More than 50 years have passed since two famous philosophers squared off against each other at England’s Cambridge University. Though their raucous debate lasted only ten minutes, it still stirs the passions of their followers.

Both men were Viennese expatriates, refugees from the rise of Hitler and the ravages of World War II. But the war was only a backdrop for the clash of ideas as they faced each other for the first time, on October 25, 1946.

One of the two, Ludwig Wittgenstein, picked up an iron poker from the fireplace and waved it at the other, Karl Popper. Or maybe he only waved it in the air for emphasis, as he shouted "Popper, you are wrong! You are wrong!" Maybe the poker was red hot, or perhaps it was cold. Although the room was packed with eminent philosophers and their students, no one could agree afterward on exactly what took place.

When the illustrious philosopher Bertrand Russell ordered Wittgenstein to put down the poker, he did so and, after exchanging a few angry words with Russell, left the room. According to some, he slammed the door. Ever since Wittgenstein laid down that poker, colleagues and students who were present, and even those born many years later, have taken up the cudgels in an argument that was left unsettled.

The argument is back thanks to a lively new book, BBC reporters, David Edmonds and John Eidinow. They were inspired to write it by a bristling exchange of letters in the London Times Literary Supplement in 1998, over who said what, and when, during that infamous Cambridge seminar.

What stirs the passions of philosophers may seem trivial to the rest of us, who get by with mere common sense. Wittgenstein had sent Popper an invitation to discuss "some philosophical puzzle." That got Popper’s goat. He had real problems on his mind, not puzzles. In fact, that was the crux of the matter. Wittgenstein insisted there were no real problems in philosophy, only the puzzling way philosophers talked about the world. After one Cambridge seminar he was heard to say, "Bad philosophers are like slum landlords. It’s my job to put them out of business."

The authors of Wittgenstein’s Poker have fleshed out the philosophical ideas with warts-and-all portraits of the protagonists and their colleagues. There are warts aplenty. Wittgenstein was regarded as an austere, domineering genius who often destroyed students’ ability to think for themselves. One student called him "an atomic bomb." Popper was no less imposing; his aggressive style of argument, said a friend, "put me in mind of a blowtorch."

And between them there’s Bertrand Russell, whose academic achievements in logic and mathematics paled before his public notoriety as the philosopher—and proselytizer—of free love. Russell had helped Wittgenstein publish his first book, composed in the trenches of World War I. He even wrote the introduction. At first, Russell saw Wittgenstein as a brilliant young successor. He told a friend, "His avalanches make mine seem mere snowballs."

No doubt Wittgenstein agreed; he thought Russell’s introduction to his book completely missed the point. Russell eventually soured on Wittgenstein, describing his former protégé’s writings as "completely unintelligible." Russell, who had also assisted Popper in getting established, ended up taking his side in the brouhaha with Wittgenstein.

Edmonds and Eidinow have told this story with an evenhanded treatment of all parties. Yet, like Russell, they’ve missed the point. They have stirred the ashes of the debate but not the fire. What that waving poker was pointing at was not a distinction between puzzles and problems, but something more urgent and relevant. It was a warning, to all of us, that whenever philosophers, or scientists, or any other intellectual elite claim to possess some truth that runs counter to common sense, they are talking nonsense.

Wittgenstein had a hard time getting this point across. The simple truth at the heart of his argument was unacceptable to thinkers convinced that philosophy could address many problems plaguing humanity. To take his point would put a lot of professors out of work. Yet he tried desperately to make himself clear, from his earliest words to his last. In the preface to his first book he wrote, "The whole sense of the book might be summed up in the following words: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence." Indeed, he has often been called a mystic.

In fact, he wanted philosophers to shut up about most of what matters in everyday life: ethics, aesthetics, nature, religion. On such subjects, formal languages like logic and science can only send us off "in pursuit of chimeras." It is because these formal languages follow strict rules and rule out contradictions that they lack common sense and give a misleading view of the world. "It is like a pair of glasses on our nose through which we see whatever we look at," he admonished his colleagues. "It never occurs to us to take them off." As for his attacks on philosophy, he said, "What we are destroying is nothing but houses of cards."

Poor Popper didn’t have a clue. He was a paragon of pure reason armed only with logic, confronting the mind of a mystic uttering paradoxes and waving a poker in the air. Popper was best known for his book The Open Society and Its Enemies, which attacked Communism and challenged Marxist theory as pseudoscience. Wittgenstein waved this off as the concern of sociology. He had more universal fish to fry. "Philosophy," he said, "is a battle against the bewitchment of our intelligence by means of language."

Although Wittgenstein, who died in 1951 at age 62, did not live to see the most striking example of this bewitchment—the pursuit of artificial intelligence in computers—his ghost sat next to me at a seminar on this subject at the Smithsonian Castle in the 1980s. Bill Woods, a scientist who had struggled to make computers understand ordinary language, offered a confession. "We assumed," he said, "we could start with simple children’s stories and work our way up to complex fields like physics and astronomy. It turned out that understanding physics and astronomy is extremely simple compared to the problem of understanding children’s stories." Bewitchment indeed, muttered Wittgenstein’s ghost.

The ghost turned up again a few years later when I was talking to another artificial intelligence pioneer, John McCarthy, at Stanford University. McCarthy was explaining his efforts to impart reason to computers. "I estimate there are only about 12 or 13 rules that are needed for the logic of common sense," he said. "I’ve figured out 5 of them, and I’m sure we’ll understand the rest in a few years. Then we can program any computer with common sense." That achievement, as it turned out, has proved elusive.

Our scientists and philosophers are still misleading us in their pursuit of chimeras. Lately, the talk of cloning people has got Wittgenstein’s ghost reaching for his poker again. We are dealing with imponderables once more, and talking as if we knew what we’re talking about when we don’t.

The actual poker Wittgenstein waved at Popper back in 1946 mysteriously disappeared after the incident. But Wittgenstein’s ghost, ever skeptical, still brandishes it.