EMERSON: THE MIND ON FIRE By Robert D. Richardson University of California Press 656 pp., $30 JOHN DEWEY AND THE HIGH TIDE OF AMERICAN LIBERALISM By Alan Ryan W.W. Norton & Co. 414 pp., $30 VIRGINIA WOOLF By James King W.W. Norton & Co. 699 pp., $35 A GENIUS FOR LIVING: THE LIFE OF FRIEDA LAWRENCE By Janet Byrne HarperCollins 504 pp., $27.50 MAYNARD KEYNES: AN ECONOMIST'S BIOGRAPHY By D.E. Moggridge Routledge 941 pp., $25 GEORGE ELIOT: VOICE OF A CENTURY By Frederick R. Karl W.W. Norton, 768 pp., $30 Conor: A Biography of Conor Cruise O'Brien By Donald Harman Akenson Cornell University Press 573 pp., $35 The traditional purpose of biography is to furnish interested readers with the story of a famous person's life. Whether the biographer aims to expose the flaws behind the public facade, or to portray an exemplary role model, or something in between, the assumption is that readers are interested in the biographical subject in the first place. Yet in an increasingly forgetful world, it often falls to the biographer to rekindle interest in important figures in danger of being relegated to obscurity. By placing a person's achievements in the context of his or her life, a good biography helps us see its subject afresh. In this respect, one of the most outstanding biographies of this past season may be Robert D. Richardson's Emerson: The Mind on Fire. Although Emerson is scarcely a forgotten figure, his very familiarity tends to disguise his amazing originality, and his protean, deliberately unsystematic mind resists attempts at classification. Even readers who love his poetically pithy essays, such as ''Self-Reliance,'' ''Compensation,'' and ''Nature,'' may find it hard to imagine the man who wrote them. But, thanks to Professor Richardson's superbly written book, Ralph Waldo Emerson (1803-1882) takes on the lineaments of a thinking, feeling, entirely believable human being: an awkward middle child initially overshadowed by his seemingly more-gifted brothers; the grief-stricken widower of an aspiring poetess who died at 19; a man who taught himself how to recover from overwhelming bouts of depression by relying on his spiritual inner resources. Whether he is describing the strange character of Emerson's remarkable aunt, Mary Moody Emerson, or Emerson's first meeting with Thomas and Jane Carlyle, or Emerson's responses to his wide-ranging readings, Richardson writes with a clarity, vigor, and liveliness that transform his meticulous research into a compellingly readable, highly intelligible story. John Dewey (1859-1952), another quintessentially American figure, was alas a much duller writer than Emerson, though certainly a more systematic thinker. The avowed aim of Alan Ryan's John Dewey and the High Tide of American Liberalism is to refocus attention on a man who in his lifetime was one of America's most revered and influential philosophers. Dewey's faith in democracy and in humankind's ability to solve - or at least alleviate - problems by means of intelligently planned action may lack the dramatic allure of flashier credos, but in the long run, Ryan notes, we could do a lot worse than reconsider Dewey's open-minded yet seriously thought-out approach to political, social, and ethical questions. Ryan's admittedly partisan, but by no means uncritical, account of Dewey's life begins with a helpful ''overview'' of his place in American history. The remainder of the book cogently portrays both the man and the age in which he lived. A pragmatist whose chief concern was finding ways to translate ideas into reality, Dewey thought long and hard about problems that still concern us, such as balancing a belief in individualism with a commitment to public responsibilities. Ryan's reconsideration is well-timed. It's probably fair to say that Virginia Woolf has been one of the least neglected literary figures of the 20th century. Studies of her work are abundant, her diaries and letters have deservedly received much attention, and her life - along with others of the Bloomsbury group - has been the subject of intense interest. Indeed, in this age it's possible that her latest biographer is the one who needs to be rescued from being lost in the deluge of Woolf-related materials. James King's Virginia Woolf holds its own very nicely, providing a moving, acutely perceptive account of Woolf's life and work. Comprehensive, convincing, and well integrated, this biography should fascinate those who are already fascinated by Woolf, while offering an excellent introduction to her character and writing for those less familiar with her. If not the focus of so much attention as Woolf, economist John Maynard Keynes, also of the Bloomsbury set, has been the subject of two major biographies - Roy Harrod's rather buttoned-down version and Robert Skidelsky's ongoing multi-volume project that deals with everything from Keynesian economics to Keynes's busy love life. Now, in a single (albeit hefty) volume, Maynard Keynes: An Economist's Biography, Canadian scholar D.E. Moggridge offers a sound, analytical, carefully researched account of the man who invented deficit spending. As a narrator, Moggridge is less of a presence than the more-convivial Skidelsky. But he sets forth the facts and issues with precision and sharp intelligence. The publisher's decision to place notes at the end of each chapter (rather than at the back of the book) is an added help to readers looking for a reliable, accessible (and at $25 for 941 pages, surprisingly inexpensive) guide to Keynes and his world. Frieda Lawrence was hardly an important figure - except, of course, to her husband D.H. Lawrence, who used her as the model for many of the women in his novels. Lawrence told the dramatic story of their elopement and passionate love match in his sequence of poems ''Look! We Have Come Through!'' and Frieda herself told the story in ''Not I, but the Wind,'' a title borrowed from her husband's poem. Born into the aristocratic German von Richtofen family, Frieda first married a British professor, Ernest Weekley, then left him and their three children for the slim, fierce coal miner's son whose genius she recognized. The story of their tempestuous marriage is dramatic enough to tempt any biographer, and Frieda's young womanhood - the years in which her decisive character took shape - coincided with many interesting developments on the German cultural scene. Janet Byrne's judicious biography, A Genius for Living: The Life of Frieda Lawrence, helpfully places Frieda in the context of the Austro-Germanic avant-garde, who were pioneering just after the turn of the century the kinds of wild behavior that became more widely popular in the 1920s. Byrne also gives a vivid picture of the Lawrences' marriage, but, oddly, short changes the last 26 years of Frieda's life, after her husband's death in 1930. There is little doubt, on the other hand, that George Eliot (1819-1880) was a great woman in every sense of the word. Frederick R. Karl's George Eliot: Voice of a Century is a major biography of a major writer. Professor Karl plunges into Eliot's life and work with the strong engagement that readers of his previous biographies of Faulkner, Conrad, and Kafka have come to expect of him. He takes on previous biographers and commentators, energetically presenting his own, essentially right-minded interpretation of Eliot as woman and as writer, and he also provides particularly fine portraits of the many other people - family, friends, colleagues, and admirers - in her life. The Eliot he presents is a truly extraordinary person, flawed yet noble, bravely unconventional but only when necessary, solidly moderate and recoiling from extremism, someone who, in the words of Matthew Arnold, ''saw life steadily, and saw it whole.'' Writing the life of someone who is still very much alive can be a challenging task, almost always prematurely undertaken. Donald Harman Akenson's lively, detailed, up-close and personal Conor: A Biography of Conor Cruise O'Brien does not avoid all of the pitfalls. This biographer's fervent esteem for the colorful and eloquent diplomat, journalist, and author, whom he considers ''the greatest living Irishman'' sometimes makes his account of O'Brien's life a trifle embarrassing. But although Akenson's tone can be disconcertingly personal, he demonstrates a solid grasp of his material. O'Brien is indeed an excellent subject. From his early career as an Irish nationalist to his involvement in African and Middle Eastern politics and his recent defense of the rights of Ulster Unionists, he has been a courageous, often controversial champion of human rights, equally ready to challenge the complacency of conservatives and the conformity of self-styled radicals. With his well-thought-out views on everything from the Irish Republican Army to Zionism, O'Brien's multifaceted career offers a unique perspective on the history of our century.