Claradoon wrote:
Ignoramus question (please be kind): Bertrand Russell refused to accept that 1+1=2 although he admitted that if it did, then the rest of mathematics followed. Do the axioms you mention remove Russell's objection? I apologize if this is archaic.
Short answer: Yes
Slightly less short answer: Bertrand Russell didn't so much refuse to accept that 1+1=2 but he wanted to create a certain type of axiomatic system from which all of mathematics could be deduced from. So in other words; it wasn't that there was a specific objection he had that needed to be overcome, it was just that the foundation of mathematics wasn't yet at a stage where a standardized axiomatic system of the type proposed by Russell was in place. He was partially successful in doing this with his book Principia Mathematica in which he derived 1+1=2 from his axiom schema but there was a problem with his system that he had discovered just before the book was published so the Zermelo-Fraenkel(-Choice) axiom schema was only completed and standardized as the common axiom schema for mathematics after Russell (although it built on his work in some ways)
12 May 2007, 4:16 pm
