The President's Committee on the Arts and Humanities held its inaugural meeting yesterday, beginning with a private lunch at the White House hosted by honorary chairman Nancy Reagan and ending with cocktails under the vaulted ceiling of Librarian of Congress Daniel Boorstin's office.

Almost all of the 29 members -- culled from business, the arts, education and the federal government -- were present, including singer Frank Sinatra, a friend of the Reagans.

"I believe that art binds us together and I need not say how necessary that is today," said Nancy Reagan in her remarks after a luncheon for committee members and other arts patrons. "On the humanities, she said, "Scholarship is a jewel that shines over the centuries. Yet I don't believe it's received a fair share of private support or public appreciation."

The committee will look into ways to increase and encourage private support of the arts. Committee chairman Andrew Heiskell pledged, "God forbid that we should become a bureaucracy."

The two-hour meeting in the Whittall Room of the Library of Congress was a predictable forum for background information on the arts and humanities and broad statements of goals.

It began with members introducing themselves by name and occupation. When it was Sinatra's turn, he said expressionlessly, "Frank Sinatra, saloon singer." "From Chicago?" cried one member over the laughter around the table. "Rancho Mirage, California," responded Sinatra.

Heiskell, chairman of the board of the New York Public Library and former chairman of the board of Time Inc., said he wasn't surprised if people didn't know exactly what the committee would do. "I don't," said Heiskell. "You walk before you run. . .I think you'll find out in two years whether we can do something or not."

However, it was made clear what the committee would not be doing. "We will not be asked to raise money," said Barnabas McHenry, who, with industrialist and Reagan friend Armand Deutsch, is a co-vice chairman of the committee. "We would hope to develop private support and promote better understanding and undertake discrete projects."

Rawleigh Warner, chairman of the board of Mobil Oil (and chairman of the Business Committee for the Arts), said that businesses would not give any "automatic" percentage -- like five percent -- of income to the arts. "Business will still give in proportion to the amount it makes," said Warner. " . . There's just no way we'll give 5 percent."

Sinatra suggested focusing on contributions from individuals. "We've been hung up on corporations for a while," he said.