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From Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer, ed. Paul Henle, Horace M. Kallen, and Susanne K. Langer (New York: Liberal Arts Press, 1951), 171-182; reprinted as the Appendix to Susanne K. Langer, Problems of Art (New York: Scribner’s, 1957), 163-180.


Abstraction in Science and Abstraction in Art 

Susanne K. Langer


All genuine art is abstract.  The schematized shapes usually called “abstractions” in painting and sculpture present a very striking technical device for achieving artistic abstraction, but the result is neither more nor less abstract than any successful work in the “great tradition,” or for that matter in Egyptian, Peruvian, or Chinese art—that is, in any tradition whatever.

Yet the abstractness of a work of art seems to be something quite different from that of science, mathematics, or logic.  This difference lies not in the meaning of “abstraction,” as offhand one might suppose; we are not dealing with a mere ambiguity.  Both in art and in logic (which carries scientific abstraction to its highest development), “abstraction” is the recognition of a relational structure, or form, apart from the specific thing (or event, fact, image, etc.) in which it is exemplified.  The difference lies in the way the recognition is achieved in art and science, respectively; for abstraction is normally performed for some intellectual purpose, and its purpose differs radically from the one context to the other.  The two characteristic processes of abstracting a form from its concrete embodiment or exemplification go back, therefore, as far as the fundamental distinction between art and science itself; and that is along way back.

There seem, indeed, to be two meanings of the word “form” involved in the two fields, respectively.  A logician, mathematician, or careful epistemologist may question what sense it makes to call anything ”form” except the logical form of discourse, the structure of propositions expressed either in ordinary language or in the refined symbolism of the rational sciences.  Wherever terms exist at all for him they can be named; the relations among them can be named (although their “names” may be indirect, may be parentheses or even mere positions in a line of print); and no matter how complex their combinations may be, those terms and relations are wholly expressible in verbal or algorithmic propositions.  Why, then, call anything “form” that is not capable of such presentation?

Yet artists do speak of “form” and know what they mean; and, moreover, their meaning is closer than that of the logicians to what the word originally meant, namely, “visible and tangible shape.”  The artists, therefore, may ask in their turn how one can speak of the “form” of something invisible and intangible—for instance, the series of natural numbers, or an elaborate mathematical expression equal to zero.  Their sense of the word has undergone refinements, too; in plastic art, it does not mean that at all.  The forms achieved by prose fiction are neither shapes nor logical systems; for although literary works contain propositions, literary form is not the systematic unity of a complex literal statement.  The artistic form is a perceptual unity of something seen, heard, or imagine—that is, the configuration, or Gestalt, of an experience.  One may say that to call such an immediately perceived Gestalt “form” is merely a metaphor; but it would be exactly as reasonable to say that the use of the word for syntactical structure is metaphorical, derived from geometry, and carried over into algebra, logic, and even grammar.

If one cannot tell which of the two meanings is literal and which is figurative, it is fairly safe to assume that both make use of a single underlying principle which is exemplified in two different modes.  The basic principle of “form” determines that close relation between apperceptive unity and logical distinctions which was known to the ancients as “unity in diversity”; But they might just as well have called it “diversity in unity”; for it is sometimes thought to relate many individually conceived things or properties each to each, directly or indirectly, producing a whole, and sometimes to distinguish many elements from one another where an all-inclusive unit is the first assumption.  The preposition “in” is an unfortunate word to designate the construction of a coherent system out of given factors; but when it serves also to designate the articulation of structural elements of a given whole, it is as bad a hyperbole for the expression of relational concepts as ever bedeviled classical philosophy.

Yet the two ideas—constructed unity and organic differentiation of an original whole—both involve the more general concept of relative distinctness.  They are specifications of this concept that arise from epistemological sources, from the nature of logical intuition and the nature of the symbols whereby we elicit and promote it.  Now the object of logical intuition is form; and although there are two ways of developing our perception of this object, and consequently two sets of associations with the word “form,” the use of it is equally and similarly justified in both contexts.

There are certain relational factors in experience which are either intuitively recognized or not at all, for example, distinctness, similarity, congruence, relevance.  These are formal characteristics which are protological in that they “must be seen to be appreciated.”  Once cannot take them on faith.  The recognition of them is what I mean by “logical intuition.”  All discourse is a device for concatenating intuitions, getting from one to another, and building up the greater intuitive apperception of a total Gestalt, or ideal whole.

Artistic intuition is a similar protological experience, but its normal progress is different.  It begins with the perception of a total Gestalt and proceeds to distinctions of ideal elements within it.  Therefore its symbolism is a physical or imaginal whole whereof the details are articulated, rather than a vocabulary of symbols that may be combined to present a coherent structure.  That is why artistic form is properly called “organic” and discursive form “systematic,” and also why discursive symbolism is appropriate to science and artistic symbolism to the conception and expression of vital experience, or what is commonly termed “the life of feeling.”

As art and discursive reason differ in their starting points of logical intuition, so they differ in all their intellectual processes.  This makes the problem of abstraction appear entirely different in the two domains.  Yet artists and logicians are equally concerned with abstraction, or the recognition of pure form, which is necessary to any understanding of relationships; and they perform it with equal spontaneity and carry it, perhaps, to equally great lengths of skillful manipulation.

There is a widespread belief—sometimes regarded as a very truism—that abstract thought is essentially artificial and difficult, and that all untutored or “natural” thought is bound to concrete experiences, in fact to physical things.  But if abstraction were really unnatural, no one could have invented it.  If the untutored mind could not perform it, how did we ever learn it?  We can develop by training only what is incipiently given by nature.  Somewhere in man’s primitive repertoire there must have been a spontaneous intellectual practice from which the cultivated variety of abstract thought took its rise.[1]

This instinctive mental activity is the process of symbol-making, of which the most amazing result is language.  All symbolization rests on a recognition of congruent forms, from the simple one-to-one correspondence of name and thing that is the dream of speech reformers[2] to the most sophisticated projection of thought into conventional systems of notation.  The logic of symbolic expression is an old story though not completely told even yet; it is still gaining precision in works like C. I. Lewis’ Analysis of Knowledge and Valuation.  But its main outlines are familiar enough to need no restatement here.  The interesting thing in the present context is that the growth of language takes place at all times in several dimensions, and each of these entails a primitive and spontaneous form of abstractive thinking.  The appreciation of pure conceptual forms as such is indeed a late and difficult attainment of civilized thought, but the abstraction of formal elements for other intellectual purposes is a natural and even an irrepressible human activity.  It permeates all thought and imagination—reason, free association, play, delirium, and dream.  And although I am convinced that some abstractions cannot be made verbally at all, but can be made by the nondiscursive forms we call “works of art,”[3] yet the basic abstractive processes are all exemplified in language at various stages of its ever-productive career. Some transcend its limitations soon, and other late; some leave it and become completely articulate only in the various media of art; some remain essentially linguistic and simply transform and develop language in their natural advance, giving it more and more of what we call “literal meaning,” more and more precise grammar, and finally the algorithmic extensions that belong rather to written language than to speech.

We have no record of any really archaic tongue; the origins of all known languages lie beyond the reaches of history.  But as far back as we can go, language has two essential functions, which may be called, somewhat broadly, “connotation” and “denotation” (the exact distinctions made by Professor Lewis[4] are indeed relevant here), but I resort to the less precise, traditional terms because, in the small compass of this essay, the roughest characterization that will serve the purpose is the most economical.)  Connotation belongs to all symbols; it is the symbolic function that corresponds to the psychological act of conception.  Denotation accrues to symbols in practical use, for the applicability of concepts to “reality” is, after all, their constant pragmatic measure.  Both conception and denotation through language are natural activities, instinctive, popular, and therefore freely improvisational and elaborative; and both involve a constant practice of abstraction from the pure experience of this, here-and-now.

The principles of abstraction that govern the making of symbolic expressions vary, however, with the purposes (conscious or unconscious) to which those expressions are to be put.  One outstanding purpose is, certainly, to attain generality in thought.  The tremendous practical value of language lies largely in its power of generalization, whereby the naming of any object immediately establishes the calls of such objects.  This is a very rudimentary abstractive function inherent in language as such, as Ribot observed more than fifty years ago,[5] and as Cassirer has demonstrated in The Philosophy of Symbolic Forms.[6]  The earliest classconcepts, therefore, are directly linked with the assignment of names to objects.

The modern empiricists, notably Locke, took it for granted that the “simple qualities”—such as colors, tones, smells and tastes, pressures—were the items most directly presented to the mind through primitive, unguided sense experience, and therefore remembered—that is, conceived—even as meaningless “data.”  Oddly enough, the development of language, which mirrors the history of those twin functions, perception and conception, gives a different view of elementary qualities.  Judging by early nomenclature, we find that colors, for instance, were not always distinguished by their actual spectrum values—that is, as “red,” “blue,” “yellow,” and so forth—but primarily as warm or cold, clear or dull.  Walde’s comparative etymological dictionary[7] renders the meaning of the IndoEuropean root ĝhel as “glänzen, schimmern, gelb, grün, grau oder blau.”  The names for definite pigments were late established, and often changed their signification completely from one hue to another.  Thus the current word “blue,” German blau, derives from blavus, a Middle Latin form of flavus, meaning, not “blue,” but “yellow.”[8]  Black is descended from bhleg, and cognate with blanc, blank, Swedish black, Norwegian blakk, meaning “white.” The oldest sense is probably preserved in “bleak.”  But what is even more surprising is that the connotation of an adjective often shifts entirely from one sensory field to another.  The German word hell, now applied literally only to light and color—that is, to visual impressions—and sometimes used metaphorically of tones, seems originally to have referred to sounds first and foremost, and to have come into use for visual effects only around the time of Martin Luther.  In fact, when Luther employs it to describe light, he always says “hell licht,” “am hellen lichten Tag,” and the old meaning is still preserved in the idiom “ein heller Haufe,” which refers not to a bright throng but a noisy one.

Yet the apparently capricious changes of meaning, often from the original quality to its very opposite, follow a perfectly obvious principle: a word designates any quality that can symbolize a certain feeling.  This seems to be the law of that metaphorical extension whereby whole groups of words arise out of one phonetic “root,” all embodying this root in their sound and deriving their meaning from its archaic sense, which Max Müller aptly called the “root metaphor.”  The original reference of adjectives especially appears to have been primarily to feeling tones, and hence, quite freely and naturally, to any sense-qualities that helped the conception of them.  Therefore extreme opposites of sensation were often designated by the same word: white and black, hot and cold,[9] high and deep (Latin altus).  Both extremes of a sensation symbolize the same intensity of feeling.  The true opposite of their value is a low-keyed sensation—dim, gray; lukewarm; flat, shallow. Primitive thought is fairly indifferent to the particular order of sensation from which the qualitative symbol is taken, so long as it conveys the subjective value of the experience to be recorded.

But language is not only an intellectual tool whereby concepts are formed; it is also a common currency for the exchange of them; and this public interest puts a premium on objective reference and develops the function of denotation.  The attachment of verbal labels to things is the major purpose of words in social use.  Every device that facilitates naming is naturally accepted and exploited; and perhaps the greatest of such devices is generalization, the treatment of every actually given thing as a representative of its kind—that is, of every “this” as a “such-as-this.”  The establishment of kinds, or classes of things, requires some easily recognizable mark of membership in otherwise diverse objects, and this interest was probably what led people from the conception of qualities through feeling-tones to the more precise observation of publicly comparable features—the hues, shapes, sizes, noises, temperatures, and the rest that modern languages honor with adjectives: blue, round, big, loud, cold, and so forth.  With this fixation of characters, the old contrast between “extreme” and “middling” would be broken down by the discovery that there are two different “extremes”; and their close association, amounting even to fusion in a single root-metaphor, would lead to a new, powerful, abstracted notion—the notion of a dimension, a range or gamut of experiences.  Then the qualities within one dimension could be distinguished, named, comparatively treated; the principles of empirical analysis supervene over the earlier recognition of feeling-tones; and language become the mighty instrument of discursive thought in which Aristotle found the laws of logic reflected.

The “simple qualities” of empiricism, the “data” that are obviously distinct for us, are so by virtue of language; and their classification in sensory orders—such as hues, sounds, tastes, and so on—is already a long step toward science.  This step is effected by the spontaneous processes of symbolic transformation that give rise to language in the first place: metaphor, which always involves a basic recognition of the common form that justifies the substitution of one image for another; and the principle of pars pro toto, exemplifying the class-concept involved.  But these primitive insights into formal conditions do not constitute “abstraction” in a strict sense.  They are abstractive processes implicit in symbol-making and symbol-using, rather than a recognition of abstracted elements as such.  Genuine abstraction is a relatively late achievement, born of reflection on the works of art and science, and fully understood only by means of the latter.  But once we attain the concept of abstract form, or pure structure apart from the things in which it is exemplified, we find that both art and science constantly tend toward the maximum revelation of abstract elements, and both for the same purpose—namely, to create more and more powerful symbols—but by different procedures, born of their different intuitive starting points.

The driving principle of science is generalization.  Its subject matter is really something perfectly concrete—namely, the physical world; its aim is to make statements of utmost generality about the world.  And generalization, as we have just seen, arises from the denotative character of language, from the fact that a named thing is at once a focus of “reality”—that is, a fixed entity—and a symbol for its kind; since a name is always a class label as well as a handle for its specific object. (Even supposedly individual, or proper, names tend to serve in this double capacity: “A Daniel come to judgment!)  The principle of classification, inherent in language, begets the logic of quantified statement that underlies the development of scientific thought.  There was good reason why a logic guided by scientific aims should have been developed in extension rather than intension; the extension of a term is the range of its denotation, and denotation is its link with the world, the object of science.  Bertrand Russell, in one of his brilliant early essays, called this extensionalism “the Principle of Abstraction . . . which  might equally well be called the principle that dispenses with abstraction.”[10] Actually, it does not dispense with them at all, but moves over them without explicit recognition, because its aim is to put all abstracted forms to further use—much as we do in making our unconscious abstractions by the common-sense use of language—and to make general statements about reality—that is, assert general facts of nature.

It was only with the development of mathematics that abstract logical forms became so apparent and, in their appearance, so interesting that some logicians turned their attention to the study of form as such and undertook the abstraction of relational patterns from any and every concrete exemplification.  Russell, despite his proposal to dispense with abstractions, was one of the first advocates of that new logic and (together with Whitehead) one of its great promoters; for, oddly enough, systematic generalization—the principle that was to obviate the need of abstraction—furnished exactly the technique whereby structures were brought to light, symbolically expressed and recognized as pure abstract forms.  Russell’s leanings toward physical science are so strong that perhaps he does not see the entire potential range of philosophical studies built on the study of relational logic.  Whitehead came nearer to it; Peirce and Royce saw it;[11] but the actual development of systematic abstraction to the point where it can be an eyeopener to philosophers has been the special task of the man to whom these essays are dedicated [Henry M. Sheffer].  In natural science, generalization is all we require, and mathematics is valued for its power of general statement and complex manipulations without any loss of generality.  But in pure mathematics the element of logical form is so commandingly evident that mathematical studies naturally lead to a theory of structure as such and to a systematic study of abstraction.  That study is logic, and its technique is progressive generalization.  The use of generalization to make abstract structure apparent was more or less accidental until Sheffer saw its possibilities and built a pure logic of forms upon it.  This work gave logic a different aim, not only from the old traditional “art and science of inference,” but even from the modern development of truth-value systems; for instead of being essentially a scientific tool, logic thus becomes an extension of human interest beyond the generalized empirical thought of science, to the domain of abstract form, where the very principles of symbolism, conception, and expression lie open to inquiry and technical demonstration.

If we now turn to the domain of the arts, it seems as though nothing comparable to logical abstractness could be found there at all, but everything were immediate, unintellectual, and concrete.  Yet a little conversance with any art quickly reveals its abstract character.  A work of art is a symbol; and the artist’s task is, from beginning to end, the making of the symbol.  And symbol-making requires abstraction, the more so where the symbolic function is not conventionally assigned, but the presented form is significant simply by virtue of its articulate character.  The meanings of a work of art have to be imaginatively grasped through the forms it presents to the sense or senses to which it is addressed; and, to do this, the work must make a forceful abstraction of “significant form” from the concrete stuff that is its medium.

But the abstractive process of art is entirely different from that of science, mathematics, and logic; just as the forms abstracted in art are not those of rational discourse, which serve us to symbolize public “fact,” but complex forms capable of symbolizing the dynamics of subjective experience, the pattern of vitality, sentience, feeling, and emotion.  Such forms cannot be revealed by means of progressive generalization; this makes the whole development of art and all its techniques radically different from those of discursive thought.  Although art and science spring from the same root, namely, the impulse to symbolic expression—of which the richest, strongest and undoubtedly oldest manifestation is language—they separate practically from the beginning.[12]

A work of art is and remains specific.  It is “this,” and not “this kind”; unique instead of exemplary.  A physical copy of it belongs to the class of its copies, but the original is not itself a member of this class to which it furnishes the class concept.  We may, of course, classify it in numberless ways, for example, according to its theme, from which it may take its name—“Madonna and Child,” “Last Supper,” and so on.  And as many artists as wish may use the same theme, or one artist may use it many times; there may be many “Raphael Madonnas” and many “Last Suppers” in the Louvre.  But such class-membership has nothing to do with the artistic importance of a work (the classification of a scientific object, on the other hand, always affects its scientific importance).

The artist’s problem, then, is to treat a specific object abstractly; to make it clearly an instance of a form, without resorting to a class of similar objects from which the form underlying their similarity could be abstracted by the logical method of progressive generalization.  The first step is usually to make the object unimportant from any other standpoint than that of appearance.  Illusion, fiction, all elements of unreality in art serve this purpose.  The work has to be uncoupled from all realistic connections and its appearance made self-sufficient in such a way that one’s interest does not tend to go beyond it.  At the same time, this purely apparent entity is simplified so that the ea, eye, or (in the case of literary art) the constructive imagination can take in the whole pattern all the time, and every detail be seen in a fundamental, unfailing context—seen related, not seen then rationally related.  Whether there is much detail or little, what there is must seem an articulation of the total semblance.  In the case of a piece that is not physically perceivable at one time, as for instance a novel, a long drama or opera, or a series of frescoes constituting a single work, the proportion of the whole has to be established at all times by implication, which is a special and technical problem.  In any event, the perception of a work of art as “significant form”—significant of the nature of human feeling—always proceeds from the total form to its subordinate features.

This manner of perception, which the work is designed to elicit, causes it to appear organic; for the evolution of detail out of an indivisible, self-sufficient whole is characteristic of organisms and is the material counterpart of their function, life.  And so the work of art seems to have organic structure and rhythms of life, though it is patently not a real organism but a lifeless subject.  If the semblance is forcible enough—that is, if the artist is successful—the impression of living form becomes commanding and the physical status of the piece insignificant.  The form of organic process which characterizes all vital function has been abstracted, and the abstraction made directly from one specific phenomenon, without the aid of several examples from which a general pattern emerges that may then be symbolically rendered.  In art, the one instance is intelligibly constructed and is given the character of a symbol by suppression of its actual constitution as painted cloth, vibrating air, or (somewhat less simply) a string of the conventional counters called “words,” whose relative values are recorded in the dictionary.  When its proper material status is cancelled by the illusion of organic structure, its phenomenal character becomes paramount; the specific object is made to reveal its logical form.

Yet it does not present an abstracted concept for our contemplation; the abstractive process is only an incident in the whole function of a work of art, which is to symbolize subjective experience—that is, to formulate and convey ideas of sentience and emotion.  The abstracted form of organic relations and vital rhythms is only an ingredient in the total expression of feeling, and remains implicit in that greater process.  But it is the framework; and, once it is established, the whole realm of sense-perception furnishes symbolic material.  Here the inherent emotive significance of sense-data comes into play.  The natural relationship between sensory qualities and feelings, which governs the extension of language by the development of “root-metaphors,” also determines the function of sensuous materials in art.  Surfaces, colors, textures and lights and shadows, tones of every pitch and quality, vowels and consonants, swift or heavy motions—all things that exhibit definite qualities—are potential symbols of feeling, and out of these the illusion of organic structure is made.  That is why art is essentially qualitative and at the same time abstract.  But the sensuous elements, often spoken of as the “sense-content” of a work, are not content at all but pure symbol; and the whole phenomenon is an expanded metaphor of feeling, invented and recognized by the same intuition that makes language grow from the “root-metaphors” of fundamentally emotive significance.

Artistic abstraction, being incidental to a symbolic process that aims at the expression and knowledge of something quite concrete—the facts of human feeling, which are just as concrete as physical occurrences—does not furnish elements of genuine abstract thought.  The abstractive processes in art would probably always remain unconscious if we did not know from discursive logic what abstraction is.  They are intuitive, and often most successful and complete in primitive art.  It is through science that we recognize the existence of pure form, for here it is slowly achieved by conscious method and finally becomes an end in itself for the entirely unempirical discipline of logic.  That is probably why so many people stoutly maintain that art is concrete and science abstract.  What they should properly say—and perhaps really mean—is that science is general and art specific.  For science moves from general denotation to precise abstraction; art, from precise abstraction to vital connotation, without the aid of generality.


[1] This fact was noted by T. Ribot in an article, “Abstraction Prior to Speech,” in The Open Court (1899), Vol. XIII, pp. 14-20.

[2] Cf. Bertrand Russell’s Philosophy (New York, 1927), Ch. IV; and his later and more elaborate Inquiry into Meaning and Truth (New York, 1940), especially the first four chapters; also G. B. Shaw’s Preface to R. A. Wilson’s The Miraculous Birth of Language (New York, 1948).

[3] Here I regret to disagree radically with Professor Lewis, who says: “It is doubtful that there are, or could be, meanings which it is intrinsically impossible for words to express.”—An Analysis of Knowledge and Valuation (La Salle, Ill., 1946), p. 73.

[4] Ibid. Ch. III.

[5] In the essay previously alluded to.

[6] See especially Vol. I, Chs. IV and V.

[7] Walde, Vergleichendes Wörterbuch der indoger-manischen Sprachen (Leipzig, 1926).

[8] Ibid.

[9] Walde gives the meanings of the root kel as: “(1) frieren, kalt. (2) warm.”

[10] Our Knowledge of the External World, 2nd ed. (New York, 1929), p. 44

[11]  C. S. Peirce, “The Architecture of Ideas,” in Chance, Love and Logic; Josiah Royce, “The Principles of Logic,” especially Sec. III, in Encyclopedia of the Philosophical Sciences, edited by Windelband and Ruge, Eng. Transl. (1913).

[12] For a full discussion of this point, see E. Cassirer, The Philosophy of Symbolic Forms, especially Vol. I, ch. I.

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