Structural Realism for Secondary Qualities

Alistair M. C. Isaac

August 14, 2012

1 Introduction

What is the relationship between the world as we experience it and the world as it is? This is

the question of perceptual realism, the question of whether or not the properties attributed

to the world in our experience are in fact the properties of the world. This question has

been most hotly debated for the property of color, but the considerations raised in that

literature apply equally to the rest of the so-called “secondary qualities.”1 My aim here is

to defend a novel position in this debate, namely structural realism.

The basic idea behind structural realism is that our experience of secondary qualities

conveys only relational information to us about the world.2 An experience of this much

warmth does not convey an absolute value of this much temperature. Rather, it conveys to

us the difference in temperature between the warmth inducing stimulus and some baseline.

This feature of warmth perception is well known: your assessment of the temperature of a

bucket of water is affected by the antecedent temperature of your hand before immersion.

Below, I argue that it is a general feature of secondary qualities that they convey only

relational information about properties in the world. Consequently, I argue, the relationship

between secondary qualities as they are experienced and as they are in the world is properly

understood as a structural correspondence.

This position is “new” in the secondary qualities debate only in that it has not been

explicitly endorsed by name. The basics of the view I will defend here, however, date at least

to von Helmholtz (1878). Many of the key ingredients are found currently in versions of

the ecological approach to color realism (Hatfield, 2003; Noe, 2004; Matthen, 2005), though

none of these has explicitly drawn the conclusion of structural realism. So, in many respects,

the view defended here can be seen as a friendly amendation / elaboration of the ecological

approach.

1I use the term “secondary quality” throughout to refer merely to a well-known category of epistemo-logically worrisome properties. I do not intend to thereby endorse any substantive theory of the primary /secondary quality distinction.

2This view should not be confused with the view that secondary qualities are “relational” in the sensethat they are defined in terms of the relation between the organism and the environment.

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Nevertheless, even if the basic ingredients are already present in the debate, it’s worth

emphasizing that they are properly interpreted as implying structural realism. This is be-

cause the realism question is epistemologically motivated: we want to understand the rela-

tionship between our experience and the world because we want to understand the extent

to which experience serves as a foundation for knowledge. The intuition that experience

provides a relatively firm epistemological foundation arguably motivates many varieties of

realism, from direct realism (Campbell, 1993) and representationalism (Tye, 2000) to more

elaborate physicalist versions (Byrne and Hilbert, 2003). Many of the ingredients for struc-

tural realism can also be found on this side of the debate (especially in the physicalism of

Churchland, 2007), but, again, the position has not to my knowledge been explicitly stated.

Emphasizing that the consequence of these well known considerations is a structural real-

ism, I hope, renders more clear the epistemological commitments implied by sophisticated

versions of both ecological and physicalist interpretations of color experience.

My argument for the structural realist interpretation of secondary qualities is by analogy

with the theory of measurement.3,4 This analogy will help to make explicit the presuppo-

sitions implicit in perceptual psychology, as exemplified by psychophysics and neurophys-

iology. Thus, the structural realist view is not bound by any particular theory of vision,

audition, etc. (as are, arguably, the various forms of physicalism), but binds itself rather to

the research protocols which have generated all such theories in modern psychology.

I begin in Section 2 with a discussion of the basic features of measurement and introduce

there two key ideas: i) the distinction between artifactual and representational structure;

ii) the concept of calibration. Next I discuss structural realism for color in more detail in

Section 3. I think the primary barrier to the explicit endorsement of structural realism for

color is the problem of metamers. The possibility of metamers seems to show that it is

precisely the structural features of color experience which fail to represent. I demonstrate

that this barrier can be dissolved by employing the distinction between artifactual and rep-

resentational structure. Furthermore, the second well known stumbling block for realist

interpretations of color experience, its context sensitivity, is demonstrated to be a conse-

quence of calibration. After discussing those positions in the color realism debate closest to

that defended here, I conclude in Section 4 with a quick survey of how the structural realist

interpretation extends to other secondary qualities, such as pitch and odor.

3The analogy between perception and measurement has been much discussed, and the comparison be-tween thermometry and color vision has been made on many occasions (e.g. Matthen, 2005; Tye, 2006).Nevertheless, I can find no such discussion which emphasizes that the correct conclusion from this analogy isstructural realism, nor can I find a discussion which identifies the importance of calibration and the distinc-tion between artifactual and representational structure for understanding the representational properties ofmeasurement outcomes in this context.

4Although structural realism has recently gained attention as a view within philosophy of science, thatliterature is not actually the motivation behind the present discussion. For those familiar with that debate,however, it is worth emphasizing that the structural realism I defend here is an epistemic structural realism,i.e. the view that all that can be known is structure, not an ontic structural realism, i.e. the view that allthere is is structure.

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2 Basic Features of Measurement

The theory of measurement analyzes the relationship between a measured space and a

measuring space established by a measurement procedure. After illustrating this analysis

with the example of thermometry, I argue that the representational relationship between

measuring and measured is best thought of as a structural one. I conclude the section by

applying this analysis to the sensation of heat, arguing that the situation is analogous, and

therefore that sensations of heat should be interpreted as measuring temperature. Since the

representational content of sensations of heat stands in a structure preserving relationship

to temperatures in the world, this analysis implies that the relationship between heat as

experienced and the physical correlates of heat in the world is one of structural realism.

2.1 Measuring Temperature and Calibration

The standard view in the theory of measurement is that a foundation for the assignment of

numerical values to the outcomes of a measurement procedure is provided by demonstrat-

ing an isomorphism from the axiomatically defined qualitative assumptions underlying the

procedure into a numerical structure such as the real line. Such a “representation theorem”

demonstrates that for any model which satisfies the qualitative axioms there exists an iso-

morphic numerical structure, and this thereby legitimates our use of a numerical structure

to represent all such models. (Krantz et al., 1971)5

In the case of temperature, the qualitative measurement procedure involves holding a

thermometer, for concreteness a glass tube filled with mercury, up against various surfaces

and noting the position of the height of the column of mercury. This procedure assumes that

the values being measured can be linearly ordered, just as the relative heights of the column

may be linearly ordered. Note, however, that the column is always there, it just responds

differently to different surfaces. Because the column is always present, the physical behavior

of the thermometer does not by itself imply a natural zero point. Because the column varies

continuously in height, it does not imply any preferred unit size. But if we want to use

our thermometer to assign numbers to our measurements, we need to specify a way to map

mercury heights into the real line. In order to do this, then, we must pick a zero point and

a unit size. Although the term has other technical meanings, for the purpose of the present

discussion, we’ll call this process calibration.

Calibration – The establishment of a baseline correspondence between states

5Recently, the standard view has come under fire from philosophers who argue that a full theory of mea-surement must also take into account the intentions of the scientist developing the measurement procedure(van Fraassen, 2008) or more details of the empirical procedure itself than just the axiomatic characterizationof its presuppositions (Frigerio et al., 2010). I set these subtleties aside here, but note in passing that thedevelopment of the analogous measurement procedure in perceptual systems took place on an evolutionarytime scale, and the appropriate analog to scientist’s intentions on the picture offered here would therebybe something like selective evolutionary pressures.

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of the measurement device and points in the measuring space such that each

state of the device determines a unique point.

By writing a scale on the side of our thermometer, we calibrate it, thereby establishing a

map from the property being measured into the real line.

In the contemporary theory of temperature, we analyze that which is measured in this

case as mean molecular motion. But the theory of temperature as mean molecular motion

is independent of the qualitative assumption behind our procedure that whatever is being

measured can be linearly ordered. Consider, for example, the caloric theory, which analyzed

temperature in terms of a special intermolecular fluid, caloric. Levels of (free) caloric in a

body can also be ordered linearly. The naıve practice of thermometry just described does

not make assumptions about whether that which is measured is mean molecular motion or

free caloric, it only assumes that some property of the body varies linearly and that different

values of this property affect the height of the column of mercury differentially.

And this is why the correct interpretation of the relationship between the numerical

values assigned by a thermometric measurement and the measured property of the body

is one of structural correspondence. The properties of caloric, mean molecular motion,

and numbers are largely disjoint. One is a concrete substance, the other a summing over

behavior, the third a set of abstract objects. What all three systems share, however, is the

structural feature of being organized linearly: there can be more or less caloric, more or less

mean molecular motion, greater or lesser numbers.

To summarize: in the case of simple thermometry, the measuring space is the space

of possible real numbers. Today, we interpret the measured space as the space of possi-

ble mean molecular motions. The only property of this space which is represented in the

measuring space, however, is the relational property that mean molecular motions can be

linearly ordered. The correspondence between the space of mean molecular motions and

the space of numbers is established by a combination of a physical process which responds

differentially to the measured space, namely the equilibrium height of a column of mercury

when a thermometer is held against a body, and a calibration procedure, which establishes

a convention for assigning relative heights unique numbers.

2.2 Artifactual and Representational Structure

So, a measurement procedure establishes a structural correspondence between two spaces.

What can we learn about the measured space by examining the measuring space? The

answer to this question depends upon the nature of the calibration procedure.

The most important thing to notice is that the measuring space must have antecedent

structure in order to play the role of measuring space. We already ordered real numbers

linearly before Galileo suggested to Sagredo that he write numbers on the side of a tube

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filled with spirits and lower it down a well.6 But because the structure of the real numbers

is present antecedent to its use as a measuring space, there is no guarantee that it will all

correspond to structure in the measured space.

Consider for example ratios between real numbers. If x and y are real numbers, then x/y

is a meaningful quantity and we can meaningfully assert, for example, that if x/y = 1/2,

then y is twice the value of x. If it is 100◦ Fahrenheit in Houston, Texas and 50◦ Fahrenheit

in Anchorage, Alaska, is it meaningful to say that it is twice as hot today in Houston as it

is in Anchorage? No, and the answer can readily be seen by translating the temperatures in

Houston and Anchorage into Celsius, namely 37.8◦ and 10◦C respectively. 50/100 = 1/2 6=10/37.8.

The problem here is that ratios inherit their meaning from the fixity of the zero point.

Since our calibration procedure set a zero point arbitrarily, however, the structure in the

real line which depends upon the significance of the zero point does not represent anything

about the structural relationship between temperatures. We can see this in the formula for

converting Fahrenheit into Celsius. If x is degrees in Fahrenheit and y degrees in Celsius,

then the two values are related by the formula

x = y(9

5) + 32.

This is an affine transformation, it both changes zero point (by adding 32) and unit size

(by multiplying by 9/5). Only structural features of the real line which are invariant across

affine transformations are meaningful as representations of structure of the measured space

of possible temperatures.

These considerations motivate a distinction between representational structure and ar-

tifactual structure:

Representational Structure – Those structural features of a measuring space

which are invariant across all mappings from the qualitative assumptions of the

measurement procedure.

Artifactual Structure – Those structural features of a measuring space which

are not invariant across all mappings from the qualitative assumptions of the

measurement procedure.

The theory of measurement organizes numerical scales in terms of their relative proportions

of representational to artifactual structure. In ratio scales, i.e. those with meaningful zero

points, like length measurement in inches, ratios are meaningful—it makes sense to say of

6Obviously, this is a caricature of the history, but the basic point is correct. Thermometry begins around1600 and the differences in calibration procedures across researchers meant a) that only claims of relativetemperature could be communicated; b) that the establishment of fixed point standards for calibrationbecame the primary goal of early thermometry (Chang, 2004, Ch. 1).

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this board that it is twice as long as that board. In interval scales such as those resulting

from simple thermometry, ratios between intervals are meaningful, e.g. if x1, x2, x3, and x4

are temperature measurements in degrees Fahrenheit, then the value

x1 − x2

x3 − x4

is meaningful because it is invariant across affine transformations (Krantz et al., 1971, Ch. 1;

see also Luce et al., 1990, Ch. 22).

Ordinal scales use even less of the structure of the real line as representational structure as

they are invariant under any monotonic increasing function. Only the ordering of assigned

values is meaningful for such a scale, not the distances between them. Since the only

representational structure we need is an ordering in the case of an ordinal scale, we could

easily use some measuring space other than the real line, so long as it has an antecedent

ordering defined over it. Consider, for example, the Mohs hardness scale, which orders

minerals by the hardest sample substance they can scratch. Distance relations in this scale

are not meaningful, only the ordering it produces. Traditionally we use natural numbers to

represent this ordering, but we could just as easily use letters of the alphabet, days of the

week, or middle names of presidents of the United States. Any structure with an antecedent

ordering could represent the exact same structure as the natural numbers typically do in

this case. An example of this practice for a non-scientific ordinal scale is the use of letters

to represent pitches in a musical scale.

In the limit, simple categorization via some specified procedure is a form of measure-

ment (the “nominal scale” of Stevens, 1946). Here the relation between measuring and

measured spaces is still “structural” although very little structure is preserved, merely dif-

ference in category membership. Consider, for example, the classification of brainwaves into

Gamma, Alpha, Beta, and Theta waves. In this example, there is antecedent structure in

the measuring space, namely the standard ordering of letters in the Greek alphabet, but this

ordering does not correspond to an ordering in the measured space—if we order brainwaves

by frequency, from greater to lesser, we get Gamma > Beta> Alpha > Theta > Delta.

It is important to notice that the distinction between representational and artifactual

structure depends on the assumptions of the measurement procedure not on absolute prop-

erties of the measured space. Once we interpret temperature as mean molecular motion,

we can theoretically define a meaningful zero point (zero motion) and thereby establish a

ratio scale for temperature, such as degrees Kelvin. This does not make ratios between

temperatures as measured by simple thermometry meaningful, however. If we convert a

measurement made in Fahrenheit into Kelvin (by first transforming it into Celsius, then

adding 273, an instance of an affine transformation), this new value is properly understood

as the outcome of a new measurement procedure, one with qualitatively different assump-

tions than simple thermometry. The assumptions of this new procedure are those of simple

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thermometry plus the theoretical assumptions which motivate the analysis of the zero point

for mean molecular motion.

This also illustrates a final point: measurement procedures can be arbitrarily complex

and theory laden. Often (typically!) measurements are “indirect,” “derived,” or made by

proxy.7 Measurement devices can be arbitrarily complex (think of a Geiger counter, or

the detectors used in a particle accelerator), yet still be understood from a measurement

theoretic standpoint as making relatively simple qualitative assumptions about the measured

domain. An illustration of this can be seen in the recent controversy over the measurement

of neutrino velocity. Velocity is assumed to be be organized into a ratio scale, but the device

which delivers numerical values on this scale for neutrinos is large, complex, and depends

upon many theoretical assumptions and technical details.

2.3 The Sensation of Heat

I claim that the sensation of heat stands in the same relationship to temperature as the

outcome of a simple thermometric measurement. Sensations of heat are linearly ordered

against a neutral baseline. Above this baseline, we describe them as more or less warm, below

the baseline, more or less cold. Just as a single thermometer can be calibrated differently

to deliver numbers on either the Fahrenheit or Celsius scale, so also the same physiological

apparatus may be calibrated against different baselines when generating sensations of heat.

If I hold ice in one of my hands for five minutes but not the other, then plunge both hands

into a bucket of water, the hand which formerly held ice will sense the water as warmer

than the hand which did not. The sensory (measurement) devices in the two hands have

been calibrated differently.

It is important to note that we need not equate the measurement procedure correspond-

ing to sensation with just the interaction between sensor and stimulus at the surface of

the skin. Just as a simple thermometric measurement may be combined with theoretical

assumptions to produce a value on the Kelvin scale, or a measurement of sensor activity in a

particle accelerator may undergo complex processing in order to deliver a value for neutrino

velocity, the neural processing of the signal returned from the nerve endings at the surface

of the skin may be arbitrarily complex. Whatever the neural correlates of this experience

may be, from a phenomenological standpoint, we clearly sense objects as more or less warm,

and these sensations are linearly ordered.

The calibration of sensory experience is largely opaque. In fact, the history of early

thermometry involves a sequence of discoveries about the heretofore unforeseen degree to

7Arguably, the only direct form of scientific measurement is length measurement (George Smith, personalcommunication); we measure the height (length) of the column of mercury directly, but only in an indirectway measure some value of the body against which we hold the thermometer. For a detailed discussionof measurement by proxy using the example of Thomson’s measurement of the charge of the electron, seeSmith, 2001.

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which sensations of heat were subject to calibration. In 1615, for example, Sagredo wrote to

Galileo in excitement at his discovery that “well-water is colder in winter than in summer

. . . although our senses tell differently” (in Entropy and Energy, Muller, Weiss - find better

source). Well water feels cooler to us in summer than in winter because the baseline ambient

temperature calibrates our sensations, but the fact of this calibration is not transparent.

Only with an external instrument, one subject to a different calibration process, could

Sagredo discover the extent to which our sensations of warmth and cold depend upon a

variable baseline.

If we accept this analogy, then it appears that the relationship between heat as we

experience it and heat as it is in the world is one of structural correpondence. The physical

causes of experiences of heat are linearly ordered, as are our sensations of heat. When

a baseline is fixed, then our sensations or greater or lesser heat veridically represent the

relative ordering of these physical causes.

3 Structural Realism for Color

The realism debate about secondary qualities has been most extensive for the example of

color. For a survey of the many positions and arguments see, for example, the introduction

to Byrne and Hilbert (1997). Rather than respond in detail to the many positions on this

issue which have already been stated, I’ll first defend the positive proposal of structural

realism for color. After a discussion of the fundamental challenge for this view, namely the

phenomenon of metamers, physically distinct but perceptually identical surfaces, I’ll turn

to a discussion of only those views most closely related to the position defended here.

3.1 Color Vision as Measurement

We perceive surfaces as colored, but how does our experience of surfaces as colored relate to

the properties of surfaces as they are? I claim that color experience measures surface prop-

erties, consequently the relationship between the colors which may possibly be attributed

to a surface and the properties which surfaces may have in actuality is one of structural

correspondence. Our experience of colors is therefore veridical only in the sense that our

organization of surfaces into different categories by color correctly corresponds to actual

differences between the surfaces (whether these differences be physical, chemical, or ecolog-

ical). (I deal with the question of whether more is measured than mere difference in the

following section.) This is structural realism about colors.

Our possible experiences of color are organized into a geometrical space commonly called

the color solid. The representation of this space most familiar to philosophers is as a spindle

with a vertical axis (lightness), a radial axis (saturation), and a circular axis (hue). The color

solid characterizes the relative distances between possible experiences of color, as determined

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through assessments of color similarity. Although these distances vary across subjects, and

even within subjects from day to day, they are fixed enough that they can be determined with

a high degree of precision by psychophysical methods such as color matching experiments.

The asymmetries of this space and the distances within it are remarkably robust across

observers.8

From the standpoint of physics, the property of a surface which determines the color

which will be attributed to it is its surface spectral reflectance profile (SSR), this is the

percentile for each possible wavelength of light in the visible range (roughly 400–700 nm)

with which that wavelength is reflected when incident on the surface. An illuminant is

characterized by its spectral power distribution (SPD), a function which gives the strength

of each wavelength in the emitted light. The color signal which arrives at the retina after

light from an illuminant I has bounced off a surface S is then given by SSRS × SPDI .

The measurement “procedure” for color perception involves the transduction of the color

signal at the retina by photoreceptor cells (rods and cones) plus later processing of this

signal in the retina, the lateral geniculate nucleus, and further cortical regions in the visual

processing chain. The crucial fact about this procedure for the present discussion is that

the assignment of color values is calibrated by the SPD of the illuminant. It is this feature

of the physiological measurement of color that generates the psychological phenomenon of

“color constancy,” illustrated by the relative fixity of baseline category assignments such as

neutral white despite gross changes in illuminant, and thus of color signal incident at the

retina.

Just as in the case of heat perception, the exact details of the processing involved in the

physiology of color perception are not fully known (although they are much better under-

stood for color than for heat!). We do know that the illuminant calibrates this procedure,

however, because models for predicting color appearance must take into account not only

the color signal incident at the retina, but also the illuminance level (and, in more elabo-

rate models, other facts about context as well, for instance absolute luminance, SSR’s for

surround and background, and even the spatial organization of the scene (Fairchild, 2005,

p. 184)). The basic fact here is summarized succinctly by Wandell: “The appearance of an

object in a scene is generally predicted somewhat better by the tendency of the surfaces to

reflect light rather than by the actual light arriving at the eye” (1989, p. 187).

So, the color solid is a measuring space. It (plausibly) measures the space of surface

spectral reflectance profiles. The measurement procedure involves not only the transduc-

tion of the color signal at the retina, but also complex processing of this signal before the

neural correlates of color experience (whatever they may be) are arrived at. This mea-

surement procedure is calibrated through adaptation, and this calibration is controlled by

the illuminant and other features of the scene. The effect of calibration is a relative fixity

8For a discussion of the history of experimental methods for investigating the color solid and an assessmentof the evidence for similarities in color experience across observers, see Isaac (forthcoming).

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in assessments of the relative differences between surfaces independent of the SPD of the

illuminant, so called “color constancy.”

3.2 Artifactual Structure in the Color Solid

I believe the reason that structural realism is not a standard position in the color realism

debate is the observation that the structural relations between colors do not seem to corre-

spond to any physically interesting structural relations between surface spectral reflectance

profiles.

The most common illustration of this fact is through the phenomenon of metamerism.

Surface metamers are physically distinct SSRs which appear identical under a specific illu-

minant. In general, the SSRs of surface metamers are not “similar” or close together in any

way naturally specificiable in physical terms. Further support comes from various structural

features of the color solid which do not obviously correspond to structural relationships be-

tween SSRs, for instance the opponency of yellow and blue, or the fact that orange is closer

to red than to green.

The first point to note here is that, even if none of the qualitative relations between

colors as experienced are mirrored in qualitative relations between SSRs, the interpretation

of color experience as measurement of SSR, and consequently the structural realist view, is

not thereby undermined. The assignment of different instances of a measured domain to

different points within a measuring domain is an act of measurement even if all the remaining

structure of the domain is artifactual (this is the case with categorization of brain waves

into Gamma, Alpha, etc.). Furthermore, the assessment of such a procedure as an act of

measurement is not undermined if the categories in the measured domain turn out to lack

significance, i.e. if the categories of SSRs corresponding to particular colors turn out to share

no feature in common other than that they are categorized together by human experience.

Consider, for example, the phrenologist’s measurement and categorization of bumps on the

skull. We now judge these bumps to be of no theoretical significance, but so long as there is

consistency in his procedure, the phrenologist still satisfies the requirements for performing

a measurement.

Nevertheless, the conclusion that all structural relations between color categories are

artifactual is way too strong. At the very least, the ordering of hues around the color solid

corresponds to the ordering of homogeneous lights by wavelength. Furthermore, if SSR1 and

SSR2 are “similar” in the sense that their curves are very close together, the corresponding

color sensations will also be close. This follows immediately from the fact that a continuous

change in the spectral power distribution incident at the retina results in a continuous change

in color experience (a fact utilized to great effect in color matching experiments). So, even

if we accept that the existence of metamers demonstrates that some structure in the color

solid is artifactual, it does not follow that all structure is artifactual.

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Finally, although I have argued that color experience measures SSRs, other interpreta-

tions of the measured space are consistent with the structural realist view.9 The relative

regularity in the assignment of colors to surfaces motivates interpreting color experience as

the outcome of a measurement, but the view that it is SSRs which are being measured is a

mere hypothesis. Taking the evolutionary perspective, we might ask: given the structural

features of the color solid, what features in the world are plausible candidates for a mea-

sured space? From this perspective, it is not physical, but rather biological or ecological

properties which are more plausible candidates.

Many of the apparently arbitrary features of color vision can be explained once one

takes the ecological perspective. For instance, Kurt Nassau has emphasized that the range

of wavelengths to which the human eye is sensitive is precisely that at which the interaction

between radiation and electrons is substantive, but not destructive, making it ideal for the

detection of chemical properties of surfaces (2001, p. 31). Furthermore, the three dimension-

ality of color space seems much less restrictive once we note that most naturally occurring

SSRs are smooth curves, and can be recovered through the linear combination of relatively

few basis curves (Maloney, 1986). For a sustained analysis of this kind of consideration, see

Shepard (1992).

3.3 Comparison with Preexisting Views

Any analysis of color experience sensitive to color science will have noted the major facts

described in Section 3.1: 1. the organization of color experiences within a color solid; 2.

the robustness of the assignment of color values to surfaces across changes in illumination;

3. the dependency of color experience upon a complex physiological process.10 These are

the only features of color vision required to motivate the structural realist position. Nev-

ertheless, other philosophers who have looked at color science have not explicitly endorsed

structural realism. I believe this is largely because the analogy with measurement has not

been correctly interpreted. I discuss the relationship between the view defended here and

several prominent views in the literature in more detail below.

9This is a general advantage of structural versions of realism, and part of the reason why they arebecoming so popular in philosophy of science. If the correspondence between theory and world is at thelevel of structure, then “incommensurable” theories such as Newtonian gravity and General Relativity maynever the less both be “true” in virtue of the fact that they both correspond veridically to structure in theworld.

10I say “a” color solid as the spindle shaped solid most familiar to philosophers is not the current bestapproximation to the color similarity judgments investigated by the psychophysics of color (a more standard,though still imperfect, analysis is the CIELAB space (Kuehni and Schwarz, 2008, pp. 167–8; Fairchild, 2005,pp. 185–94)). I have not discussed these details here as they are irrelevant for the conclusion of structuralrealism about color (as are the complex details surrounding the scientific investigation of the phenomenonof color constancy). This is because the structural realist view is not motivated by the details of currentscience, but rather by the presuppositions which underlie the research program on color (and other perceptualqualities) and these presuppositions have been fixed at least since the mid-nineteenth century codificationof psychophysical methodology (by Fechner, 1860) and arguably long before that. This point will becomemore clear in Section 4.

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3.3.1 Physicalist Views

Physicalism is the view that color properties just are surface spectral reflectance properties.

A significant motivation for this position is the desire to preserve the apparent veridicality

of everyday color assessments. The major insight of structural realism here is that this

veridicality can be preserved without identifying color properties with surface properties.

Just as my claim that it is 100◦F in Houston today may be true without any further insistence

that mean molecular motions just are real numbers. In fact, this further, unnecessary, step

obscures the true epistemological status of the assignment of numbers to temperatures

via an act of measurement, just as the assertion that colors are SSRs obscures the true

empistemological relationship between color attributions and surface properties.

Byrne and Hilbert. Alex Byrne and David Hilbert have developed the most philosoph-

ically nuanced and scientifically sensitive version of physicalism. On their view, colors are

types of reflectance properties. Although many of Byrne and Hilbert’s arguments can be

endorsed by the structural realist position, I’m afraid the point of actual disagreement is

rather deep. In particular, it hinges on the relation between epistemology and semantics,

a topic too broad and complex to give sufficient attention here. Acknowledging that more

discussion is needed, I think the essential point can be made by noting how Byrne and

Hilbert distinguish experience from its contents:

An experience of a tomato is an event, presumably a neural event of some kind,

and although it represents the property red, the experience is certainly not red,

any more than the word “red,” which refers to the property red, is itself red. If

anything is red it is the tomato. (2003, p. 5)

As should be clear from the above discussion, I take red to be a property of experience,

not the property represented by experience. Consequently, I am happy to accept the claim

that red experiences represent surface reflectance properties, but in doing so, take Byrne

and Hilbert’s point that the word “red” is not itself red to apply mutatis mutandis to the

relationship between red experiences and the properties of surfaces which they represent.

It is not clear to me how much Byrne and Hilbert’s rejection of this point hinges on:

i) the too quick reductionist view stated in this passage that experiences are neural events

(I certainly agree that neural events are not colored!); ii) their rejection of the existence

of “sense data,” interpreted as some realm of third things mediating between the object

and experience (p. 5); or iii) the simple linguistic observation that “experience of color”

as a syntactic construction presupposes “color” as independent of experience, something

experiences are of (which plays a major role in Byrne and Hilbert, 2011). I take (ii) to turn

on questions about how to provide a semantics for experience, but it is distinct from the

question I am addressing here, namely the epistemological relationship between experience

and world. I take (iii) to be a straightforward holdover from ordinary language philosophy,

12

and thus am legitimately surprised that it should play a serious role in the defense of

physicalism, given that the spirit of reductive physicalism is prima facie contrary to the

general commitments of the ordinary language movement, which would seem much more

simpatico with direct realism of the sort endorsed by Campbell (1993).11

Finally, it is important to emphasize that, despite their obvious sensitivity to the details

of the science, the physicalist position defended by Byrne and Hilbert, if taken seriously,

renders color science impossible. For, if one refuses to countenance a distinction between

color experience and properties in the world, one also thereby removes the possibility of the

systematic examination of the relationship between color experiences and these properties,

which is precisely the project of color science. Having conflated color experience with surface

reflectance, the distinction must be made anew if color science is to proceed. This point is

succinctly made by Davida Teller in response to Byrne and Hilbert’s target article:

Now, as far as I can see, color realism is the view that of the vision scientist’s three

entities—surface spectral reflectance, neural signals, and perceived color—one is

color, and the other two are not. But if you ask a color scientist which of the three

entities is color, she will answer that the question is ill-posed. We need all three

concepts, and we need a conceptual framework and a terminology that makes it

easy to separate the three, so that we can talk about the mappings among them.

Color physicalists can call surface spectral reflectance physical color if they want

to, although surface spectral reflectance is a more precise term. But to call it

color (unmodified) is just confusing and counterproductive, because for us the

physical properties of stimuli stand as only one of three coequal entities. (2003,

p. 48)

Again, these considerations are presented much too quickly, and certainly deserve further

elaboration. Nevertheless, I hope I have made clear that despite our shared commitment

to a philosophical theory of color which is sensitive to scientific details, the disagreement

between the structural realist position defended here and the physicalism of Byrne and

Hilbert is deep, and involves wide ranging questions about philosophical methodology.12

Paul Churchland. Churchland (2007) defends a version of physicalism which is very

close to the structural realism defended here. In particular, he takes the question of color

realism to turn on the production of a “structural homomorphism” between the space of

possible color experiences as represented by the color solid and the space of possible surface

reflectance profiles. The existence of such a map would establish a “second-order resem-

blance” between these two spaces. Stated as such, the position is exactly that defended here.

11For a critique of the use of ordinary language considerations in the color realism debate, see Hatfield,2007, Section 5.

12For a sustained discussion of the entangled semantic and metaphysical commitments of Byrne andHilbert, and an argument that their response to Teller fails, see Wright, 2010.

13

However, Churchland interprets the significance of such a map differently. Here, I have ar-

gued that it motivates a claim of structural realism; Churchland, however, interprets such

a map reductively, arguing that it shows that “the objective color of an object is identical

with the electromagnetic reflectance profile of that object” (p. 142).

Churchland’s reductionist commitments blind him to the full power of a second-order

resemblance based approach. In particular, Churchland does not recognize the distinction

between artifactual and representational structure. Consequently, he believes that the es-

tablishment of a structure preserving map between color experiences and surface reflectances

depends upon finding a three dimensional characterization of surface reflectance space. His

attempts to do so have been severely criticized for their insensitivity to the scientific details

(Isaac, 2009; Wright, 2009; Kuehni and Hardin, 2010). Finally, Churchland is committed

to two reductions: the first between possible experiences and possible neural states; the

second between possible experiences and the world (c.f. Churchland, 2005). The structural

realist position, by analogy with the theory of measurement, insists on keeping these three

structures distinct.

3.3.2 Ecological Views

The ecological approach to color takes inspiration from considerations about the evolution of

color vision. If color vision was subject to evolutionary pressures, then it should have evolved

to represent features of the world of functional importance for the organism. These features

are not necessarily those of physics, but may instead be ecologically interesting properties

such as edibility, availability for mating, or dangerousness. These considerations by them-

selves do not fully determine a position in the color realism debate, however, and ecology

inspired theories range from variants of direct realism (e.g. Noe, 2004) to dispositionalism

(e.g. Hatfield, 2003).

Inspiration for the ecological view can be traced to the work of J. J. Gibson. It is perhaps

worth noting that many of the considerations discussed here appear in Gibson as well. For

example, he uses the term “calibration” in essentially the sense elucidated above when

discussing the perception of heat (1966, p. 131), and he frequently identifies the information

picked up by perceptual systems with “structures” or “patterns” that are “invariant” in

the stimulus. In the case of color, Gibson roughly identifies it with pigmentation in the

environment and denies the significance of spectral colors as “there is no advantage whatever

for any animal to be able to see rainbows, or sunsets” (Gibson, 1966, p. 183).

Mohan Matthen. Matthen (2005, 2010) defends a view with all the components of the

one developed here but a different conclusion. He emphasizes the importance of the struc-

tural relationship between colors for understanding their representational content, and he

acknowledges the crucial point that successful denotation does not depend upon the denoted

object possessing the attributed property, as when a radar operator successfully refers by

14

uttering “the red plane” to a plane which itself is not red, though its icon on his screen

is. He calls this latter form of denotation “projective” denotation, and summarizes these

two points with the thesis that “Color experiences constitute a structured projective de-

notational system” (Matthen, 2010, p. 79). Likewise, Matthen acknowledges the analogy

between perception and measurement, and even uses the term “calibration” in a sense very

similar to that developed here (Matthen, 2005, p. 259). Nevertheless, like Byrne and Hilbert,

he takes colors as properties of the world rather than of experience (2005, p. 141) and, like

Churchland, he seeks an external basis for color similarity judgments, which he identifies as

the substrate for conditioning (2010, p. 82).

The point at which Matthen’s analysis and my own diverge can best be seen by ex-

amining our different uses of the analogy with measurement.13 Matthen is led astray by

resting his analysis of measurement too closely on a discussion by Dretske (1995). Dretske

emphasizes the role of the instrument maker’s intentions in the calibration of a measure-

ment device (p. 47). But taking this view leads Dretske away from the structural realism

argued for above, and into a direct realist interpretation of measurement outcomes. This

emphasis on intentions, however, obscures the fact that the fundamental presuppositions of

a measurement procedure are necessarily structural, and thus the same measurement pro-

cedure may be valid for different theoretical interpretations of the measured domain (mean

molecular motion vs. free caloric) provided they i) exhibit the same structure, and ii)

causally determine the state of the measurement apparatus. Calibration does not determine

interpretation, and thus it cannot justify realism.

Matthen emphasizes the possibility of “auto-calibration” (2005, pp. 261–3), calibration

without the intervention of an instrument maker, but presumes this still requires “an expli-

cation” of what is measured. His response is to identify that which is measured with the

pattern of inductive generalizations supported by performing measurements with the device

in different contexts, citing Wittgenstein’s dictum that meaning is use (p. 262). This line

of reasoning leads him to identify colors with the physical surface differences by which an

organism can be conditioned, and thus which can lead to differential action. This implies a

“pluralistic realism”: the surface features by which an organism can be conditioned differ

across species, but this does not undermine the claim of realism for those features (p. 207).

On the analysis presented here, it is not the calibration but the measurement procedure

which supports any such inductive generalizations. This point is crucial for motivating the

structural realism conclusion. A child with a Celsius thermometer and one with a Fahrenheit

thermometer may both make the same inductive generalizations as they experiment with

their thermometers, yet they may disagree about whether an object is 10◦ or 50◦. In order

13Matthen also draws analogies with Tarskian semantics, and calls his view a “semantic” theory of color.Many of the points made in discussing Matthen’s use of the analogy with measurement could be mademutatis mutandis in discussing his analogy with semantics. In the interests of minimizing space whilemaintaining clarity, however, I will discuss only the measurement analogy here.

15

to understand that this disagreement is spurious, they must acknowledge that numerical

assignments by themselves are not significant for their inductive generalizations, but rather

only those structural relationships between numerical assignments which are invariant across

all possible calibrations of their measurement devices.

Gary Hatfield. Hatfield (2003, 2007) defends a ecological theory of color which is both

dispositionalist and objectivist. Unlike Byrne and Hilbert, he countenances a distinction

between phenomenal color experience and whatever that experience may represent. He

rejects the straightforward analysis of this representational content in terms of SSRs because

of the problem of metamers (2007, p. 331). Without a straightforward physical analysis of

representational content, it appears that “[t]he existence of color as an attribute of objects

depends on the normal effects of objects on perceiving subjects” (2003, p. 290). This view

is relational, color content is only definable in relation to the organism, consequently, any

physical basis for this content must be analyzed in terms of its disposition to produce

color sensations in the organism. However, Hatifeld’s view is still objective because color

categories “sustain factual claims” and “pertain to publicly available states of affairs” (2003,

p. 295).

A crucial difference between Hatfield and other ecological views is in his analysis of the

function of color vision. On the ecological approach, a functional analysis is necessary to

understand the content of a representational state, and evidence for this analysis is to be

found in the evolutionary history of the organism. Where Noe (2004) and Matthen (2005)

cash color function out in terms of elaborate counterfactual patterns of expectation and

conditioning, respectively, Hatfield sticks to the straightforward view that the function of

color vision is simply discrimination:

The functions of color vision are served merely if color vision enables us to better

discriminate some objects from other objects, and enables us to reidentify them

as those objects when we encounter them again. (2007, p. 337)

This view, combined with a distinction between phenomenal color experience and its repre-

sentational content, motivates the conclusion that the information about the world provided

by color vision is purely relational.14

Beyond the implication that, with conditions held constant, surfaces that look

different chromatically are different in some way, color qualia of themselves don’t

contain further content about the properties of surfaces. (2007, p. 334)

Hatfield’s analysis is largely consistent with the discussion above. Furthermore, his con-

clusion, that color experiences provide purely relational information about surface properties

14i.e. relations between color experiences tell us something about relations between surface properties—again, not to be confused with the view that color is a relational property, c.f. footnote 2.

16

(though he does not use those terms), is precisely the conclusion of the structural realist.

The only real disagreement between the view developed here and that endorsed by Hatfield

is on the issue of whether color is a relational property. On the view developed here, the

space of possible color experiences is innately determined by the physiology of the organ-

ism and the space of possible surface properties is some fact about the world. The causal

relationship between these two spaces of properties induced by the organism’s perceptual

apparatus determines a structural correspondence between them, but the establishment of

this correspondence does not imply that either type of property is defined only through its

relationship with the other.

4 Other Secondary Qualities

In the introduction I claimed that structural realism for secondary qualities is not motivated

by any particular theory, but rather by the presuppositions implicit in the research protocols

employed by modern psychology. This point is perhaps best illustrated by demonstrating

how the analysis defended so far for warmth and color perception applies to other secondary

qualities, especially ones as yet poorly understood. I briefly discuss the examples of pitch

and odor. The psychophysics of pitch illustrates how different calibrations can connect the

same space of physical stimuli to different measuring spaces. The history of research on

odor demonstrates that the determination of the structure of both the measured and the

measuring space is a driving force behind odor science.

4.1 Pitch

A measurement device may be used to measure in different ways. Consider again our

thermometer. Instead of noting the height of the column of mercury when touching it to

an object, we might instead lay the thermometer end to end noting how many times are

required to reach the end of the object. By using the same physical device, a tube filled

with mercury, a different way, i.e. as a ruler, we thereby establish a different measurement

relationship.

Perceptual organs are similar in that they may establish different correspondences be-

tween world and experience preserving different structural relations depending upon how

they are calibrated and used. Consider, for example, the perception of pitch. Boring (1942)

attributes the discovery of the correspondence between pitch and the frequency of vibrations

in the air to Galileo (p. 323). Both pitch and frequency may be linearly ordered and this

ordering constitutes part of the structure veridically represented by pitch sensations. What

additional structure is represented, however, depends upon calibration.

If pure tones (i.e. sine waves) are used as stimuli and presented to the subject using

traditional psychophysical methods, we can determine the ratio between the just noticeable

17

difference between stimuli and the absolute value of a comparison stimulus (the “Weber

fraction”). As with other sensory modalities, the ability to discriminate between frequencies

varies with the comparison frequency. While some sensory modalities exhibit ranges of

relative fixity in this relationship (i.e. the Weber fraction remains stable), the Weber fraction

for pitch varies dramatically across the range of audible frequencies.15

But this data has a puzzling implication. In standard psychophysics, it’s common prac-

tice to assume that just noticeable differences are psychologically equal. This assumption,

combined with the data on frequency discrimination, implies that frequencies which are

“equal” distances apart are perceived in experience as different distances apart, including,

crucially, octaves.16 For example, the perceptual distance between c′ and c′′ is significantly

greater than that between C and c, because a greater number of distinct changes in stimulus

frequency can be discriminated between c′ and c′′. This result is puzzling because we are

quite good at veridically perceiving octaves (otherwise we couldn’t tune instruments!) and

do in many circumstances judge the distance between C and c and that between c′ and c′′

as “the same.”

These considerations motivated the development of psychophysical techniques for inves-

tigating pitch perception in a musical context. For example, rather than just presenting sine

waves in random order (the method of constant stimuli), one might first play a short musical

passage to the subject, then present him with stimuli for comparison. Some of the crucial

developments in this project were due to Roger Shepard, including both methods (e.g. the

“Shepard tone,” developed as a stimulus for these studies) and theory. On the theoretical

side, a major contribution was Shepard’s proposal that musical pitch space should be repre-

sented by a torus. The toroidal representation incorporates several facts about perception

of pitch within a musical context: i) frequencies separated by an octave are perceived as

“the same”; ii) frequencies separated by a fifth are perceived as “close together”; iii) steps

in a diatonic scale are perceived as equivalent in distance (even though some are whole steps

and some are half steps) (Shepard, 1982).17

In the traditional color realism debate, a constant point of contention has been the

interpretation of color similarity judgments. Realists have struggled to argue for these as

externally motivated, while antirealists have reveled in their apparent subjective basis. But

if we try to reconstruct the arguments in this debate for the example of pitch perception, it

is unclear how they apply. In particular, are frequencies separated by an octave similar in

15For a recent summary of data on the Weber fraction for pitch see Moore, 2008, 196–204.16More specifically, octaves are equal log distances apart. The crucial point is just that the octave is a

physically, musically, and prima facie psychologically meaningful interval, yet it does not fall out of standardpsychophysical methods as a perceptual invariant, motivating the need for further investigation.

17Of course, I elide many details here. In particular, similarity judgments between stimuli which are not“pure” sine waves, but more complex waves exhibiting harmonics, have a physical basis in the agreementof the harmonics across different base frequencies. This consideration provides a physical basis for theassessment of fifths as “similar.” Furthermore, a full account would discuss the physiology of the earand its acoustical properties, as these are less well known to philosophers than the physiology of the eye.Nevertheless, the basic points should be clear without these details.

18

a sense the realist needs to explain or not? In the context of pitches presented in a musical

context, they are judged similar; in the context of pitches presented in a random order,

they are not. Which is the correct context for the realist debate about similarity between

pitches?

The structural realism account has no trouble with this example. In a musical context,

the measurement procedure performed by the ear and auditory cortex is calibrated differ-

ently than in a non-musical context. Musical calibration establishes a mapping between

frequencies and the musical pitch torus, whereas the default calibration for auditory percep-

tion merely establishes a mapping from frequency space into a linear pitch space. The two

measuring spaces have different structures and these correspond to different aspects of the

structure of the space of possible frequencies. There is no meaningful question of whether

frequencies separated by an octave are similar simpliciter. Rather, there are some physical

features they share and some they do not, and the map into musical pitch space veridi-

cally represents (some of) the former, while the map into nonmusical pitch space veridically

represents (some of) the latter.

4.2 Odor

Compared to color and pitch, odor perception is extremely complex and relatively poorly

understood. In the ongoing research program on odor perception, however, the same three

basic ingredients which can be found in color science also appear: 1. an attempt to char-

acterize the space of possible odor experiences (the measuring space); 2. an attempt to

characterize the set of stimuli which cause odor experiences (the measured space); and 3.

an attempt to analyze the physiological structure of the organ of smell and its associated

cortical areas (the measurement device). Whereas in the case of color, early progress on 1

and 2 drove predictions about 3, the complexity of odor perception frustrated efforts on all

three tasks until relatively recently.

Odor is classified with taste as a “chemical sense” since the perceptual response is driven

by the microstructure of molecules, in the case of odor, those that are volatile. Despite

attempts at the systematic categorization of odors and the search for a molecular basis for

them in the late 19th and early 20th century, in 1942 Boring could assert of the failure

to confirm any systematic relationship that “[t]he failure to make the analysis is simply a

phase of the failure to make the crucial discovery about smell, to find the essential nature

of its stimulus” (p. 449). The simple knowledge that odor receptors respond to molecular

structure is not enough to understand the “essential nature” of what is measured because

it does not provide a characterization of the systematic variation in molecular structure

which drives differences in odor perception, a characterization which is needed to extract

quantitative conclusions about odor space from psychophysical methods.

In recent years, the most progress has been made on understanding the nature of the

19

odor receptors and the features of molecules with which they interact, due largely to the

development of increasingly sophisticated techniques for controlling and analyzing both the

molecular structure of stimuli and the pattern of neurophysiological responses.18 Neverthe-

less, progress has still been difficult on the characterization of the space of possible smell

experiences. There is clearly some antecedent structure in this space, but an increased

understanding of the physiology of odor receptors does not help in characterizing psycho-

logical smell space, so long as it provides no guidance on the organization of the nominal

measurements made by individual receptors into a structured scale.

In the early 20th century, Henning asked subjects to order odor samples with respect to

degree of similarity. These experiments motivated his proposal of the Henning odor prism in

1915, the surface of which was offered as an analysis of the space of possible odor experiences

(Boring, 1942, p. 445). Immediate attempts to experimentally confirm the prism concluded

that, although its gross features could be recovered, the prism was not a sufficiently close

approximation to smell space to support quantitative measurements of distance such as

those which which had been made in the color solid. For example, Macdonald (1922) both

found stimuli which produced sensations which could not be located within the structure

of Henning’s prism and failed to find stimuli which could fill out specific regions of it,

concluding that “the solution may lie in some other geometrical construction” (p. 551).

Another tradition characterized the response to odor stimuli by asking subjects to rank

them against a number of smell-related adjectives. Boring discusses the late 19th century

efforts along these lines by Dutch physiologist Zwaardemaker (pp. 441–4). A mid-century

summary of efforts in this direction can be found in Harper et al. (1968) and a significant data

set has been collected by Dravnieks (1985). Such a data set provides a characterization of

smell space with as many dimensions as there were adjectives used (Dravnieks, for example,

used 146 adjectives, giving a 146 dimensional smell space). But which of these adjectives

characterize the fundamental dimensions of smell space and which do not? Or what if none of

them do? One approach to a high dimensional data set such as this is to use a mathematical

technique such as principal components analysis to find a space of reduced dimensionality

that preserves relative distances between points in the space. Alexei Koulakov (2012) has

recently performed such an analysis on the Dravnieks data set, discovering that distances

can be preserved on a 2 dimensional curved “potato chip” shaped surface embedded in

three space. Although this analysis implies that, despite the large number of receptors, smell

space need not be high dimensional, Koulakov has as of yet failed to find any psychologically

significant characterization of the dimensions of the reduced space.

The point of this discussion is just that the same basic features of color science which

18For example, Zhao et al. (1998) used an adenovirus to increase expression of a particular olfactoryreceptor in rat nasal cavities. They found a single compound amongst fifty tested which increased neuralfiring in the infected tissue, motivating the conclusions that the specific receptor expressed detects thatcompound.

20

motivated the structural realism conclusion can be found also in odor science. If anything,

the fact that we as yet lack characterizations of either the measured or measuring spaces for

smell makes the structural realism conclusion even more vivid. The search for these char-

acterizations drives odor science, as it is the presupposition of a structural correspondence

between psychological smell space and some space of possible molecular configurations upon

which the methods for studying smell perception are themselves based.

5 Conclusion

What is the relationship between the world as we experience it and the world as it is?

The structure of our possible experiences corresponds to the structure of possible ways the

world can be, and attributions of properties to the world are veridical or not insofar as the

corresponding properties obtain or not. Since this correspondence is only at the structural

level, the correct analysis of the epistemological status of secondary qualities is in terms

of structural realism. The fundamental lesson of structural realism is that the veridicality

of secondary quality attributions does not depend upon the ascription of the properties

experienced to the world, the car as it is in the world need not be colored in order for my

experience of the car as red to be veridical.

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