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. His Principia is an attempt to suppress his Paradox, and win the day for the logicist program. It is long, dense, unreadable by most, and its mission was defeated by Gödel’s Theorems - themselves proven by the existence of sentences similar to Russell’s Paradox: “the set of all sets that do not contain themselves” and “ ‘is not provable when applied to its own quotation’ is not provable when applied to its own quotation.” Russell tried to ban self-reference, but self-reference is inherent in arithmetic, given coding.

The Principia is long, heavy, obsolete, incomplete, incomprehensible, and failed. The Paradox is short, sweet, witty, and can be adapted to relevant topics. For instance: the watchmen watch all those, and only those, who do not watch themselves. Who watches the watchmen?

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 lesson in pragmatic memetics. The rule is: Keep It Simple, Stupid.