*The Monist*, 68 (4), October 1985, 491-506.

Austen Clark

Department of Philosophy U-54

University of Connecticut

Storrs, CT 06269-2054

Although the capacity to discriminate between different qualia is typically admitted to have a definition in terms of functional role, the qualia thereby related are thought to elude functional definition. In this paper I argue that these views are inconsistent. Given a functional model of discrimination, one can construct from it a definition of qualia. The problem is similar in many ways to Goodman's definition of qualia in terms of 'matching', and I argue that many of his findings survive reinterpretation into a physicalistic basis which employs 'indiscriminability' as its primitive term. I show how one can identify the critical properties to which discrimination capacities are sensitive, and then identify their order. A problem arises concerning the different ways in which qualitatively distinct experiences can differ (hue, shape, and so on). Physicalist accounts have often been accused of relying in a circular fashion on some antecedent understanding of phenomenal properties in order to specify those differences. This account avoids such an accusation: ordering of critical properties is determined by the dimensionality of discriminations, and the latter is given by the structure of the discrimination pair lists. Once a topology of quality is constructed, qualia names can be defined by their relative location within the order. In the conclusion I argue that psychophysics employs physicalist techniques to define a topology of quality, and that it can provide what Thomas Nagel calls an "objective phenomenology."

The qualitative content of experience is commonly thought to elude functional definition, as qualia seem to have intrinsic non-relational properties. In contrast, the relationship of qualitative similarity is typically ceded to functionalism, as there seem to be no intrinsic non-relational properties involved in the capacities of discrimination. In this paper I will argue that these intuitions are inconsistent. If one admits the possibility of a functional definition of qualitative similarity, one can construct from it a definition of qualia.

The key moves in this construction are
inspired by Goodman's *Structure of Appearance*.
<Note 1.>
Starting from a phenomenalistic base, Goodman showed how identity
criteria for qualia could be framed given the following conditions:

(N) Ifxandydo not match,xandypresent distinct qualia,

and

(S) Ifxandypresent distinct qualia, then there is somezwhich matchesxbut noty.

It is difficult to see how either (*N*) or (*S*) could
sensibly be denied. Denial of (*N*) would amount to the claim
that *x* and *y* may sometime present identical qualia
even though they do not match. (*S*) is much weaker than
the claim that matching provides a sufficient condition for qualitative
identity; to deny it one must find instead that *x* and *y*
each match the same sets, yet fail to be qualitatively identical.
Denying either condition seems implausible. But Goodman showed
that with them one can achieve the seemingly implausible project
of defining "qualia."

This achievement has important consequences for the debate concerning functionalism and qualia. For example, physicalist accounts of secondary qualities and sensations have repeatedly been accused of circularity. The physicalist has traditionally attempted to define phenomenal properties in terms of phenomenal similarities. Smart analysed "I have a yellowy orange afterimage" as "Something is going on in me like what goes on when I see an orange." This account was challenged as not specifying the respect in which the experiences were alike. <Note 2.> Having a yellowy orange after image is like seeing an orange in one respect, but it is also like seeing a basketball. To define phenomenal color, one must somehow specify that it is the latter aspect that is relevant, not the former. But, the argument goes, to do that, one must name the phenomenal property which the experiences share. So any physicalist reduction of phenomenal properties is circular, resting ultimately on unanalyzed phenomenal properties.

A major task to this paper is to show how a definition of phenomenal properties can avoid such circularity; how, that is, one can specify the way in which two experiences need be like one another without presupposing any notion of their having the same phenomenal properties.

Goodman's system employed a phenomenalistic, nominalistic, and
realistic base; the qualia debate now typically assumes a vocabulary
which is physicalistic, platonistic, and particularistic. However,
in this paper I will show that constructions from the latter base
have the wherewithal to ensnare qualia. If one accepts a functional
definition of discrimination capacities (as is plausible), and
the physicalist analogs of (*N*) and (*S*) (as are also
plausible), a consequence is a constructional definition of qualia.

To begin, we allow primitives referring to things, to parts of
things, and to the relations 'simultaneous with' and 'later than'.
A slice or stage can be defined using those primitives: *x*
is a slice if *x* is a part of some thing *y*, and all
parts of *x* are simultaneous. Our variables range over space-time
regions of finite extent, so we count things and thing-slices
as their values, but not space-time points.

We need certain predicates to describe relationships between slices.
The first is that of a 'generalizable slice sequence' which obtains
between part of a slice *x* and part of some later slice
*y* just in case there is a sequence of slices from *x*
to *y* which instantiates a law. Suppose between subslices
*x* and *y* there is a chain of subslices related to
one another by contiguity and temporal succession.
For
example, *x* is contiguous to some *u* and some
successor of *u* has a part contiguous to *y*. If that
sequence is an instance of a law, then between *x* and *y*
there is a 'generalizable slice sequence.' <
Note 3.>
Each later stage *z* in the sequence between *x* and
*y* is an instance of some generalizable principle of association:
some function projecting *x* to *z*.

We need a predicate to describe the information-theoretic notion
of one slice *x* signalling or encoding occurrence of some
other slice *y*. This notion requires specification of an
input ensemble, an output ensemble, and a collection of contingent
probabilities relating inputs to outputs. An ensemble can be considered
a class of event classes. To signal *y*, slice *x* must
fall in a class of slice types which is one member of the output
ensemble--a class of such classes. Furthermore, there must be
relations of dependence between ensembles, so that (roughly) the
conditional probability of some input event *y*, given *x*,
is different from the a priori probability for *y* alone.
One can give a fully explicit definition
of 'signal' in terms of the conditional probabilities relating
input events to outputs. <Note 4.>

Finally, the basis will include the resources of second order logic, so that we can quantify not just over things and slices, but also over sets of things and slices.

The key psychological predicate needed in order to define qualia
is "indiscriminable," or I(*x*,*y*,*p*),
holding between stimuli *x* and *y* for person *p*
when *p* cannot discriminate between *x* and *y*.
It means something different than "matches" or "looks
the same," and the differences are important to specify at
the outset.

By "indiscriminable" I mean that the subject *p*
literally cannot tell the difference between *x* and *y*.
It does not mean that on casual or even scrupulous inspection,
the subject avers that *x* and *y* 'look the same,'
for the subject may aver that even if, in some situation, the
subject could tell *x* from *y*. "Match" is
closer in meaning, but still does not carry the implication that
there is no way in which the subject can tell the difference between
stimuli *x* and *y*.

How does one assess indiscriminability? One method uses a forced-choice task. Label one stimulus the 'target', and present both simultaneously, altering the placement of target from left to right in a random way. Require the subject to identify the target each time. If, over a sufficiently large number of trials, the subject's identification of the target is not statistically distinct from a random distribution, then the two stimuli are indiscriminable for the subject. If, however, the subject can pick out the target at a better than chance level, then he or she can discriminate the two stimuli.

Discriminability is a purely physical notion. It is a term which can immediately be admitted into a physicalist vocabulary, as it merely ascribes a certain statistical relation among classes of stimulus events and choice behavior.

Information theory provides a useful perspective on discriminability.
Consider stimuli *x* and *y* the input ensemble, and
choice behaviors ('left' vs. 'right') the output. Now if *x*
and *y* are discriminable, then there is a statistically
significant difference between the distribution of choices and
a random distribution. There is a higher
contingent probability that the target is on the left, given the
choice 'left', then the a priori probability that the target is
on the left. <Note 5.> Hence the
choice behavior signals the input, and a channel exists between
event ensembles. The information concerning the difference between
*x* and *y* is retained by the system and is reflected
statistically in behavior.

In order to explain information transfer,
one will naturally posit some generalizable slice sequence between
the stimuli *x* and *y* and behavior.
<Note 6.>
Suppose there is such a sequence. If *x* and *y* are
discriminable, then in each slice in the sequence the effects
of *x* and *y* must have some different properties,
which retain the information that they are distinct. For suppose
that at some slice effects of *x* had all the information
bearing properties of effects of *y*. Then no successive
slice could yield different effects for *x* than for *y*,
and the information concerning their distinctness could never
reliably be regained. So if *x* and *y* are discriminable,
then at every stage between presentation of stimuli and behavior,
information bearing properties of the effects of *x* must
differ (in some way) from those of *y*.

Is the converse true as well? That is, if *x* and *y*
are indiscriminable, must there be some stage at which effects
of *x* and *y* are identical with respect to all their
information bearing properties?

If indiscriminability of *x* and *y* implied that at
some stage effects of *x* and *y* had such identical
properties, then indiscriminability would be transitive. Suppose
*x* and *y* are indiscriminable, so that (by hypothesis)
encodings of *x* and of *y* at some stage *u* have
identical information bearing properties. Suppose also that *y*
and *z* are indiscriminable, so that encodings of *y*
and *z* have identical information bearing properties at
stage *u*. Then there would be a stage at which *x*
and *z* are encoded identically, and so *x* and *z*
would be indiscriminable.

But indiscriminability is intransitive. Two pairs may each be
indiscriminable, but the endpoints (*x* and *z*) sufficiently
different to be discriminated. The difference between *x*
and *y* may be just small enough that the subject cannot
reliably tell them apart. Likewise, the difference between *y*
and *z* may be below a threshold for discrimination of differences.
Yet the accumulated differences between *x* and *z*
may allow reliable discrimination. A simple example is hue discrimination,
where the difference in wavelengths of monochromatic stimuli *x*
and *y* is below the threshold for hue difference, as is
the difference between *y* and *z*, but the sum of the
differences (from *x* to *z*) is not.

Since indiscriminability is intransitive, it is consistent with
there being no stage at which effects of *x* and of *y*
have identical information bearing properties. They may have distinct
properties at every stage of processing yet remain indiscriminable.
Indiscriminability is not co-extensive with identity of properties
of encodings at some stage of processing. Presence of distinct
encodings is a necessary condition for discriminability, but not
a sufficient condition. To develop the latter we need to consider
further the channel between stimuli and behavior.

A stimulus is an event occurring at one or another sensory transducer: retinal rods, muscle stretch detectors, cochlear membrane cells, and so on. A thing or slice within the proximity of a person is no stimulus unless it affects a sensory neuron in some way, and rather than attempt to identify which element of the causal path leading to that effect is the stimulus (the illumination, the reflectance properties of the surface, the reflected light, the light entering the eye, or the light absorbed by light-sensitive cells), one can simply specify stimuli as the furthermost afferent events in the nervous system.

This causal path can be extended into the brain. For example,
events in retinal rods are related to later events in retinal
bipolar cells by generalizable functions, and thence to events
in retinal ganglion cells. At each stage there is some later subsection
*z* such that the relation between *x* and *z*
is an instance of some generalizable principle of association:
some function projecting *x* to *z*. These functions
are determined by the biophysical workings of the cells. We need
not assume that the function is deterministic; it may, for a given
slice, yield no unique successor, but only a probability distribution
for a range of potential successors. Nevertheless, a stochastic
function satisfies the definition for generalizable sequences.

I shall call the function mapping stimulus events to properties
of sections of later stages an* encoding function*. There
is an encoding function from *x* to *y* if and only
if *x* is a stimulus event and there is both a signal relation
and a generalizable slice sequence between *x* and *y*.
For *y* to be a 'code' for *x*, both must be members
of classes found in ensembles, and between the ensembles there
must be an information channel. Furthermore,
this informational relationship must be instantiated in a
physical channel (a generalizable slice sequence) to rule out
the possibility that it is a mere 'ghost' channel arising from
some common cause of both *x* and *y*.
<Note 7.>
No particular anatomical claims are implied concerning encoding:
we do not require that the function always be subserved by the
same biological structures.

Now we are ready to describe a necessary condition for indiscriminability.
Recall that a sufficient condition for *x* and *y* to
be indiscriminable is that at some stage the information bearing
properties of encodings of *x* and *y* be identical,
so that the system loses the information that *x* and *y*
are distinct. However, the converse does not hold, since there
can be indiscriminable differences between encodings of *x*
and *y* at every stage. Since a necessary condition
for indiscriminability
is just a sufficient condition for discriminability, we ask: what
general definition can be given for the conditions under which
*x* and *y* can be discriminated?

An informal presentation will be given first. To
discriminate is to compare. At some stage of processing there
must be a 'discriminal process' in which properties of encodings
are compared. <Note 8.> Some differences
between properties of encodings of stimuli are insufficient to
surpass the threshold of the discriminal process, in which case
the respective stimuli are indiscriminable. Other differences
are sufficient to reject a match. Properties of encodings sometimes
sufficient to reject a match and assure discriminability of the
respective stimuli will be called 'critical' properties. For example,
color sensations presumably have critical properties corresponding
to hue, saturation, and brightness. If encodings share all critical
properties, then there is no discrimination between their stimuli,
and they match. If encodings differ in a single critical property,
then their comparison does not yield a match, and the stimuli
they encode are discriminable. A sufficient condition for discriminability
is that encodings of *x* and *y* differ in at least
one critical property.

This would all be thoroughly circular unless one could give a
noncircular way of specifying the critical properties, but the
latter can be done. Roughly, a critical property is any property
which if not shared by both encodings makes their respective stimuli
discriminable. Slices *u* and *v* encode indiscriminable
stimuli if they both share any property which, if missing in either,
would make those stimuli discriminable. Note that this is not
a mere tautology. Let us suppose *u* is an encoding of some
stimulus *x* (for which I will write *u* = e(*x*)),
and *v* is one of *y*. Property *P* is a critical
property of *u* just in case there is a *v* such that
a difference between *u* and *v* in *P* is alone
sufficient to assure the discriminability of the stimuli *u*
and *v* encode. One way to capture the force of *P*
being alone sufficient to assure discriminability is if *u*
and *v* match in all properties *Q* other than *P*
which can assure discriminability among any stimuli. So *P*
is a critical property of *u* if and only if there are stimuli
*x*, *y* and encoding *v* such that:

(i) *u* = e(*x*) & *v* = e(*y*)

(ii) ~(*Pu* º *Pv*)

(iii) ~(*Pu* º
*Pv*) É
~*Ixy*

(iv) (" Q)("
*s,t,w,z*)(
(*s *= e(*w*) & *t *= e(*z*) & (~(*Qs*
º* Qt*)
É
~*Iwz*) & ~(Q = P) ) É
(*Qu º Qv*) )

What makes *P* critical is that encodings *u* and *v*
fail to match in it (ii), that failure is sufficient to make their
respective stimuli discriminable (iii), and furthermore that it
alone suffices to make them discriminable, since *u* and
*v* match in all other properties *Q* which could account
for that discriminability (iv). Using '*P* is critical' to
abbreviate that condition, our minimal theory of discrimination
is:

Ixy É ("P)( (Pis critical & (~(PuºPv) É ~Ixy) ) É (PuºPv) )

and

("P)( (Pis critical) É (PuºPv) ) ÉIxy

The first says that if *x* and *y* are indiscriminable,
then their encodings match in all those critical properties which
if not matched would suffice to make *x* and *y* discriminable.
The second says that if their encodings match in all critical
properties (not merely those that would make *x* and *y*
discriminable, but all of them), then *x* and *y* are
indiscriminable. Neither conditional is a logical truth since
both relate properties of encodings to discriminability of stimuli.
But the first is a truism, while the second is not. It is a truism
that if *x* and *y* match, then if the failure of encodings
of *x* and *y* to share some critical property would
lead to a mismatch, then encodings of *x* and *y* share
that critical property. But the second conditional is not a truism.
The mere absence of any guarantee of discriminability does not
alone guarantee indiscriminability.

It would, however, if we assume that stimuli are indiscriminable unless proven otherwise. That is, the discriminal process initially presumes no difference between stimuli, and proceeds on that basis until a difference in critical properties is found. Absence of evidence that the stimuli are distinct is then sufficient for them to be indiscriminable. What are the critical properties? Just the ones which, if present, constitute sufficient evidence that the two stimuli differ. If there is some way of defining what makes a property 'critical' which does not rely on its being sufficient for discrimination, then this construction is absolved from the threat of circularity. Such a definition will be provided in the next section.

The presumption favoring indiscriminability explains several characteristics
of qualia. One consequence is the intransitivity of matching.
That both pairs (*u*,*v*) and (*v*,*w*) share
all properties which if absent in one would lead to a detectable
difference does not show that the pair (*u*,*w*) also
share all such properties. Clearly *v* may have some property
*P* which differs from any found in *u* but which does
not render *u* and *v* discriminable, and *w* may
have some further property* P' *distinct in the same way
from properties of *u*, while *P' *may suffice to render
*u* and *w* discriminable.

Second, identity of critical properties of encodings parallels Goodman's definition of identity of qualia: not merely that the two stimuli are indiscriminable, but rather that they both match (are indiscriminable with) the same sets of stimuli. <Note 9.> They may differ indiscriminably in certain ways, and identity is only guaranteed by indiscriminability with the same collection of other terms.

How can one define the critical properties of encodings of stimuli? Thus far our only criterion is that a critical property is any property of encodings which if not shared by both members of a pair suffices to make their respective stimuli discriminable. While it logically follows that indiscriminable stimuli lead to encodings which share all critical properties, unless some independent definition for 'critical' is given, the sufficient condition for discriminability is circular.

Critical properties will reveal themselves indirectly in the data
concerning matches. If there were just one critical property relevant
to the matching of a set of stimuli, then all encodings of those
stimuli could be ordered in terms of that property. Any two encodings
sharing it will encode matching stimuli: there is no other difference
which could occasion discriminability. If there are two critical
properties, then even though encodings *u* and *v* may
be alike in one of them, they can still differ in the other, and
therefore still be discriminable. For example, things matched
in brightness may differ in hue. Similarly, if there are three
critical properties, then encodings *u* and *v* can
match in two critical properties and still be discriminable, since
they may differ in some third respect.

The dimensionality of discrimination pair lists clearly gives
a lower bound for the number of critical properties of encodings
of stimuli. Does it give an upper bound as well? To say that *P*
is a critical property of encodings is to say that there are stimuli
*x* and *y* such that mismatch in *P *of encodings
*u* and *v* alone suffices to make *x* and *y*
discriminable. Can such a property fail to appear as a dimension
of the discrimination pair list? Suppose that *u* and *v*
share *n* critical properties but fail to share *P*,
and that *x* and *y* are discriminable. In terms of
the *n* dimensions provided by critical properties of *u*
and *v*, *x* and *y* are in the same 'place'; but
the fact that they are discriminable implies they cannot be in
the same place. Such a supposition implies a failure in
*n*-dimensionality
of the pair list. Since this is true of every critical property,
there are no critical properties not revealed by the dimensionality
of discriminations; and so the latter provides an upper bound
for the former.

Critical properties are therefore revealed as dimensions along
which encodings can differ. If there are *n* + 1 critical
properties among encodings, then *u* and *v* can match
in n properties and their stimuli remain discriminable. The key
to avoiding circularity is that dimensionality will reveal itself
in the structure of the list of pairs <*x*,*y*>
which are judged to be indiscriminable. By examining that list,
the dimensionality of the similarity judgments can be determined;
and the latter provides the means to identify the critical properties
of encodings.

How is a two dimensional structure revealed in the pair list?
Suppose we have three stimuli such
that *Ixy*, *Iyz*, and *~Ixz*. Encodings of *x*
and *z* are discriminable, and *y* is 'between' them.
<Note 10.> If such encodings have
but one critical property, then any stimulus *u* indiscriminable
from both *x* and *z* will also be indiscriminable from
*y*. (If *u* is 'between' *x* and *z*, then
it must be indiscriminable from that point *y* which is indiscriminable
from both.) But with two dimensions, this condition fails. Then
there can be some *u* indiscriminable from both *x*
and *z* and discriminable from *y*. Intuitively, *u*
does not lie on the line between *x* and *z* (as it
must, if the encodings have one critical property) but rather
somewhere else in the (two dimensional) plane. So the encodings
are shown to be two dimensional.

Two dimensionality is demonstrated by the failure of some point to be colinear with others. Failure of colinearity is shown by the discriminability of two stimuli which are both indiscriminable from the same pair of points. Three dimensionality will be shown by a failure of some point to be coplanar with others, by its failure to lie within a square.

These definitions generalize in an easy way. We show discriminations
are *N* + 1 dimensional by showing that the pair list could
not be *N* dimensional. Failure in *N* dimensions is
demonstrated by finding an *N* dimensional structure (line,
plane, cube, and so on) and a point which is not co-*n*-dimensional.
Each corner is indiscriminable from adjacent corners and discriminable
from all non-adjacent corners. Each edge represents the relation
of indiscriminability, and any distance longer than an edge represents
a relation of discriminability. We find a point contained 'within'
the n dimensional structure (i.e., indiscriminable from its far
corners) yet failing to match any other corners. Since it cannot
both be within the structure and fail to match some other corner,
the discriminations cannot be *N* dimensional.

A slightly easier construction employs relative similarity. First
we define relative similarity in terms of indiscriminability.
A stimulus *x* is more similar to *y* than to *z*
(which I will write '*Sxyz*') if and only if the power of*
I *(indiscriminability) holding between *x* and *y*
is less than the power of *I *holding between *x* and
*z*. Intuitively, *x* is closer to *y* than to
*z* because the number of steps required to get from *x*
to *y* is less than the number required to get from *x*
to *z*.

Relative similarity then gives a easy definition of dimensionality.
Topologically, relative similarity corresponds to distance, so
that if *x* is more similar to *y* than to *z*,
then *x* is 'closer' to *y* than to *z*. Dimensionality
is revealed in the structure of the triples list of relative similarity.
Once again the definition is recursive and proceeds by setting
a minimum dimensionality to the structure. Certain combinations
of triples are impossible if the structure is *n* dimensional,
and show it to be at least *n* + 1 dimensional. The construction
proceeds by defining when one point is co-*n*-dimensional
with other points (co-linear, co-planar, co-3-dimensional, and
so on), and then defining the dimensionality of the list as the
smallest *N* such that all terms are co-*N*-dimensional.

Before proceeding it is worthwhile to show that the definitions in the last section are workable, and provide the basis for psychophysical techniques determining the critical properties of encodings.

Judgments of relative similarity provide the basis for a family
of procedures used in so-called 'multidimensional scaling.' Subjects
are given a list of objects and asked to judge relative similarities:
whether *x* is more similar to *y* than to *z*.
One can then determine the number of dimensions required to describe
the data, and plot the objects in a space defined by those dimensions
using matrix algebra. Distances in that plot correspond to relative
similarity. In this way our intuitions on the attributes of sensation
can be subjected to empirical test. This has been done, for instance,
with color. Numerous triples of color chips were presented to
subjects, and the only data collected were judgments of relative
similarity: whether *x* was more similar to *y* than
to *z*. The resulting structure
was found to be three dimensional, and calculated distances between
chips were in close agreement with more direct psychophysical
approaches. <Note 11.>

The somewhat simpler two-place predicate 'indiscriminable' or 'matches' provides the foundation for the classical psychophysical techniques, including the method of limits, the method of adjustment, and the method of paired comparisons. In the method of limits the experimenter creates ascending and descending series of stimuli proceeding in indiscriminably small steps, and repeatedly assesses the point at which the subject says the series matches or fails to match the target. In the method of adjustment the subject is provided with a target and a method of adjusting physical parameters of a second stimulus, and is asked to adjust those parameters until the stimuli match. Finally, in paired comparisons the experimenter simply presents the subject with many pairs of stimuli and asks the subject whether they match or not. <Note 12.>

The payoff from all these techniques is a topology of quality: an ordering (in terms of physical parameters) of all the potentially detectable differences between stimuli. One gives a physical description of just those conditions under which stimuli are discriminable.

In short, the dimensionality of discriminations can be determined relatively directly via multidimensional scaling, or less directly via a definition of distance and subsequent model fitting. Since dimensionality determines the number of critical properties, and dimensionality can be empirically established by various psychophysical procedures applied to the discriminations, it is clear that the definition of 'critical property' is not only noncircular but also empirically useful.

With necessary and sufficient conditions for 'critical property' defined, we can now present analyses of a host of notions including qualitative similarity, perceptual qualities, and qualia.

a. The first provides physicalist analogs for Goodman's principles
(*N*) and (*S*) above. The relationship 'presents the
same qualia' has (at least in one standard sense of 'qualia')
exactly the extension of 'has the same critical properties', as
given in the account above.

First we should clarify the meaning of the relationship 'presents
the same qualia,' which I will also call 'qualitative' or 'phenomenal'
identity. It is the relation which obtains if *u* presents
just the same phenomenal appearance as *v*.
Visually
such a relation is that of 'looking phenomenally the same';
in bodily sensations it is that of 'feeling the same'. I shall
use 'seems(ph)' to stand for the general notion. <
Note 13.>
It is a relation obtaining between encodings of stimuli, not between
stimuli.

Clearly qualitative differences bear some relation to discriminability, and I shall argue that the relation they bear to discriminability is exactly that satisfied by critical properties of encodings.

First suppose that *u* presents exactly the same qualitative
content as *v*, so that *u* and *v* are qualitatively
identical. The subject then could not tell apart the stimuli occasioning
*u* and *v*, and they would be indiscriminable. Put
another way: if the subject can discriminate *x* from *y*,
then there must be some difference in the qualia they present.
So qualitative identity is sufficient for indiscriminability.

Suppose conversely that *x* and *y* are indiscriminable.
Must *x* and *y* then present the same qualitative content?
While indiscriminability is intransitive, qualitative identity
presumably is not; hence we must allow indiscriminable qualitative
differences. What assures qualitative
identity is not merely that *x* and *y* be indiscriminable,
but that they each be indiscriminable from the same set of stimuli.
This is precisely Goodman's definition of identity of qualia,
<Note 14> and it is precisely coextensive
with identity of critical properties as developed above. That
is, if *u* and *v* differ in some critical property,
then there is some w indiscriminable from one but not the other;
so if *u* and *v* are indiscriminable from the same
set, then they share all critical properties. Qualitatively identical
encodings offer no proof to the discriminal process that their
respective stimuli are different.

To defeat this identification one must either show qualitatively identical experiences which are nevertheless discriminable, or experiences which both are qualitatively identical to the same sets yet which are qualitatively distinct. Since neither seems plausible, Goodman's definition survives interpretation on a physicalist basis.

b. Since qualitative identity is transitive, we can form equivalence classes using it. Sensory qualities correspond to classes of objects whose encodings fall into an equivalence class with respect to qualitative identity. A color predicate, for example, is a predicate applied to stimuli which are encoded in such an equivalence class. Two things are in the same color class if the visual encoding function maps both into the same equivalence class with respect to seems(ph).

Color cannot be defined as a physical attribute of things or a psychological state of observers. A relational account is required, which identifies physical attributes in terms of the relations they bear to human visual processing. A color is a power of a thing to affect your visual system in a certain way. This is similar to the classical definition of secondary qualities, but differs in that the similarity of effects which two things of the same color have is not described as 'leading to experiences of the same kind', but rather as 'falling in the same equivalence class with respect to phenomenal identity'. Two things have the same color if they are encoded so as to match in all critical properties. Since critical properties can be identified from the dimensionality of discrimination pair lists, this account does not rest on any circular definitions of 'same kind of experience'.

c. When it comes to defining a particular perceptual quality (such
as red), the relation of qualitative identity does not enable
one to name any particular equivalence class. To attach names
to classes some further step is required. This can be done indexically.
We define 'red' by (at some time) picking out some red exemplar,
and allowing 'red' to characterize the class of things whose encodings
fall in its equivalence class with respect to qualitative identity.
The paradigm and all other red things cause sensory codes which
match in all critical properties. Let '*p*' name the ostended
paradigm and '*Suv*' mean that *u* and *v* are
qualitatively identical. Then

red(x) º ($u)(u= e(x) &S(u,e(p)) )

That is, the encoding of *x* is within the same equivalence
class relative to phenomenal identity as is the encoding of the
ostended paradigm. So

red(x) º ($u)(u= e(x) & ("P)(Pis critical É (PuºPe(p)) ) )

To use color names, the structure of color similarity must be attached to things at several points, and this can only be done by ostension. The use of indexicals within definitions is perfectly legitimate, however, as shown by recent work on natural kinds. <Note 15.>

One way in which the analysis is idealized is that a thing can be red without being literally indiscriminable from any red exemplar ever ostended, as long as it is relatively more similar to the red exemplars than to others. The analysis also requires as many paradigms as there are discriminable colors. A simple way to avoid both difficulties is to employ the relationship of relative similarity. We pick out five or six exemplars or paradigms of colors. Then 'red' is the class of things which are more similar to the red exemplar than to any of the other exemplars. The occurrence of the term 'red' in the definiens is again eliminated by ostension. The judgments of relative similarity need to be judgments of similarity in respect to hue (and not shape, for example), but that can be guaranteed by identifying the appropriate dimensions in the discrimination pair list.

d. Qualia are properties of sensations; and if one asks "which properties?" the immediate answer is that they are those properties which enable one to differentiate different sensations and identify similar ones. Similarities and differences among sensations are related to judgments of similarity and difference among things. If two things present identical qualia then the things are judged to look the same or match. If two things present different qualia, then the two things do not match the same set of things. In short, qualia can be identified with critical properties of encodings of stimuli.

To say that *u* is a red sensation is to say that *u*
is the encoding of some *x* and that *u* has all those
properties which are such that if *u* lacked one, *x*
would be discriminable from some paradigm red thing. So *u*
and the encoding of the paradigm share all properties which if
absent in either encoding would make *x* and the paradigm
discriminable. Let *p* name some ostended paradigm of a red
thing. Then *u* is a sensation of red if and only if

($x)(u= e(x) & ("P)( (Pe(p) & (~ (PuºPe(p)) É ~Ixp) ÉPu) )

Red qualia are universals instantiated in red sensations: the
properties *P* ascribed to *u* in virtue of which *u*
is qualitatively identical to some *v* which is the encoding
of a red exemplar:

Red quale(*Q*) º *Q* =
{*u*: ($*x*)
("*P*)(
*u*=e(*x*) & (*P*e(*p*) & (~(*Pu*
º *P*e(*p*))
É
~*Ixp*)) É *Pu* )}

A red quale is just a set of red sensations *u* as defined
above. Intuitively, qualia are whatever properties are such that
a code has those properties if and only if its referent seems
the same as some red exemplar.

Qualia are properties of Sellarsian 'sensa' or 'impressions' in that they are properties of internal states involved in perception, which help to explain 'looks', and which have similarities and differences that are structurally similar to similarities and differences among colored things. <Note 16.> They are properties of sensation which can play a certain role in the discrimination of objects.

The properties of sensa are not literally sensory qualities: colors,
smells, and so on. Sensations of color are not themselves colored,
but rather underly discriminations between things which are colored.
Since dimensionality of the pair list yields the critical properties
of encodings, those properties can be identified by their place
within a network of discriminations and differences. A structural
definite description of the form 'the set of all *u* such
that *u* is an encoding of some *x* and *u* bears
*S* to ...' can yield the extension of such a property.

The account here developed in effect identifies qualia with dimensions of the discriminability pair list. It purports to give an objective characterization of phenomenal properties. It seems an easy target for the kinds of criticisms Nagel raises in 'What is it like to be a bat?', and as a summary it will be useful to contrast its treatment of bat qualia with phenomenalistic constructions, and see how well it deals with Nagel's worries. <Note 17>

Whatever their differences, one thing is common to all accounts
of qualia: namely that qualia describe what something looks like,
feels like, or in general, seems like from a given creature's
point of view. Nagel argues that there
are intractable difficulties in giving any objective characterization
of facts of this sort, and hence that qualia--as descriptions
of the immediate subjective character of experience--cannot be
characterized objectively. The difficulty is that facts concerning
what it is like to be *B* "embody a particular point
of view" <Note 18>--namely
that of *B*--and they are inaccessible except from the point
of view of *B*. It seems that
no objective characterization can capture facts of this sort,
since the 'real nature' of experience cannot be described by leaving
behind the creature's point of view, but only by retaining it,
and in fact, by experiencing things from that point of view.
<Note 19.>
So we cannot expect to be able to describe
bat phenomenology with any current methods. That task requires
a new discipline: one of "objective phenomenology."
<Note 20.>

How would the theory developed above attempt to construct a bat phenomenology--for bat sonar, say? By studying discrimination thresholds and the structure of the discrimination pair list; in other words, by constructing bat psychophysics. One can test discrimination capacities among non-verbal creatures by making receipt of food (for example) dependent upon choosing the correct stimulus in a choice task and successively decreasing differences between the choices. To what features is the sense organ sensitive? To what differences is the creature differentially sensitive? While technically difficult, experiments to answer these questions (even for bat sonar) are possible.

And, I would argue, they would give an answer to "what is
it like to be a bat?" If bat *B* can discriminate *x*
from *y* (in the behavioral sense) then even from the bat's
point of view, *x* cannot seem to *B *to be just the
same as *y*. So an ability to discriminate shows that what
it is like to be a bat experiencing *x* is not phenomenally
the same as what it is like to be a bat experiencing *y*.
If there are qualitative differences between bat experiences of
*x* and of *y*, then there will be some *z* for
the bat indiscriminable from *x* but not from *y*, and
so the structure of the pair list will reveal sufficient conditions
as well for qualitative similarity from the bat's point of view.
In short, all the qualitative, phenomenal, or subjective likenesses
and differences among experiences of the bat could be identified
extensionally from the structure of its discriminations. So we
get an 'objective' characterization of what it is like to be a
bat. Of course such a description does not enable us to experience
the world the way the bat does, so in that sense it does not answer
the question "what is it like to be a bat?", but it
does suffice to defeat Nagel's claim that no objective characterization
is possible.

Indeed, such a feat must be possible for us even to recognize that bat sonar (or in general, an alien sensory modality) would be phenomenologically different from any of our sensory modalities, and so it must be possible even for us to recognize that there is a problem about bat sonar. The reason we know that what it is like to be a bat is not like what it is like to be a person is simply that the bat can discriminate stimuli which to us are indiscriminable (sizes, distances, and shapes when your eyes are closed) and fails to discriminate stimuli which to us look different (e.g. colors). Since we can know that, we have a purchase on alien phenomenology; and if the constructions above are sound then in principle nothing bars an extensional identification of its sensory phenomenology.

In short, then, there is no need for a new discipline of 'objective
phenomenology'--of objective characterization of the modes of
appearance of the world--for psychophysics already *is* that
discipline.

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1. Nelson Goodman, *The Structure of
Appearance*, 3rd edition (Boston: Dordrecht Reidel, 1977).
<Back.>

2. See J.J.C. Smart, "Sensations and
brain processes" and James Cornman, "The identity of
mind and body" both reprinted in C.V. Borst (ed) *The Mind-Brain
Identity Theory* (London: Macmillan, 1970). <
Back.>

3. This is similar to Reichenbach's space-time
'signal' relation. See Rudolf Carnap, *Introduction to Symbolic
Logic and its Applications*, New York, Dover, 1958, pp. 201-203.
I reserve the term 'signal' for the sense deriving from information
theory. <Back.>

4. See Fred Dretske, *Knowledge and the
Flow of Information*, Cambridge Massachusetts, MIT Press, 1981,
pp. 12-26. <Back.>

5. If the choice distribution is non-random then there is a statistically significant relationship between target presentation and choice; and hence there is a non-zero contingent probability linking events in the two ensembles. <Back.>

6. That is, one posits a physical channel to explain the information channel. Note that the latter may exist without the former in cases of 'ghost' channels where both input and output ensembles have a common cause. See Dretske, loc. cit., pp. 38-39. <Back.>

7. Note that a generalizable slice sequence alone is insufficient to establish a signal relation between its endpoints. See Dretske, loc. cit., pp. 33-38. <Back.>

8. The term derives from L.L. Thurstone,
'A Law of Comparative Judgment', *Psychological Review*,
34 (1927), pp. 273-286. See also W.*S*. Torgerson, *Theory
and Methods of Scaling*, New York, John Wiley & Sons, 1958,
pp. 156-158. <Back.>

9. Goodman, loc. cit., pp. 196-197. <Back.>

10. This utilizes Goodman's 'rule of order' to the effect that "every quale between two matching qualia matches both". See Goodman, loc. cit., p. 213. <Back.>

11. See Warren *S*. Torgerson, *Theory
and Methods of Scaling*, New York, 1958, pp. 291-292.
<Back.>

12. See Torgerson, op. cit., pp. 41-60;
J.P. Guilford, *Psychometric Methods*, 2nd edition, New York,
1954. <Back.>

13. The subscript emphasizes that the
similarity in question is not a matter of judged similarity in
the properties of objects (the epistemic sense of 'seems'), but
rather of the immediate appearances they present. See C.W.K. Mundle,
*Perception: Facts and Theories*, London, Oxford University
Press, 1971, p. 20. <Back.>

14. Goodman, loc. cit., p. 196. <Back.>

15. See Hilary Putnam, 'Meaning and Reference',*
Journal of Philosophy 70 *(1973), pp. 699-711.
<Back.>

16. See Wilfrid Sellars, 'Empiricism and
the Philosophy of Mind' in his *Science, Perception, and Reality*,
London, Routledge & Kegan Paul, 1963, p. 193.
<Back.>

17. In Ned Block, (ed.) *Readings in
the Philosophy of Psychology*, vol. 1, Cambridge Massachusetts,
Harvard University Press, 1980, pp. 159-168.
<Back.>

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