FLATNESS has been one of modernism's greatest assets - and one of its most persistent dogmas. It all began when Cezanne, Gauguin, Seurat, and other Post-Impressionists decided that their canvases were no longer ''windows'' through which the viewer could peer at mountain vistas or lifelike heroic events but flat surfaces upon which depth, volume, and the appearances of nature could only be implied through various rigidly controlled formal devices.

Cezanne's tiny, exquisitely orchestrated wedges of paint, Gauguin's flat areas of color, and Seurat's modulated clusters of dots led to even more strictly horizontal structurings by the Cubists and Constructivists and to a kind of glorification of two-dimensionality by Mondrian and Kandinsky.

Flatness was ''in.'' To be ''modern'' one had to avoid Renaissance perspective, illusion of depth or volume, and, particularly, straightforward depictions of actual people, places, or events.

The dogma of flatness permeated every aspect of the modernist world. Even such powerfully expressive figures as Picasso, Kokoschka, and Beckmann modified their imagery to conform to the prevailing orthodoxy. Only the Surrealists resisted, making a virtue out of heresy by emphasizing deep space, three-dimensionality, and precise renderings of objects and human beings. They were, however, frowned upon by the modernist purists, and were generally respected more for their impact upon such artists as Miro, Gorky, and Pollock than for their own work.

Abstract Expressionism, for all its passion and improvisational freedom, was still based upon the sanctity of the flat picture plane. Pollock's labyrinthian images, Kline's formal collisions, Rothko's color vibrations, and Stamos's secret rustlings all took place in a pictorial universe that was skin-deep. What these artists brought into being was carried further by the second-wave Abstract Expressionists, by the Hard Edge painters, and, later, by the Minimalists.

Even the Pop artists took flatness to heart, if not so much during the first years of the movement, then certainly as each of them brought his individual style to maturity. Lichtenstein and Rosenquist, in particular, achieved monumentality by moving their forms laterally on increasingly huge canvases. Warhol, not to be outdone, expanded his serial approach by arranging up to two dozen identical and equal-size images on the surface of his canvases.

The first real break with the dogma of two-dimensionality in recent years came with the Photo-Realists, who needed spatial depth and volume to produce their meticulous, photo-inspired paintings. Richard Estes was especially dependent upon traditional perspective devices for his sharply detailed studies of city streets. And most of his colleagues established their reputations by creating the illusion that the viewer could step into their compositions.

By the early '70s, even more painters had rejected flatness for depth and three-dimensionality, and by 1980 hundreds of exceptionally talented younger artists had turned their backs on the modernist position entirely in order to devote themselves to the frank depiction of the world around them. Some youngsters had begun in an abstract or minimalist mode, others had tried their hand in a variety of other up-to-date styles. But all were finally united in the view that a painting could once again be a ''window'' through which the viewer could look.

The modern purists, as was to be expected, were not pleased. All such work, to them, was suspect if not regressive. There isn't much they can do about it, however, for our younger painters are more open to alternative approaches than were their elders. Those who feel comfortable in a ''flat'' mode work in that fashion and those who don't, cast about for other means.

Two- vs. three-dimensionality has itself become the subject of some intriguing and effective prints by M. C. Escher, who devoted much time to examining the paradoxes of spatial illusion. It has also challenged Clarence Carter, who has fashioned a number of pictures in which flatness and depth meet head on to produce extremely handsome images that are both subtly decorative and illusionistic.

In his 1981 ''Labyrinthine,'' we look down a flight of stairs to the next landing, and then down another flight to the level below that. The angle is steep, and the depth is considerable, and yet we cannot get over the impression that the image is actually flat.

This illusion is heightened by Carter's use of color. The bannisters are yellow, the wall immediately below is a rich orange, and the wall on the left is a deep red. Since both orange and red are warm, ''advancing'' colors, their presence on the lower floor conflicts with our downward perspective reading of the stairs. This creates a spatial contradiction that Carter neatly stabilizes by a few blacks, browns and bluish-grays, and by arranging the work's primary shapes as though the picture were a flat design.

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