PHOTOGRAPHY is either the craftiest of the arts or the artiest of the crafts, and either way it's irritating, because photographs tend to tell too much or too little.

Two new photo exhibitions in town, one at the Museum of American Art and the other at the Corcoran, illustrate the extremes very well. A third, at the National Portrait Gallery, will be of interest to those who are insatiably curious about presidential offspring.

"LIFE, the Second Decade, 1946- 1955" at American Art is an overwhelming reminder of how powerfully Henry Luce's picture magazine imposed itself on our life and times. Our memory of many events is not what happened but the pictures Life chose to show us. And no matter how clearly and powerfully a photograph might speak for itself, Life's legions of editors made sure, in laboriously crafted captionsand text blocks, that we understood the picture properly. Underlying this overwriting, according to a retired Lifer who attended the exhibit preview, was "an utter, if avuncular, contempt for the reader. We were always terribly afraid you'd miss the point."

But such talent as appeared on the pages of Life -- and there were few top photographers who didn't -- could not fail to inform, instruct and delight. Witness Eliot Elisofon's witty strobe sequence of painter Marcel Duchamp "Viewed Descending a Staircase." And Philippe Halsman's pungent portraits of the powerful, Margaret Bourke-White's farmers and warriors, and Henri Cartier-Bresson's er, um, Henri Cartier-Bressons.

There are about 200 photographs displayed, which is too many to take in at once but too few to be fully representative of 520 issues of the magazine. After a bit it gets a bit blurry; but one comes away struck by the thought that you don't see pictures like that anymore, hardly.

You never did see such pictures as appear in the Corcoran's show of five photographers of "The New York School, 1935-1963," because nobody ever printed them, hardly. Alexey Brodovitch, Louis Faurer, Sid Grossman, Helen Levitt and Lisette Model aren't names to conjure with because they took a lot of pictures about which, lacking Lifestyle captions, we don't understand how to think.

This is Part One of the exhibit; two more are to follow, and then there'll be a catalogue to explain what the Corcoran calls their "unique documentary style," which involves, in many cases, not focusing the camera and not holding it steady and not pointing it at anything in particular.

Finally, there's the National Portrait Gallery exhibit of "Presidential Children," which is a display of portraits of the 23 living Americans whose fathers have been president. Somebody at the new Life Magazine decided it would make a nice spread, and commissioned Harry Benson to take them. He did so, very dutifully.

Ho hum, except for the somewhat surprising news that sons of Hoover, Coolidge and Cleveland, and a daughter of Taft, are still alive. Little Amy Carter has grown up, of course, but not enough to suit Life; she posed for Benson in a stained blouse, but Life retouched it to spotlessness before it appeared in the magazine. One wonders, for just a moment, why they did that.

LIFE: THE SECOND DECADE, 1946-1955 -- Through May 12 at the Smithsonian Museum of American Art, Eighth and G streets NW. Open daily, 10 to 5:30. Gallery Place station of Metro's Red and Yellow lines.

THE NEW YORK SCHOOL: PHOTOGRAPHS 1935-1963 -- Through April 14 at the Corcoran Gallery of Art, 17th and New York Avenue NW. Open Tuesday through Sunday 10 to 4:30 and Thursday evenings until 9. Farragut West station of Metro's Blue and Orange lines.

PRESIDENTIAL CHILDREN -- On view indefinitely at the Smithsonian National Portrait Gallery, Eighth and F streets NW. Open daily 10 to 5:30. Gallery Place station of Metro's Red and Yellow lines.