Friday, April 12, 2013

The Sack of Samarkand: A Lesson in the Abuse of Logic.

Note: The following legend is as imaginary as the paradox it illustrates.

Genghis Khan was a good man at heart, and he hated to massacre a city without warning it first. So when he reached the gates of Samarkand one Sunday evening, he summoned a messenger from the city. "One day this week," he said, "I will sack the city. I'm not going to tell you which day it will be, because it will be a surprise attack. But tell your king to be prepared." The terrified messenger raced back to the city and went into the royal court, where he told the Shah the bad news. To his great surprise, the Shah laughed.

"Open the gates," he said. "The city is saved."

"How is that?" asked the vizier.

"Genghis Khan," said the Shah, "is an honest man, and I expect him to keep his word that he will attack us by surprise. But he can't surprise us! Imagine that that it were Thursday night, and that Genghis Khan had not attacked. That would mean that the attack would have to be on Friday. But that can't be, because he said it will be a surprise, and we would know that it was coming. Genghis, therefore, cannot logically attack on Friday. But if it's not on Friday, then we know that it can't be on Thursday either. For if Wednesday night arrived without an attack, then we would know (since it couldn't be on Friday) that it had to be on Thursday. Again, that wouldn't be a surprise. The same logic means, in fact, that it can't be on Wednesday either, or on Tuesday, or on Monday! It is therefore logically impossible for Genghis to launch a surprise attack next week. Glory to God!"

A banquet was immediately prepared, and the city spent the night celebrating. And it was to everyone's astonishment when Genghis Khan attacked at noon on Tuesday. Facing no resistance, his soldiers burned the mosque, murdered the city's citizens, and stacked their heads in towering pyramids. Genghis gave a hearty laugh: he had counted on the Shah's cleverness all along.

This seems like a paradox. On the one hand, the Shah's reasoning was flawless. It should have been logically impossible to catch the Samarkandians by surprise. But he did surprise them in the end—how can that be?

Perhaps there is a problem with the Shah's reasoning or with Genghis's original promise. A sprawling Wikipedia article documents the efforts of philosophical contortionists to point these problems out. "Genghis's definition of surprise changes," says one. "He unwittingly shifts his ground!" "Surprise is a meaningless concept," charges another. "This paradox shows its fundamental instability." "This paradox," says the most grotesque of them all, "shows us that we don't really know what a surprise is. If we work harder and think more clearly, we'll find a way out of our confusion."

But the way to solve the problem involves no logical analysis. We must instead pay attention to what we already know: the real function of the concept surprise in speech. Genghis, in particular, applies the term to an event that he thinks is likely to catch the city off guard. Since he's speculating about the behavior of other people, it's not something that he can guarantee, but it is something that he can predict.

How should we test Genghis's proposition? We must not attempt to tease out what the city's preparedness logically must be. People, after all, don't get surprised in logical space. If I drew a picture of a toothless alligator, it wouldn't protect me in the Everglades.

Instead, we must determine the real likelihood that the attack will shock the Samarkandians. Genghis's own probabilistic analysis, which is reasonably good, goes like this:
Case I: If the Shah is an untutored ignoramus, then he will tremble in fear, prepare the city, and be surprised by the attack whenever it comes.
Case II: But if the Shah is a master of logic, then he will deduce that the attack just can't happen, and end up just as surprised. 
No matter what the Shah does, Genghis is justified in believing that his attack will be a surprise. And the Shah goes wrong when he concludes that Genghis Khan can't surprise him—not because his logic is flawed, but because it's completely disconnected from reality.

Does anyone still see a paradox?
Logic always loses to life.

Tuesday, April 9, 2013

The Two Symposiums: A Lesson in the Life of the Mind.

One starry night two thousand years ago, a group of free Greek citizens gathered for a symposium at the poet Agathon's house. Sitting on a ring of comfortable couches, the men ate a hearty banquet and prepared for the customary night of entertainment. This night, though, was different from all other nights. Choosing intellectual over physical pleasure, the men sent away the flutist, renounced wine, and dedicated the night to the pleasures of the mind. The program: all the guests were to give a speech expounding on and praising love.

Phaedrus opened by praising the unshakable courage that love confers on mortals. Pausanius was next, explaining the difference between earthly and heavenly—that is, intellectual—love. The last speech belonged to Socrates, who gave the West one of its most penetrating insights and greatest follies. Earthly desire, he said, is the lowest rung of an intellectual ladder whose top is the ultimate truth of the world. But at the end of the night, a drunk and enthusiastic Alcibiades burst into the room; mocking Socrates, joking with the guests, and reminding everyone that pleasure doesn't exist for abstract intellectualism: its real importance lies in colorful, earthly delight.

Alcibiades arrives late.
Once upon a more recent time, a group of American scholars gathered at a modern university for another symposium. The theme this time: Towards a Critical Interpretation of Socratic Dialogue.
After a lunch of turkey sandwiches speared with cellophane-wrapped toothpicks, the first to speak was Professor Max Fischentgraeter from St. Louis. The professer, a balding fifty-one-year-old, talked for an hour and a half about the destabilizing rhetorical techniques employed in the Phaedrus. Next, Professor MarĂ­a Rallavacas gave a frame-shifting talk on the drama of gender in Agathon's Symposium speechAt the end of her presentation, a middle-aged man, name-tag draped over his pot-belly, stood up and rambled for three minutes about his own research. Professor Rallavacas patiently panned a question out of his remarks and gave a detailed, fifteen-minute answer. The audience shifted in their seats, waiting for the next speaker.

At the end of the conference, the bespectacled organizer stood up on stage. Everyone was invited, he said, to submit papers to the annual conference of the Midwestern Institute for Classical Studies, which would be held in October in St. Paul.

Which of the symposiums, do you think, came closer to wisdom? Which advanced the human race farther? Which was more filled with foxlike cunning, ancient resplendence, and innocent delight? And woe to the University of Chicago! I've been to its symposiums, and I haven't seen any drinks or music to abstain from.