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.