On Sat, 22 Jul 2006 12:53:00 -0600, Virgil <email@example.com> wrote:
>In article <firstname.lastname@example.org>, > Lester Zick <DontBother@nowhere.net> wrote: > >> On 21 Jul 2006 16:59:48 -0700, "Jiri Lebl" <email@example.com> wrote: >> > Simple >> >Further the fact >> >that either A or not A is true is an AXIOM (given that A is a well >> >defined statement that is either true or false in some system)! It is >> >an ASSUMPTION! Further some people reject this assumption, for it >> >leads to non constructive proofs. >> >> Well this point is well taken: the tautological exhaustion of truth is >> an assumption. However the point I would make in this connection is >> whether there can be any alternative. In other words can there be an >> alternative to the tautological exhaustion of truth that is actually >> "not a tautology"? > > >Those who reject the axiom of the excluded middle in favor of >constructive mathematics make, and,implement just such an assumption. > >Thus Zick must assume something to get anything.
I think you deleted just the part of my reply which shows there can be no alternative to tautologies in mechanical terms. Whether you assume the exhaustive truth of tautologies is another issue. The excluded middle and constructive math are other issues than whether there can be alternatives to tautologies.