Russell’s Two Legacies

             Russell’s Two Legacies

 

             Bertrand Russell has two legacies: his Paradox and his Principia. His Paradox is concisely stated, wittily illustrated with a quaint tale, and logically devastating. He asked: consider the set of all sets, and only those sets, that do not contain themselves. Does it contain itself, or not? The answer is: yes as much as no!

            Russell illustrated his Paradox with a quaint tale about a village’s  barber. The barber shaves all those, and only those, who do not shave themselves. Does the barber shave himself? Yes as much as no!

            You can tell similar tales. For instance, that village is watched by a watchman, who watched all those, and only those, who do not watch themselves. Who watches the watchman? The watchman watches himself as much as he does not.

            The village jester laughs at all those, and only those, who do not laugh at themselves. Does the jester laugh at the jester? The answer to this question is, yes as much as no.

            Related to these is Gödel’s Paradox: “ ‘is not provable when it quotes itself’ is not provable when it quotes itself.” That statement uses coding to call itself unprovable. This yields a paradox unless proof does not equal truth.

            Russell’s Principia is an attempt to suppress Russell’s Paradox, and win the day for the logicist program. It is long, dense, unreadable by most, and its mission was defeated by Gödel’s Paradox. Russell tried to ban self-reference, but self-reference is inherent in arithmetic, given coding.

             Russell’s Principia is long, dull, obscure, unreadable, specialized, and failed. Russell’s Paradox is short, sweet, clear, witty, adaptable, and effective. I think that Russell’s Paradox will long outlive his Principia, which will be remembered only for taking hundreds of pages to prove that 1+1=2.

I see in this a kind of Shakespearean family tragedy. Lord Russell had two brainchildren: Principia Mathematica, the legitimate heir, and Russell's Paradox, the by-blow conceived in youthful folly. The two waged war, and the bastard defeated the legitimate heir. 

            I also see in this an object lesson in pragmatic memetics:

Keep It Simple, Stupid.

            And why? Because all men are mortal. We don’t have time for windy nonsense; we only have time for witty nonsense.
 

 

Paradox-logic addendum:

            The Kleenean-logic solution to the paradox of the jester is that the jester only half laughs at the jester, with a forced and rueful chuckle. The Diamond-logic solution is that there are two jesters, who laugh loud and long at each other.