In 1951, a Professor at Princeton, Carlos Baker (who indicatively refers to himself in the third person) approached Hemingway about doing a critical study which became Hemingway: The Writer as Artist. Now he has written the definitive biography, factually validated throughout, running to 750 pages. A long labor, but not one necessarily of love or even with the catching admiration of the proprietary Hotchner memoir. . . . Ernest Miller Hemingway at three said he was ""fraid a nothing""-spent all his life proving it in his pursuit of blood sports including war (le metier triste, also his definition of writing). The first American casualty in Italy in World War I, he returned with 227 scars on his leg. This was just the beginning of a succession of significantly disabling experiences. Hemingway believed he was ""living not one life but two"" and he needed his second life to fuel his first as an artist. Mr. Baker rarely injects his own views of either the man or the writer, drawing from all the widely available materials--diverging from Hadley, his first wife, who found him ""hulky, bulky, something masculine"" to Martha Gellhorn, his third, who declared his egotism went beyond the call of genius. Certainly as time went on, Hemingway became more and more brash, boorish and bibulous, intensifying the childish Papa pose he extended to all who came to lionize the beard. The writing of each book and its critical reaction is documented chronologically; but it was a long time ago that a Russian diagnosed Hemingway as a ""mens morbida in corpore sano"" which became evident in the last years of internal disorders of every kind. He was also a man spooked by death even though at nineteen he had said, ""Dying is a very simple thing."" Mr. Baker is a seemingly scrupulous custodian and recorder but at times one suspects that in putting everything in--something has been left out, or that the complete Hemingway diminishes the essential Hemingway. This, however, is the official biography and it will be an obligatory referral for a long time to come. It is also the Book-of-the-Month Club selection.