PRINT November 1979

Nothing/Not Nothing/Something

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actually cross (not unlike lengths of molding) inside the depiction.

Van Gogh’s combination in a single work of just-touching border bands, an entirely nonobjective square in the very corner, and narrower bands that do cross within the representation, points toward the active neutralization that Mondrian described, since even what is represented conforms to his flat topology. In several of Mondrian’s own canvases, painted from about 1927 onward, a comparable construct can be found. In some of these, from around 1929, the L-shape, consisting of two side bands and their adjacent squares, approaches the remainder of the canvas in width, so that the whole tends to be foursquare.

In Abstraction, a drawing by Frantisek Kupka, perhaps from about 1933 (Paris, Musée National d’Art Moderne), two broad bands enter the field from the top and the left side, nearly touching, so as to isolate a large blank square in the upper lefthand corner of an already square sheet, with a small implied square in the grip of the ends of the bands and a medium-sized solid, painted square the lower right. This is more thoroughly visual in its operation than El Lissitzky’s famous page layout About 2 Squares, for his book The Story of Two Squares (1922); About 2 Squares is as verbal as a rebus, not so much for including the word “about” and the numeral “2” as for descriptively appropriating one square, as if to say, “About two of the following forms, one of which is pointed to.”

In later painting rectilinear bars that meet to produce diagonal checkering can also be found. In Leon Polk Smith’s Diagonal Passage No. 3, 1949, a post-Mondrianesque square canvas rotated to a lozenge format, an asymmetrical nine-unit grid pattern is shifted off center. Interesting ambiguities result, as where the bands defining the configuration shift back and forth between being the inside edges of some zones and the outside edges of others, which makes for a peculiarly balanced, high-strung but well-tuned, version of a thoroughly asymmetrical idea.

If we isolate the points where pairs of right angles touch points in diagonal symmetry, as in Smith’s painting, we find a configuration that in the theory of ornament is referred to as two “gammas”; this motif is a reduction from a fourfold device that had once represented the four corners of the universe, and which, when Christianized as a cross in swastika form, was called the gammadion.3 The architect Alvar Aalto was interested enough in the diagonally interacting “double gamma” to sketch twice an ancient Egyptian (hieroglyphic?) version of the motif, in a notebook drawing of The God Thot from the Temple at Luxor, Egypt, of 1954–55.4 Opposed, diagonally symmetrical angles of this sort also had an obvious fascination from the point of view of Structuralist binary classification. In his Structural Anthropology (1958) Claude Lévi-Strauss discusses a device used in body painting by the Cudaveo Indians of South America, in which the open-ended spaces between two lines intersecting at right angles are bisected, with two different designs filling diagonally opposite zones and every other wedge-shaped zone left blank.5 For Lévi-Strauss this counts as asymmetry, which indicates social hierarchy, whereas symmetry is identified with social reciprocity. However, the matter must be more complicated, since the Cudaveo face paintings include asymmetrical forms on a par with symmetrical ones, yet subject them to symmetry along the diagonal axes: Michael P. Carroll has now criticized Lévi-Strauss on this very point, suggesting that such designs, which combine symmetry and asymmetry, “are most likely to be found in societies whose members cannot clearly define their society as being stratified or not,” and expanding the consideration, interestingly, to European heraldic devices.6

Some ambiguity is present wherever a foursquare arrangement implies a Greek cross in its abutments, or, vice versa, where a cross implies adjacent rectangular fields. In the same sense, grid painting in general involves an ambiguity as regards the compartments identified with the surface and whatever bands, lines or internal edges separate them: one recalls Samuel Johnson’s amusing doubly negating definition of a “network,” in his Dictionary (1755): “Any thing reticulated or decussated, at equal distances, with interstices between the intersections.” Actually, grid painting probably lacks interest unless the merely ambivalent relation between what divides and what is in between is somehow compounded.

To compare Morris Louis’ Ladder, 1950, with Garry Rich’s Hot Link, 1973, is to observe the refinement and then collapsing fragility of the grid as a structural theme in painting. In the early work by Louis the grid is a modified, spontaneously irregular, version of the structural armature of regular unit squares that had once supported traditional—and intact—and then Cubist—and fragmented—pictorial elements, these elements having subsequently been removed, as it were, by a transitive procedure of abstraction, leaving the armature behind. The handmade, bulging irregularity of this grid united it with the otherwise hysterically diffuse forms of the rest of the composition, which it might simply have overlaid. Significantly, Louis’ grid does not extend uniformly over the surface; in fact, he allows his basically square grid, of roughly four units by four, to assert itself vertically, touching the top and bottom, just as the ground spreads out horizontally, which mutually involves the rectilinear weave of the grid and the loose lateral spread of the other forms.

There is a confidence in Louis’ abstract use of a Cubistic (and older) device that is met by a provisional or skeptical attitude in Hot Link and related works by Garry Rich. The grid, which by this time had lost its affirmative structural strength, now breaks down into unhinged clusters of only partly connected units, of different colors—although these units now seem easier to distribute in an allover way than had been the case before. By the turn of the 1960s the grid idea had even been treated with sarcasm, as in Robert Rohm’s floppy wall-mounted rope grids with the ropes partly cut and left drooping, and by such works of Alan Shields as Wadle II (Roman), 1970, where a large asymmetrical grid of painted cloth strips hangs from the ceiling in real space: both artists seem to have resorted to quasi-sculptural effects in order to criticize painting.

Checkering is in some fundamental sense an issue of colors in fixed relations, even if the units in question are only either black or white, despite E. H. Gombrich’s panicky insistence, in his (rather disorderly) The Sense of Order (1979), that a checkerboard pattern is something essentially ambivalent, in ceaseless optical fluctuation between equal and mutually competing areas of figure and ground. To say that because strips of diagonal squares, fivesquare Greek-cross clusters, X-patterns and even framed isolated squares can all be picked out of regular checkering,7 is not to say that artists do not have one or more of these configurations specifically in mind, whether we look to the colored squares in the checkered grid of an 18th-century Tantric ritual and contemplative painting,8 or to all the little foursquare, fivesquare and other formations picked out of the checkered grid in many paintings by Kandinsky. (Gombrich, satisfied with the notion, borrowed from design theory, of “counterchange,” concentrates on so much inferior 20th-century art, from the tedia of M. C. Escher through all available Optical Art.) Anyway, many chessboard grids in modern painting are colored, from the earliest abstract examples through Pollock’s Tea Cup, 1946, to the present, while modern art theory also testifies on black and white as colors in checkering.

Van Gogh thought of black and white in terms of color, as well as thinking, for instance, of the cross in analogy with window mullions, and of checkered fabric in relation to alternating colors in landscape painting. In a letter to his brother Theo, written at Arles in June of 1888, he described a hypothetical landscape consisting of a whitewashed cottage with a black door, windows and “little cross on the ridge of the roof, set against an orange field and a blue sky.” These elements, he considered, would “produce a simultaneous contrast of black and white just as pleasing to the eye as that of blue and orange.” He elaborated: “Or let us take a more amusing motif: imagine a woman in a black-and-white-checked dress in the same primitive landscape with a blue sky and an orange soil—that would be a rather funny sight, I think. In Arles they often do wear black and white checks. Suffice it to say that black and white are also colors, for their simultaneous contrast is as striking as that of green and red, for instance.” Two small sketches in the middle of the letter illustrate both suggested compositions: in the first there is an obvious analogy between the cross against the sky and the white crossbars that partition the window into a foursquare design, as there is also between a white square indicating a chimney and the solid black door; in the second, the figure of the woman in a heavily checked dress intersects at the center with the areas identified as blue/orange at the horizon.9

Henry Havard’s La Décoration (2nd ed., 1892?), a book which Matisse seems likely to have known, includes an illustration of the optical interaction of black and white, in the form of a square checkered into four alternating subsquares. Havard notes that careful examination will reveal, at the point of intersection, that the two white squares seem joined together by “a sort of dot of the same color,”10 which interested him as a case of color interaction more than for any possible ornamental application that either checkering or foursquare composition might suggest. When Roger Fry saw David Bomberg’s Ju-Jitsu, 1913 (Tate Gallery), he was less pleased by this “colossal patchwork” of the checkered grid, in which “glimmers a dazzling veil of black squares and triangles“ than he was in its suggestion of ”new plastic possibilities, and a new kind of orchestration of colour.”11

Franz Boas, considering the diagonally relating alternations of square or rectangular units in the ancient Peruvian textiles, in his classic Primitive Art (1927), made a point of the fact that, beyond the alternation of recurrent motifs positioned within the grid, changes in color increased the complexity of the alternation, “so that even when the form is the same, the tints and the color values will not be the same.”12 Much of the visual richness of these designs comes from the fact that they consist of checker and other grid patterns whose color alternation is as regular and logical as in a simple checkerboard, but of a higher order of complexity.

Matisse wrote, in an essay “On Modernism and Tradition” (1936): “A picture is the coordination of controlled rhythms, and it is thus that one can change a surface which appears red-green-blue-black for one which appears white-blue-red-green; it is the same picture, the same feeling presented differently, but the rhythms are changed. The difference between the two canvases is that of two aspects of a chessboard in the course of a game of chess. The appearance of the board is continually changing in the course of play, but the intentions of the players who move the pawns remain constant.”13 Later, in his “Testimonial” of 1952, Matisse remarked that the reason he had never been interested in playing chess was that “the signs” (meaning the identity of the pieces) never change. It is no accident that Matisse was here discussing his cut-outs, where there is often a binary opposition between forms of a single color (especially blue) on a white ground, as with the chessboard.

The main point, as Matisse put it, was that he disliked chess because its signs are all fixed: “ . . . The sign for which I forge an image has no value if it doesn’t harmonize with other signs which I must determine in the course of my invention and which are completely peculiar to it. The sign is determined at the moment I use it and for the object of which it must form a part. For this reason I cannot determine in advance signs which never change, and which would be like writing: that would paralyze the freedom of my invention.”14 Kate Linker, relying on these passages, elucidates the semiology of the chessboard for the painter: “In Matisse’s analogy, it symbolizes a painting’s formation, delineating the oppositions of elements which engender meaning through differential readings.”15 In contrast, Duchamp, who loved to play chess, explained the cerebral appeal of the game in a coloristic pun on the black-and-white polarity of the chessboard, saying that the beauty of chess is entirely in “the gray matter” (la matière grise).16

Wittgenstein thought of the checkerboard while reflecting, in 1950–51, on the question of black and white as colors: “We wouldn’t want to call a medium white if a black and white pattern (chess board) appeared unchanged when seen through it, even if this medium reduced the intensity of the other colours.”17 He asked and answered a related question: "To what extent can we compare black and white to yellow, red and blue, and to what extent can’t we? If we had a checked wall-paper with red, blue, green, yellow, black and white squares, we would not be inclined to say that it is made up of two kinds of parts, of ‘coloured’ and, say, ‘uncoloured’ ones.”18

The Byzantines were aware of the possibilities for coloristic as well as formal elaboration in checkering. Vered Lieb has called my attention to a 5th-century mosaic pavement in the church at Shavey Zion, in Israel, showing a foursquare pattern defined by an alternation between light and dark squares and elaborated by incorporating two motifs—a square knot with four lobes and a quatrefoil like those made when toying with compasses—in the four sub-squares. No two of the motifs are really the same, since each otherwise similar paired element is both inverted in its form and rotated 45 degrees: as a result, each horizontal and vertical pair (consisting otherwise of categorically opposed motifs) has something in common, while the diagonal pairing of knots and quatrefoils is equally active, thanks to having one element of each type rotated on the diagonal. Color, too, plays a part in this, the knot motifs containing yellow and red besides black (actually violet) and white, which also serves to equate “black-and-white” with alternations of other colors. The same system of binary oppositions extends to the microstructure of the ancient painting: one zone of all orthogonally set tesserae is paired with one entirely set on the diagonal, whereas in the other two squares, (both quatrefoils) the tesserae modulate from the orthogonal into curves; furthermore, the single, regularly spaced white squares that punctuate the square, orthogonally placed knot recur, carefully rotated, in its partner. One may speculate that this complex, checkered, foursquare design includes a kind of crypto-cruciformality, not only overall, in the intersecting lines implied by the abutting squares, but also in the two innocuous small Greek crosses found at the centers of both quatrefoils: a law of 427 (not strictly obeyed) had forbidden the representation of crosses on floors.19

In Cubist painting the motif of the chessboard was important not only for its intrinsic abstract potential, as furnishing anti-pictorial subject matter on a par with numerals and letters, but also for extending the proto-abstract theme of cerebral activity that was implicit in Cézanne’s various Card Players. This tendency was passed along through Duchamp’s extreme mentalism (first in early paintings, then in his increasingly detached and ironic art activities, even as he pursued the actual game of chess with a passion) and on to Conceptual art.

From the beginning, however, the chessboard also suggested that profoundly new reconstruction of the painting surface, by more or less alternating the more or less regular fragments of previous pictorial composition, which the Cubists pursued: witness paintings with chessboards painted by Gris, Marcoussis and others. Even on the provincial fringes of the movement, the excitement of this new analytical vision, and its new possibilities for painting, were felt, as in Ezra Pound’s violent Vorticist poem “Dogmatic Statement on the Game and Play of Chess (Theme for a Series of Pictures)” (1913), where the moves of the chess-pieces “break and reform the pattern” of a board "alive with light.”20

An etching called Chessboard, of 1920, by Jacques Villon (Duchamp’s brother, and one of the sitters in Marcel’s more depictively cerebral Chess Game, 1910, in the Philadelphia Museum), uses the chessboard motif to effect a thorough revision of the field as a system of interrelated units. Checker motifs were used with a high degree of abstraction by Marsden Hartley, especially in analogy with emblems in his Military Symbols drawings of about 1913–14, but Villon’s identification of chessboard and the field as a whole also developed in America. Charles Demuth’s Sketch for the Poster Portrait “Homage to Wallace Stevens,” c. 1925, consists almost entirely of a rotated chessboard pattern in which, interestingly, the squares do not simply alternate, light and dark, but are picked out and grouped into supersquares (each a foursquare cluster) that do alternate. Also pertinent here is an otherwise trivial magazine decoration that Ad Reinhardt drew while still an undergraduate at Columbia (between 1931 and ’35; Archives of American Art): where a checkerboard is also rotated diagonally, like an ironic modern version of a grid indicating perspectival recession, while vertical bands along the side edges propose a contradictory interference to recession.21 More pictorially, Charles Sheeler used a backgammon board (centuries ago chess was played on such a board) on a tabletop in his Americana 31, 1931, as though in analogy, as a represented patterned field, with a rug having an Andre-like parquet pattern of striped squares alternating on both axes, as well as a plaid fabric on a couch in the same room. A sophisticated European parallel for Sheeler’s image is Braque’s Woman Playing“Patience_,” 1941, where the figure plays cards seated at a table, with a chessboard on a chair opposite, as though suggesting the game she would play if she had a partner. More in the line of Villon’s Chessboard is Man Ray’s abstraction called Knight’s Move, 1942, where diagonal Cubist vectors crisscross a chessboard banded with black, as though the whole painting were like a chessboard across which knights’ moves might be made; in the fullness and seriousness of its dominant abstract idea, Knight’s Move links Delaunay’s great “Window” paintings with the Jasper Johns of the “Targets.”

Naturally, checkering is prevalent in the Constructive art that developed out of Cubism, but the collages of the Arps had an early and special importance. Jean Arp’s Squares Arranged According to the Laws of Chance (Museum of Modern Art), 1916–17, consists of torn, irregular “squares” of paper spaced unevenly but with an overall rectilinear order, as a system of solid rectangles masking a ground that shows through as an irregular grid in negative: this is a kind of homemade Mondrian of around 1917, and it anticipates compositions by Ellsworth Kelly, who met Arp in Paris, and the Canadian painter (later a conceptual artist) Michael Snow, that would otherwise seem exclusively Constructivistic. A Geometric Collage by Arp, from 1916, more regular in its forms but still rhythmically animated, is remarkable for isolating one checkered foursquare device within a composition that reads as an incomplete checkered whole. Its equalization of pairs of square units with single blocks two squares long—which also checker with regard to one another—and its division of one square into alternating equal stripes—along with a doubled square having similar stripes that are twice as wide—are interesting modifications of the regularity of the checkered grid that also evoke the procedures of some present-day painters (James Juszczyk, Joanna Pousette-Dart). The famous Duo-Collage, 1918, executed by both Jean Arp and Sophie Tauber-Arp, with its checkered grid of vertical oblongs. one or possibly two of which are split in two, has also proved to be of importance for later painting.

Schwitters also made use of the foursquare checker. His Albert Finslerbild, 1926, subjects the device to a kind of mock-Cubist torque, wrenching it off the horizontal, in analogy with a wittily concrete play on the switchovers, in Cubist painting, where the edge of a motif or form is cut off by another line and has its value reversed. (Checkering, indeed, may be considered only a special type, if the most abstract, of this procedure). In Schwitters’ painting this alternation even subsumes a raised trapezoidal form affixed to the canvas. The stylistic differences between this conception and that of Van Doesburg’s Simultaneous Counter Composition, 1930, are not enough to distract from the structural similarities, especially the skewing of a foursquare device and the use of black bands like fragments of Mondrianesque structural grids, plus the locking of a vertical rectangular form into the lower right. In both cases we even find a diagonal edge in the upper left and the placement of the largest form, a truncated quadrilateral, in the lower lefthand corner.

Van Doesburg’s painting is like an attacked, criticized, somewhat dismantled version of a canvas like his own Simultaneous Composition of 1929 (Yale University Art Gallery). Recent artists seem to have taken this dismantling even further, to consider Paul Huxley’s Untitled No. 80, 1967, where a large polygonal form at the bottom seems to render a single element of the Schwitters or Van Doesburg perspectivally, in the context of a fragmentary but stable foursquare device. This pseudo-perspectivalism is carried to an even more specialized and detached extreme in Ellsworth Kelly’s Black Green, 1968, with a Minimalist literalism: Tony Smith, whose sculpture around the same time dealt articulately with cubic faceting, had already exhausted the interest of a flat but perspectivally allusive cubic form in a very early painting, Untitled A, 1933. Must one resist the inference that the sequence, in this comparison of Schwitters, Van Doesburg and Kelly, runs downhill? This is not a simple matter, Van Doesburg’s Counter Composition, for instance, being if anything, more inventive than his earlier but relatively inhibited Composition.

Duchamp’s identification of chess with purely cerebral activity in the name of art and to the exclusion of plastic manifestations, which become legendary in the 1920s, was more than a stylistic matter. Interested enough in the theory of chess to write, with V. Halberstadt, L’Opposition et les cases conjuguées sont reconciliés (1932; Opposition and Sister Squares are Reconciled), a treatise on the endgame, Duchamp had for some time given the impression that for him chess had displaced art. He was not, however, alone among the moderns in eschewing the masterly touch in art. In the otherwise distinct realm of Constructivism László Moholy-Nagy, in 1922, ordered five paintings by telephone from a sign factory (and depending on graph paper and standardized color charts to do it). Moholy recalled later “it was like playing chess by correspondence.”22 By the late 1950s, Naum Gabo, reflecting back on his own esthetic, maintained that the chessboard offers only one kind of order, while still remaining loyal to regularities discoverable in the real world as models for art: “Nature is not a chessboard and we are not pieces moving on it within strictly prescribed coordinates. The patterns of Nature can be as many as our consciousness is capable of drawing on it.”23 Gabo’s remark has a defensive tone, no doubt because at the time his own de-emphasis on the manual would have been at odds with the insights of current expressive painting. Still, his phraseology is symptomatic, in its inorganic and cerebral emphasis, of a whole attitude of withdrawal from physicality, whether by Duchamp or by the classical Constructivists, and in this the appeal of chess imagery is significant. For Otto Rank, writing in his Art and Artist: Creative Urge and Personality Development (1932), the history of chess itself shows how—"the degradation of the bodily faculties, the foot-soldier, peasant, runner, in favor of the head and king, who is more spiritual, finally gave the game its wholly intellectual character; and it is probably connected . . . with the decay of the body and its parts, which are now survived only by the spirit in its immortal works.”24

Still, the possibilities for abstract painting with the chessboard as a motif, with its nondescriptive interior boundaries, can be indicated by considering it as one principal answer to the desire for a new kind of imagery whose boundaries might be as compositionally concrete as the concrete edge of the canvas. As Apollinaire wrote in a 1913 notice on Picasso, “The object, either real or trompe-l’oeil, will doubtless be called upon to play an increasingly important role. It constitutes the internal frame of the painting, marking the limits of its depth just as the frame marks its exterior limits.”25 In contemporary painting, this compares readily with the concept of an “internal edge” as when Jeremy Gilbert-Rolfe wrote of Ryman’s Untitled No. 13, 1960 (Amsterdam, Stedelijk Museum), that an internal edge "undermines the continuity between inside and outside otherwise implied in the interaction between the work and the wall. . . .”26 Such a view, needless to say, is more comprehensive and dialectical than what Apollinaire had in mind in 1913. The difference is a function of the history of abstraction. But it is also a matter of understanding oppositions, of which a line or edge within the field and the outside edge of the stretched canvas is but one. Here is where checkering, where forms are evident exclusively in their mutual opposition, shades into philosophy.

Aristotle appreciated the antithetical element in, at least, natural creation, as the Physics testifies: “. . .Whenever anything is created or destroyed it necessarily passes out of or into either its opposite or some intermediary state. And since each group of intermediates is derived from some pair of opposites (colors, for instance, from black and white), it follows that whatever comes into existence by a natural process is either itself one of a pair of opposites or a product of such a pair” (I.v).27 And this principle traces back further to the Pythagorean “table of oppositions” (odd/even, light/darkness, square/oblong, etc.).

However, the dualistic Manichean heresy, founded in the 3rd century by Mani, who, interestingly enough, was a painter, has always tempted the European mind to consider the world as categorically dual, with everything physical belonging to a sovereign power of evil (T. S. Eliot said that Manicheanism is the heresy most characteristic of the West). We come close to Manichean duality in the Polish Constructivist Wladyslaw Strzeminski’s notion of the “mutual neutrality of forms,” exposed in his essay “B-2” (1924)28 and visually evident in those of his paintings which divide into two asymmetrical but balanced areas, each of a different color—a procedure that appeared recently in some paintings by Leon Polk Smith. That Strzemiński claimed to have derived his principle from positivism, especially from the consideration of progressive formal elaboration, helps to explain its undialectical character, since then it evokes what Mao Tse-Tung, in his famous essay “On Contradiction” (1937), called “metaphysical mechanistic materialism and vulgar evolutionism.” We come even closer to outright Manicheanism in Theo van Doesburg’s Principles of Neo-Plastic Art (1925), from which the following text will suffice to show the persistence of such thinking even in modern art theory: “The religious principle is in fact another form in which fundamental reality is expressed. The duality of this reality is symbolized in the Christian religion in the antithesis God-Devil (Christ-Judas, position and counterposition).”29 Needless to say, our concern here is not with proving that van Doesburg was a heretic, but to show that the Manichean principle of a world divided between two distanced and opposed forces, with mankind suspended, helplessly, between them, is always available.

In its general workings, the complex binary mutual distinction of units that prevail in other checkering and abstract configurations, can be compared with traditional discrimination in thought, from the Aristotelian tradition as passed on by St. Thomas Aquinas—“. . . One negative difference is restricted by another that marks a distinction from more things”30—to William James—“Difference, commonly so called, is thus between species of a genus.”31 The remark by St. Thomas precedes a chapter of his Summa contra gentiles (written 1259–64) entitled ”That in God There is No Composition,“ while James’s comes from a section entitled ”Are All Differences Differences of Composition?“ in the fascinating chapter on ”Discrimination and Comparison“ in his Principles of Psychology (1890). In our time, Robert Rauschenberg’s comment on his own all-white paintings, made in a letter to Betty Parsons in 1953, that “they are large white (one white as one God) canvases,”32 is notably close to St. Thomas’ principle ”that in God there is no composition."

For Luther the opposition of, especially, adjacent contraries, was a central theological consideration, not only in such sublimely comprehensive matters as the apparent paradox of Christ’s being both hidden (absconditus) and revealed (revelatus) in the abasement/glory of the Cross, but also in the close reading of specific texts. In his 1517–18 Lectures on the Epistle to the Hebrews Luther observed (of Heb. 12.11): “Frequently in the scriptures there are two opposite ideas side by side. For example, judgment and righteousness, wrath and grace, death and life, evil and good. This is what is referred to in the phrase ‘. . . An alien work is done by him so that he might effect his proper work’ (Isa. 28.21),”33 which is to indicate that in such oppositions some dynamic analysis is called for.

Paul Overy has already applied to De Stijl abstract composition the famous dictum of Spinoza that “‘all determination is negation’—things are defined by reference to their boundaries, that is, where they change into something else. (There is a constant insistence in the writings of the De Stijl artists on relations rather than things).”34 This is also the form in which Engels gives the same quotation, in his Anti-Dühring (1878): “Long ago Spinoza said: Omnis determinatio est negatio—every limitation or determination is at the same time a negation.”35 Although traditional, this would seem to be an imprecise transmission of Engels’ remark, which occurs in a letter written at The Hague to Jarig Jellis on June 2, 1674, and which, it happens, is more suggestive still for the esthetics of painting, especially as regards figure/ ground relationships. There, after explaining that ”he who says that he perceives a figure merely indicates that he conceives a determinate thing, and how it is determinate,“ and that ”this determination, therefore, does not appertain to the thing according to its being, but, on the contrary, is its non-being," Spinoza continues: “As then figure is nothing else then determination, and determination is negation, figure, as has been said, can be nothing but negation.”36

Engels’ discussion, in Anti-Dühring, of negation, drawing on Hegel and arguing for dialectics and against metaphysics, suggests an issue of mere, simple negation in some contemporary art. Engels investigates the triviality of a mere negation of a negation, in comparison with concrete negation. “I negate a grain of barley,” he writes,

. . . when I grind it down, an insect when I crush it underfoot, or the positive magnitude a when I cancel it, and so on. Or I negate the sentence; the rose is a rose, when I say: the rose is not a rose; and what do I get if I then negate the negation and say: but after all the rose is a rose?—These objections are in fact the chief arguments put forward by the metaphysicians against dialectics, and they are eminently worthy of the narrow-mindedness of this mode of thought. Negation in dialectics does not mean simply saying no, or declaring that something does not exist, or destroying it in any way one likes. . . . If I grind a grain of barley, or crush an insect, it is true I have carried out the first part of the action, but I have made the second part impossible. Each class of things therefore has its appropriate form of being negated in such a way that it gives rise to development, and it is the same with each class of conceptions and ideas. . . . It is clear that in a negation of the negations which consists of the childish pastime of alternately writing and cancelling a, or of alternately declaring that a rose is a rose and that it is not a rose, nothing comes out of it but the stupidity of the person who adopts such a tedious precedure.37

It is worth digressing to point out briefly the surprising adumbration by Engels in this passage of, yes, Gertrude Stein’s famous monogrammatic dictum “A rose is a rose is a rose,” which she wrote into her play Sister Emily in 1913 (published in Geography and Plays, 1922). In the same year, in his Art (preface dated November 1913; preface to the 2nd edition, dated October 1948, claims that the 1st edition records “what I thought and felt in 1911 and 1912”), Clive Bell asked the question, in formulating the notion of significant form, “For, after all, what is a rose?” Bell compared the work of art to a rose as being “the result of a string of causes.” Has the Stein text, or Clive Bell’s for that matter, any connection with Engels’ passage?

In any event, Engels’ exposition of constructive negation may apply illuminatingly to the turn away from painting and sculpture, on supposedly radical grounds, that was seen in the later 1960s and earlier 1970s, when some artists sought not only to leave plastic art behind but also to negate it at the same time. (Historically, this tendency gained momentum by riding in the wake of Duchamp, whose “Rose” [later “Rrose] stage-name was adopted in 1920.) Especially if we consider grid painting as the last procedural approach to abstraction that many artists were to be willing to acknowledge, a particular work by Joseph Beuys takes on special importance at a time when the crisis was not yet even widely apparent. Beuys’ Ghengis Khan’s Flag, of 1961 (Krefeld, Kaiser-Wilhelm-Museum) remains a painting—pigment of some kind on cloth—even as it separates itself from conventions governing what painting generally looks like. However far-fetched this might seem, it even opens itself to comparison with a well-known feature, admired by Vasari, of one of the great monuments of the pre-history of grid painting, as well as of bourgeois Humanist realism, the crisp rectangular folds in the tablecloth of Leonardo’s Last Supper, 1497 (Milan, S. Maria delle Grazie). At the same time, consisting as it does of a (Cézannesque?) partly filled in system of rectangles, it points up ”process" as well as commenting on grid composition.

By comparison, other types of art—whether hiding out as sculpture or remaining within the realm of painting but, as it were, on strike against it—came closer to Engels’ idea of undialectical negation. One of the most important works of art of this kind from the 1960s was Dennis Oppenheim’s Directed Seeding—Cancelled Crop, executed at Finsterwolde, in the Netherlands, in 1969, which comprised the planting of a wheat field and its subsequent harvesting in an enormous “X” pattern. Here allusions to painting were deliberate, although made from a position outside the discourse of painting: in Oppenheim’s words, “Planting and cultivating my own material is like mining one’s own pigment (for paint)—I can direct the later stages of development at will. In this case the material is planted and cultivated for the sole purpose of withholding it from a produce-oriented system. Isolating this grain from further processing (production of food stuffs) becomes like stopping raw pigment from becoming an illusionistic force on canvas.”38 What was it Engels had said about grinding down a grain of barley? Oppenheim’s cancelling ”X“ can be found as a recurrent motif, with the clear function of negation, in works by the prolific Spanish Marxist painter Antonio Tàpies, and, in the last few years, in Katherine Porter’s paintings, Swann’s Song, 1975 (Pittsburgh, Carnegie Institute), for example. The motif obviously originates in the making of working drawings, where the artist changes his mind and crosses out a division or zone, or where he merely wants to make an area apparent (as when workmen soap an ”X" on windows in buildings under construction). As such, some of the most interesting examples of this device are Mondrian’s little abstract sketches on opened out cardboard cigarette packages, works such a Classical Drawing No. 17: Blue Line Cigarette Pack Cover, 1939.

The crisis in painting and sculpture dates back at least a decade earlier than its most ostentatious manifestations of around 1970. This is not ultimately a matter of style, and not even primarily a function of the fabulous success of the few best known practitioners of one or two discrete styles, although those who think that it did not manifest itself in style also oversimplify. More profoundly, it had to do with a posture of detachment from large issues of meaning and from all deep analysis except the most psychologistic. Take a distinguished example, William Empson’s classic Seven Types of Ambiguity (1955), describing the most ambiguous of the ambiguities in Empson’s taxonomy, that where “the two values of the ambiguity are the two opposite meanings defined by the context, so that the total effect is to show a fundamental division in the writer’s mind. . . . The criterion . . . becomes psychological rather than logical, in that the crucial point of the definition has become the idea of a context, and the total attitude to that context of the individual.” Furthermore:

A contradiction of this kind may be meaningless, but it can never be blank; it has at least stated the subject under discussion, and has given a sort of intensity to it such as one finds in the gridiron pattern in architecture because it gives prominence neither to the horizontals nor to the verticals, and in a check pattern because neither [N. B.] colour is the ground on which the other is placed; it has at once an indecision and a structure, like the symbol of the Cross.39

Even astute literary or artistic analysis can be content with operational consideration, a description and classification, removing itself as far as possible from the moral content of contradiction.

It is a newer mistake to assume that a teleology of reduction governs the progress of the modern tradition. If, here, we have seen checkers and grids breaking down before our very eyes, it will be useful to observe how certain younger artists, not even very closely related in stylistic terms, may subject a preexisting, in this case, Constructivist, idea, to subtler elaboration than the last generation was prepared to do.

The starting point here is the square with one of its quarters isolated or removed, an interesting variant of the foursquare checker idea in which the relation of part to whole is not indicated, either by four comparable lines or linear abutments or by positive-and-negative alternations between the four subsquares, but is instead only inferred. This special kind of foursquare has sculptural as well as pictorial possibilities, no doubt because it can be used in a structurally supporting way, whereas a square physically cut into four subsquares results in four simply separate squares of material. One of the masterpieces of Polish Constructivism, Katarzyna Kobro’s small painted steel sculpture Space Composition 2, 1928 (Lódz, Muzeum Sztuki), seen in the Guggenheim’s great exhibition “The Planar Dimension: Europe 1912–1932,” perfectly exploits the sculptural possibilities of this idea. In our own time, Christopher Wilmarth’s Wyoming, 1972, where a square of steel is cut and folded so as to support a square of etched glass, one of its quarters corresponding with one quarter of the overlaying glass, we see comparable incarnation of the same idea, made at a time when Kobro’s sculpture was unknown to American artists.

In painting, Ellsworth Kelly’s 1970 Two Panels: White Square with Black must be the most simplistic possible presentation of the same idea. True, an uninflected Minimal obviousness seems to the point in this work, whose general air of negation would have been even more thorough if even the basest colorism of black and white could have been denied (Kelly being otherwise one of our greatest colorists). Interestingly, this painting, whose single square of white is embraced by an “L” of three times its area in black, might be likened to just the extreme corner of one of Noland’s square lozenges, such as Go, 1964. But its square of white embraced by three squares’ worth of black (Kelly seems to assume the ubiquitous white walls of the 1960s and ’70s, against which a black square bracketed by white would look like a small square merely pictorially set against a larger one), more interesting still, constitutes the exact inverse of a vivid literary metaphor that came to St. Augustine’s mind when he was trying to explain the Manichean conception of the cosmos: “ . . . Lest . . . [the region of darkness] appear to be a fraction equal in amount to half of that representing the region of light, they narrow it . . . on two sides. As if, to give the simplest illustration, a piece of bread were made into four squares, three white and one black; then suppose the three white pieces joined as one, and conceive them as infinite upwards and downwards, and backwards in all directions: this represents the Manichean region of light.”40

Younger painters have dealt with this elemental formal notion from a more critically optimistic impulse, acknowledging the end of Minimalist insight, to challenge its more complex possibilities. Sean Scully’s series of untitled gouache drawings of 1976, for example, revives plastic issues that also operate in Kobro’s sculpture, especially the fact that the pairing of sub-squares, by painting them a different color from other pairs, necessitates intuitive choices. In one Scully drawing, for instance, the four subsquares paired in three different ways, share either solid white or gray stripes or solid black: in each case two squares are united by each decision, the results overlapping, with all four subsquares further differentiated as as result. Yet solid white and solid black cannot overlap, so we must be content with their indirect connection as the pair not overlaid by gray stripes. The sculptural equivalent of this decisive complexity in Kobro’s work is apparent if we consider the discrepancies between its front and side elevations and the plan, seen from above. Jeremy Gilbert-Rolfe’s foursquare canvases of the last three years engage similar issues with respect to four colors, without admitting the graphic inflection of, in Scully’s drawings, the stripes that, in Scully’s paintings, cover the whole surface. At present, such paintings by Gilbert-Rolfe entertain a remarkably varied range of colors and yet maintain systems of interrelation between the various quarters. What Scully and Gilbert-Rolfe, both of whose ongoing work has other preoccupations, share, is an involvement with the synthetic possibilities—the possible richness and complexity—of such a fundamentally simple configuration, which Katarzyna Kobro would understand, and which hardly amounts, in a Minimalist way, to something about which nothing analytical or critical could be said. Theirs are not “paintings of nothing.”

In the next, and final, essay in the present series various other encouraging developments in the modern tradition can be considered.

Joseph Masheck



1. Joseph Masheck, “Pictures of Art,” Artforum, May 1979. pp. 26–37; the fourth in a series of Artforum articles of which the present essay is the fifth and next to last. The first three were “Cruciformality,” Summer 1977, pp. 56–63; “Hard-Core Painting,” April 1978, pp. 46–55; and “Iconicity,” January 1979, pp. 30–41.

2. Piet Mondrian, “Plastic Art & Pure Plastic Art,” in Robert L. Herbert, ed., Modern Artists on Art; Ten Unabridged Essays, Englewood Cliffs, N.J., 1964, pp. 114–30.

3. Archibald Christie, Traditional Methods of Pattern Designing; an Introduction to the Study of Formal Ornament, 2nd ed., Oxford, 1929, pp. 40–41.

4. Illus., Alvar Aalto, Sketches, ed. Göran Schildt, trans. Stuart Wrede, Cambridge, Mass., 1978, fig. 60 on p. 120.

5. Claude Lévi-Strauss, Structural Anthropology, trans. Claire Jacobson and Brook Grunfest Schoepf, New York, 1963, p. 252, with fig. 20.

6. Micheal P. Carrot. “Claude Lévi-Strauss on Art,” The Dumb Ox (Northridge, Calif.), No. 8 (Winter 1979), pp. 18–21.

7. E.H. Gombrich, The Sense of Order; a Study in the Psychology of Decorative Art (The Wrightsman Lectures, IX), Ithaca, N.Y., 1979, p. 131 with fig. 142.

8. Illus., Ajit Mookerjee and Madhu Khanna, The Tantric Way; Art, Science, Ritual, Boston, 1977, fig. on p. 89.

9. Vincent van Gogh, Complete Letters, Greenwich. Conn., 1958, vol. III, p. 490; facsimile of letter, illus., p. 487.

10. Henry Havard, La Décoration (Les Arts de l’ameublement), 2nd ed., Paris, n.d. (1892?), pp. 109–10, with fig. 87 on p. 110.

11. Roger Fry, “Two Views of the London Group,” The Nation (London), March 14, 1914, pp. 998–99; qu. in William Lipke, David Bomberg; a Critical Study of his Life and Work, New York, 1968, p. 42.

12. Franz Boas, Primitive Art, New York, 1955, p. 38, with detailed analytical tabulations.

13. Henri Matisse, “On Modernism and Tradition,” fr. The Studio, May 1935, in Matisse on Art, ed. Jack D. Flam, New York, 1978, pp. 71–73.

14. Matisse, “Testimonial,” in Matisse on Art (previous note), pp. 136–37.

15. Kate Linker, “Matisse and the Language of Forms,” Arts Magazine, May 1975, pp. 76–78.

16. Pierre Cabanne, Entretiens avec Marcel Duchamp, Paris, 1967, p. 24; thanks to Bert M. P. Leefmans for pointing to this remark.

17. Ludwig Wittgenstein, Bemerkungen uber die Farben / Remarks on Colour, ed. G. E. M. Anscombe, trans. Linda L. McAlister and Margarete Schättle, Berkeley and Los Angeles, n. d., Pt. 1, par. 47, p. 8e.

18. Ibid., Pt. III, par. 37, p. 22e.

19. Ernest Kitzinger, Israeli Mosaics of the Byzantine Period, New York , 1965, p. 8. (not discussing the cruciformal idea).

20. Ezra Pound, “Dogmatic Statement on the Game and Play of Chess (Theme for a Series of Pictures),” Blast (London), November 1913, p. 19.

21. On microfilm: New York, Archives of American Art (Smithsonian Institutional), Reinhardt archive, Reel N69–100, frame 19.

22. László Moholy-Nagy, “Abstract of an Artist” (1945; 4th rev. ed., 1947), in his The New Vision and Abstract of an Artist (Documents of Modern Art), New York, 1947, pp. 65–87, here p. 79.

23. Naum Gabo, Of Divers Arts (The A. W. Melon Lectures in the Fine Arts,1959) (Bollingen Series, XXXV/8), Princeton, 1962, p. 57.

24. Otto Rank, Art and Artist: Creative Urge and Personality Development, New York, 1932, pp. 315–16.

25. Guillaume Apollinaire, “Pablo Picasso” (1913), in Apollinaire on Art, ed. Leroy C. Breunig, trans. Susan Suleiman (Documents of 20th-Century Art), New York, 1972, pp. 279–91, here p. 279.

26. Jeremy Gilbert-Rolfe, “Appreciating Ryman,” Arts Magazine, December 1975, pp. 70–73.

27. Aristotle, Natural Science, excerpted in Aristotle; Containing Selections from Seven of the More Important Books, ed. Philip Wheelwright, rev. ed., New York, 1951, p. 7.

28. Wadysaw Strzemiński, “B-2,” quoted and discussed in Andrzej Turowski. “Strzemiński, le group ‘a. r.’ et ses contemporains” (Fr. summary), in the Muzeum Sztuki catalogue Grupa "a. r.,” Lodz, 1971, pp. 46–49; I am grateful to the Muzeum Sztuki for a copy of this.

29. Theo van Doesburg, Principles of Neo-Plastic Art, trans. Janet Seligman, New York, 1968, p. 25.

30. St. Thomas Aquinas, The Summa Contra Gentiles, trans. English Dominican Fathers, London, 1924, Vol. I, ch. xiv, p. 34.

31. Williams James, The Principles of Psychology, 1904. Vol. I, p. 529.

32. Qu. Lawrence Alloway, “Rauschenberg’s Development,” in the Smithsonian Institution catalogue Robert Rauschenberg, Washington, 1976, p. 3.

33. Martin Luther, Lectures on the Epistle to the Hebrews, in his Early Theological Works, ed. and trans. James Atkinson (The Library of Christian Classics), Philadelphia, 1962, pp. 233–34; qu. Regina Prenter, “Luther’s Theology of the Cross,” fr. Lutheran World, VI (1959–60), pp. 222–23, repr. as a tract, Philadelphia. 1971, pp. 1–2.

34. Paul Overy, De Stijl, London. 1969, p. 37.

35. Frederick Engels, Herr Eugen Dühring’s Revolution in Science (Anti-Dühring), trans. Emile Burns, ed. C. P. Duff, New York, 1939, p. 155.

36. Benedict de Spinoza, Philosophy of Benedict de Spinoza, trans. H. M. Elwes, New York, 1936, Letter 50, pp. 374–76. In the Latin original the last sentence reads “Quia ergo figura non allud, quam determinatio, & determinatio negatio est; non potent, ut dictum, aliud quid, quam negatio else”, Spinoza, Opera, ed. Carol Gebhardt, Heidelberg, 1925, Vol. IV, pp. 238–41, here p. 240.

37. Engels, Anti-Dühring (note 35), pp. 155–56.

38. Dennis Oppenheim, “Catalyst 1967–1974,” in Alan Sondheim, ed., Individuals; Post-Movement Art in America, caption to illus. of the work on p. 50.

39. William Empson, Seven Types of Ambiguity, New York, 1955, pp. 217–18.

40. St. Augustine of Hippo, “Against the Epistle of Manichaeus Called Fundamental,” trans. Richard Stothert, in his Writings Against the Manicheans and Against the Donatists (A Select Library of the Nicene and Post-Nicene Fathers of the Christian Church, 1st set., IV), New York, 1887(?), repr. Grand Rapids, 1974, p. 139.

I am grateful to the John Simon Guggenheim Memorial Foundation for supporting this and related investigations.