Toward a Unified Theory of the Arts

Originally published in the journal Semiotica, in 1993 – reissued with additional commentary in Music Theory Online, 1996

          With the great successes of structuralism, semiotics and poststructuralism during the past three decades, the theory of the sign-function and the ideological issues associated with it threaten to dominate the entire realm of aesthetic discourse.  This paper presents the essential ingredients of a unified theory of the arts which, while reflecting the very real insights of structuralism and its offspring, seeks to move beyond them to a realm where the aesthetic can find a meaningful place.  The theory is 'unified' in the sense that it is intended ultimately to encompass:  1. any and all art forms; 2. the full historical and ethnological range of artistic expression, non-Western as well as Western, modernist and postmodernist as well as 'traditional'; 3. semiotic as well as aesthetic principles.

          A complete elucidation of such a theory would be beyond the scope of this paper.  For now I would like simply to define and discuss certain fundamental principles and possibilities with respect to two important areas:  the pictorial arts (painting, drawing, etc.) and music.  The reader should bear in mind that my intention, in this context, is simply to convey a clear idea of the general outlines of the theory, not present a carefully reasoned set of arguments in its defense.[1]

                                                         

An Analogy

Consider Figure 1.  From an iconographic point of view, the most we can say is that it is rhomboid, essentially geometrical and flat.

          Adding some lines (Figure 2) we can immediately recognize the sign, however crude, for 'house.'  Our rhombus has become one side of the house.  It is, moreover, no longer perceived as flat, but polarized in a particular direction with respect to three dimensional space:  rearward to the right.

          Consider the variation in Figure 3.  The same rhombus is now perceived as polarized in a completely different direction:  rearward to the left.

          Now let us attempt to combine the two (Figure 4).  Something is clearly wrong.  The figure contains all the elements of the sign for house, but does not make sense.  The difficulty centers on the original rhombus, which can no longer be perceived as having an unambiguous spatial orientation of any kind.  The result can be described as 'ungrammatical.'

          Withholding, for the moment, any attempt at analysis, let us move to what seems an entirely different realm. 

Imagine listening to the unaccompanied musical line of Figure 5.

          Harmonized in the key of G Major (Figure 6), the line is clearly polarized in a particular tonal direction.  Note how the final 'A' sounds 'up in the air.'  Figure 7 presents the same notes polarized toward a completely different tonal center (A Major), giving them a musical meaning very different from that found in Figure 6.  In this context, the line ends with a sense of finality and repose.

          Finally, in Figure 8, which superimposes the two previous settings, we have something that sounds, from the 'common practice' point of view, wrong, 'ungrammatical.'  Unrelated to any key, the line cannot be oriented in tonal space.  Its musical meaning is therefore unclear and, from a traditional standpoint, it sounds out of place.

                                                   The Syntactic Field

          While the above visual and musical situations may not strictly parallel one another, there is a close analogy nonetheless.  In the pictorial examples, a particular figure took on a different meaning and a different appearance depending on its apparent orientation within pictorial space.  In the musical examples something very similar happened, but this time in the context of what we must call 'tonal space.'  In both cases, instances which could not be understood within any given 'spatial' context seemed in some sense to violate a 'grammatical' rule and were understood as meaningless.[2]

          Similar examples could doubtless be drawn from, say, 'color space,' the 'space' of musical time ('metric space'), sculptural space, architectural space, cinematic space, cinematic time, etc.  What they would all have in common can be summarized in the following, which I call the 'first semio-aesthetic principle': any object of perception can signify (take on meaning) only in relation to a controlling syntactic field.

          The notion of syntax is appropriate for more than one reason:  it is associated with the rules of 'grammar' to which we have already referred -- in this sense pictorial or musical 'space,' by analogy with linguistic syntax, can be regarded as the source of a set of rules determining pictorial or musical signification; the term implies a purely formal, structural entity, functioning independently of any possible content; the derivation of the word suggests the useful notion of a structure (tax) which brings-together (syn) -- in this sense a syntactic field must be understood as having a unifying function.

          The notion of a syntactic field should not present serious problems.  A field is a kind of invisible controlling spacelike region or extent within which certain types of activity have the potential to take place.  In the physical sciences, prior to the field idea, bits of matter and the forces between them were considered fundamental.  For Faraday, followed by Maxwell and Einstein, what is fundamental are the fields (e.g. electromagnetic, gravitational) through which forces and matter can be understood to operate.  Similarly, we can consider a syntactic field as a controlling, determining fundamental entity or function by means of which syntax and signs can be understood to operate.

           Principle one does not, of course, follow inevitably from our analysis of Figures 1-8.  However, these examples do provide simple, readily apprehensible illustrations of the workings of syntactic fields in the pictorial arts and music.  In figure 2, a spatial syntactic field is produced from a few carefully placed lines just as an electromagnetic field would be produced by a small burst of electrical current.  A differently oriented field is produced in figure 3.  Figure 4 is 'ungrammatical' simply because it cannot be unambiguously oriented within a field.  Since the differences between figures 2 and 3 relate to orientation in depth, we know that these fields are equivalent to three dimensional spaces.  Since the figures have been drawn on a two-dimensional surface, the fields in question can only be understood as virtual, that is essentially mental, imaginary.  The most highly evolved example of this sort of thing can be found, of course, in perspective space, where invisible 'lines of force' control the syntactic field of an entire picture.

          Figures 6 and 7 produce analogous syntactic fields in tonal space.  Since the difference between the fields produced by the two keys cannot be accounted for with reference to one dimensional (high to low) pitch 'space,' the tonal field must also be regarded as virtual.  In its most highly evolved form, the 'common practice' tonal system of Western culture during the Eighteenth and Nineteenth centuries, virtual 'lines of force' deriving from the Circle of Fifths control the syntactic tonal field of an entire musical composition.

          The same tradition has produced an equally systematic method of controlling musical time.  Virtual 'lines of force' in the form of measures orient each note within a metric field.  Thus, for example, a note occurring on the first beat of a measure will sound different and carry a different musical meaning from the same note occurring on the second beat, even if both are played in exactly the same way.

          A second principle arises naturally from the first:  before any perceptible can function as a sign, it must be apprehended as a gestalt, i.e. a form or figure perceived against a ground. 

          In other words, insofar as a syntactic field is also a perceptual field syntax must be first and foremost organized according to the laws of gestalt psychology, where figures are perceived against grounds and wholes are greater than the sum of their parts.  The field itself functions as the ground within which sign-gestalts are placed.  It would, indeed, be difficult to imagine how one would attempt to describe or deal logically in any way with a sign that was not also perceptible as a gestalt. 

          In the rush to establish semiotics as a theory of everything this rather obvious point seems to have been lost.  (There is no reason, however, to deny to semiotics the complementary notion:  every gestalt must signify.)

          Gestalt principles are, of course, the basis for the traditional pictorial art of the West and many other cultures as well, as reflected, for example, in relations between shapes and backgrounds or, in more modern terms, positive and negative space.  While not so obvious, analogous relations are found in traditional Western music, where, for example, various kinds of figurations and motives generate gestalts, as do points of closure such as cadences.[3]

          A third principle is the result of poststructuralist insights:  every syntactic field is a construct with an ideologically determined basis. 

          In other words, there is no such thing as a passive or even neutral ground.  The fields associated with all signifying processes are the products of culture and reflect ideologically determined value systems enforced by explicit or implicit rules.       Principle four:  in the absence of a clearly defined syntactic field, there arises a context of free floating, ambiguous implication which functions as though a syntactic field were present. 

          Thus one cannot defeat the ideological effect of the syntactic field simply by breaking the rules, invoking rhetoric or bricolage as a substitute for logic, making random marks or random sounds, etc.  While such devices may not unambiguously signify, they will always imply the existence of some transcendent field within which their ambiguities can be resolved and a kind of mystical sign function can arise.  This is undoubtedly the source of the special appeal of Surrealism.

                                              Signification vs. Aesthesia

          Let us pause for a moment to ponder some issues raised by the above.  The examples with which we began illustrate how pictorial and musical meaning is related to a process of signification within a syntactic field.  What is most remarkable and disturbing about this process is the fact that the shifts in meaning produced shifts in the way our figure and our notes were actually perceived.  When understood as 'side of a house,' our rhombus is seen as a rectangle oriented in a certain direction.  When understood as 'in the key of G,' our melodic line is heard as ending 'up in the air.'  Indeed, in such a context meaning and perception can hardly be distinguished.

          For traditional semiotics this sort of thing reveals a surprisingly intimate connection between signification and perception.  For the more radical poststructuralists it leads to a profoundly disturbing metaphysical gap.  From this point of view all perception is completely dependent upon codes of signification -- we literally cannot see or hear anything that is outside a signifying process. 

          In terms of the principles outlined above, we could say that all perception is dependent upon syntactic fields and, since such fields are controlled by ideologically determined thought processes, we are inherently incapable of perception per se.  In more radical terms, not only perception, but reality itself falls away in favor of a purely mental process devoted exclusively to the decoding and encoding of 'empty' signs.

          In the present context we can leave aside the difficult metaphysical issues raised by this position.  We cannot, however, avoid an obvious question:  in view of the total absorption of perception into signification, what is the status of the work of art or, more specifically, how does the art work differ in kind from any other coded entity?

          Let us recall that the word aesthetic, derived from the Greek aesthesia, originally meant 'of or pertainable to things perceptible by the senses, things material as opposed to things thinkable or immaterial' (The Oxford Dictionary 1989:206).  Indeed, the Eighteenth Century philosopher Alexander Baumgarten, in establishing aesthetic for the first time as an autonomous field of study, specifically relates the term to 'things perceived' as opposed to 'things known' (Baumgarten 1954:78).  We will be using the word in this original sense throughout the remainder of this essay.  Though the provenance of this term has broadened considerably since Baumgarten, it would be difficult to imagine an aesthetic theory in any sense of the word which excluded the sensory world. 

                                              Signification and its Other

          Semiotics, poststructuralism, 'deconstruction' etc., in denying the ultimate validity of sensory experience, remove thereby any basis for an autonomous theory of the arts.  If perception is reduced to a mode of signification, aesthetic must simply take its place within a system of essentially linguistic codes, hardly distinguishable from an intensified rhetoric.[4]

          While it is not our intention, here, to 'deconstruct' poststructuralism, it is necessary to put this issue in historical perspective.  The conflict between perception and signification is an old one and, consciously or unconsciously, has always posed a problem for the artist.  The issue came to a head with the development of naturalist painting in late Nineteenth Century Europe, which entertained the naive hope of a perfectly straightforward, unmediated representation of the material world.

          Naturalism came to grief during a remarkable period when artists such as the Impressionists, Cezanne, Braque and Picasso delved progressively farther into the most fundamental problems of observation and representation.  Finally, in the crucible, or should we say 'cyclotron,' of Cubist art, aesthetic and semiotic collided, the atom of cognition was split, and a new sensibility was born.  Structuralism and modern semiotics can trace much of their ancestry to the Russian Formalist school of linguistics, born as a response to this sensibility as expressed in Futurism and Constructivism, direct outgrowths from Cubism.[5] 

          In our view, the remarkable group of paintings and constructions produced by Picasso and Braque in the years 1908 to 1914 already encompass the central issues not only of semiotics but also deconstructionism.  As a result, these works, which became the foundation stones of modernism (and postmodernism), also provide a key to the functioning of 'traditional' pictorially based sign-systems.

                                                 Disruption of the Sign

          Space does not permit an adequate analysis of the Cubist achievement in these pages.  I will make do, instead, with a few comments which, if they are so brief as to appear dogmatic, will at least, hopefully, clarify my point of view.

          Cubism begins as an extension of the project of Cezanne, i.e., the use of painting as part of a relentless struggle to observe the material world directly, free of any representational  scheme (such as perspective).  Like Cezanne, the Cubists proceed by breaking up pictorial space to do justice to the unique space generated by each object.  The various contending spaces are linked by areas of 'passage,' a time-honored device in which painters have traditionally linked foreground and background elements in order to create vague areas of transition that could, among other things, mask spatial discrepancies.  As Cezanne learned, extreme use of passage leads to distortion.  Seeking to resolve this problem, the Cubists radically fragment space into ever smaller 'facets,' so that each can absorb some of the distortion.

          Extreme fragmentation and passage, coupled with devices such as reverse perspective, cause forms to disintegrate, details to be emphasized at the expense of the whole.  As a result, the syntactic field breaks into its constituent signs and sign-parts.  No longer visible as gestalts, however, these fragments cannot fully signify.  At this point Cubism becomes a self-referential meditation on the relation between perception and signification, playing a thousand different games with the now defused signs for spaces and things.

          With the disruption of the three dimensional syntactic field, areas such as the rhombus of figure 1 can no longer be 'read' as polarized in any direction and begin to reveal themselves simply as patches of color on an intensified surface.  A new kind of space begins to emerge from such areas and the areas of passage surrounding and infiltrating them:  'negative space,' the space between forms. 
 

          As Cubism moves into its so-called 'synthetic' phase, fragments of negative space resolve into large, flattened areas of solid color or collage, punctuated by forlorn, thoroughly deconstructed sign fragments.   As Cubist energies wane, the project is taken up by Mondrian, who methodically eliminates all reference to signification in an effort to equilibrate the newly acquired space through control of proportion.  With Mondrian, the realist ambition ultimately becomes transformed into the project of determining perception itself.   
  

                                                 The Musical Analogue

          Parallels with the development of music over a somewhat broader time span are striking.  Musical 'modulation,' a transitional device linking more or less distant keys is, of course, analogous to pictorial passage, which links more or less distant spaces.  Modulation is usually characterized by the use of 'pivot chords,' ambiguous harmonies which have a function in both the old and the new key. 

          During the Nineteenth Century, as composers seek to incorporate farther ranging tonal relationships, increasing emphasis is placed on a group of dissonant, inherently ambiguous pivot chords which can afford ready 'passage' to distant keys via enharmonic relationships:  the chord of the diminished seventh, the 'French,' 'Italian' and 'German' Sixths and the so-called 'Tristan' chord.  By the late Nineteenth Century, these and other transitional harmonies are enabling composers to fragment tonal space through frequent, almost routine, modulation.  In the process, as with painting, forms begin to disintegrate and details, in the form of a host of new, highly colored dissonant harmonies, increasingly appreciated in and for themselves as sounds, begin to assert themselves at the expense of the whole.

          Finally, in the work of Arnold Schoenberg, the tonal system itself breaks down.  With Schoenberg's 'emancipation of the dissonance,' the ambiguous chords which originally functioned as musical 'passage' take on a new role as stable, unambiguous landmarks of a new 'negative' tonality:  atonality.

          The new musical space, designed to prevent any one note from becoming a stable tonal center, defeats the tendency, illustrated in Figures 6 and 7, for every note to be polarized in a particular tonal 'direction.'  Notes and chords begin to be heard, not in terms of musical 'meaning,' but as sounds with unique and interesting properties of their own.

          Atonality, in which the notes repel one another, initially functions as a fundamentally disruptive strategy, comparable with analytic Cubism.  The systemization of atonality by Schoenberg's twelve tone method, by analogy with synthetic Cubism and the later work of Mondrian, builds a completely new, multipolar 'space' in which all elements (notes of the series) are in equilibrium.[6]

          Despite his radical break with the tonal system, Schoenberg is reluctant to completely do away with rhythmic and motivic gestalts.     The final break comes in the work of his disciple Anton Webern, whose opening out of the motive-gestalt, liberation of timbre and rhythm, and acceptance of the ephemeral, eventually inspire the most influential compositional movement of the Twentieth Century:  total serialism.

          The serialists, led by Pierre Boulez and Karlheinz Stockhausen, continue the process of radical fragmentation, increasingly emphasizing (as in 'moment form') the ephemeral part at the expense of the transcendent whole, the audible 'surface' (the 'sound object') at the expense of tonal 'depth' and (as with Mondrian's treatment of space) attending carefully to the proportional division of musical time.[7]        

                                                     Negative Syntax

          The striking parallels between the pictorial and musical developments outlined above encourage us to draw up a set of principles which might clarify this new situation:

          Principle five:  a syntactic field is always associated with an opposing, usually hidden field, which, by analogy with negative space, we will call the negative field. 

          As demonstrated by Cubism, negative space is more than simply the space between forms.  The latter is only a fragment of a larger entity, repressed by the syntactic field which it threatens.  As Cubism develops, this new space, first perceived as a distortion of three dimensional 'positive space,' emerges as a 'negative field' of the surface, functioning in direct opposition to the gestalt structure of the more familiar 'positive' syntactic field. 

          Principle six:  while the syntactic field is virtual, i.e., fundamentally conceptual, the negative field is material, i.e., fundamentally sensory, defined in terms of what Kant has called 'Transcendental Aesthetic,' the 'two pure forms of sensuous intuition':  space and time (Kant 1966:22,23). 

          In painting, the negative field is the two dimensional space of the canvas itself, which must be suppressed to permit representation in depth.  In this context, negative space, if noticed at all, is always perceived as part of the material (sensual) two dimensional surface, never as part of the virtual (mental) three dimensional space-in-depth.

          In music, the negative field is the simple, one-dimensional pitch 'space' of the sound-spectrum (as opposed to the multidimensional syntactic 'space' of the tonal system, with its functions and class identities) coordinated with the time of simple duration (as opposed to the multi-leveled time of the metric system, with its hierarchically structured periodicities).[8]  The 'negative times' of music (analogous to the 'negative spaces' of painting) are the actual durations of sounds or the silences between them as opposed to the 'figures' created by attack-points.[9]

          We must be careful to distinguish (as Kant did not) between the virtual, abstract space and time of the syntactic field, and the space and time of the negative field, perhaps best described as experiential or even existential.

          Principle seven:  the negative field disrupts signification -- to the extent that sign elements are present in a predominantly negative field they will be multireferential.

          While its value to purely aesthetic experience should never be minimized, the negative field also has an important role to play in the opening out of the ideological forces behind the signifying process.  Unlike simple ambiguity, which only tends to mystify the sign, the negative field, in defeating gestalt perception, totally disrupts the sign, revealing the rich, multiple play of interconnected, often contradictory, channels of reference hidden within the apparently straightforward message of any 'text.'  It should thus be of interest to the poststructuralists, whose attack on semiotics is based largely on the latter's neglect of the 'polysemic' implications of the sign-function.

Principle eight:  the negative field, normally suppressed by the process of signification, can only be liberated by a structural principle in direct opposition to syntax -- we can refer to this principle as negative syntax (or antax).         

          Though we have left it for last, negative syntax is especially important, the key to the liberation of the negative field.  Its operation has, to some extent, already been described in our earlier discussions of the development of Cubism and serial music.  Initially, negative syntax is a repellant force, working against the tendency of positive syntax to promote gestalt perception and unify the syntactic (positive) field.  Negative syntax opens the gestalt, promotes the part at the expense of the whole, perception at the expense of signification, disunifying the (positive) syntactic field while, at the same time, unifying the (negative) aesthetic field.  Ultimately, after its analytic moment has been supplanted by a synthetic moment, negative syntax is equivalent to what can be called the 'aesthetic determination' of the negative field, a pure sensory play of rhythm, proportion and surface.

          The above description of this extremely complex and revolutionary structural principle is only partially adequate.  To pursue the matter further, we must take a detour into the past.

                                                  Ars Analogi Rationis

          Strangely enough, the position we have arrived at via the practice of some of the most advanced minds of our century betrays a remarkable affinity with the thought of an obscure Eighteenth Century metaphysician, the aforementioned Alexander Baumgarten.  Usually considered the founder of aesthetics as an independent discipline, Baumgarten is nevertheless so rarely read his major work has apparently never been translated from the original Latin.

          For Baumgarten, aesthetica, the knowledge of the 'lower' faculties of cognition (i.e., the senses), cannot be reduced to the categories of logical thought, but must be treated independently, as an ars analogi rationis ('art of the analogy of reason').  Reversing the priorities of his rationalistic forbears, he concentrates not on the clarities of the mind, with its distinct, 'intensive' categories, but the clarities of the senses, with their potential for apprehension of conceptually confused but vividly observed 'extensive' particulars.  It is in the 'lower' faculty that we can find the 'perfect sensate discourse' of 'the poetic,' analogous but opposed to the 'perfect conceptual discourse' of 'the rational.'[10]

          While the greater part of Baumgarten's argument is all too heavily indebted to the rationalism (and artistic taste) of his day, its core remains remarkably fresh, providing us with a valuable insight into the meaning of the very similar analogies we have drawn.  Indeed, negative syntax can be understood as in some sense equivalent to Baumgarten's aesthetica.  Both seek to balance the cognitive equation.

                                                The Aesthetic Function

           Baumgarten, in treating aesthetic as an artifice or construct, not, as did his contemporaries, an inborn faculty for direct, unmediated knowledge a priori, places the object of his concern beyond the reach of the perennial debate over the status of the 'real.'  Instead of attempting, as have so many others, to use sensory experience as both an empirical given of thought and that which can only be redeemed by thought, he opens for sensory processes a balanced, symmetrical relation to mental processes in which neither is given, neither exists as anything more (or less) than a function.

          Taking our cue from Baumgarten, we must define negative syntax as a function analogous to (though also in opposition to) logic.  As logic can be said to determine thought, so negative syntax (aesthetic) can be said to determine perception.  Thus negative syntax promotes perception by determining it, not valorizing its supposedly privileged position with respect to 'reality' or 'presence.'

                                                 Axioms of Perception

          Moving deeper into our analogy with an analogy, we are faced with some difficult questions.  If negative syntax is, indeed, ars analogi rationis, then:  1. what aspects of negative syntax resemble what aspects of logic?  2. how does a 'logic' operating in opposition to logic work?  3. how can such a 'logic' determine sensory experience?  While an attempt to provide more or less complete answers to such questions would take us far beyond the limitations of this essay, let us suggest some paths of research which might prove fruitful.

          Of all the visual artists whose work we have thus far discussed, the only one to make a serious theoretical contribution was Mondrian.  An important clue to the workings of negative syntax can be found in his notion of dynamic equilibrium, 'a dynamic rhythm of determinate mutual relations which excludes the formation of any particular form' (Mondrian 1945a:58).  While Mondrian's meanings are often far from clear, it is possible to distill from his writings, as a key to dynamic equilibrium (and negative syntax), the following sequence:  neutralization of representation through abstraction; opening of forms (i.e., gestalts, which, even when abstract, can still signify) to space; determination of equilibrated proportions in space (equivalent to the determination of perceptual space itself).

          In 'logical' terms, this could be equivalent to:  abstraction (e.g., dealing with logical symbols or numbers rather than, say, apples); analysis (the basic tool of logical thought); ratio (the traditional term for reason itself, apparently conceived as a proportioning of logical 'space').

          Studying Mondrian's artistic development, from the earliest influence of Cubism in 1911 to the period just before his emigration to America in the early Forties, we see his principles at work in a process of reduction and distillation leading to a group of paintings that can, in fact, be characterized as axiomatic with respect to perceptual experience.  The result is a dynamic, balanced interplay of line, plane and color which cannot be perceived in terms of figure-ground and contains no gestalt.

          As a logical axiom is a single thought, self-evident to the mind, an aesthetic axiom must be a single (non-hierarchical) image, 'self-evident' to the senses.  Aided by his theoretical principles, Mondrian simplifies to the point that he can determine proportions (and, of course, colors) exclusively by eye, with no recourse to logic, representation, geometry or system of any kind.  We can compare this to the process with which Euclid arrived at his axioms by a similarly reductive, purely mental process, with no need for empirical (perceptually confirmable) input.

          The musical equivalent of Mondrian's axiomatic paintings would undoubtedly be the highly reductive, extremely brief works of Webern's early, pre-serial period (e.g. the Five Pieces for Orchestra, Six Bagatelles for String Quartet, Four Pieces for Cello, etc.).

          The tone row itself can, in a different sense, also be regarded as a kind of musical axiom.  A twelve tone series is an essentially disjunctive, equilibrated arrangement (proportioning) of the twelve pitch classes which, as the basis for an extended composition, functions as an axiom.  As with a logical proof, the entire construct inherits the properties of the axiom(s).  Thus in a well made twelve tone work, the entire piece inherits the disjunctive tonal space of the row, in addition to any special motivic/harmonic characteristics a particular row may have.  While in the hands of many composers the row can function conjunctively as a substitute for positive tonal syntax, this is not the case for Webern, whose treatment of the row always remains a fundamentally disjunctive system-for-the-disruption-of-system.

Negative Syntax, Art and Signification

          From the point of view presented here, contrary to the conventional wisdom of the 'postmodern' era, the modernism of the Cubists, Mondrian, Schoenberg, Webern, etc. is more than a style period to be followed by the next style period.[11]  It represents the founding of a new sensibility, a new mode of awareness and, like all fundamental paradigm shifts, alters our view of past and future alike.

          The modernist attack on the sign-function reveals the presence, in the words of Mondrian, of 'liberated and universal rhythm distorted and hidden in the individual rhythm of the limiting form' (Mondrian 1945b:31).  Thus negative syntax does not produce something completely new, but liberates that which has always been present but repressed.[12]

          We must think, therefore, of negative syntax (aesthetic) and positive syntax (logic, representation, signification, semiosis) as two poles of a dialectic which must pervade any but the most thoroughly sublimated sign system.  In substituting a dialectical, semio-aesthetic process for a monistic, rule-based semiotics, we may even be able to win back for systematic theory a portion of the territory now claimed by deconstructionist bricolage.[13]

          A complete elaboration of a semio-aesthetic theory of expression/communication would, of course, be a major undertaking.        At the present time, we must be satisfied with the following somewhat disconnected thoughts:

          1. In most cases of more or less traditional expression, negative and positive syntax may be seen as opposing (or, in another sense, complementing) one another on many levels.  On the lowest level, negative syntax produces the disruptions that articulate (analogous to, say, the 'phonetic' stream).  Positive syntax pulls these articulations together to produce the next ('phonemic') level.  On higher levels, the same process is repeated, negative syntax opposing the positive field just enough to make perceptible the differences which positive syntax will bring together to produce thinkable (meaningful) gestalts on the next level.

          2. The above dialectic resembles the workings of the Japanese game of go, where each side tries to incorporate space previously carved out by the other.  In all but modernist discourse, positive syntax always wins.  Thus, in traditional works of art, all the space, even that once occupied by the negative field, ends by belonging to the positive field.  The negative is usually present only in repressed, all but subliminal form.

          3. Whenever negative syntax is incorporated into the process of signification by the unification of its disruptions through positive syntax, the portion of the negative field that has been (provisionally) revealed is then 'understood' as having some sort of expressive value or adding to the impact, vividness or drama of the result.  The stronger the pull of negative syntax, the more dramatic the effect will be.  (Of course, negative syntax that has not been incorporated by positive syntax will not be understood at all and will convey only the notion that either 'something is wrong' or 'this is modern art.')

          For example, many Futurist paintings incorporate the extreme spatial fragmentations of Cubism, but use geometric structure (positive syntax) to pull the fragments together into an ultimately positive totality.  Such paintings, essentially far more conventional than those of the Cubists, have a very exciting, hyperdramatic quality, gained through appropriation of a powerful negative field.

          More traditional works are replete with less extreme, but very similar effects, where distortions, spatial disruptions, coloristic anomalies, etc. are understood as 'expressive' where and when they are comprehended positively on a higher structural level.  Negative syntax also contributes to the degree to which local relationships or particular details hold their own with respect to the whole.

          4. Negative syntax must be distinguished from weaker ad hoc devices that can have a disruptive function.  Negative syntax is a structure, albeit a structure which disrupts structure.  The key to differentiating a structure from a simple device is that the former is always associated with a field. 

          5. Of all expressive means, language alone is not fully grounded in either space or time, hence lacks a true negative field.  This is not to say that the sounds of spoken or the marks of written language do not exist in time and space, but that they are not precisely defined therein.  As soon as one attempts to be precise with the time of spoken language one begins to turn it into music (e.g., chant).  As soon as one attempts to be precise with the space of written language it becomes visual art (e.g., concrete poetry).  The precisions of language exist exclusively within the realm of signification and the logic (positive syntax) which grounds it.

          Thus, while a truncated form of negative syntax is certainly present in language and can even manifest itself strongly (e.g. Mallarme, Artaud, Joyce, Stein), language based art forms can never completely resolve onto a negative ground, thus can never move beyond essentially rhetorical devices such as overcoding or code shifting (see Eco 1979:261-275).  This may be the reason why structuralists, semioticians and poststructuralists, primarily linguists or literary scholars, have tended to either explicitly or implicitly place all artistic expression within the realm of rhetoric.

          The limitation of language with respect to the negative field has consequences for the deconstructionist enterprise, which uses language in an attempt to negativize the signifying process from within (rather than outside itself, from the realm of the senses, as is the case with, say, Cubism).  This essentially ungrounded, self-reflexive strategy can result in a fascinating, if unending, play of paradoxes and witty 'openings' of the sign, but can never resolve, as, lacking a negative field, it lacks any ground but that of the logic it seeks to demystify.[14]  Consequently, what begins as a bid for expressive freedom ends with reincorporation within the bonds of the positive.  Postmodernist art operates according to essentially the same model, choosing to ignore or minimize potential negative fields in favor of a play of mutually negativising positivities.

          There is a certain advantage to be gained from such play, which, by travelling in circles, need never fear reaching a 'dead end.'  But it is unfair and, indeed, repressive of the deconstructionists, on the basis of the limitations of language, to insist that all expressive forms share the same limitations and that, as a result, logic (ideology) can be attacked only from within itself.  Such a policy leads to mystifications as disturbing as any deconstructionism seeks to overcome.

          6. While positive syntax always reflects culturally accepted and controlled procedures and values (ideology), negative syntax seems to work against them, toward a universal experience which is not culture bound.  Initially, of course, negative syntax opposes positive syntax and, in so doing, becomes a kind of image (albeit a negative image) of that which it has engaged.  Ultimately, however, negative syntax disrupts the ideologically controlled signifying process in favor of a liberated sensory play.  The extent to which this play will reflect socially determined value systems can, of course, only be decided by examination of its function in a variety of cultural settings. 
           

          If, as it would seem, negative syntax is resistant to such local variation, it would be extremely valuable as a tool for isolating universals in cross-cultural studies of the arts and communication.  Negative syntax may, indeed, have something to do with the fact that all art forms with the exception of those that are language-based may be appreciated, if not understood, trans-culturally.  In fact, the crucial difference between the appreciation and understanding of a work of art may derive from the distinction between negative and positive syntax.

7. The discourse of the traditional Western arts, with their elaborate hierarchical structures, would seem to be far more heavily positivized than that of non-Western or 'folk' cultures.  Would careful study of the arts of these 'simpler' societies reveal a compensatory development of the negative?

                                                          Summary

          Semiotic and poststructuralist theory argues that all aesthetic experience must take its place within the essentially language-based, ideologically controlled codes of the signifying process.  While acknowledging the validity of much of this argument, we have taken exception to the notion that the world of the senses cannot be independently grounded.  Determining that any signifying process must be based on what we have called a 'syntactic field,' we found, in certain modernist paintings and musical compositions, a structural principle which disrupts this field to promote sensory experience and multireferentiality:  negative syntax.

          Following the lead of Alexander Baumgarten, for whom aesthetic is the basis of perception, we have attempted to understand negative syntax as, in his words describing aesthetic, 'ars analogi rationis.'  Indeed, certain paintings of Mondrian seem to function as 'axioms of perception,' and certain examples of twelve tone music operate, like (anti)logical proofs.

          While negative syntax was first revealed in, and can help us to analyze, modernist art, it also clearly plays an important role in traditional art, if not all forms of expression and/or communication.  In this regard, we have attempted to speculate on the manner in which negative and positive syntax operate dialectically within 'normal' communication and the meaning such a dialectic might have cross-culturally.

          These speculations are intended to stimulate further thought and should, of course, be regarded as provisional.  Sorting out the role of aesthesis vis a vis semiosis in traditional Western art and discourse, not to speak of the traditional arts of non-Western cultures, is bound to be a technically difficult, intellectually challenging and time consuming task.  Perhaps this paper will convince some readers that such a task would be worthwhile.

                                                                      References

Baumgarten, Alexander (1954).  Meditationis philosophicae de        nonnullis ad poema pertinintibus, trans. by K. Aschenbrenner         and W. B. Holther.  Berkeley: University of       California      Press.

de Man, Paul (1979).  Semiology and Rhetoric.  In Textual    Strategies, Josu Harari (ed.), 121-140.  Ithaca: Cornell     University Press.

Derrida, Jacques (1978).  Structure, Sign and Play in the      Discourse of the Human Sciences.  In Writing and Difference,    Jacques Derrida, trans. A. Bass.  Chicago: Chicago    University Press, 278-293.

Eco, Umberto (1979).  A Theory of Semiotics (=Advances in Semiotics).  Bloomington: Indiana University Press.

Grauer, Victor (1982a).  Modernism/Postmodernism/             Neomodernism.  Downtown Review 3 (1 & 2), 3-7.

-(1982b).  Montage, Realism and the Act of Vision. Unpublished      monograph.

Hodier, Andre (1961).  Since Debussy.  New York: Grove Press.

Kant, Emmanual (1966).  Critique of Pure Reason, trans. by Max    Muller.  New York: Doubleday.

Kramer, Jonathan (1978).  Moment Form in Twentieth Century Music.            Musical Quarterly 64(2), 177-187.

Kristeva, Julia (1980).  From One Identity to Another.  In Desire       in Language, Julia Kristeva, 124-147.  New York: Columbia      University Press.

Meyer, Leonard (1956).  Emotion and Meaning )in Music.  Chicago:           University of Chicago Press.

Mondrian, Piet (1945a).  Plastic Art and Pure Plastic Art.  In Plastic Art and Pure Plastic Art, Piet Mondrian.  New     York: Wittenborn.

-(1945b).  Pure Plastic Art.  In Plastic Art and Pure Plastic     Art, Piet Mondrian.  New York: Wittenborn.

The Oxford English Dictionary (1989).  Second edition, volume        one.  Oxford: Clarendon Press.

Steiner, Peter (1984).  Russian Formalism.  Ithaca: Cornell   University Press.

Wessel, Leonard P. (1972).  Alexander Baumgarten's Contribution to the Development of Aesthetics.  In Journal of Aesthetics   and Art Criticism 30(3), pp. 333-342.

                                                             Notes

[1]. An ext­­ensive, carefully argued treatment and defense of crucial aspects of the theory can be found in Grauer (1982b).

[2]. The so-called 'abstract' nature of music should not confuse the reader into thinking that because musical notes or passages cannot be translated into words they cannot have meaning.  We need not look for lexical meanings in music any more than we would look for musical meanings in language.  To say, for example, that a certain passage functions as a 'cadential figure' is already a perfectly sufficient statement about its signification within musical discourse.

[3]. For a thorough treatment of the role of the gestalt in music, see Meyer (1956).

[4]. Such is the impression given by the discussion of art in Eco (1979:261-276).  Eco treats the 'aesthetic text' as a means of 'overcoding' and/or 'code-changing', categories that appear as part of the more extensive discussion of rhetoric which follows (Eco 1979:276-298).

     Julia Kristeva, in an attempt to carve an independent place for the 'poetic language' of modernism in a spirit very close to our own, nevertheless concludes that it must posit 'its own process as an undecidable process between sense and nonsense, between language and rhythm . . ., between the symbolic and' that which is prior to symbolization.  Essentially, her notion of poetic language involves a process of continual mutation within signification, a function hardly distinguishable from that of rhetoric (Kristeva 1980).

     Further arguments for rhetoric as the basis of aesthetic experience can be found in de Man (1979).



[5]. For documentation of the links between the artists and poets of the Futurist/Constructivist school and the linguists of the Russian Formalist group, as well as the latter's influence on the development of structuralism and semiotics, see Steiner (1984).

[6]. Additional, equally relevant developments should also be mentioned:  Stravinsky's tonal bipolarities and rhythmic fragmentations disrupt the tonal/metric gestalt as effectively as atonality; Schoenberg's ironic, self-referential treatments of traditional musical materials in, for example, Pierrot Lunaire or the Serenade, mirror the 'semiotic' playfulness of Cubism; likewise Stravinsky's Le Histoire du Soldat and, of course, all his subsequent neoclassical work.

[7]. Interest in sound for its own sake drew Boulez to the concept of the 'sound object' (Hodier 1961:136-142).  For a discussion of moment form and its role in the proportional determination of time in the work of Stravinsky, Messiaen and Stockhausen, see Kramer (1978).

[8]. See Kramer (1978:181-183) for a convincing analysis of temporal 'flattening' in certain modernist compositions.

[9]. Note how effectively a piano arrangement of any traditional Western art music conveys its essential 'logic' or 'meaning' despite the instrument's very limited ability to sustain.  The greater part of Twentieth Century music, which places more emphasis on  'negative time,' where the release is as important as the attack, would not be well served by piano arrangements, and in fact they are rare.

[10]. See Baumgarten (1954), especially propositions 3, 9, 14, 15, 17, 19, 22, 112, 113.  My summary of Baumgarten owes a good deal to Wessel (1972).

[11]. For an extended discussion of the meaning of postmodernism with respect to some of the issues raised in this paper see Grauer (1982a).

[12]. A remarkably similar point of view is revealed in Julia Kristeva's notion of the chora.  See, for example, Kristeva (1980:133-137).

[13]. The paradoxes of a purely semiotic (i.e. logic-based) attack on the ideology of the signifying process are discussed in Derrida (1978).  Derrida argues that ideology can only be 'deconstructed' by an informal, anti-systematic process of disruption-from-within which he calls bricolage.


[14]. See Derrida (1978:278-281) for the classic statement on this founding paradox of deconstructionism.