carney 1981_wittgenstein's theory of picture representation

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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-







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







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







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








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







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








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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