Katherine Frank has a theory, which has sent her foraging across oceans in quest of wild geese and red herrings. She believes that Daniel Defoe based Robinson Crusoe not on the lonely ordeal of Alexander Selkirk, a cantankerous buccaneer dumped by his shipmates on an island off Valparaiso in 1704, but on the mishaps of Robert Knox, a trader taken captive by a native chieftain in Ceylon in 1660. Following Knox's trail, Frank even travelled to St Helena, where during the 1680s the accident-prone Knox was again captured (for a few days only, which hardly makes his experience comparable with the 28 years Crusoe spends on his island) while attempting to buy a cargo of slaves.

Selkirk receives only a couple of grudging mentions in Frank's book, since she prefers to believe that Defoe, "a congenital plagiarist", was cannibalising Knox's Historical Relation of Ceylon. With her blinkers on, she ignores the existential oddity of Selkirk, which is what impressed Defoe. The essayist Richard Steele, who met Selkirk on his return to England, said that his experience was unique in human history: no man had ever been so terrifyingly tested by solitude, which threatened to erode his reason and to undermine his very humanity.

In a century that regarded individuals as their own creation and not the copy of some divine prototype, Selkirk was a symbol of modern man's proud, plaintive autonomy. For Defoe the Londoner, who understood the cellular self-sufficiency of contemporary city dwellers, he also pointed to the way all men would live in the future  alienated from their fellows, recoiling in paranoid terror from the over-populated streets.

Robinson Crusoe is about the hero's management of a solitude that should have deranged and destroyed him. Knox, by contrast, was never alone, never menaced by a maddening solipsism. His life story was a narrative of a different kind, replete with exotic adventures and daring escape bids. Crusoe's enemy is duration  the passage of those drearily uneventful decades  and he triumphs because of his capacity for endurance. He retains his rationality by writing. Determined not to regress, he constructs his own small civilisation; indefatigably ingenious, he even reinvents the umbrella. Unlike Crusoe, who wears breeches and a jacket, refuses to go barefoot and keeps his hair and beard trimmed, Knox went native, stripping to a loincloth and allowing the sun to burnish his skin.

Frank admits that Knox's Historical Relation is a drearily prolix ramble, but she seems to admire it more than anything Defoe wrote: she regards the great novelist as a hack with overdue bills to pay, who "churned out" an "astonishing surfeit of work" while simultaneously breeding cattle, raising corn, tanning leather, importing anchovies and selling metal buttons. She misreads the books and mistakes their tone: convinced that Defoe's characters are thoughtless, go-getting profiteers, she overlooks Robinson Crusoe's battle against despair, the nonchalant fatalism of Moll Flanders, and the ghostly detachment of the narrator who wanders at night through a stricken city in A Journal of the Plague Year.

Although Knox and Defoe lived within a few miles of each other in London, they never met; Defoe read Knox's book, though the novel in which he makes use of it was not Crusoe but Captain Singleton, the story of a sailor who marches across Africa, panning rivers for gold and accumulating a hoard of ivory, pausing to gun down any natives who challenge him. Given the lack of any further connection between the two men, how can Frank justify forcibly coupling them in this dual biography? Only, I'm afraid, by over-stretched analogies and questionable metaphors. Because she has so little respect for Defoe's imagination, she treats Robinson Crusoe as a reflection on the novelist's internment in debtors' prison, not a reverie about Selkirk: "You don't have to go to sea to be shipwrecked," she remarks, as it's possible to "come to grief on dry land, as Defoe did". Knox, too, beached in London at the end of his life, "is like a castaway: alone with his thoughts". The same all-purpose cliche returns in Frank's account of Defoe's sad end: "He was in the midst of life's last and greatest storm and he was going under." Actually, it is Frank's theory that by this stage has foundered hopelessly.

Most depressing of all is her inability to appreciate the difference in quality between Knox's memoir and Defoe's novel. The myth that her subtitle invokes is our culture's most authoritative story about the glory and misery of individualism, about the ego's domination of the world and its reduction of other people to ownable, usable things, like Crusoe's compliant Man Friday. Frank treats this as just one more tired paraphrase of the devalued American dream: Knox and Defoe, she says, wrote interchangeable tracts about self-help, "books that tell you that no matter what your situation, you can survive and succeed". It's as if Crusoe were the winner of I'm a Celebrity, Get Me Out of Here! Myths and fables, despite their extremism and their stretching of probability, tell us the truth about ourselves; the feel-good moral Frank propounds is a fatuous lie.