It is not a war memorial, exactly. Or maybe it is. It is a grave site, but it should not feel like a graveyard. It must honor the dead, but it should be for the living. It will list the names. But it must express far more.

Some memorials console, some teach. And the Sept. 11 memorial proposed for the World Trade Center site may eventually do both. But after the announcement on Wednesday of the eight final designs in the competition, New Yorkers remain deeply split over the memorial's most basic outlines: What is its purpose? Whom is it for? And when should it be done?

Many say they want something therapeutic, to help heal the wounds of survivors. Others want something educational, drawing lessons for the future. Some want a memorial that illuminates individual victims' lives; others say too many specifics will eclipse any sense of collective meaning. For some, the process is too long -- or not long enough.

''I think this is the worst time in our history to have to come up with a memorial,'' said Art Spiegelman, the cartoonist and creator of ''Maus,'' a novel of the Holocaust in comic book form, which won a Pulitzer Prize. ''Because the meanings of the tragic events of Sept. 11 have been so hijacked themselves. Whatever we try to make of this event right now will be distorted by the deep fissure in our political life in America.''

In interviews conducted in the two days since the Lower Manhattan Development Corporation named the finalists and put their designs on display at the World Financial Center in Lower Manhattan, several dozen New Yorkers talked in detail about what they believe the purpose of the memorial should be and what the experience of visiting it should be like.

They were divided over the degree to which the memorial should be cathartic or educational; over the extent to which it should be for the immediate survivors or ''a history book in stone,'' as one put it; and over how much the 9/11 memorial should dwell on specific details of the day and of the dead -- or on broader, even global themes.

Nicholas Christopher, a poet and novelist who lives in Greenwich Village, said several of the finalists' proposals reminded him of cemeteries. He would prefer a simple park and a wall of names, along with ''buildings with living people working and carrying on what the people who died were doing, from drinking their coffee to daydreaming to doing their jobs.''

Yury Komisar, a Russian immigrant who lives in Brighton Beach and manages a car service on Atlantic Avenue in Brooklyn, insisted: ''It's a cemetery. You don't build on a cemetery. You have to give respect to the people buried there.'' He said the memorial must be large enough to have emotional power: ''It should go to your heart. So when you see it, you'll never forget.''

Jose E. Rodriguez, a sculptor born in Puerto Rico and living in Manhattan, said he would prefer that the emphasis be ''more about peace or understanding or learning to live with each other in this world.'' Focusing exclusively on the American end of the 9/11 experience, he said, ''is almost an easy way out. It would be more difficult to talk about the world issues.''

''And if it's going to be about the loss,'' he added, ''maybe it would be good to make parallels with other tragedies that have happened around the world because of war and economics and similar things.''

For much of American history, memorials celebrated heroes, not victims. They followed what historians describe as a didactic or pedagogic model. But in the second half of the 20th century, the focus shifted from heroes to victims. The stated purpose of many recent memorials became a kind of community or group therapy and healing.

Kirk Savage, an art historian at the University of Pittsburgh who has traced the evolution of what he and others call therapeutic monuments, said a turning point was the Vietnam Veterans Memorial in Washington. Devoid of the traditional celebration of heroic sacrifice, the monument had as its express purpose encouraging the process of healing.

Professor Savage said the focus on victims intensified even further at the Oklahoma City National Memorial, where images of the 168 people killed in the 1995 bombing are on display. If the idea of the ''therapeutic or traumatic memorial'' is taken to its extreme, he said, there is a risk of losing the sense of a broader meaning.

''In the end, there has to be a collective meaning to this event that justifies their memorialization,'' he said of the victims. ''That's why I think the therapeutic monument has to be didactic in some way, has to have a rationale, a meaning that justifies the collective focus on this event.''

Some New Yorkers said they imagined the 9/11 memorial primarily as an expression of loss. Others wanted it to convey resilience, defiance or hope. Anthony D. Meyers, an advertising salesman from Morris Park in the Bronx, said he would like something educational, along the lines of the 16th Street Baptist Church in Birmingham, Ala., incorporating oral history.

Martin B. Duberman, a professor of history at the City University of New York, said he wished the memorial would present an alternative to ''the model of human depravity'' used to explain awful events. It might instead challenge the notion of ''intrinsic depravity'' by exploring recent findings that compassion and the need for affiliation are intrinsic to human nature.

''I would like to move it beyond a simple memorializing of those who were lost,'' Professor Duberman said. ''If we want to prevent more victims in the future, we need to involve ourselves in some kind of thought about what human beings are like, and is this indeed inevitable and necessary, this kind of slaughter?''

Kenneth T. Jackson, editor of the Encyclopedia of New York City and president of the New-York Historical Society, said he leaned more in the direction of memorial as therapy. He said Sept. 11 would have meaning for almost everyone in the world; many watched it on television. ''It's like D-Day,'' he said. ''You don't need a lesson.''

Some argued for waiting because the meaning of 9/11 will evolve.

''Right now, it's just so much a symbol of this war on an abstract entity called terrorism that it's hard to see past that to what this may actually mean for Western civilization,'' Mr. Spiegelman said. ''At which point, if it's meaningful, the names of the individuals who died at Dunkirk or the twin towers are less urgent than they might seem close up.''

Barbara Petak, a 60-year-old retiree who lives in Brooklyn Heights, said: ''I don't think it needs to be done immediately. Maybe by doing something, it makes people think we're healing ourselves. But I think we need to heal ourselves and then do something. We're such an action-oriented society. We feel we must do, rather than reflect and pause.''

Pauline Grant took the opposite view.

''Eventually you have to do it,'' said Ms. Grant, a baby-sitter from Brooklyn. ''So let's get it over with.''

Photo: Visitors examined panels of the eight finalists in the World Trade Center memorial design competition at the Winter Garden of the World Financial Center yesterday. (Photo by Ting-Li Wang/The New York Times)(pg. B4)