Wittgenstein's Theory of Picture Representation James D. Carney The Journal of Aesthetics and Art Criticism, Vol. 40, No. 2. (Winter, 1981), pp. 179-185. Stable URL: http://links.jstor.org/sici?sici=0021-8529%28198124%2940%3A2%3C179%3AWTOPR%3E2.0.CO%3B2-D The Journal of Aesthetics and Art Criticism is currently published by The American Society for Aesthetics.
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J-4MES D. CARNEY
Wittgenstein 's Theory of
Picture Representation
WHATIS IT for one thing to be a picture of another thing? I t seems that most paintings and pictures represent or depict things. For example, a Georgia O'KeeHe painting represents or depicts a cow's skull, or Cezanne's T h e Card Players represents or depicts three men playing cards. What must be true for a picture P to represent or depict x? And of what importance for art criticism and art appreciation is this question? In this paper I will outline and defend the theory of picture representation found in Ludwig Wittgenstein's early work, Tractatus Logico-
philosophic us.^ As Nelson Goodman has remarked, "Nothing is intrinsically representational; status as representational is relative to symbol systems."z Attempts to answer the question what it is for a picture t o depict something that do not posit rules or conventions as necessary for picture depiction seem open to grave objections. Max Black has reviewed some of these attempts and has commented effectively on their weaknesses.3 For example, to suppose that P depicts x if and only if P imitates x or looks as if one is actually seeing x, Plato's view, is open to the objection that most pictures that depict something d o not look like what they depict. Monroe Beardsley proposes that P represents x if and only if P contains an area that is more similar to the visual appearance of x than to objects of any other class.4 D . CARNEY is professor of philosophy at Ari. zona State University.
JAMES
This view seems to imply that if P resembles x more than anything else, then P represents x. But as Nelson Goodman and others have pointed out, resemblance is a symmetrical relation.5 T h a t is, if P resembles x, then x resembles P. So if P depicts x if P resembles x, then any tree, for example, represents any naturalistic picture of a tree. Also, nothing resembles a painting so much as a reproduction 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 misfire, so on this analysis P could depict x even if nothinq in the painting warrants us to suppose it depicts x. Also even if someone, 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 playing cards. No theory of representation can be fully convincing unless it accommodates or explains our intuition that not any picture can represent or depict anything. Any adequate theory of representation, it seems, ought to accommodate our intuition that for P to represent x some sort of resemblance between P and x is needed. T h e recent promising attempts to analyze representation, by Goodman and Kendall Walton have made rules or conventions central to picture representation.6 Representation or depiction is seen as something we do with objects. So, independently of conven-
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tions, nothing could represent anything. But these promising attempts have been justly criticized as having the consequence that any picture can represent anything.' T h e reason for this is that both Goodman and 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 postulate any resemblance between pictures and what they depict."g Goodman writes that "the plain fact is that a picture, to represent an object, must be a symbol for it, stand for it, refer to it; and that no degree of resemblance is sufficient to establish the requisite relationship of reference . . . Denotation 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 Wittgenstein calls the "logical form" of x (2.18).10 I believe that the beat way to explain Wittgenstein's theory of picture representation is by making use of some simple diagrams." What relation must exist between the diagram below
1
1
Diagram 1. and a cat being on a mat, for diagram 1 to be a picture that depicts a cat on a mat?lz Wittgenstein rejects the answer that a picture must look like a cat on a mat. And he should, since surely a picture can depict
x without looking like x. For example, diagram 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 tc. stand for a cat, and the relation between the circle and the square in the diagram to stand for x being physically on y. We may be inclined to say that though diagram 2 could depict a cat on a mat if we suppose appropriate rules, diagram 1 just naturally depicts a cat on a mat without our having to suppose any rules at all, since it looks like a cat on a mat. This account is also rejected by Wittgenstein. On his analysis of picture depiction, rules are supposed if a picture is to depict. Rules are thus supposed with diagram 1 if it depicts, but the rules we suppose with diagram 1 are simply better known and more easily read from the picture. If we make explicit these better known rules, what would they look like? We take diagram 1 to depict how a cat on a mat might look from such-andstands such a perspective, thus for the for the mat (a rule), cat (a rule), and the relations in the diagram stand 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 consisting of a dot with no other distinguishable parts:
Q~
Wittenstein's Theory represented. (Wittgenstein calls these rules "latvs of projection" [4.0141].) Representation in pictures, on the theory of Wittgenstein, 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 objects and artifacts provide IVittgenstein's theoretically required multiplicity i n P for P to represent x. Wittgenstein uses the expression "logical form" in the statement of his 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 the world." (2.19) Simply put: P can represent Diagram 3. or depict x if and only if P has the same logical form as x. A P does represent or Let us not count the space enclosed around depict x when we choose a set of rules which the dot as a part of the picture. For IVitt- correlate the elements and relations of x genstein diagram 3 cannot represent or de- with elements and relations of P. It is mispict a cat on a mat, for, according to his leading and inaccurate to state Wittgentheory, we need at least two distinguishable stein's theory of representation simply in parts and a relation between the parts in these terms: P represents or depicts x if and order to establish the appropriate rules. Ac- only if P has the same logical form as x. cording to IVittgenstein, diagra~n 3 lacks For a picture can depict any reality whose the needed "logical multiplicity" to repre- form it has (2.172). T h u s diagram one can sent or depict a cat on a mat. Even if dia- depict a cat on a mat or a pink elephant gram 3 cannot represent a cat on a mat, on a cloud or a cloud on a pink elephant, a part of a picture may in fact be a dot depending on how we choose to set u p the which represents a cat on a mat, but onl) rules. Nelson Goodman in his review of in the context of the whole picture. For E. H. Gombrich's Art and IIlusion suggests example, a picture can include a series of that with suitable principles of correlation, pictorial representations of cats reclining on "Constable's landscape painting could promats and beconling smaller and eventually vide an enorlrlous amount of information fading off into tlie far distance, appearing about a pink elephant." 13 On IVittgenstein's as a dot at the end of the series. I n such a theory, if we suppose such rules, Constable's context, a dot can represent a cat on a mat.13 landscape would represent a pink elephant. However, such a part of a pictorial structure It is worth noting that on Ilrittgenstein's can acquire representational status only from theory, representation is not a synlmetrical the context provided by the entire composi- relation. For the chosen rules typically cortion. O n any theory of picture representa- relate elenlents of P to elements of x and tion, including Wittgenstein's, the theory is not vice versa. Categories of art, in a Ilrittgenstein analyabout whole picture depiction. T h e theory of pictorial representation sis of representation, would be construed as which emerges from these examples may be different sets of rules o r conventions. Imagsimply stated as follows: ,2 picture repre- ine a cat on a mat as it would be depicted sents or depicts a subject when and only in a Fifth-dynasty Egyptian style, or as it when the parts of the picture have the same would be depicted in an analytical Cubist logical multiplicity as the parts in the sub- painting. T h e Egyptian painting would be ject represented, and appropriate rules are strongly linear, where the artistic image is assumed relating picture parts and relations an assembly of the most obvious parts of to the parts and relations of the subject cats and mats. Here the elements in the
a
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picture are taken to stand for objects and one as imitative and thus take the relations relations as known rather than as they ap- in diagram one to stand for relations we see pear. I n the Cubist painting the three di- when we view a cat on a mat from a certain mensional cat and mat is reduced to two di- perspective. It is natural to think that there mensional shapes, where a cat on a mat is are no rules since we have never thought shown from more than one viewpoint at of any rules in our recognizing what is deone time and where aspects, especially angu- picted in imitative pictures. 'I'hey have been lary aspects of cats and mats, are empha- internalized as part of cultural conditionsized. I t is easy to see the rules involved if ing. But following a rule need not be an we construe the Cubist style within the explicit, conscious act. A regularity in acWittgenstein theory. tion can be convention-following behavior Representation is creative, rather than without the convention nzeding to be conimitative, on Miittgenstein's theory of rep- sciously thought, if certain conditions are resentation. T h e artist must either suppose fulfilled. David Lewis has outlined such consome system of conventions or modify or ditions in his Convention.1s Briefly and create new conventions. In turn the viewer roughly, a regularity in behavior, R, is a needs to understand the historical conven- convention for members of a population, tions to grasp what is depicted in a picture. P, if the behavior of members of P conMany who first see a Cubist portrait do not forms to R, if members of P expect others realize that the squarish shapes no more to conform to R, and if members of P prefer represent angularity of facial structure than to conform to R. do the thin sculptured figures of Giacometti Second objection: T h e Wittgensteinian represent very thin and very long bodies. analysis of picture depiction is circuIar or Understanding rules in representation is like incomplete since it supposes an unanalyzed learning a new language. And often when "stand for" relation with respect to rules one learns new rules the viewer may notice connecting elements and relations between aspects and features of subjects that he may a depicting picture and the thing depicted. never have noticed before. By employing T h e analysis is not circulzr since the "stand new rules for representation the artist can for" relation is not same logical form but alter our perception of the world, can get rather a denotational relation, the kind of us to notice certain features that we may relation that exists, for example, between have overlooked. I n short, many by now the word "cat" and cats. And this relation commonplace insights about art find sup- seems unproblematical in the context of art port i n ItTittgenstein's theory. theory. Third objection: An adequate theory of Even though Tvittgenstein's analysis of picture-depicting may have certain attrac- picturing should not exclude representing tions, is it not also open to grave objections? an object with a nonrelational or monadic It does have its difficulties, but, I believe, property, for example, blackness. As the none of them are fatal. I will now briefly theory is characterized above, properties repconsider some objections to the theory. Ob- resented by a picture must be relations jection one: It is implausible to say that among the parts of x. This seems to rule we follow rules or conventions with respect out representing monadic relations such as to pictures like diagram one where the pic- x is black, and surely no such theory of ture looks like what it depicts. Pel-haps rules picture representation is adequate. Wilfrid are supposed in Cubism and Egyptian art, Sellars has proposed that the picture theory but not in imitative art. T h e reply that can of propositions can accommodate such r e p be given to this objection is that look-alike resentation (and thus the Tractatus need not pictures are as conventional as any other be committed to bare particulars).l6 Applysort of picture. I t is merely that the con- ing this to pictures, we need to suppose proventions governing such pictures are better jection rules which correlate a monadic known and more easily read than with property of a part of the picture with a Egyptian or Cubist art. As part of our West- monadic property of x. This can be done, ern cultural inculcation, we take diagram for example, by correlating the black of a
Wittenstein's Theory square with the black of the cat, or a style of painting the square with the black of the cat-say thick, dark lines. And a simple and obvious restatement of the explication of "representa~tion"o n page 181 would accommodate 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 depicting x but misdepicting or misrepresenting x. For example, a portrait of Washington which depicts him may represent a stylized Caesar with hardly any resemblance at all to 'CVashington. A portrait of Washington need not have a likeness-that is, it may attribute any number of qualities to Washington which IVashington did not have. But, again, can anything be a picture of Washington? If human intentions were sufficient for a picture to depict its subject, then anything can represent the subject. But, as argued earlier, this view of representation is open to grave objections. It seems that some rninimal sameness or resemblance is needed for a picture to depict Washington, and the same logical form provides the absolute minimal sameness. I n addition, this minimal sameness is sufficiently flexible so that almost anything can represent anything so long as it meets the logical multiplicity requirement. 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 picturecat 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 depicted are parts of logical form? T h e answer is that the viewer needs to single out whatever feature or features the depictor desires. An audience learns what features of a picture and depicted subject are relevant by knowing the rules assumed by the artist. We thus need to come to understand the rules
supposed (the art category) when the picture is produced. If in order to properly appreciate a depicting picture one must know what it depicts, then to properly a p preciate a depicting picture, one must understand 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 knorvs its correct historical art category. Art criticism can be equally creative as art production in that the art critic can implicitly or explicitly suppose new rules in interpreting the art, and in this way construe P as depictin; something that it does not depict, supposing historical rules. In this way there can be more in a work of art than the artist might have imagined. Sixth objection: T h e Tractatus account of picturing is intended to show how language works. T h e picture theory of the Tractatus covers pictures and representations of all sorts. But will it do to talk about representation in art in the same terms as technical drawings, diagrams, language, and all these other things? E. H. Gornbrich in Art and Illusion proposed that P represents or depicts 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 see P as x. When Gombrich uses the term "illusion" he is referring to the "seeing-as" phenomenon. Illusion is, of course, the typical kind of depiction that occurs in objective art. TVittgenstein in the Philosophical Znvestigations suggests that seeing-as typically involves both seeing and thinking. In a key passage he writes: "What I perceive in the drawing of an aspect is not a property of the object, but an internal relation between it and other objects." 17 When things appear as 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 Eor Gombrich type illusions, then the kind of representation connected with ordinary objective art 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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analysis of picture depicting important for art criticism? T h e important consequences for art criticism that follotcr from Wittgenstein's analysis are the same that follow from any rule analysis of picture depicting such as Nelson Goodman's and Kendall Walton's. For example, one cannot dismiss unfamiliar pictures as not depicting anything. T h e unfamiliar picture may be a depicting picture, but the conventions may not be widely known or not easily read from the picture. Since an important element in the proper appreciation of a depicting picture 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 (its art category). Consider abstract expressionism, 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 canvas, permitting himself to be directed by inner 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 multiplicity, then one could interpret hTumber1 4 as an attempt at depicting emotions on Wittgenstein's analysis of picture representation. For Susanne K. Langer a work of art is an expressive form where what is expressed 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, Wittgenstein's account of logical form.18 Whether it is intelligible to think of emotions as having the requisite Iogical multiplicity is a question I will not go into in this paper. Some recent work in psychology suggests that it may be plausible to regard emotions as having the needed logical multiplicity.lg Even so, one is left with the puzzling praspect that there is a method of rule projection that could "decode" a Jackson Pollack's painting. In any case Wittgenstein's theory of picture representation first opens up the intriguing possibility that nonobjective art can be, after all, representational art. Second, on his theory the difference between
expression and representation could be located in terms of what is represented. Though Goodman writes that no degree of resemblance is necessary for a picture to represent or depict x, he also adds that "almost anything" can represent anything. Why, for Goodman, cannot anything represent anything? According to Goodman, the distinguishing mark of pictures, as contrasted with symbol systems in language, is "density."20 A scheme, according to Goodman, is dense if "it provides for infinitely many characters so ordered that between each two there is a third."21 On this account if a depicting scheme is dense, as pictures are for Goodman, differences in pictorial aspects make a difference with respect to what is depicted. For example, the differences in size, color, and spatial relations make no difference in symbols used in language-only same spelling matters-but such differences can be relevant in representation. T o 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 symbols.22 We need now merely add that some elements in a dense set are relations in order for it not to be the case hat anything can represent anything, and, interestingly in order to obtain "same logical form" and thus a minimal resemblance between pictures 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 picture is regarded as depicting x we in a makebelieve way see x when we look at the picture. But in either case such make-believe presupposes rules or conventions. It is necessary 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. [Valton 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 internalize, and more likely to be adopted (explicitly or otherwise) than others" if P resembles x.23 SO, to use his examples, the
Wittenstein's T h e 0 9 rule that the pie contains a raisin if the glob of mud contains a pebble is just more natural than the rule that the pie contains a raisin if the glob does not contain a pebble o r the rule that the pie contains a raisin if the glob of mud is light-colored. No doubt in the latter two cases there is an absence of visual P-resemblance. But, nevertheless, the mud has the needed logical multiplicity and with appropriate rules has the same logical form as what it depictsa pie with a raisin. I n the latter case there is the mud glob and color, while in the former case there is the glob and there is a pebble-free glob. Nothing Tl'alton writes provides a reason to think that P-resemblance in the formal, abstract sense of same logical form need not be present for his P-depicting. And each of his examples can be construed as having P-resemblance of the Wittgenstein kind. I n recent literature, conventional or rule theories of how a depicting picture depicts have received a great deal of attention. Such theories have interesting consequences for art criticism and appreciation. However, a ctifficulty found in these theories is that they appear to have the consequence that any picture can depict or represent anything. It'ittgenstein's analysis of picture depicting in the Tractatus is an analysis where rules or conventions play a key role that avoids this consequence. O n this analysis of picture representation, same logical form, a minimal, abstract kind of nonimitative resemblance, is required between a depicting picture and what it depicts in order for the picture to ctepict or represent. Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London, 1961). Nelson Goodman, Languages of Art (Indianapolis, 1968), p . 226. Max Black, "How Do Pictures Represent," E. H . Combrich, Julian Hochberg, and Max Black, Art, Perception, and Reality (The Johns Hopkins University Press, 1970), pp. 95-129. ' Monroe Beardsley, Aesthetics (New York, 1958), p. 270. Languages, op. cit., p. 4. ' Kendall TZTalton, "Pictures and Make-Believe," Philosophical Review, vol. 32, no. 3 (1973), 283-319. ' W. E. Kennick makes this criticism in Art and Philosophy, 2nd ed. (New York, 1979), pp. 379-80. Ibid., p. 226.
"anguages, op. cit., p. 5. lo1Yittgenstein's account of picture depicting is found in 2.12-2.19 of the Tractatus. Important clarifying remarks and examples are found in his 1929 paper, "Some Remarks on Logical Form," Aristotelean Society Supplementary, kol. 9, Knowledge, E X perience, and Realism (London, 1929), pp. 162-71. l1 Jay F. Rosenberg in an excellent article on Wittgenstein's picture theory of language makes use of such diagrams to explain the theory, "Wittgenstein's Theory of Language," American Philosophical Quarterly, vol. 5, no. 1 (January, 1968), 18-30. l2 TVittgenstein's theory of picture representation, like the theories mentioned earlier, are attempts to give an account of what obtains when a picture represents or depicts something. But, as almost all tvriters on this subject have pointed out, saying what a picture depicts or represents is highly ambiguous. Sometimes we state what kind of picture P is. Sometimes we state that P denotes something. There are pictures of centaurs, but there are no actual centaurs to picture. Many pictures of cats are such that there are no cats which they picture. For example, Andre Masson's T h e Cat is not a picture of any actual cat, but it is correctly described as a picture of a cat. Tt'hen one says that P is a picture of x, we sometimes suppose that there is an actual x, and sometimes we d o not. If a picture is a picture of some actual existing x, we can say it denotes x. If a picture is a picture of a cat in the sense in which its being a picture of a cat does not depend on there being an actual cat which it pictures, we can say P is a cat-depicting picture. Theories of representation, including Wittgenstein's theory, are primarily concerned with representation in the sense of picture kind, x-depicting pictures, for, presumably, the analysis of P denoting x presupposes that P is an x-depicting picture. T h a t is, to say that P denotes x tvould be at least to say that P is an x-depicting picture and x actually exists. ' T h i s example appears in Robert Howell's "Ordinary Pictures, Mental Representations, and Logical Forms," Synthese, 33 (1976), 149-74. "Nelson Goodman, "Review of Gombrich's Art and Illusion," T h e Journal of Philosophy (September, 1960). 598. " David Lewis, Convention: A Philosophical S t u d y (Harvard University Press, 1969), p. 42. '' Wilfrid Sellars, "Naming and Saying," Philosophy of Science, vol. 29, no. 1 (1962), 7-26. " Ludwig Wittgenstein, Philosophical Znvestigations (Xew York, 1958), p. 212. Problems of Art (London, lRSusanne K. 19.371. l 8 Michael M. Piecho\vski, "The Logical and the Emp~ricalForm of Feelings," T h e Journal of Aesthetzc Educatzon (January, 1981). ")Languages, op. cit., pp. 225-28.
" Ibid., p. 136.
22 Ibid., 228.
?3 "Pictures," op. cit., p. 318.
anger:
h.
I wish to thank this journal's referee for some valuable corrections and for raising several obpctions that I try to meet in this paper.
