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Wittgenstein's Theory of Picture Representation
Author(s): James D. CarneySource: The Journal of Aesthetics and Art Criticism, Vol. 40, No. 2 (Winter, 1981), pp. 179-185Published by: Wiley on behalf of The American Society for Aesthetics
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JAMES D. CARNEY
Wittgenstein sh e o r y o
i c t u r e Representation
WHAT SIT for one thing to be a picture ofanother thing? It seems that most paintingsand pictures represent or depict things. For
example, a Georgia O'Keeffe painting rep-resents or depicts a cow's skull, or Cezanne'sThe CardPlayers representsor depicts threemen playing cards. What must be true fora picture P to represent or depict x? Andof what
importancefor art criticism and art
appreciation is this question? In this paperI will outline and defend the theory of pic-ture representation found in Ludwig Witt-
genstein's early work, Tractatus Logico-
Philosophicus.1As Nelson Goodman has remarked, Noth-
ing is intrinsically representational; statusas representational is relative to symbol sys-tems. 2 Attempts to answer the questionwhat it is for a picture to depict somethingthat do not posit rules or conventions as
necessary for picture depiction seem opento grave objections. Max Black has reviewedsome of these attempts and has commented
effectively on their weaknesses.3 For exam-
ple, to suppose that P depicts x if and onlyif P imitates x or looks as if one is actuallyseeing x, Plato's view, is open to the objec-tion that most pictures that depict some-
thing do not look like what they depict.Monroe Beardsley proposes Ithat P repre-sents x if and only if P contains an area
that is more similar to the visual appearanceof x than to objects of any other class.4
JAMESD. CARNEYs professor of philosophy at Ari-
zona State University.
This view seems to imply that if P resemblesx more than anything else, then P representsx. But as Nelson Goodman and others have
pointed out, resemblance is a symmetricalrelation.5 That is, if P resembles x, then xresembles P. So if P depicts x if P resembles
x, then any tree, for example, representsany naturalistic picture of a tree. Also, noth-
ingresembles a
paintingso much as a re-
production of it, but a reproduction of P
does not depict P. Perhaps P represents x
if and only if the artist intends P to be
about x. But this view is also open to grave
objections. An artist's intentions may mis-
fire, so on this analysis P could depict x
even if nothing in the painting warrants us
to suppose it depicts x. Also even if some-
one, for example, puts a dot on paper and
intends this to be a picture of three men
playing cards, this is not sufficient for the
dot on the paper to depict three men play-
ing cards. No theory of representation can
be fully convincing unless it accommodates
or explains our intuition that not any pic-ture can represent or depict anything. Any
adequate theory of representation, it seems,
ought to accommodateour intuition that for
P to represent x some sort of resemblance
between P and x is needed.The recent promising attempts to analyze
representation, by Goodman and Kendall
Walton have made rules or conventions cen-tral to picture representation.6 Representa-tion or depiction is seen as something we do
with objects. So, independently of conven-
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CARNEY
tions, nothing could represent anything.But these promising attempts have been
justly criticized as having the consequencethat any picture can represent anything.7
The reason for this is that both Goodmanand Walton reject resemblance between a
depicting picture and what it depicts as a
necessary condition for depicting. Walton
writes that his theory does not itself postu-late any resemblance between pictures andwhat they depict. 8 Goodman writes that
the plain fact is that a picture, to representan object, must be a symbol for it, stand
for it, refer to it; and that no degree of
resemblance is sufficient to establish the req-uisite
relationshipof reference ... Denota-
tion is the core of representation and is
independent of resemblance. 9
Neither Goodman nor Walton considers
the abstract or formal kind of resemblance
that occurs when P has what Wittgensteincalls the logical form of x (2.18).10I be-
lieve that the best way to explain Wittgen-stein's theory of picture representation is by
making use of some simple diagrams.1'What
relation must exist between the diagram be-
low
Diagram 1.
and a cat being on a mat, for diagram 1 to
be a picture that depicts a cat on a mat?12
Wittgenstein rejectsthe answer that a pic-
ture must look like a cat on a mat. And
he should, since surely a picture can depict
x without looking like x. For example, dia-
gram 2
Diagram 2.
does not look like a cat on a mat, yet it can
depict a cat on a mat. How? We can tak:the square to stand for a mat, the circle tostand for a cat, and the relation betweenthe circle and the square in the diagram tostand for x being physically on y.
We may be inclined to say that thoughdiagram 2 could depict a cat on a mat ifwe suppose appropriate rules, diagram 1
just naturally depicts a cat on a mat withoutour having to suppose any rules at all, sinceit looks like a cat on a mat. This accountis also rejected by Wittgenstein. On his
analysis of picture depiction, rules are sup-posed if a picture is to depict. Rules arethus supposed with diagram 1 if it depicts,but the rules we suppose with diagram 1
are simply better known and more easilyread from the picture. If we make explicitthese better known rules, what would theylook like? We take diagram 1 to depict howa cat on a mat might look from such-and-
such a perspective, thus stands
for the mat (a rule), for the
cat (a rule), and the relations in the diagramstand for the relations we could see from a
certain perspective if we looked at a cat on
a mat (additional rules).Let us consider another diagram consist-
ing of a dot with no other distinguishable
parts:
180
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Wittenstein's Theory
.
Diagram3.
Let us not count the space enclosed aroundthe dot as a part of the picture. For Witt-
genstein diagram 3 cannot represent or de-
pict a cat on a mat, for, according to his
theory, we need at least two distinguishableparts and a relation between the parts inorder to establish the appropriate rules. Ac-
cording to Wittgenstein, diagram 3 lacksthe needed logical multiplicity to repre-sent or depict a cat on a mat. Even if dia-
gram 3 cannot represent a cat on a mat,a part of a picture may in fact be a dot
which represents a cat on a mat, but onlyin the context of the whole picture. For
example, a picture can include a series of
pictorial representations of cats reclining on
mats and becoming smaller and eventually
fading off into the far distance, appearingas a dot at the end of the series. In such a
context, a dot can represent a cat on a mat.13
However, such a part of a pictorial structure
canacquire representational
statusonly
from
the context provided by the entire composi-tion. On any theory of picture representa-tion, including Wittgenstein's, the theory is
about whole picture depiction.The theory of pictorial representation
which emerges from these examples may be
simply stated as follows: A picture repre-sents or depicts a subject when and onlywhen the parts of the picture have the same
logical multiplicity as the parts in the sub-
ject represented, and appropriate rules are
assumed relating picture parts and relationsto the parts and relations of the subject
represented. (Wittgenstein calls these ruleslaws of projection [4.0141].) Representa-
tion in pictures, on the theory of Wittgen-stein, is, in part, a function of conventions,and is, in
part,a function of what is
found,so to speak, in nature. That is, natural ob-
jects and artifacts provide Wittgenstein'stheoretically required multiplicity in P forP to represent x. Wittgenstein uses the ex-
pression logical form in the statement ofhis theory. What any picture, of whatever
form, must have in common with reality,to be able to depict it . . . is logical form.
(2.18) Logical pictures can depict theworld. (2.19) Simply put: P can representor depict x if and only if P has the same
logical form as x. A P does represent ordepict x when we choose a set of rules whichcorrelate the elements and relations of xwith elements and relations of P. It is mis-
leading and inaccurate to state Wittgen-stein's theory of representation simply inthese terms: P represents or depicts x if and
only if P has the same logical form as x.For a picture can depict any reality whoseform it has (2.172). Thus diagram one can
depict a cat on a mat or a pink elephant
on a cloud or a cloud on a pink elephant,depending on how we choose to set up the
rules. Nelson Goodman in his review of
E. H. Gombrich's Art and Illusion suggeststhat with suitable principles of correlation,
Constable's landscape painting could pro-vide an enormous amount of informationabout a pink elephant. 14 On Wittgenstein'stheory, if we suppose such rules, Constable's
landscape would represent a pink elephant.It is worth noting that on Wittgenstein's
theory, representationis not a
symmetricalrelation. For the chosen rules typically cor-
relate elements of P to elements of x and
not vice versa.
Categories of art, in a Wittgenstein analy-sis of representation, would be construed as
different sets of rules or conventions. Imag-ine a cat on a mat as it would be depictedin a Fifth-dynasty Egyptian style, or as it
would be depicted in an analytical Cubist
painting. The Egyptian painting would be
strongly linear, where the artistic image is
an assembly of the most obvious parts ofcats and mats. Here the elements in the
181
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182
picture are taken to stand for objects and
relations as known rather than as they ap-
pear. In the Cubist painting the three di-
mensional cat and mat is reduced to two di-
mensional shapes, where a caton a mat
isshown from more than one viewpoint at
one time and where aspects,especially angu-
lary aspects of cats and mats, are empha-sized. It is easy to see the rules involved if
we construe the Cubist style within the
Wittgenstein theory.
Representation is creative, rather than
imitative, on Wittgenstein's theory of rep-resentation. The artist must either supposesome system of conventions or modify or
create new conventions. In turn the viewer
needs to understand the historical conven-tions to grasp what is depicted in a picture.
Many who first see a Cubist portrait do not
realize that the squarish shapes no more
represent angularity of facial structure than
do the thin sculptured figuresof Giacometti
represent very thin and very long bodies.
Understanding rules in representation is like
learning a new language. And often when
one learns new rules the viewer may notice
aspects and features of subjects that he may
never have noticed before. By employingnew rules for representation the artist can
alter our perception of the world, can getus to notice certain features that we mayhave overlooked. In short, many by now
commonplace insights about art find sup-
port in Wittgenstein's theory.Even though Wittgenstein's analysis of
picture-depicting may have certain attrac-
tions, is it not also open to grave objections?It does have its difficulties, but, I believe,
none of them are fatal. I will now brieflyconsider some objections to the theory. Ob-
jection one: It is implausible to say that
we follow rules or conventions with respectto pictures like diagram one where the pic-ture looks like what it depicts. Perhaps rules
are supposed in Cubism and Egyptian art,
but not in imitative art. The reply that can
be given to this objection is that look-alike
pictures are as conventional as any other
sort of picture. It is merely that the con-
ventionsgoverning
such pictures are better
known and more easily read than with
Egyptian or Cubist art. As part of our West-
ern cultural inculcation, we take diagram
CARNEY
one as imitative and thus take the relationsin diagram one to stand for relations we see
when we view a cat on a mat from a certain
perspective. It is natural to think that there
are no rules since we have neverthoughtof any rules in our recognizing what is de-
picted in imitative pictures. They have been
internalized as part of cultural condition-
ing. But following a rule need not be an
explicit, conscious act. A regularity in ac-
tion can be convention-following behavior
without the convention needing to be con-
sciously thought, if certain conditions are
fulfilled. David Lewis has outlined such con-
ditions in his Convention.15 Briefly and
roughly, a regularity in behavior, R, is a
convention for members of a population,P, if the behavior of members of P con-
forms to R, if members of P expect others
to conform to R, and if members of P preferto conform to R.
Second objection: The Wittgensteinian
analysis of picture depiction is circular or
incomplete since it supposes an unanalyzedstand for relation with respect to rules
connecting elements and relations between
a depicting picture and the thing depicted.
The analysis is not circulzr since the standfor relation is not same logical form but
rather a denotational relation, the kind of
relation that exists, for example, between
the word cat and cats. And this relation
seems unproblematical in the context of art
theory.Third objection: An adequate theory of
picturing should not exclude representingan object with a nonrelational or monadic
property, for example, blackness. As the
theory is characterizedabove, properties rep-resented by a picture must be relations
among the parts of x. This seems to rule
out representing monadic relations such as
x is black, and surely no such theory of
picture representation is adequate. Wilfrid
Sellars has proposed that the picture theoryof propositions can accommodate such rep-resentation (and thus the Tractatus need not
be committed to bare particulars).16Apply-
ing this to pictures, we need to suppose pro-
jection rules which correlate a monadic
property of a part of the picture with amonadic property of x. This can be done,
for example, by correlating the black of a
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Wittenstein's Theory
square with the black of the cat, or a styleof painting the square with the black of the
cat-say thick, dark lines. And a simple and
obvious restatement of the explication of
representation on page 181 would accom-modate such monadic representation.Fourth objection: For a depicting picture
and what it depicts, is having the same
logical form or same anything really needed?After all, we can have cases of P depictingx but misdepicting or misrepresenting x.
For example, a portrait of Washingtonwhich depicts him may represent a stylizedCaesar with hardly any resemblance at all
to Washington. A portrait of Washingtonneed not have a likeness-that is, it
mayattribute any number of qualities to Wash-
ington which Washington did not have. But,
again, can anything be a picture of Wash-
ington? If human intentions were sufficient
for a picture to depict its subject, then any-
thing can represent the subject. But, as ar-
gued earlier, this view of representation is
open to grave objections. It seems that some
minimal sameness or resemblance is needed
for a picture to depict Washington, and the
same logical form provides the absolute
minimal sameness. In addition, this mini-mal sameness is sufficiently flexible so that
almost anything can represent anything so
long as it meets the logical multiplicity re-
quirement.Fifth objection: A depicting picture may
have the same logical multiplicity as the
subject depicted, and yet it is usually the
case that both the picture and the subject
depicted have further discernible parts. For
example, diagram one represents a cat on
a mat, yet cats have claws while the picture-cat has no claws. Also, we can discern that
the picture-cat is located a certain distance
from the diagram frame, yet this is not true
of the subject of diagram one. So how does
one determine which parts and relations of
the picture are components of logical form
-and which parts of the subject depictedare parts of logical form? The answer is
that the viewer needs to single out whatever
feature or features the depictor desires. An
audience learns what features of apictureand depicted subject are relevant by know-
ing the rules assumed by the artist. We
thus need to come to understand the rules
183
supposed (the art category) when the pic-ture is produced. If in order to properly
appreciate a depicting picture one must
know what it depicts, then to properly ap-
preciate a depicting picture, one must un-derstand the category of art in which the
picture was produced. These last remarks
should not be taken to suggest that one is
somehow cut off from appreciating a work
of art unless one knows its correct historical
art category. Art criticism can be equallycreative as art production in that the art
critic can implicitly or explicitly supposenew rules in interpreting the art, and in
this way construe P as depicting somethingthat it does not
depict, supposinghistorical
rules. In this way there can be more in a
work of art than the artist might have imag-ined.
Sixth objection: The Tractatusaccount of
picturing is intended to show how languageworks. The picture theory of the Tractatus
covers pictures and representations of all
sorts. But will it do to talk about representa-tion in art in the same terms as technical
drawings, diagrams, language, and all these
other things? E. H. Gombrich in Art and
Illusion proposed that P represents or de-picts x when P is a kind of illusion for x
where no error in belief occurs. That is, for
Gombrich P depicts x where one can seeP as x. When Gombrich uses the term illu-
sion he is referring to the seeing-as phe-nomenon. Illusion is, of course, the typicalkind of depiction that occurs in objectiveart. Wittgenstein in the Philosophical In-
vestigations suggests that seeing-as typicallyinvolves both seeing and thinking. In a key
passage he writes: What I perceive in thedrawing of an aspect is not a property of
the object, but an internal relation between
it and other objects. 17When things appearas if they have to be connected, this shows
that we are bringing them under a rule, and
we have an internal relation. So rules are
seen as necessary for certain kinds of visual
experience. If rules are to be brought in
for Gombrich type illusions, then the kind
of representation connected with ordinary
objectiveart is subsumed under the kind of
representation found in diagrams, language,and many other nonart t)pe representation.
Final objection: How is Wittgenstein's
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CARNEY
analysis of picture depicting important for
art criticism? The important consequencesfor art criticism that follow from Wittgen-stein's analysis are the same that follow
from anyrule
analysisof
picture depictingsuch as Nelson Goodman's and Kendall
Walton's. For example, one cannot dismiss
unfamiliar pictures as not depicting any-
thing. The unfamiliar picture may be a de-
picting picture, but the conventions maynot be widely known or not easily read from
the picture. Since an important element in
the proper appreciation of a depicting pic-ture is to understand what is depicted, one
may be cut off from proper appreciation of
unfamiliar
pictures
unless one can come to
understand the supposed conventions (itsart category). Consider abstract expression-ism, for example, Jackson Pollack's Number
12. For many of us, this painting does not
seem to be a depicting painting. Yet Pollack
reports that when he poured the paints for
such a painting he allowed his hands to
wander freely across the surface of his can-
vas, permitting himself to be directed byinner impulses. His method of painting was
his way to express his basic emotions in the
most vivid and direct way that he could.If our basic emotions have a logical multi-
plicity, then one could interpret Number 12
as an attempt at depicting emotions on
Wittgenstein's analysis of picture represen-tation. For Susanne K. Langer a work of
art is an expressive form where what is ex-
pressed is human feelings. A work of art
expresses a feeling, for Langer, when it is
an iconic symbol for a feeling. Her account
of expressive form is, or should be, Witt-
genstein's account of logical form.'8 Wheth-er it is intelligible to think of emotions as
having the requisite logical multiplicity is
a question I will not go into in this paper.Some recent work in psychology suggeststhat it may be plausible to regard emotions
as having the needed logical multiplicity.19Even so, one is left with the puzzling pros-
pect that there is a method of rule projec-tion that could decode a Jackson Pollack's
painting. In any case Wittgenstein's theoryof
picturerepresentation first opens up the
intriguing possibility that nonobjective artcan be, after all, representational art. Sec-
ond, on his theory the difference between
expression and representation could be lo-
cated in terms of what is represented.Though Goodman writes that no degree
of resemblance is necessary for a picture to
representor
depict x,he also adds that al-
most anything can represent anything.
Why, for Goodman, cannot anything rep-resent anything? According to Goodman,the distinguishing mark of pictures, as con-
trasted with symbol systems in language, is
density. 20 A scheme, according to Good-
man, is dense if it provides for infinitely
many characters so ordered that between
each two there is a third. 21 On this ac-
count if a depicting scheme is dense, as pic-tures are for Goodman, differences in pic-torial aspectsmake a difference with respectto what is depicted. For example, the dif-
ferences in size, color, and spatial relations
make no difference in symbols used in lan-
guage-only same spelling matters-but such
differencescan be relevant in representation.To have a dense symbol system, one needs
rules connecting a dense set of elements
with denotata; though the rules may not
result in an actual denotata for the sym-bols.22We need now merely add that some
elements in a dense set are relations in orderfor it not to be the case that anything can
represent anything, and, interestingly in
order to obtain same logical form and
thus a minimal resemblance between pic-tures and what they depict.
Walton construes picture depicting in
terms of make-believe games. As children
make-believe that a stone in a pile of mud
is a pie with a raisin in it, so when a pictureis regarded as depicting x we in a make-
believe way see x when welook at the
pic-ture. But in either case such make-believe
presupposes rules or conventions. It is nec-
essary for the children to let the stone stand
for a raisin and the mud to stand for a pie.So for different categories of art there would
be supposed different sets of rules in order
to make the make-believe seeing possible.Walton writes that P-depicting does not
require P-resemblance but that some rules
of make-believe are more natural, simpler,and easier to learn, remember, and inter-
nalize, and more likely to be adopted (ex-plicitly or otherwise) than others if P re-
sembles x.23 So, to use his examples, the
184
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Wittenstein's Theory
rule that the pie contains a raisin if the
glob of mud contains a pebble is just morenatural than the rule that the pie containsa raisin if the glob does not contain a
pebble or the rule that the pie contains araisin if the glob of mud is light-colored.No doubt in the latter two cases there is anabsence of visual P-resemblance. Bult, nev-
ertheless, the mud has the needed logicalmultiplicity and with appropriate rules hasthe same logical form as what it depicts-a pie with a raisin. In the latter case thereis the mud glob and color, while in theformer case there is the glob and there isa pebble-free glob. Nothing Walton writes
providesa reason to think that P-resem-
blance in the formal, abstract sense of same
logical form need not be present for his
P-depicting. And each of his examples canbe construed as having P-resemblanceof the
Wittgenstein kind.In recent literature, conventional or rule
theories of how a depicting picture depictshave received a great deal of attention. Suchtheories have interesting consequences for
art criticism and appreciation. However, a
difficulty found in these theories is that theyappear to have the consequence that any
picture can depict or represent anything.Wittgenstein's analysis of picture depictingin the Tractatus is an analysis where rulesor conventions play a key role that avoidsthis consequence. On this analysis of picturerepresentation, same logical form, a mini-
mal, abstract kind of nonimitative resem-
blance, is required between a depicting pic-ture and what it depicts in order for the
picture to depict or represent.
Ludwig Wittgenstein, Tractatus Logico-Philo-sophicus (London, 1961).
2Nelson Goodman, Languages of Art (Indianap-olis, 1968), p. 226.
3 Max Black, How Do Pictures Represent, E. H.Gombrich, Julian Hochberg, and Max Black, Art,Perception, and Reality (The Johns Hopkins Uni-
versity Press, 1970), pp. 95-129.4Monroe Beardsley, Aesthetics (New York, 1958),
p. 270.
Languages, op. cit., p. 4.8 Kendall Walton, Pictures and Make-Believe,
Philosophical Review, vol. 32, no. 3 (1973), 283-319.7W. E. Kennick makes this criticism in Art and
Philosophy, 2nd ed. (New York, 1979), pp. 379-80.8Ibid., p. 226.
185
9Languages, op. cit., p. 5.
10Wittgenstein's account of picture depicting is
found in 2.12-2.19 of the Tractatus. Important clar-
ifying remarks and examples are found in his 1929
paper, Some Remarks on Logical Form, Aristote-
lean Society Supplementary, vol. 9, Knowledge, Ex-perience, and Realism (London, 1929), pp. 162-71.
11Jay F. Rosenberg in an excellent article on
Wittgenstein's picture theory of language makes useof such diagrams to explain the theory, Wittgen-stein's Theory of Language, American Philosoph-ical Quarterly, vol. 5, no. 1 (January, 1968), 18-30.
12Wittgenstein's theory of picture representation,like the theories mentioned earlier, are attempts to
give an account of what obtains when a picture rep-resents or depicts something. But, as almost allwriters on this subject have pointed out, saying whata picture depicts or represents is highly ambiguous.Sometimes we state what kind of picture P is. Some-
times we state that P denotes something. There arepictures of centaurs, but there are no actual cen-taurs to picture. Many pictures of cats are such thatthere are no cats which they picture. For example,Andre Masson's The Cat is not a picture of anyactual cat, but it is correctly described as a pictureof a cat. When one says that P is a picture of x, wesometimes suppose that there is an actual x, andsometimes we do not. If a picture is a picture ofsome actual existing x, we can say it denotes x. If a
picture is a picture of a cat in the sense in whichits being a picture of a cat does not depend on there
being an actual cat which it pictures, we can say Pis a cat-depicting picture. Theories of representa-tion, including Wittgenstein's theory, are primarilyconcerned with representation in the sense of pic-ture kind, x-depicting pictures, for, presumably, the
analysis of P denoting x presupposes that P is an
x-depicting picture. That is, to say that P denotes xwould be at least to say that P is an x-depictingpicture and x actually exists.
'1This example appears in Robert Howell's Or-
dinary Pictures, Mental Representations, and Log-ical Forms, Synthese, 33 (1976), 149-74.
14Nelson Goodman, Review of Gombrich's Artand Illusion, The Journal of Philosophy (Septem-ber, 1960), 598.
'1 David Lewis, Convention: APhilosophical Study(Harvard University Press, 1969), p. 42.
6Wilfrid Sellars, Naming and Saying, Philos-
ophy of Science, vol. 29, no. 1 (1962), 7-26.7 Ludwig Wittgenstein, Philosophical Investiga-
tions (New York, 1958), p. 212.1 Susanne K. Langer, Problems of Art (London,
1957).1 Michael M. Piechowski, The Logical and the
Empirical Form of Feelings, The Journal of Aes-thetic Education (January, 1981).
2oLanguages, op. cit., pp. 225-28.21Ibid., p. 136.
Ibid., p. 228.23
Pictures, op. cit., p. 318.I wish to thank this journal's referee for some
valuable corrections and for raising several objec-tions that I try to meet in this paper.
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