“A Sense of Abstraction” at the Alan Klotz Gallery in Chelsea, a well thought out exhibition of more than 70 photographs, explores what happens when it no longer matters what pictures are pictures of, but are concerned with formal properties of design. Some are pictures of recognizable subjects that are just more artfully arrayed than usual, in others it is impossible to tell what the object before the camera lens was – total abstractions.

The initial response to these works tends to be cerebral. You begin by asking, “What is it?” In the case of Aaron Siskind’s “Feet 102” (1957), we know what “it” is, but have to puzzle out what Siskind has made of it. There is a monumental foot, seen in profile, the heel at the bottom of the picture balanced on the big toe of another foot, of which we see only a few toes. It sounds silly, but Siskind has transformed anatomy into biomorphic sculpture, something like a work by Henry Moore. It is silly, but it is also grand and intriguing.

When I was in Paris a few years ago, I saw among the office towers of La Defense the worst piece of public art that has ever been placed in the way of pedestrians, an enormous, realistic bronze statue of a thumb. The trouble was, it never became anything other than a thumb: It was just unavoidable thumbness. Siskind’s foot is poetic, graceful, and bafflingly allusive. There is no context for the foot – the background is a blank light gray that is probably sky – and it reads at first as a silhouette, although there is enough modeling to see some of the bones and get a sense of volume. It is like the visual illusion that is alternately a vase and two facing profiles: This is a foot, then an abstract shape, then a foot again. Siskind must have had great fun taking this picture, and wants us to have fun looking at it. I think.

Several Siskind pictures in the exhibition are of signs, but unlike the pictures of posters, signs, and graffiti taken by, say, Walker Evans, they contain nothing of sociological interest. “Chicago 30” (1949) seems to be a close-up of part of a black letter that seems to be painted on white sheet metal. There are some scratches and screwheads that give texture to the surface, but the figure might be an “R” or a “Q” or not a letter at all. It looks like a shape Alexander Calder would use in one of his stabiles.

“Lima 86” (1975), seems to be something painted in black and gray on a light background with some squiggles and inscriptions in chalk. It reminds me of Japanese calligraphy, or the playful doodads of a Zen master of brush and ink. Like the similar “Lima 80 (100)” (1975), it is part of the “Homage to Franz Kline” series. The dedication of these photographs to a leading figure of the New York School of Abstract Expressionists ties Siskind’s work to a larger mid-century art universe in which abstraction played a central role.

Siskind (1903-91) began his career as a Social Realist closely associated with the left-wing Photo League in New York City. He did important documentary projects on the Bowery and in Harlem, but grew increasingly unhappy with the communist-influenced league. In 1943 and 1944 he began shooting symbolic and abstract photographs based on discarded objects he found on Martha’s Vineyard and in Gloucester, Mass., and this radically altered the nature of his work. Many suggest abstraction was a refuge from politics: Maybe so, but if so, so what?

In 1951 Harry Callahan invited him to join the faculty of the Institute of Design of the Illinois Institute of Technology in Chicago. This put him in contact with Laszlo Moholy-Nagy, the school’s founder, and through Moholy-Nagy with the tradition of the Bauhaus and the whole of European Modernism. Siskind in turn became an important teacher of another generation of photographers.

There are three pictures by Callahan (1912-99) in the Klotz exhibition: “Chicago” (1947) is a close-up of three stones on a sandy beach; “Royal Oak, Michigan” (1945), a picture of the delicate tracery made by dimly seen willow branches; and “Wall, Chicago” (1947), the pattern of what seems to be black paint splattered on white. The protean Callahan was rigorous in whatever he did, and each of these photographs is precise, sensitive, and appears just right.

Minor White (1908-76) explored the sacred and spiritual aspects of photography. White was baptized a Catholic by a chaplain while serving in the Army in World War II but was also influenced by his studies of Zen, Gestalt psychology, and the teachings of G.I. Gurdjieff, as well as by his associations with Ansel Adams and Edward Weston. His pictures, 10 of which are in the show, have a mystical, transcendental quality: “One Wave, Matchstick Cove” (1947), “Ritual Branch, Frost on Window” (1958),”Sun Spot in Cracked Mud, Capital Reef, Utah” (1961), and the rest are all portents of something simultaneously lucid and impenetrable. It is clear in most instances what they are pictures of, but White has isolated, framed, and shot them in light that turns them into deep mysteries.

Wynn Bullock (1902-75) encountered Moholy-Nagy’s works while studying music in Paris in the late 1920s. A subsequent interest in symbolism led him to give his photographs a runic cast: “Rock (Stone Mask)” (1973), “The Shore” (1966), “Floating Logs” (1957), and “Leaves in Cobwebs” (1968) are examples. Eliot Porter (1901-99) is represented by four dye-transfer color prints, including “Pool in a Brook, Pond Brook, near Whiteface, New Hampshire” (1953), ostensibly about some leaves floating on water but in fact an exquisitely sophisticated picture of reds and yellows and greens and whites. It draws as much on the Romantic English painter J.M.W. Turner as on Eliot’s contemporary, Helen Frankenthaler.

There is more in the Klotz show. Our first reaction to these works is likely to be cool, as we try to puzzle them out. But a successful abstraction draws us in, our speculations lead in many directions, and we do not disengage until we have found some significance.

Until July 2 (511 W. 25th Street, between Tenth and Eleventh Avenues, 212-741-4764). Prices: $2,200-$50,000.