On Fri, 21 Jul 2006 14:14:26 -0600, Virgil <firstname.lastname@example.org> wrote:
>In article <email@example.com>, > Lester Zick <DontBother@nowhere.net> wrote: > >> On Thu, 20 Jul 2006 21:37:01 -0600, Virgil <firstname.lastname@example.org> wrote: >> >> >In article <email@example.com>, >> > Lester Zick <DontBother@nowhere.net> wrote: >> > >> >> On Thu, 20 Jul 2006 13:12:21 -0600, Virgil <firstname.lastname@example.org> wrote: >> > >> >> >In mathematics, all assumptions (axiom systems) are merely conditional, >> >> >to see what will follow from them. When what follows proves useful or >> >> >interesting, one tends to codify those assumptions. but that never >> >> >requires that one claims them true is any absolute sense. Such >> >> >assumptions are always "what if's". >> >> >> >> It's clear in faith based math >> > >> >"Faith based"? There is no "faith" required for axiomatic based >> >mathematics, only logic. >> >> Sure. And assumptions of truth of axioms doesn't make axiomatic math >> faith based. Yadayada whatever. >> >> ~v~~ > >Truth of "If P then Q" need not require assuming the truth of "P".
Never said it did. I just said the truth of any Q demonstrated of P requires the assumption of truth for P. Otherwise the truth of Q remains problematic. It's an old and ongoing problem in Aristotelian syllogistic inference: the truth of any conclusion is only supported by the truth of the premises involved.
>If P and Q are compound statements such that Q is false whenever P is >false, then "If P then Q" will be true regardless of the truth of P.
Don't quite follow the logic here. The whole "If" conditional is an assumption of truth on the face of it.
>All one is assuming is that formal logic works as advertised, which is >not. strictly speaking, a mathematical assumption at all.