On Sat, 22 Jul 2006 14:07:50 -0600, Virgil <email@example.com> wrote:
>In article <firstname.lastname@example.org>, > Lester Zick <DontBother@nowhere.net> wrote: > >> 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: > >> >> 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"? > >For any assumption, one can refuse to make that assumption. >And the refusal to assume an excluded middle, which constructionists >have refused to assume, is an alternative to Zick's "tautological >exhaustion of truth"
I never said anyone has to make any assumption. They can continue to wallow in syllogistic inference and faith based mathematics as they please.
>> >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. > >One cannot demonstrate anything without having something on which to >base that demonstration. So how does Zick propose to demonstrate that >"there can be no alternative to tautologies in mechanical terms"?
Any alternative to tautologies would form a tautology: "tautology, not tautology".
>I only snipped a section in which no such demonstration occured.
I guess we'll just have to take your word for it.
>> Whether you assume the exhaustive truth of tautologies is another >> issue. > >That is merely another form of the excluded middle, which, as we have >seen, need not be assumed.
Nothing need be assumed in faith based mathematics.