Steven Pinker -- How the Mind Works - Hampshire High Italian ...

98 | HOW THE MIND WORKSThe Emperor's New Mind was pointed out by Dennett. Penrose's denunciationof the computational theory of mind turns out to be a backhandedcompliment. The computational theory fits so well into our understandingof the world that, in trying to overthrow it, Penrose had to reject mostof contemporary neuroscience, evolutionary biology, and physics!REPLACED BY A MACHINEIn Lewis Carroll's story "What the Tortoise Said to Achilles," the swiftfootedwarrior has caught up with the plodding tortoise, defying Zeno'sparadox in which any head start given to the tortoise should rilake himuncatchable. (In the time it would take for Achilles to close the gap, thetortoise would have progressed a small amount; in the time it took toclose that gap, the tortoise would have moved a bit farther, ad infinitum.)The tortoise offers Achilles a similar paradox from logic. Achilles pulls anenormous notebook and a pencil from his helmet, and the tortoise dictatesEuclid's First Proposition:(A) Things that are equal to the same are equal to each other.(B) The two sides of this Triangle are things that are equal to the same.(Z) The two sides of this Triangle are equal to each other.The tortoise gets Achilles to agree that anyone who accepts A and B and"If A and B then Z" must also accept Z. But now the tortoise disagreeswith Achilles' logic. He says he is entitled to reject conclusion Z, becauseno one ever wrote down the if-then rule on the list of premises he mustaccept. He challenges Achilles to force him to conclude Z. Achillesreplies by adding C to the list in his notebook:(C) If A and B are true, Z must be true.The tortoise replies that he fails to see why he should assume that just becauseA and B and C are true, Z is true. Achilles adds one more statement—(D) If A and B and C are true, Z must be true.—and declares that "Logic [must] take you by the throat, and force you"to accept Z. The tortoise replies,