To be taken seriously, does American art have to be solemn?

By and large, major American art is easier to respect than to like. From Copley, Cole, Homer, and Eakins to Hopper and Pollock, it has tended to be serious and somewhat stern - and to possess a touch of austerity that would have done the Pilgrim forefathers proud.

Whistler decided he would have none of that - and left to establish a career in England. And Sargent, America's most brilliant and flamboyant artist of the late 19th century, has still not been fully forgiven for his refusal to settle down and become a truly ''serious'' painter.

It's difficult to say why this is so. Perhaps because of the influence of the Puritan forefathers. Or perhaps we still believe - at least to a degree - that art, unless it is high-minded and solemn, is of no real importance. But whatever , it is true that Americans at heart still have a hard time taking someone like Calder altogether seriously, and prefer to give the mantle of artistic importance to those whose art is more monumental, solemn, and ''serious.''

I was reminded of this while viewing the large Philip Pearlstein retrospective at the Brooklyn Museum here. Its more than 100 paintings, watercolors, and drawings prove conclusively that Pearlstein is an important figure in contemporary American art. And that his work has the qualities Americans generally deem essential for major art.

His paintings are serious, weighty, well crafted, and monumental. They are the products of considerable talent and intelligence, reflect a no-nonsense attitude toward art, and could only have been painted by an artist of great determination.

Interestingly, however, almost all are of nudes - and of very obviously posed studio models at that. They stand, lounge about, or lie on the floor, and make no attempt whatever to suggest that they represent anything allegorical or morally uplifting.

They do, however, represent a very serious attempt to create significant art out of the nude human body as it relates in terms of composition with other bodies, or with such nearby objects as chairs, rugs, draperies, sofas, or ladders. Its style fuses precise draftsmanship, dramatic foreshortening, extremely compact compositions, and an approach to color that is distinctly cool and detached.

The extraordinary thing is that it works, and that it does so with increasing impact as Pearlstein's career advances.

The truth is, I was very impressed by this exhibition and felt after leaving it that those who insist Pearlstein is a major American artist may very soon be proved right.

I say this even though there are things about his work I do not like. It's a bit too cold and calculated for my taste, and too academic in its draftsmanship. Details sometimes tend to be gross or out of proportion. Even so, extraordinary things are happening in his recent paintings that indicate he is just now beginning to produce his finest work.

Pearlstein has always had a special ability to create tightly interlocking compositions out of one or more figures and a few simple objects, and to have the result be both human and richly patterned. During the past five years, however, this ability has become downright uncanny. No one alive today can relate the tones and rhythms of the human body to the colors and patterns of fabric, woodwork, or furniture better than he. And no one can surpass him in the creation of images that come increasingly close to satisfying both ''realistic'' and ''abstract'' ideals and demands.

In this he is unique and stands as a kind of mediator trying to reconcile the two most extreme positions in contemporary art. It cannot, of course, be done in an absolute sense, since the two are by definition contradictory. But the attempt itself is an extraordinary one, for it proves that significant compromises can still be accomplished in art. And that there still are those among us who will try.

It is this quality, and the way it translates into his work, that impresses me most about Pearlstein's art and that leads me to see him as a likely candidate for major artistic status.

I haven't forgotten that there are things about his work I do not like, but they seem of relatively little importance in the face of the increasingly extraordinary paintings he is now producing. Such recent works as ''Female Model on Platform Rocker,'' ''Two Female Models in Hammock,'' and ''Model in Kimono on Eames Chair'' are, without doubt, among the best paintings any American has produced in the past decade.

Even so, I find that his work - in the tradition of other major American art - is easier to respect than like. That's also the way I generally feel about the paintings of Copley, Eakins, and Hopper.

This excellent exhibition was organized by the Milwaukee Art Museum and traces Pearlstein's career from his student work to the present. Included are several of his early Expressionist landscapes of the 1950s, a few portraits, and a handful of recent urban and mountain landscapes.

After its closing at the Brooklyn Museum on Sept. 18, the show travels to the Pennsylvania Academy in Philadelphia (Dec. 15-Feb. 26, 1984); the Toledo Museum of Art (March 18-April 29); and the Museum of Art, Carnegie Institute, Pittsburgh (May 19-July 15).