April 28, 2010
Formal logic is seductive. You start with a handful of indisputably true statements and a set of rules. You apply the rules to the statements and derive more rules and statements. Brick by logical brick, you can build rooms, houses, streets, cities and worlds. And, smugly surveying all these edifices, you soon get the idea that you can build anything. I’m fairly sure that my undergraduate logic professor only taught the introductory course so he could watch students’ crestfallen reactions when he introduced KURT GÖDEL (1906-78) in the final week. With his cheekily paradoxical incompleteness theorems, Gödel pointed at the cracks in formal logic’s edifices and revealed that the bricks are made of sand. More formally, he proved that, in any system of mathematical logic that claims to be able to prove all truths, there will always exist truths that it can’t prove. When he first dropped this intellectual atom bomb in 1931, at a time when theoreticians like Bertrand Russell thought they were close to finding the Holy Grail, the explosion was devastating. Gödel had a uniformly dazzling career as mathematician, philosopher and even physicist — when he fled Nazi-run Austria for the US, he became Einstein’s favorite sparring partner at Princeton — but he will be remembered mostly for bursting into the room and pulling the rug out from beneath our quest for truth.
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