It's finals time for seniors at St. John's College. Like nearly everything else at this bastion of the liberal arts, it's different from other schools. Here there are no real final examinations.

St. John's isn't much on tests and grades, anyway. The presumption is that after four years of intensive study in a school so small there's no place to hide, the worth of a student already has been proved.

So finals are a formality--literally. A graduating senior arrives in black robes to be introduced with a flourish to a panel of three robed tutors in the Persian-rugged King William Room. The senior discourses on some weighty matter ("Leibniz's Living Force: Is Its Primitive Nature Physical?") and for an hour the theories are probed and poked in a friendly, conversational way. Tutors and student are equals. It is a coming of age.

A dwarf sitting on a giant's shoulders is said to see farther than the giant. This is the theory of learning at St. John's, where tutors and students soar daily atop the thinking giants of Western history. For four years students read and talk and talk and read; when it's over they are supposed to have learned how to think.

It isn't a program that always appeals to the top high school students. Steve Werlin had to ponder for a moment when asked why he enrolled at St. John's. "I guess," he finally said, "because I didn't get in anywhere else."

Werlin was rejected, or his acceptance was delayed, by Georgetown, George Washington and Johns Hopkins universities. Yet, St. John's, which with its sister school in New Mexico, is rated along with Harvard, Princeton and Yale universities among the 35 most selective schools in the nation by "The Comparative Guide to American Colleges," accepted him immediately, without qualification.

Werlin explained: "Almost anyone can get into St. John's if they're willing to fill out the application. It says right in the catalogue, 'St. John's doesn't select students; students select St. John's.' "

Last year, only 220 prospects completed the grueling application to the 400-student college, and 180 were approved. They were judged on five lengthy essays describing education to date, goals and interests. They weren't even asked to submit Scholastic Aptitude Test scores, the requirement for most college admissions.

If the selection process sounds unusual, the program that follows is downright revolutionary by most modern American standards. St. John's, which costs students a total of about $10,000 a year, is so unlike other U.S. colleges that it finds it cannot accept any transfer credits. The only way to enter is as a freshman.

Once in, students sit at conference tables instead of desks and speak up in tutorials and seminars instead of taking notes at classes and lectures. They almost never face written tests.

They are asked their opinions on matters that have puzzled man since civilization began; their answers and questions are taken seriously and discussed exhaustively by their tutors and peers. Their progress is measured at "don rags," where tutors offer critiques face-to-face.

All students take the same classes without electives and read the same crushing load of great books. They sing Bach fugues in choir and read the music of Mozart; for entertainment they have waltzes and play croquet under a 600-year-old tulip poplar tree.

Following a program instituted almost 50 years ago and essentially unchanged, they learn to reason by reliving the cogitations of the great reasoners and achievers of Western history.

"The following teachers will return to St. John's next year," reads an admissions pamphlet. The list is 108 names long and includes Homer, Aeschylus, Sophocles, Plato, Thomas Aquinas, Galileo, Newton, Melville, Moliere, Dante, Chaucer, Shakespeare, Thoreau, Mark Twain, Dostoevski, Kafka, Baudelaire and Einstein.

St. John's students don't read about these people, they read the original works, and by discussion and demonstration in small groups attempt to retrace their thought processes.

Nor are the tutors immune from learning. They are expected to teach all courses at St. John's, regardless of their initial field of expertise.

So it was that a freshman mathematics class of 12 students, assisted by tutor William Mullen, a doctor of literature, wrestled recently with Ptolemy's theory that the earth is at the center of the universe and all other things revolve around it.

The students spent 70 minutes on five paragraphs of Ptolemy's complicated geometric reasoning, a period punctuated by such exclamations as, "Maybe he was trying to say . . . " and, "I think he meant . . . "

The fact that the entire theory was disproved years later mattered not; sharing the thinking process did. Not until sophomore year would the students get to the works of Copernicus and Galileo, which debunked Ptolemy's. As juniors they would read Newton and by senior year they'd be on to Einstein. Similar chronological courses are followed in languages, starting with Greek, and the great books and sciences.

Why no notes and exams? "We're supposed to be learning to think, not just remember facts," sniffed junior Karl Walling.

Thus a student asks another before afternoon class, "What time does your watch say it is?" and is told, "Well, all time is relative, but my watch says it's 1:15."

It is clearly not a program for everyone, but school officials say it lights a fire under some students who are uninspired by conventional tactics. Others who could have been accepted almost anywhere choose St. John's because it's the only place that offers what they want.

"I spent a lot of time in high school thinking about how classes ought to be," said senior Marion Sharp. "Then I got junk mail from St. John's describing exactly what I was thinking of."

Interestingly, while more than half the current freshmen were in the top 20 percent of their graduating high school classes, almost 10 percent came from the bottom 40 percent. Students come from 30 states, four foreign countries and Puerto Rico. About two-thirds of departing students go on to graduate school, according to school records.

The New York Times 1982 Selective Guide awarded St. John's 13 stars--the maximum five each for academics and quality of life, and three for social life. ("We don't want any more than three for social life," said a college official.) Only Stanford and Brown, rated the best private universities, and Virginia as the best public school, rated higher with 14 stars.

Dean Samuel Kutler said the willingness to accept a broad range of applicants is a strength. "I believe we'd have a very good freshman class if we just took the first 105 who applied," he said.

On the other hand, Kutler said, "If we could somehow find the 105 best high school students in the country and lure them here, it would be a disaster." He said high school valedictorians often prove poor students at St. John's.

Kutler said St. John's attracts some extraordinarily bright students, a lot of good students and a few late bloomers.

So through a process the school calls "self-selection," inquisitive young minds find their way to this descendant of the third college in the nation, King William's, founded in 1696.

In the mid-1930s it had a standard curriculum and was in fiscal ruin. St. John's President Stringfellow Barr (whose later achievements included a satirical review of American colleges, "Purely Academic," that made the New York Times best-seller list) authorized a new program emphasizing the great books.

The curriculum went in place in 1937 and remains, still known as "The New Program." In some circles it is considered experimental. "That's the worst misconception," tutor Peter Kalkavage said. "The program is reactionary to the core."

This spring, as they have for almost a half-century, tutors and students gather in clusters around the broad green fields that slope down to College Creek and debate the complicated questions at the heart of Western knowledge.

And how do the students feel, now that another demanding year draws to a close?

"Tired," sighs junior Joey Goodwin, who will spend the summer on a farm, picking berries and recuperating. "Very tired."