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For certain purposes sameness can be treated as a relation.2 So treated it
is of special interest because, although there is only one kind of real
sameness relation, hence only one kind of sameness in the real world,
and only one kind of sameness on the level of intermediaries (interme-
diaries are, after all, supposed to be real in their own realm) there are
two separate relations corresponding to sameness on the level of inten-
tional content. A visaging might involve (1) two or more presentations
of what is the same content in fact or (2) two or more presented con-
tents visaged as being the same. Call the first of these a “visaging of
sames,” the second a “visaging of sameness.” Either can occur without
the other “ as I will slowly try to make clear “ or they can occur to-
gether. Compare other internal relations. One might visage a tone, say,
middle C, and also visage a different tone, say, A above C, but not vis-
age one being a fifth higher than the other though of course it is. Or
one might visage that one color was brighter than another without vis-
aging either of these as a definite brightness or even as very definite
hues. Imagine, for example, that the lighting is poor and peculiar, so one
can™t really tell “what the colors are.” The passive picture theory of per-
ception (Section 8.2), however, with its projection of properties of the

1 Some portions of this chapter were revised from “Perceptual content and Fregean myth”
(Millikan 1991) and “Images of Identity” (Millikan 1997b), with the kind permission of
Oxford University Press, and from “On unclear and indistinct ideas” (Millikan 1994), in
Philosophical Perspectives, 8, Logic and Language, with the kind permission of Ridgeview Pub-
lishing Company.
2 It is not in fact a relation, as I argue in Millikan (1984, Chapter 12).

visaged onto the intermediaries of the visaging, requires that visaged
sameness should correspond to real sameness in intermediaries, that is,
that sameness should be represented by sameness. This is what I have
called the “repetition” theory of the act of reidentifying (Section 8.1).
Similar remarks go for real difference versus visagings of difference.
Although there is only one kind of difference that is real, we must dis-
tinguish “visaging differents” from “visaging difference.” Consistently
held, the passive picture theory of perception would imply that visaged
difference should correspond to difference in intermediaries, that is, that
difference should always be represented by difference. When coupled
with the above thesis that sameness must be represented by sameness, it
would imply that no mistakes could ever be made concerning identity
versus difference in visaged contents. Let us look at these moves now in
more detail.


Because there are two possible kinds of visaging for same and two for
different, there are two kinds of internalizing and two kinds of exter-
nalizing moves (Section 8.3) for each. One can internalize sames, or one
can internalize sameness, in either case positing both sames and corre-
sponding sameness on the level of intermediaries. One can internalize
differents or internalize difference, in either case positing both differents
and corresponding difference on the level of intermediaries. One can
externalize sames or externalize sameness, projecting assumed sameness
of intermediaries into visaged content in either of these ways. One can
externalize differents or externalize difference, projecting the assumed
difference of intermediaries into the visaged content in either of these
ways. Externalizing sames is equivalent to internalizing differents, for if
the same vehicles always produce visagings of the same contents then
visagings of different contents can only have been produced by differ-
ent vehicles. Similarly, externalizing differents is equivalent to internal-
izing sames. But we must be careful, for externalizing sameness is not
the same as internalizing difference, nor externalizing difference the
same as internalizing sameness. These would be equivalent only on the
assumption that visagings are always consistent. In that case, if sameness
of vehicle produces a visaging of sameness, assuming it is impossible to
visage identity and difference as both obtaining between two things,
sameness of vehicle will not be compatible with a visaging of differ-

ence, so a visaging of difference would have to have been produced by
a difference in vehicle.
The following four simple importation moves (Section 8.3) are pos-
sible for same and different.

• One can import sameness. First internalize sames, yielding sames in inter-
mediaries hence sameness in intermediaries, then externalize this sameness.
The result is
(1a) what are the same contents are always visaged as the same contents.
It follows that
(1b) if you don™t visage contents as being the same it must be different
contents that are being visaged.
• One can import sames. First internalize sameness, yielding sameness in in-
termediaries hence intermediary sames, then externalize these sames,
(2) what are visaged as the same contents always are determinate con-
tents that are indeed the same.
(For example, you could not hear that two pitches are the same without
hearing what pitch they are.)
• One can import difference, yielding
(3a) what are different contents are always visaged as being different
It follows that
(3b) if you don™t visage contents as being different they must be the
• One can import differents, yielding
(4) what are visaged as different contents always are determinate con-
tents that are indeed different.
(For example, you cannot see that two things are different colors without
seeing what colors they are, these visaged colors being different.)

Each of these moves yields to a different demand for content com-
pleteness, that is, a demand to fill out content with logically necessary
aspects so that what is envisaged is a fully determinate state of affairs.
But no one of these moves strictly implies any of the others.
If we also apply the demands for determinacy and consistency to vis-
agings of same and different we get the strong result mentioned earlier
(Section 9.1) that no mistakes can ever be made concerning sameness
or difference among contents of visagings. The demands for determi-
nacy and consistency arise from the necessity that intermediaries, being
real, must themselves be determinate and consistent, and from projecting

this back into the intentional world of the visaging. By the law of non-
contradiction, intermediaries are never both the same and different in
any respect, hence that two things are both the same and different in
some respect cannot be visaged. By the law of excluded middle, two
things are always either the same or different in a given respect, hence
intermediaries must be determinate in all respects, hence are always vis-
aged as being either the same or different. For example, if my visaging
is of two colored items, it must either be a visaging of them as same in
color or else as different in color. (“They all look the same in the dark”
“ because they don™t look different.) Thus when either the demand for
consistency or for determinacy is added in, various of the four content-
completing moves listed above will imply various of the others, even
though when taken merely in pairs, the moves are logically indepen-
dent. For example, there is no logical connection between content-
completing move (1) (what are the same contents are always visaged as
the same contents) and move (3) (what are different contents are always
visaged as being different contents) because there is none between ex-
ternalizing sameness and externalizing difference, nor between internal-
izing sameness and internalizing difference.


Nelson Goodman (1966) attempted to exploit dissociations between in-
ternalizing and externalizing different and same in defining identity for
qualia. Goodman began by calling attention to an apparent paradox
concerning the nontransitivity of identity over appearances. One thing,
A, can appear to be the same color as a second thing, B, and the second
appear the same as a third, C, yet A appear to be a different color from
C. The paradox will result from conjunction of these two internalizing
moves. (1) Internalize sameness: If B is visaged as remaining the same
while being compared first with A and then with C, it corresponds to
an intermediary that remains the same over the comparisons. (Alterna-
tively, this might be treated as an example of internalizing constancy “
Section 8.5.) Also, if A is visaged as the same as B, then their interme-
diaries are the same; likewise for A and C. (2) Internalize difference: If
A and C are visaged as different, their intermediaries are different.
Goodman calls his intermediaries or their relevant qualities “qualia.” A
clarification is needed here, however. Qualia are not external objects or
their properties, but recline before the mind. And on classical views,
what reclines before the mind should not have any part of its nature

hidden from mind. Nor can something real lying before the mind have
a contradictory nature. Clearly Goodman is conceiving of his qualia
here as themselves dividing into two aspects, the real qualia and the ap-
pearances of the qualia, only the appearances of the qualia being trans-
parent to mind. The appearances of the qualia are thus the visagings of
qualia and the qualia themselves are the vehicles. (Amazing!)
Goodman does not, of course, explicitly analyze the paradox the way
I have. But he tries to avoid it, in effect, by now internalizing difference
but not sameness and then externalizing sameness but not difference.
Qualia ± and β are identical just in case every quale γ that matches ei-
ther ± or β also matches the other (Goodman 1966, p. 290), where
“ . . . to say that two qualia are so similar that they match is merely to
say that on direct comparison they appear to be the same” (1966,
pp. 272“3). (Notice that qualia, quite explicitly, can appear to be other
than they are.) Being very careful, it is not merely difference that is in-
ternalized here but lack of sameness, that is, sameness is also external-
ized. The assumption is that “on direct comparison” qualia that are the
same never fail to produce visagings of sameness, so that not appearing
the same on direct comparison “ not matching “ can be a criterion of
qualia difference.
Now the sorts of things Goodman calls “qualia” originally were con-
ceived in the tradition to be intermediaries explaining the intentional
contents of perceptions of ordinary external objects. Just as Peacocke
had to split perceptual intermediaries into two levels with two levels of
properties (Section 8.5), if we opted not to be phenomenalists, Good-
man™s reflections would tempt us to make the same sort of split. The
level that contains the appearances of Goodmanian qualia, these being
the intentional contents projected by qualia themselves, is the same as
the level that acts as intermediary for the perception of the external
world. In a moment I will discuss a similar dissociation between the
handling of same and different in the Fregean tradition, and a similar
split between levels of intentional content engendered.
It is easy to produce paradox by combining internalizing of constan-
cies with internalizing of visaged samenesses and differences. Suppose,
for example, that between two identically colored objects a colored
band is inserted, one that is subtly graded in color from side to side.The
effect may be that while it appears that nothing has been changing
color, still what started out looking like two samples of the same color
now look like samples of different colors. Or suppose while you are
watching, someone draws arrow ends on each of two equal parallel

lines, turning them into Müller-Lyer arrows. While appearing not to
grow or to shrink, the lines will begin by appearing the same length
and end by appearing different lengths. Again: those trees in the distance
looked the same size until I noticed the men standing beside them.
Now they appear to be quite different sizes, yet things appear not to
have changed. If we internalize constancy, sameness, and difference, such
visagings would appear to be impossible.The demand here, of course, is
for content consistency.
An entirely explicit externalizing and internalizing of the sameness
relation occurs in Peacocke™s discussion of manners of perception
(1986). Using perception of distances as his example he writes “if µ is
the manner in which one distance is perceived and µ' is the manner in
which a second distance is perceived by the same subject at the same
time, and µ = µ', then the distances are experienced as the same by the
subject (they match in Goodman™s sense)” (1986, p. 5). Granted that
modes of presentation are supposed to be some kind of real thing, real
abstract object, real disposition, real process, real adjectival or adverbial
property, real relation, or whatever, as opposed to being merely inten-
tional objects, this externalizes sameness. Next, “ . . . the same manner
can enter the content of experiences in different sense modalities.You
may hear a bird song as coming from the same direction as that in
which you see the top of a tree: we would omit part of how the ex-
perience represents the world as being were we to fail to mention this
apparent identity” (1986, p. 6). That is, a visaging of sameness of direc-
tion is produced by some kind of sameness in real intermediaries
(sameness in “manner”) responsible for these visagings, regardless of the
differences between these intermediaries with regard to modality. This
internalizes sameness. Thus, Peacocke claims, there are cross-modal
manners of perception. I believe that Peacocke intends these moves to
be stipulative, defining what constitutes sameness of perceptual manner.
But such stipulations do not come for free. That there is any such cor-
related sameness existing on a nonintentional level must be argued. What
is the argument that the appearance of sameness can only result from
the presence of some kind of real sameness? For example, is the ap-
pearance of sameness necessarily transitive, as would be required if the
appearance of sameness is always associated in this way with the same
real manner of perception?
Another way of externalizing sameness is suggested when Evans
(1985a) gives a tentative “yes” answer to Molyneux™s question. His rea-
soning is that if perceptions of shape by sight and by touch produce

parallel behavioral orientations in the space surrounding one, hence
constitute perceptions of space for the same reason, then they are un-
derstood to be perceptions of the same. Because “[t]here is only one be-
havioral space” (Evans 1985a, p. 390) within which grasp of visual and
felt shapes are manifest, there could be no problem about identifying
across these modalities. Again, relevant sameness in relevant intermedi-
aries “ the intermediaries here are dispositions to orient oneself in space
or the states in which these are rooted “ is externalized to yield a vis-
aging of sameness. Behaving the same in response to visual and tactual
perceptions is grasping content sameness.


Now perhaps we are warmed up enough to discuss sameness and differ-
ence in the more abstract context of theories of thought or conception.
Frege™s senses (or more accurately but awkwardly, “graspings” of
these) are his “intermediaries,” given our gloss, for beliefs about the
world. Graspings of senses of the kind Frege calls “thoughts” are what
stand between mind and world, making errors in thought possible when
harnessed by mental acts of assertion. Also, senses are what move the
mind, as vehicles should. Differences among various grasped senses ac-
count for differences in mental movement if the mind is rational. Senses
also actually constitute a level of intentional content “ they are inten-
tional contents “ just as Peacocke™s intermediary for perception has not
only “sensational properties” but also “representational properties” (Sec-
tion 8.5), and just as Goodman™s qualia, if freed from phenomenalism,
would serve both as vehicles for visagings of the ordinary world and as
things that are themselves visaged (Section 8.7). But let us put the lat-
ter feature of Fregean senses aside for the moment and consider them
merely in their role as vehicles for reference to the world.
Frege certainly did not explicitly intend to project properties of
things as thought of “ call these “conceptually visaged properties” “
upon his intermediaries. Contrast Hume, who took thoughts to be
copies of impressions, themselves clearly picture-like. Frege™s senses are
modeled, very abstractly, on sentences and sentence parts, not pictures.
Given this model, the only internalizing/externalizing games that can
still be played are with sameness and difference.

3 I am no Frege scholar. I speak here to the understanding philosophers have mostly had of
Frege, not to his texts.

First, Frege externalizes sames, hence internalizes differents (Section
8.7). That is, he assumes that if the vehicles are the same “ that if the
senses grasped are the same “ then the referents are the same. Grasping
a sense is a way of conceptually visaging something. And the way of vis-
aging is not separable from the thing visaged. One cannot visage two
different things in the same way. Repeating a way of visaging also re-
peats the thing visaged.
Is any alternative to such a view possible? Is it possible not to exter-
nalize sames in the case of thoughts? In Chapter 10, I will argue that
there are many alternatives to externalizing sames. Here let me suggest
just an analogy. In natural language, sames are not always externalized.
The pronoun “he” might stand for any male person. Also, there are lots
and lots of people named “Jane.” But the issue is complex. I will discuss
it in Chapters 10 and 11.
If sames are externalized as Frege does, and then senses or ways of
visaging are taken to be transparent to mind, the immediate result is in-
ternalism concerning thought content. Thus Frege™s senses determine
their own referents, each distinguishing its referent from all other things,
and nothing external to what is grasped within the mind is relevant to
this determination. This view contrasts sharply with the thesis of this
book. Suppose that Frege is right to externalize sames. Suppose that it
is a psychological fact that human conceptual systems are designed to
use the same vehicle again only to represent the same content again.
Still, what the human cognitive systems were designed to do and what
they in fact manage to do would be two separate things. Mistakes in
reidentification are surely possible, in which case the same vehicle again
may not represent the same content again.
Frege externalizes not only sames but also sameness. If senses are the
same, then the corresponding referents are necessarily conceptually vis-
aged as same, or necessarily available to the rational mind as same. That
is why the rational mind cannot take contrary intentional attitudes to-
ward referents conceptually visaged under the same mode of presenta-
tion. And that is why identity judgments are uninformative when the
sense of subject and predicate terms is the same. It follows, of course,
that whenever referents are not conceptually visaged as same, the corre-
sponding senses are always different. And in accord with the demand for
consistency in content, when referents are visaged as different they are
not also visaged as same, hence, senses are again different.
The thesis that grasped senses™ merely being the same is equivalent
to visaging their referents as the same is the passive picture theory of

cognitive grasp of identity and a form of the repetition view of the
act of reidentifying. I will discuss alternatives to this view in the next
two chapters. Here let me merely note that if one adds to the exter-
nalization of both sames and sameness the assumption that senses or
ways of visaging are transparent to mind, the result is that where
senses are the same, sameness of reference in thought is known a pri-
ori and with certainty. This particular Fregean thesis might be viewed
as the central target of this book. If I accomplish nothing else, I
should like at least to make clear that this thesis is a substantive claim,
not a necessary truth.
Frege externalizes sames and sameness but, like Goodman, he does
not externalize either differents or difference. Referents may be taken to
be the same even though the grasped senses are different. For example,
this is how the thoughts Cicero and Tully are related for one who knows
that Cicero is Tully. Where senses are different, their referents may be
conceptually visaged either as same or as different, or neither visaged as
same nor as different. Since difference is not externalized, failure to vis-
age difference is not internalized nor, in accord with the demand for
consistency in content, is sameness internalized. Conceptual visaging of
sameness can be accomplished actively through identity judgments as
well as passively through sameness in grasped sense. Identity judgments
can visage sameness of reference despite difference in sense.
On the other hand, Frege introduces a second level of content (like
Peacocke and our nonphenomenalist version of Goodman) onto which
he projects sames, sameness, differents, and difference, indeed, on which
no distinctions at all are drawn between content and vehicle. The sense
contents in Ayer™s Language, Truth and Logic were like Frege™s senses in
this way.They were their own intentional objects, lying passively within
awareness and being visaged (intended) by mind in the same act. For
Frege, differences in vehicle, differences in sense, become differences in
content on this second level. Senses are intentional contents. On this
level, thought forms an ideal vehicle, nonredundant and unambiguous,
one thought one content, one content one thought. The fact of same-
ness or difference in content can be read off the sameness or difference
of thoughts and vice versa. Thus for the rational thinker no misidentifi-
cations of thought content should ever occur. Contradictions show up
right on the surface of thought so that no inconsistencies should occur
either. The relation between thought and its content is perfectly trans-
parent, indeed, it entirely disappears. There is no vehicle moving the
mind but the very content itself.

Why does Frege introduce a second level of content onto which dif-
ferents and difference can be projected in this way? What happened in
Frege™s mind is clearly documented. First, he saw that in the case of dif-
fering definite descriptions referring to the same there was a way in
which they did, but another in which they didn™t, have “the same con-
tent.” They referred to the same thing, but they got there by different
routes and from different starting points, from initially different visag-
ings of referents. They made their contributions to truth values in
different ways. But this does not give us a distinction among levels of
content for the starting points, or not without regress. It does not give
us a difference in content between the thought Tully and the thought
Cicero, for example.Why then did Frege generalize? Why did he project
two levels of content upon apparently simple thoughts?
Frege™s second move is continually rehearsed in the literature. Cicero
is Tully is an informative thought whereas Cicero is Cicero is not, so these
thoughts must have different contents. But, quite transparently, that begs
exactly the question at issue. Of course the thoughts corresponding to

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