages with a BCT for ORANGE or whether it appearsuniversally. Unfortunately, we do not yet have the answersto these deceptively simple questions.

Whether derived and composite BCTs are grounded incolor experience may seem like a fine point, but, as Table 1shows, it has crucial implications for the possibility of be-



Table 1. Basic color terms over three reflectional symmetriesa

Reflectional transformations

BCT (KayMcDaniel) RG BY/BkWh RG/BY/BkWh

RED (R) (G) (R) (G)GREEN (G) (R) (G) (R)BLUE (B) (B) (Y) (Y)YELLOW (Y) (Y) (B) (B)

BLACK (Bk) (Bk) (Wh) (Wh)WHITE (Wh) (Wh) (Bk) (Bk)

GRAY (GrWh&Bk) (Wh&BkGr) (Bk&WhGr) (Bk&WhGr)PURPLE (PR&B) (G&B ) (R&YO) (G&Y )ORANGE (OR&Y) (G&Y ) (R&BP) (G&B )BROWN (BrY&Bk) (Y&BkBr) (B&WhGb) (B&WhGb)PINK (PkR&Wh) (G&Wh ) (R&Bk ) (G&Bk )GOLUBOI (GbB&Wh) (B&WhGb) (Y&BkBr) (Y&BkBr)

WARM (WmRvY) (GvY ) (RvB ) (GvBC)COOL (CGvB) (RvB ) (GvY ) (RvYWm)LT-WARM (LWWhvRvY) (WhvGvYO) (BkvRvB ) (BkvGvBDC)DK-COOL (DCBkvGvB) (BkvRvB ) (WhvGvY ) (WhvRvYLW)

a& fuzzy logical AND; v fuzzy logical OR; no corresponding BCT; symmetric BCT present; no symmetric BCTpresent.


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haviorally detecting color transformations. If BCCs are notreflected in color experience, or if only primary BCCs arereflected, then the prior conclusion stands that there are atleast three transformations of color space that may well es-cape behavioral detection. If composite and/or derivedBCCs are relevant, then no form of the color transforma-tion argument will actually work.

1.5. Asymmetries in color similarity. Thus far, we havebeen assuming that all aspects of color experience can be

naturally represented within a spatial model such as the oneshown in Figure 2, but this is not necessarily true. One po-tential problem concerns systematic asymmetries in color-similarity relations. An axiomatic property of all metric di-mensional spaces is that distances between points aresymmetrical: The distance from A to B is the same as thatfrom B to A (Krantz et al. 1971). If spatial distance is to rep-resent experienced (dis)similarity, then color similarity re-lations must also be symmetrical.

Rosch (1975) has reported similarity results that contra-dict this assumption with respect to focal versus nonfocalcolors (which correspond approximately to unique and bi-nary colors, respectively). When Rosch had subjects indi-cate the perceived similarity between one color (the target)and another (the standard), she found small but systematiceffects: Nonfocal targets were perceived as more similar tofocal standards than vice versa (e.g., off reds were judged tobe more similar to true red than true red was to off reds).Although these effects were not large, they are noteworthyfor at least two reasons. One is that they create a seriousproblem for capturing all relations among colors in a purelyspatial model. The other is that they may constitute anotherkind of evidence that color categories influence color expe-rience.

Even so, Roschs results do not necessarily rule out thepossibility that certain color transformations can escape be-havioral detection. There are two issues. The first concernshow these asymmetries in similarity are distributed in colorspace. The focal colors for the primary BCCs are essentially

the unique primaries, and we have already noted that thethree transformations of Figure 3 preserve their unique-ness. Asymmetrical distortions in distance relations withrespect to these unique points can also be preserved by cer-tain transformations, as illustrated in Figure 4. This dia-gram shows a hypothetical representation of asymmetriesin similarity relations within the color circle that would bepreserved by the same reflections that preserve the fourunique points. The magnitude and direction of the asym-metries are represented by vectors indicating the direc-tional difference in similarity between the four primary fo-cal colors (large circles) and various comparison colors(small circles with arrows). This diagram shows that suchasymmetries in similarity could be symmetrically distrib-uted in a color space with respect to the primary focal col-ors. We simply do not have enough information on this is-sue to arrive at a firm conclusion.

The second critical issue for the behavioral detectabilityof color transformations is whether asymmetrical similari-ties to focal colors hold just for primary categories or

whether they also hold for derived categories. As we havealready noted, derived categories break all global symme-tries of color space, so asymmetries in similarity with re-

spect to these focal colors (e.g., ORANGE, PURPLE,PINK, BROWN, and GOLUBOI) would allow detection ofany color-to-color transformations. On this point, I know ofno evidence. Rosch found asymmetries in color similarityusing only the primary focal colors RED, GREEN,BLUE, and YELLOW but did not test for asymmetriesin derived color categories. The primary focal colors aresymmetrically distributed and thus may cause no problemsfor any of the candidate symmetries of color space in Fig-ure 3. A further question is whether these asymmetries areactually caused by color categories or color composition,

which has a clearer and more obvious bearing on color ex-perience. Again, we do not yet know the answer.

1.6. Metrical asymmetries. There are other potential sourcesof asymmetry in color space that might reflect nonhomo-geneities in color experience that could be detected be-haviorally. One concerns the metrical structure of colorspace as measured by the discriminability of color samples.Suppose, for example, that unique red is perceived to bemore different from unique blue than unique blue is fromunique green. Given that they are all unique versions ofchromatic primaries, it seems plausible that they are, insome sense, equally different, and this is the rationale forplacing them at opposite poles of orthogonal diameters ofthe color circle in Figure 1. But there are other ways of de-termining distances in color space psychophysically, such ascounting the number of jnds between pairs of colors. Each

jnd is measured psychophysically by finding the differencethreshold: the smallest difference along a continuum thatcan just barely be detected. Using this method, red andblue might well prove to be more different from each otherthan blue and green. Munsell color space, which is basedon measurements of equally spaced differences in hue,represents this difference in discriminability by a greaterdistance between red and blue, and MacLaury (1997a) hasreported data supporting the same conclusion. Other met-rical differences might also prove to be asymmetric whenmeasured by counting jnds, and, if they are reliably differ-ent, they break what otherwise might be plausible sym-metries.



Figure 4. A symmetrical distribution of distance asymmetries.Roschs (1975) results show that nonfocal colors are judged to bemore similar to focal colors than the latter is to the former. The ar-rows represent the degree and direction of asymmetry betweenthe four primary focal colors (large circles) and nonfocal colors(small circles with arrows attached).


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Let us summarize our discussion about the possibility ofdetecting color transformations empirically. There are justthree candidate transformations that survive the most basicbehavioral constraints concerning color experience as re-flected in the global structure of color space: red-green re-

versal, blue-yellow and black-white reversal, and reversal ofall three axes (red-green, blue-yellow, and black-white), asillustrated in Figure 3. If the color space depicted in Figure2 is at least roughly accurate, then all three transformations

will preserve the similarity relations among colors, the di-mensional description of colors in terms of hue, saturation,and lightness, the decomposition of colors into the six Her-ing primaries, and the distinguished points of the six uniquecolors.

Adding color categories and color-naming data into themix makes the situation more complex. The same threetransformations survive further constraints owing to theprimary BCCs and BCTs, including the distribution of thesix primary color categories in color space and the asym-metries in similarity relations around the focal colors for thefour chromatic primary color categories. Composite andderived BCCs rule out all transformations, however, bybreaking their symmetries, but only if they are the result of

intrinsic properties of the color system (i.e., based on expe-riential factors) rather than to extrinsic ecological factors(i.e., based on the physical environment or sociolinguisticcommunity).

I have argued that the crucial issue in assessing the va-lidity of the transformed-color argument is the existence ofsymmetries in an empirically accurate model of color expe-riences. Because no such model presently exists, the exer-cise is premature for reaching firm conclusions. I have usedcolor spaces as the focus of this enterprise because they areby far the dominant modeling tool for this domain and be-cause the nature of global transformations is particularlytransparent within them. The argument from symmetry isnot limited to spatial models, however; it can be applied to

neural-network models, abstract-propositional models, orany other sort of model. The only requirements are that theset of possible color-to-color transformations can be speci-fied in the model and that the results of such transforma-tions can be assessed in terms of the requisite empiricalconstraints. If the behavior of the model is invariant overthe transformation, it is symmetric with respect to thattransformation, and the transformed-color argument will

work.

2. The isomorphism constraint

The questions to which I now turn concern which aspectsof mental life scientists can hope to study and understand

objectively and which we cannot, using color experiences asthe example. In the present section I will discuss the limi-tations of behavioral science, and in section 3, I will con-sider the possibility that biological science can take us be-

yond these limits.

2.1. The subjectivity barrier. It is universally agreed thatthere is a behaviorally defined subjectivity barrier with re-spect to how much others can know about our experiences,and color experiences are no exception. Some aspects of ex-perience can be shared across observers, whereas otherscannot be. We know that many aspects of color experiencemust be shared across observers because normal trichro-

mats agree in their linguistic statements and other sorts ofdiscriminative behavior with respect to colors. Color-blindindividuals also agree with others having the same form ofcolor deficiency, but they do not agree across color-defi-ciency classes or with normal trichromats. These aspects ofcolor experience are therefore objectively shared and fullyavailable to behavioral science. Other aspects are indeter-minate in this respect, however, in that they appear to befree to vary without affecting any known aspect of behavior.They are purely subjective and therefore unavailable to be-havioral science. Even if they happen to be identical acrossobservers, scientists would never know with certainty thatthis was the case. In this section I attempt to define this bar-rier between objective and subjective phenomena with re-spect to behavioral science.

I suggest that the two relevant aspects of experience arethe intrinsic qualities of experiences themselves versus therelational structure that holds among those experiences.These two aspects are normally so completely intertwinedthat it may seem perverse to advocate separating them, butif they lie on different sides of the subjectivity barrier, as Isuggest, then it is important to make the distinction.

The most obvious aspect of visual awareness is certainly

the nature of the experiences themselves, such as the sen-sory quality of redness or circularity, to pick two examplesat random. It seems that the quality of these experiences isflat-out impossible to define behaviorally, given that wehave access to no ones experiences but our own. This is whycolor-to-color transformations are a legitimate problem inthe first place: The quality of individual experiences lies be-

yond the behavioral subjectivity barrier.One might suppose that there is at least one aspect of ex-

periences that can be specified behaviorally, namely, theirindividuality. The set of colors that a person can individu-ate (discriminate), for example, determines whether some-one has full trichromatic color experience or a restricted setowing to some form of color blindness. Notice, however,

that experiences can be individuated behaviorally only byasking people to discriminate between two stimuli, re-sponding same or different to various pairs. Color-blindindividuals reveal their reduced set of color experiences byperforming at chance in discriminating between certaincolor samples that normal individuals distinguish quiteeasily. Thus, even individuating experiences behaviorally isactually about the relation between two (or more) experi-ences by designating whether they are the same or different.

2.2. The importance of relational structure. The secondaspect of experience is one to which behavioral science doeshave access: namely, structure among experiences carriedby their relations to each other. Regardless of what the ex-

perience of red itself is like, normal trichromats agree thatit is more like orange than green. Likewise, sighted ob-servers agree that a circle looks more like a regular octagonthan an equilateral triangle. These relations among experi-ences are just as important as the qualities of experiencesper se and in certain respects, even more so becausethey determine thestructure of experience, which can beshared despite the subjectivity barrier. If experiences hadno relational structure, they would simply be a collection ofcompletely different and totally unrelated mental states,like the blooming buzzing confusion that William Jamessuggested is the nature of sensory experience in infants(James 1890/1950). Without relational structure, for ex-




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ample, we would not experience colors as a coherent do-main of experience, more similar to each other than theyare to shapes: Redness would be as much like circularity asit is like greenness or middle-C, or the smell of freshlyground coffee, or the taste of pumpkin pie.

Relational structure is even more crucial within a singledomain of experience such as color. Without it we wouldnot experience white as being lighter than gray or gray asbeing lighter than black; we would experience them only asdifferent colors, and equally different at that. Because oflighter-than relations among color experiences, we areaware of the ordering of colors in terms of the continuousdimension of lightness, ranging from black to white. In-deed, the entire structure of color space (see Fig. 2) is de-termined by relations among colors, particularly relations ofcomposition and similarity. These relations provide therich, complex dimensional superstructure of color experi-ence. It is quite literally unimaginable what color experi-ence would be like without this structure.

I have argued at some length that it may not be possibleto be sure that my experiences of colors are the same as yourexperiences of colors strictly from our behavior, becausemine could just as easily be some structure-preserving

transformation of yours. We can (and do) agree on basiccolor terms that refer to them I call roses red, violetsblue, and so forth so that we can communicate effec-tively about individual colors. This is an objective behav-ioral fact about color experience, but it tells us absolutelynothing about the quality of those experiences except thatthey are discriminably different from others. It is an ex-ceedingly weak constraint in the same sense that a nominalscale is the weakest type of measurement system (Stevens1951). We merely learn to attach the same labels to our cor-responding internal experiences that arise from viewing thesame collections of wavelengths, regardless of what our par-ticular internal experiences might be.

Further constraints are introduced, however, once we

begin to consider binary or higher-order relations amongexperiences (Krantz et al. 1971). Both you and I can makejudgments about the relative similarity of two colors to athird, or the relative lightness of two colors, for example.These inherently relational judgments are also objective inthat normal trichromats agree about them, at least withinsome margin of error. This is not to say that my relationalexperiences are the same as yours or that we can even de-termine whether or not they are. My experiences of colorsimilarity relations might be as wildly different from yoursas my individual color experiences are from yours, but thestructure of our experiences and relations can neverthelessbe identical.

Preserving relational structure appears to be a necessary

condition for one set of objects to represent another(Palmer 1978). Indeed, model theory formalizes the situa-tion in which one set of objects models another in terms ofthe existence of a function that maps objects in the first setto objects in the second set, so that corresponding rela-tions are preserved in a precise, set-theoretic sense (Tarski1954).8 This requirement explains why the same three-di-mensional color solid is able to model color experiences forall normal trichromats, even if they happen to have wildlydifferent color experiences: It captures exactly the rela-tional structure among the color experiences for each indi-

vidual by mapping them onto points in space so that re-lations among color experiences are preserved by spatial

relations among points in the color solid (see Fig. 5). Thisis not to say that my experience of white is literallyabovemy experience of black, even though the point represent-ing white in the color solid is above the one representingblack in the conventional color solid. However, my experi-ence of white is lighter than that of black, and the relationabove in canonical color space corresponds to the relationlighter than in color experience and preserves its structure.

The emerging picture is that the nature of color experi-ences cannot be uniquely fixed by objective behavioralmeans, but their structural interrelations can be. Thismeans that, logically speaking, any set of underlying expe-riences will do for color, provided the experiences relate toeach other in the required way. The same argument can beextended quite generally to other perceptual and concep-tual domains, although both the underlying experientialcomponents and their relational structure will be different.The experience of musical pitch, for example, could begrounded in any of an infinite variety of experiential di-mensions, but it would always have to have the same dou-ble-helical structure characteristic of perceived pitch rela-tions (Shepard 1982). Although these are both cases in

which there is a clear geometrical structure associated with

the experiential domain, this need not be true. The only re-quirement is that there be some kind of relations among theexperiences that constitute their structure.

2.3. Symmetry, isomorphism, and relational structure. Insection 1, I argued at some length that the existence of sym-metries in color space is the key issue in assessing the va-lidity of color-transformation arguments. I now return tothis topic to ask why this might be the case and how the an-swer relates to the above discussion of the structure of ex-periences.

Mathematically, symmetries are functions that have twospecial properties, known as automorphism and isomor-



Figure 5. The color/space isomorphism. Color experiences aremapped to points in a multidimensional space (see Fig. 2) suchthat color relations (e.g., lighter-than, redder-than) are preservedby corresponding spatial relations (e.g., higher-than, closer-to-

unique-red-point).


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phism. They are automorphisms because they map a givendomain onto itself in a one-to-one fashion. In the case ofsymmetries in color space, the automorphic function there-fore maps a color space onto itself. Automorphism is criti-cal for Lockes (1690/1987) argument because, as was men-tioned at the outset, it assumes that the two observers inquestion have the same overall set of color experiences. Theonly question is whether their color experiences might havedifferent causal connections to the outside world.

The second special property of symmetries is that theyare isomorphisms. Isomorphism, which means roughlyhaving the same structure, is a mathematical function in

which, intuitively speaking, one set of entities is mappedonto another set of entities such that the structure of rela-tions among the first set is preserved by the structure of cor-responding relations among the second set (e.g., Tarski1954).9 Figure 5 illustrates the general requirements for anisomorphism to hold using the (presumed) isomorphic re-lation between color experience and color space as an ex-ample. The function maps color experiences onto points ina dimensional color space such that relations among colorexperiences (lighter than, more similar than, etc.) are pre-served by corresponding relations among corresponding

points in space (higher than, closer to, etc.). This allows adirect and valid translation from facts about the relationsamong color experiences into facts about the relationsamong points in color space. The only thing missing is thecapability to say anything about the nature of the color ex-periences themselves (or the nature of the points them-selves) except that they satisfy corresponding relations. Thefact that such an isomorphism can be constructed is theprincipal reason that spatial models are good representa-tions of color experiences. Notice further that, because iso-morphism is both transitive and symmetric, if your color ex-perience and my color experience are isomorphic to thesame color space, then our color experiences are necessar-ily isomorphic to each other.10

Isomorphism is crucial for the transformed-color argu-ment because, I suggest, the only kinds of differences thatcan be detected behaviorally are differences in relationalstructure, and relational structure is precisely what is pre-served by isomorphism. I can say (or otherwise indicate be-haviorally) that color A is lighter than color B, but I cannotin any way communicate how light either one appears to mein absolute terms. I can also say with confidence that red ismore similar to orange than it is to green, but I cannot ex-press either similarity in absolute terms. It might seem thatone can make absolute ratings of, say, the lightness of in-dividual color samples on a rating scale, but such ratingsare, in fact, always relative to the range of possibilities.

Both automorphism and isomorphism are required to

satisfy the assumptions of Lockes (1690/1987) original in-verted spectrum argument. There are other versions of themore general color question that do not require the auto-morphism component, however. If you and I both have colorexperiences, for example, but they are not the same overallset, then automorphism does not hold. The nonoverlap can

vary from minimal to complete. It would be minimal, for ex-ample, if everything seemed just a bit lighter to me than to

you. In this case, no new dimensions are involved, just dif-ferent values over an expanded range of lightness. My ex-perience of pure white would then be lighter than any ex-perience you have ever had, and your experience of pureblack would be darker than any experience I have ever had.

This mapping between our experiences is not automorphicbecause there are some color experiences my white and

your black unique to each of us.More radically, though, my color experiences might be

totally different from your color experiences in ways neitheryou nor I can imagine. This would be the case if my expe-riences of the three dimensions of color space were qualita-tively different from yours, as though we lived in completelydifferent subspaces of some hypothetical experiential hy-perspace. I would have chromatic dimensions for what weall call red-green and blue-yellow variations, just as you

would, but they would span hue dimensions qualitativelydifferent from any you have ever experienced. The exis-tence of such additional experiential dimensions of colorcan be inferred from comparative studies of color vision,

which show that some animals have four or even five di-mensions of color experience (see Thompson et al. 1992).At least some of the dimensions of chromatic experiencesof such animals, whatever they may be, must be qualita-tively different from any of yours or mine. There is certainlyno logical requirement that my experiences of the range ofhues (or saturations or lightnesses) be anything like your ex-periences of them. Biological considerations can be brought

to bear, as we will discuss shortly at some length, but thereare enough differences between the brains of different per-ceivers to undermine an a priori assumption that the colorexperiences they give rise to are necessarily the same, ex-cept in extraordinary circumstances such as exact clones.

Such considerations lead me to conclude that automor-phism is not central to understanding the general questionof behavioral detectability of differences in color experi-ences, even though it is required for Lockes inverted spec-trum argument. Isomorphism, however, appears to be keyin evaluating the detectability of any color transformationsunder any circumstances. If your color experiences are iso-morphic to mine, your experiences will be undetectably dif-ferent from mine, because the structure in the relations

among your color experiences is the same as that in the cor-responding relations among my color experiences. And ifonly relations can be assessed by behavioral means, thenisomorphism is the strongest form of equality that can beclaimed for color experiences across observers based on be-havior. The relations that must be structurally preserved in-clude (at least) color similarity, color composition, unique

versus binary colors, and dimensional ordering.I will call this condition of structural equality to the level

of isomorphismthe isomorphism constraint and will sug-gest that it constitutes a fundamental limitation on what canbe discovered about experience by behavioral methods. Itmeans that, even if all the dimensions of my color experi-ences are qualitatively different from yours, we can still be-

have identically with respect to colors as long as our expe-riences are isomorphic.11 My experiences would clearlyhave to be three-dimensional; would have to include sixunique reference experiences (for the unique colors) at thepoles of three axes; would have to include an angular di-mension for hue, a radial dimension for saturation, and alinear dimension for lightness, and so forth. If all the rele-

vant conditions were met, then my color experiences couldbe arbitrarily different from yours without the differencesbeing behaviorally detectable.

Again, it is important to understand that none of theseconclusions depends on there being spatial models of thecognitive domain. Experiential domains in which there are




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viable spatial models make good illustrations because theidea of isomorphism is particularly clear in such cases, butspatial models are by no means necessary. The internal re-lations among experiences could even be fundamentally in-compatible with spatial representations, conforming tonone of the fundamental axioms of metric dimensionalspaces. The only requirement is that, whatever the qualita-tive nature of your internal experiences and the relationsamong them may be, the relations among my correspond-ing experiences must have the same structure.

If the shared aspects of experience do indeed coincideexactly with structural relations that is, what is preservedby an isomorphism the argument thus far can be sum-marized as follows: Objective behavioral methods can de-termine the nature of experiences up to, but not beyond, thecriterion of isomorphism. The subjectivity barrier wouldthen coincide precisely with the isomorphism constraint.

It is interesting that this criterion of isomorphism is notunique to the subjectivity barrier or to behavioral science;it also exists in axiomatic formulations of mathematics. Inclassical mathematics, a domain is formalized by specifyinga set of primitive elements (e.g., points, lines, planes, andthree-dimensional spaces in geometry) and a set of axioms

that specify the relations among them (e.g., two pointsuniquely determine a line, three noncollinear points aplane, etc.). Given a set of primitive elements, a set of ax-ioms, and the rules of mathematical inference, mathemati-cians can prove theorems that specify many further rela-tions among mathematical objects in the domain. Thesetheorems are guaranteed to be true if the axioms are true.

However, the elements to which all the axioms and the-orems refer cannot be fixed in any way except by the natureof the relations among them; they refer equally to any enti-ties that satisfy the set of axioms. That is why mathemati-cians sometimes discover that there is an alternative inter-pretation of the primitive elements, called a dual system,in which all the same statements hold. For example, the

points, lines, planes, and spaces of projective geometry inthree dimensions can be reinterpreted as spaces, planes,lines, and points, respectively, because all the same rela-tions hold when the elements in the latter system are sub-stituted systematically for their corresponding dual ele-ments in the former system. All the same axioms hold;therefore, all the same theorems are true. An axiomaticmathematical system can, therefore, be conceived as a com-plex structure of mathematical relations on an underlying,but otherwise undefined, set of primitives that are free to

vary in any way. As Poincar (1952) observed: Mathemati-cians do not study objects, but the relations between ob-

jects; to them it is a matter of indifference if these objectsare replaced by others, provided that the relations do not

change (p. 20). The same can be said about behavioral sci-entists with respect to consciousness: We do not study ex-periences, but the relations among experiences. It is (orshould be) a matter of indifference to behavioral scientistsif the experiences of one person differ from those of an-other, provided that the relations among experiences arethe same.

2.4. Relation to functionalism. The analysis we have justgiven of color experience bears important relations to cer-tain aspects of functionalism. One salient characterizationof functionalist accounts of the mind is that they are basedon the causal relations among mental states and their input

and output relations to the external world (Dennett 1978;Fodor 1968; Putnam 1960). Two cognitive systems thathave the same causal relational structure (i.e., that have cor-responding causal relations among all their correspondingmental states) and the same causal relations to the external

world (on both the input and the output ends) are func-tionally equivalent. Functionalist doctrine claims that suchsystems, which we can call causally isomorphic (but notcausally equivalent), are therefore mentally equivalent.

However, the analysis in section 1 suggests that this is notnecessarily so. In particular, two systems having the samecausal relational structure (including input-output relationsto the environment) can have radically different consciousstates. There are at least two ways in which this can happen.One was discussed at length in section 1, namely, the pos-sibility that the experiences of two people may be quite dif-ferent even though they have the same relational structure,as in the behavioral undetectability of causally isomorphiccolor experiences. The other is that one of the systemsmight have the same causal relational structure over its in-ternal states and their relations to the world, yet have noconscious experiences whatever. Let us now consider thislatter case more carefully.

Suppose we were to create a working color machinethat actually processes information from light in the sameway that people do and that responds as people typically do.This is a reasonable goal. Figure 6 illustrates one way toconstruct the front end of such a machine. It analyzes in-coming light using prisms, cardboard masks, photometers,electronic adding and subtracting circuits, and so forth toprocess color information according to the principles ofcolor perception as they are currently understood. The de-tails of how we now believe receptor outputs are integratedto compute the dimensional values of color space may be

wrong, of course, but the crucial issue is whether substitut-ing the right computations would result in the machine hav-ing color experiences. For such a machine to respond be-

haviorally to light patches, it would have to be extended byadding processes to produce basic color terms for the col-ors it is shown, to analyze the composition of colors intotheir compositions in terms of the Hering primaries, tomake color-similarity ratings, and so forth. Moreover, it

would have to do all this in a way that is behaviorally andcomputationally equivalent to the way in which people per-form these tasks. Supposing that such a machine could beconstructed and it would not be very difficult to do itseems almost bizarre to claim that, because it derived thecorrect coordinates in color space for, say, unique red,named it red, judged it more like orange than green,agreed that it was a warm rather than a cool color, andso on, it necessarilyhad an experience of intense redness.

Rather, the machine appears tosimulate color experienceswithout actuallyhaving them. This difference between hav-ing and simulating experience underlies Searles (1980) dis-tinction between weak AI and strong AI.

Even so, it is surprisingly difficult to prove that this ma-chine fails to have color experiences. A card-carrying func-tionalist would claim that such a machine does have colorexperiences purely by virtue of the computations it per-forms. That may seem unlikely to readers not in the grip offunctionalism, but can it be refuted? The underlying diffi-culty is the problem of other minds. Because we do nothave access to the experiences of any other entity be it aperson, animal, or machine how can we tell whether the




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color machine actually has color experiences as a result ofperforming these computations? There seems to be a logi-cal possibility that it might, but Searle (1980) has arguedthat it cannot. Let us therefore consider an adaptation of hisargument to the present topic of color experience.

2.5. The color room. Searles original thought experiment,known as the Chinese room argument, was not concerned

with color perception but with understanding foreign lan-guages. He asked whether a computer could literally un-derstand Chinese if it were programmed so that when it wasasked questions in Chinese, it answered in a way that wasindistinguishable from native speakers of Chinese. Theclaim of strong AI is that such a computer actually un-derstands Chinese, including whatever conscious experi-ences go along with such understanding, but Searle hasclaimed it does not.

Searles argument can be adapted to make a correspond-ing, and in some ways simpler and more compelling, point

about the insufficiency of performing information-process-ing operations to produce color experiences. Consider asystem that takes as input the quantum catches of the threedifferent types of receptors responsible for color vision (thecones sensitive to short, medium, and long wavelengths)and gives as output the name or description of the color insome language. The claim of strong AI is that such a systemmust be having color experiences rather than justsimulat-ing them. This is a form of functionalism, because the claimis that if the machines internal color states and processesare causally isomorphic to peoples color states and pro-cesses, then the machine literally has the analogous mentalstates, including any experiential component.

The thought experiment is to imagine yourself inside acolor room. You receive an ordered set of three numbersthrough the input door. You then consult a rule book thattells you how to perform the various numerical calculationsnecessary to arrive at three other numbers (corresponding

to hue, saturation, and brightness of a light, although youdo not know that this is what they represent). Ultimately,the rules in the book tell you how to use these values to se-lect one of a particular set of letter strings to hand out theoutput door. If the language of color naming is German, andif you do not know German, these would be meaninglessstrings of letters to you: schwarz, weiss, rot, grn,blau, and so on. You sit in the color room, carrying out

your computations flawlessly, but totally mechanically, be-cause nothing you are doing has any meaning, other thanthe fact that you are performing various arithmetical oper-ations and following certain logical rules that govern whichletter strings you pass through the output door.

Unbeknownst to you, however, people outside the room

interpret the three numbers you receive as inputs to be thequantum catches of the three types of color-sensitive re-ceptors in the retina in response to a colored light. They alsointerpret the meaningless (to you) letter strings you sendout as basic color terms in German. Thanks to the rules inthe book, the letter strings you send out in response to thethree numbers turn out to be the appropriate Germannames for the color patches that produced the three inputnumbers.

Let us suppose that you become so well practiced at yourtask that your performance is indistinguishable from that ofGerman speakers with normal color vision. Let us also sup-pose, for the sake of argument, that the rules you are fol-



Figure 6. A color machine. A system of mirrors, prisms, cardboard masks, photocells, and computational circuits can derive values cor-responding to the coordinates of colors in color space.


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lowing in the book conform precisely to the established op-erations the visual nervous system uses to arrive at internalrepresentations of colors and color names. These two factsmean that you have satisfied the usual functionalist criteriafor claiming that you have mental states associated withcolor perception and naming. The key question is whethercarrying out these computations would necessarily cause

you to have the color experiences you normally would havewhen viewing the corresponding patch of color.

Most peoples intuitions on this question are perfectlyclear. Performing these computations, no matter howclosely they might correspond to visual information pro-cessing in response to patches of color, would not give riseto anything like the experiences of color that would sponta-neously arise if you were actually looking at the patch oflight.

The force of this argument is that it avoids the problemof other minds in deciding whether a color machine hascolor experiences. By inserting yourself into the color roomsystem of rules and computations, you know that there is aconscious agent within it who could have color experiencesif that were indeed a necessary consequence of doing theright computations. Defenders of strong AI have at-

tempted to refute Searles (1980) argument on a number ofgrounds. We will not consider these arguments here; theyare fairly involved and readily available in the commen-taries following Searles original article, together with hisresponses to them. Their translation into the color room

version is straightforward.It appears that behavioral methods are deficient, not only

in determining the qualities of internal experiences but alsoin determining whether there are any internal experiencesat all. They can determine the relational structure amongexperiences, but not their subjective quality, including

whether they are simulated (i.e., nonexistent) or real. Thisappears to be a great deal less than one expects from a fullscientific understanding of consciousness.

3. Biology to the rescue?

Having considered the inherent limitations of behavioralapproaches to understanding color awareness, let us nowconsider the prospects for going further via biological ap-proaches, as suggested by neuroscientists (e.g., Crick 1994).

Will physiology succeed in penetrating the subjectivity bar-rier? In particular, will it allow us to go beyond the isomor-phism constraint to get a handle on the quality of color ex-periences within and across individuals? If so, how? If not,

why not?

3.1. Correlational versus causal theories. In considering

the status of physiological hypotheses about experience,it is important to distinguish two different sorts, which Iwill call correlational and causal claims. Correlationalclaims concern the type of brain activity that takes place

when experiences are occurring and fails to take place whenthey are not. Claims that conscious experiences arise only

when there is brain activity at a particular location, withinsynapses employing a particular neurotransmitter, or firingat a particular rate would all be correlational, because theyprovide no causal explanation of how this particular kind ofbrain activity produces experience. They fail to fill the ex-planatory gap between ordinary physical events and expe-rience (Levine 1983), because they merely designate a sub-

set of neural activity with which consciousness is associated.No explanation is given for this association; it simply is thesort of activity that accompanies consciousness.

At this point it would be appropriate to contrast such cor-relational claims with a good example of a causal one: a the-ory that provides a scientifically plausible explanation ofhow a particular form of brain activity actually produces ex-perience.12 Unfortunately, no examples of such theories areat hand. In fact, to this writers knowledge, no one has eversuggested any theory that the scientific community regardsas giving even a remotely plausible causal account of howexperience arises from neural events. This does not meanthat such a theory is impossible in principle, only that wehave yet to find a serious candidate.

A related difference between correlational and causal bi-ological theories of experience is that they are likely to dif-fer in generalizability. Correlations are inherently specificto the particular biological system within which they havebeen identified. In the best-case scenario, a good correla-tional claim about the neural substrate of human con-sciousness might generalize to chimpanzees and certainmonkeys, possibly even to dogs or rats, but probably notto frogs or snails simply because their brains are too differ-

ent. If a correlational analysis were to show that humanconsciousness is associated with, say, gammabutyric acid(GABA) activity, would that necessarily mean that creatures

without GABA are not conscious? Or might some otherevolutionarily related neural transmitter serve the samefunction in brains without GABA? If so, what featuresmight they have in common? Even more drastically, whatabout extraterrestrial beings, whose whole physical make-up might be radically different from our own? In such cases,a correlational analysis is almost bound to break down. Acausal theory of consciousness might have a fightingchance, however, because the structure of the theory itselfcould provide the lines along which reasonable generaliza-tions might flow.

3.2. The DNA analogy. It seems conceivable that we willsomeday attain a full enough understanding of the brainthat the biological mechanisms underlying conscious expe-rience will be discovered and understood, even though wecurrently have few clues regarding what they might be like.The best we can do right now is appeal to an analogy to theunderstanding of the nature of life that was achieved by dis-covering the molecular structure of DNA.13

The facts to be explained by a theory of life concern cer-tain differences in macroscopic properties of living organ-isms versus nonliving objects, particularly their abilities togrow, sustain their internal functions, and reproduce. Thebasic mechanisms available for a truly causal theory to ex-

plain such life functions are the physical behavior of ordi-nary matter. Prior to the discovery of the structure of DNAby Crick and Watson (1953), however, there was a huge ex-planatory gap between the known physical laws and thesemolar properties of living organisms. The gap was largeenough that some theorists claimed there must be a specialvital force that pervades living tissue and endows it withthe requisite properties. Other theorists rejected this view,of course, insisting on a mechanistic theory devoid of mys-terious, nonphysical forces.

In retrospect, the facts about living organisms thatturned out to be most important for discovering the mech-anisms of life concern their ability to reproduce. Especially




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pertinent were the lawful inheritance relations betweencharacteristics of offspring and characteristics of their par-ents. The general nature of these regularities was workedout by the brilliant Austrian monk, Gregor Mendel, in hispainstaking experiments with garden peas. His results en-abled him to propose, test, and refine a theory of inheri-tance based on hypothetical physical entities, now calledgenes, that were combined in reproduction and ex-pressed in offspring according to lawful principles. He

worked out this genetic theory without ever directly ob-serving the physical basis of these genes. Mendels work isa beautiful example of how a molar behavioral analysis cangive insights into underlying molecular mechanisms with-out those mechanisms being directly observed.

Mendels genetic theory did not fill the explanatory gap,however, because the physical mechanism was not yet spec-ified. Many years later, when sufficiently powerful micro-scopes enabled biologists to observe the internal machineryof cells directly, correlational hypotheses correctly sug-gested that the nucleus of cells was crucial in their self-replicating abilities. More refined correlational conjecturesfocused on the strands of chromosomes within the nucleusas the crucial structures involved in cell reproduction. Even

so, the explanatory gap remained, because there were noserious candidate theories about how the properties of liv-ing cells might arise from chromosomes, whose internalstructure was unknown.

The gap-filling discovery was made by Crick and Watson(1953) when they determined the double-helical structureof DNA. It revealed how a complex molecule, which wasmade of more basic building blocks, could unravel andreplicate itself in a purely mechanical way. As further im-plications of this structure began to be worked out, it be-came increasingly clear how purely physical processescould form the basis of not only genetics, but cellular repli-cation, protein synthesis, and a multitude of other uniqueand previously inexplicable properties of living tissue. The

current biological understanding of life is thus a good ex-ample of how a truly causal theory can fill a seemingly im-mense explanatory gap in science. It did not appear magi-cally, but was historically preceded by molar analyses oforganismic phenomena and by correlational observations ofthe underlying biological mechanisms. Indeed, if Crick and

Watson had worked out the structure of DNA prior to theseother discoveries, its importance would very likely havegone completely unnoticed. Thus, all levels of theorizing

were important in the historical development of a scientifictheory of life.

In this analogy, our present knowledge of the biologicalsubstrates of conscious experience is best thought of as pre-Mendelian. After decades of actively ignoring the problem,

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