Carroll Sockwell's abstract art is precisely paradoxical. It suggests assorted certainties and then gracefully eludes them. His present show at the Harry Lunn Gallery, 406 7th St. NW, is elegant and anguished, somber and yet playful, rigorous yet free.

Sockwell, like his pictures, is not easy to pin down. He has painted here for years. In 1963, when he was only 20, he did a 40-foot-long mural at D.C. General Hospital. A slim, slim-fingered man, he regularly appears at Washington art openings, art parties and artists' bars. His tailoring, at all times, is stylish, impeccable. Yet his art contains disorder. It has always been difficult to label. Perhaps because it draws from a variety of styles, and belongs to no one school, he has never quite received the recognition he deserves.

His champions have been many. They include Walter Hopps, who guest-curated this show. And James Harithas, who'd just become director of the Corcoran Gallery of Art when he showed Sockwell's L-shaped canvases in an exhibit of new talent (with Michael Clark, Bob Newmann and Ken Wade) in 1968. And dealer Harry Lunn, who is departing for Manhattan, chose to display Sockwell's work in his final Washington exhibit of local art.

Though Sockwell's art has in it something of New York--his calligraphic freedom recalls '50s action painting--his work in many ways is distinctly Washingtonian. Its small scale calls to mind the pictures at the Phillips. Its openness and air and its Euclidian geometries also adhere firmly to Washington traditions. Sockwell may be viewed as a sort of latter-day Washington Color Painter. But that label, tied to Sockwell's work, seems oddly indistinct.

Sockwell doesn't often paint. He rather tends to draw with charcoal stick or pencil. Often he makes collages. Though he's loyal to geometry, to parallels, diagonals, triangles and squares, the formal shapes he uses are often incomplete or broken. And the colors he deploys so well are wholly unlike those of other Washington Color Painters.

They are rarely ripe or startling. Sockwell's palette runs from white through gray to black. Though he also plays with primaries--tiny, subtle touches of red and blue and yellow twinkle in his fields--he seems to work with shadows rather than with sun. His art is rarely bold. Despite its hints at chaos, it is delicate and intimate. His pictures may be dark, but they billow and they breathe.

Even when he uses scraps--bits of wrinkled metal, awkwardly bent nails, or torn parts of cigarette packs--his pictures keep their elegance. More than most locally made abstractions, they gracefully allude to works by other artists-- Robert Motherwell, for instance, or Kandinsky or Kurt Schwitters. Hopps, asked to pick a phrase to describe Sockwell's art, finally came up with one: "Classicism in despair." The show at Lunn's is handsomely installed. It closes June 4. The Museum Guards' Exhibit

No Washington museum is more gracious than the Phillips Collection, and one reason for its graciousness is its nonofficious guards. Most of them are young. None of them wear uniforms. They seem to like and understand the pictures they protect. Not surprisingly, lots of them are painters: 27 members of the Phillips staff are now exhibiting together at the Art Barn, 2401 Tilden St. NW.

Their show is called "The Museum Muse." The objects on display, like those at the Phillips, tend to be non-shocking, subtly colored, small. Few of them are awesome, and none of them are fierce.

Among the most appealing are Barbara Grupe's little dappled landscapes. Wendy Feltman Garner's "Sunflower in the Morning" and Anne Highton's watercolor still lifes are comparably restful. Though well-known Willem de Looper is an exception, as is Shahla Arbabi, most of the artists in this show avoid complete abstraction. (De Looper, come to think of it, gives lots of his abstractions a sort of landscape air.) Karen Schneider's little picture looks abstract at first glimpse, but at second it appears to show a bright island in dark seas.

The collection of the Phillips may have influenced many of these artists. Perhaps it influenced their teachers. More than half of the artists in this exhibition studied at George Washington or American universities, schools where Duncan Phillips' taste has ruled for many years. The show closes May 29. Photos of Mayan Ruins

Because she shows us eerie things--jungle-nibbled ruins redolent of ancient gods and sacrifical victims--Marilyn Bridges' photographs, now at Meridian House, 1630 Crescent Place NW, ought to seem mysterious. But they don't. Because she took them from the air, while buzzing Mayan ruins with her single-engine Cessna 172 Skyhawk, they ought to look surprising. But the more of them one sees, the more one's surprise dims.

These now-empty courtyards, stone walls and bold stepped pyramids stamp clean and forceful forms on the chaos of the jungle. But these photographs are all pretty much alike. Bridges prints in such high contrast that foliage becomes little more than blackness while stone work seems to glow. Her compositions seem a bit ill-considered, as if her pictures were (as, of course, they were) snapped quickly on the wing. Her subjects are more interesting than her images. They are all right as documents. They are not much as works of art.