In article <firstname.lastname@example.org>, "Jesse F. Hughes" <email@example.com> wrote:
> david petry <firstname.lastname@example.org> writes: > > > On Wednesday, January 30, 2013 1:58:25 PM UTC-8, Toni...@yahoo.com wrote: > > > >> How in the world can a serious MATHEMATICIAN _claim_ that something > >> written in a book/paper has proved "once and for all" that so and so and > >> then, later, he whines he has no expertise, interest and etc. in the > >> paper/book's claims TO DO SO?? > > > > > > The word "proof" has two meanings: > > > > 1) Informally, a proof is a compelling argument using the > > intuitively understood reasoning that we have acquired from our > > experience in the real world. It is entirely possible that that > > intuitively understood reasoning has never been completely and > > accurately formalized. > > > > 2) A purely formal construct that is inspired by the informal notion > > of proof but may not be an entirely accurate model of that informal > > notion. > > > > > > When we debate the question of whether ZFC has accurately captured > > our intuitive notion of what a proof is, we must rely on the first > > definition. It is reasonable for mathematicians to get involved in > > such a debate. > > WM has bigger fish to fry. > > He thinks that he's proved ZF is inconsistent, and hence the second > meaning is closer to the relevant sense. > > I don't know if that's what he's doing on p. 112, mind you, but at > least sometimes, he is presenting what he mistakenly believes is a > valid, mathematical proof.
One of the problems with WM's "proofs" is that he quite often sneaks in his conclusion, or at least a large part of it, as an assumption in his arguments. --