On Sun, 23 Jul 2006 14:38:37 -0600, Virgil <firstname.lastname@example.org> wrote:
>In article <email@example.com>, > Lester Zick <DontBother@nowhere.net> wrote: > >> >If you could demonstrate them, as opposed to merely give good reasons >> >for believing in them, then they wouldn't be called axioms. You have to >> >start somewhere. >> >> Of course. The difference is that it would be nice to start with >> something true instead of something just assumed to be true. > >If wishes were horses. beggars would ride.
Which is undoubtedly why you ride.
> I don't >> know what the etymology and exact meaning of "axiom" are but I see no >> special reason axioms should be inherently undemonstrable except that >> the process of sylllogistic inference provides no mechanism for >> demonstrating the truth of premises except in terms of more elementary >> premises. Which just regresses the assumption of truth to the more >> elementary premises. > >Until Zick, or someone else, can provide a way of finding a basis for >everything in absolute truths, one has to start with some collection of >premises. In mathematics such ur-premises are collectively called an >axiom system.