“Others abide our question. Thou art free,” wrote Matthew Arnold in a sonnet to Shakespeare. This Shakespearean difference, the unaccountability that sets him apart from even the greatest writers, only becomes more mysterious with time. His contemporaries were already aware of it: Ben Jonson, his colleague and rival, refused to compare Shakespeare even with Chaucer and Spenser, declaring, “He was not of an age, but for all time!”

But as Shakespeare the man disappeared from memory, the imaginative freedom of his work became more and more inexplicable: Readers began to wonder how any human being could have owned such semi divine powers of creation. What started out as a critical problem for writers like Dryden and Johnson became a psychological, and even metaphysical, one for Coleridge, Freud, Joyce, and Borges. It was inevitable that finally a critic like Harold Bloom should declare that Shakespeare actually “invented the human”: no smaller metaphor seems to do him justice.

Yet the attempt to explain Shakespeare’s freedom always threatens to degrade into an attempt to explain it away. If no writer is as revered, likewise, no writer is so insolently manhandled by criticism. There is no school of critics committed to showing that Virgil did not write the “Aeneid,” or Dante the “Commedia”; yet there is an unending supply of people willing to argue that Shakespeare’s plays were written by the Earl of Oxford, Francis Bacon, or Christopher Marlowe. Such theories, inane and childish in themselves, are significant only as negative tributes to Shakespeare’s freedom. The “authorship controversy” seeks to tame his imagination by re-assigning it to someone richer, more famous, or simply better documented – as though this would make the work itself any easier to explain.

Such speculations are able to flourish because Shakespeare cannot be known in the way we know, for example, Charles Dickens. There are no letters, memoirs, or anecdotes to reveal his personality, no reviews or sales figures to document his career. All the facts we know for certain about Shakespeare can be numbered on two hands. Inevitably, then, every biographer of Shakespeare turns to the works – the poems, sonnets, and above all the plays – to try to understand the man who wrote them.

Yet even in the most acute and scholarly of biographies, this is necessarily a self-canceling enterprise. First, it is tautological: The only thing that emerges about Shakespeare is that he was the kind of man who could write the plays of Shakespeare. And second, it is reductive: because no one ever wrote like Shakespeare, we can’t really know what kind of man that is. All we can do is apply our own intuitions to the problem; and since our intuitions are inevitably less fine than Shakespeare’s, we end up with a vulgarization, a caricature.

The only fruitful activity left to the biographer, then, is historical: to fill in the social and cultural background that has been effaced by time. Stephen Greenblatt’s “Will in the World” (W.W. Norton, 406 pages, $26.95) does this with the expertise one would expect from the scholar who invented the so-called New Historicism – a critical approach that seeks insight into a literary work by studying its linguistic, intellectual, and cultural context. Yet while Mr. Greenblatt is frequently fascinating on the world of Elizabethan England, he offers little new insight into Will.

In part this is because the events of Shakespeare’s life are far from clear, and probably never will be. All that is known for certain are those moments when he appears in official records: his baptism in 1564, his marriage, the births of his three children, his tax and real estate transactions, and his burial in 1616.We know that he was a shrewd businessman, who grew rich from his own labors and bought the biggest house in his hometown. And we know that he could not have seen much of his family, who remained in Stratford while he lived and worked in London, as a playwright and actor in the Lord Chamberlain’s Men (later the King’s Men) from the early 1590s until a couple of years before his death.

Beyond that, almost everything is speculation – in Mr. Greenblatt’s case, some of it quite ingenious. For instance, various scholars over the last 60 years have advanced the theory that Shakespeare’s childhood was spent in a clandestine Catholic milieu. Several teachers at the Stratford grammar school during his youth went on to become Jesuits; two of his possible early employers were Catholic magnates; and there once existed a document, now lost, purporting to be his father’s confession of Catholic faith. In pursuing these clues, Mr. Greenblatt paints a vivid picture of the dangers faced by underground Catholics during the reign of the Protestant Queen Elizabeth.

The problem, however, is not just that all this is highly inferential – there is no proof, for instance, that Shakespeare actually went to the Stratford grammar school or worked for those Catholic noblemen. The problem is that, even if it were all true, it reveals very little about the religious sensibility of Shakespeare’s plays, which cannot be described as either Catholic or Protestant. The question of Shakespeare’s Catholicism is, in this sense, emblematic of all the biographical questions Mr. Greenblatt raises – about Shakespeare’s marriage, his relationship with his father and his children, his attitude towards love, money, and politics. Nothing outside the work is certain; and even if it were, it wouldn’t help to explain the work. Biography comes to seem like the ether, an element that touches everything and affects nothing.

“Will in the World” is least satisfying when Mr. Greenblatt essays psychological analysis of the Shakespeare he has half-deduced and half-invented. He is very concerned, for instance, with whether Shakespeare had a happy marriage: “It is, perhaps, as much what Shakespeare did not write as what he did that seems to indicate something seriously wrong with his marriage. “The tone of moralizing concern here seems just as inappropriate as the later reassurance that “Shakespeare was not necessarily doomed to a life without love.”

In both cases, Mr. Greenblatt treats Shakespeare as though he were a 21stcentury American who ought to consider seeing a marriage counselor. But when a man has created Romeo and Juliet, Antony and Cleopatra, Macbeth and Lady Macbeth, who would presume to pronounce on “his trust, his happiness, his capacity for intimacy”? Shakespeare, who has eluded so many hunters, is not to be caught in nets of such coarse weave. At the end of “Will in the World,” he remains free as ever.