On Wed, 19 Jul 2006 14:47:00 -0600, Virgil <firstname.lastname@example.org> wrote:
>In article <email@example.com>, > Lester Zick <DontBother@nowhere.net> wrote: > >> On Tue, 18 Jul 2006 15:26:43 -0600, Virgil <firstname.lastname@example.org> wrote: >> >> >In article <email@example.com>, >> > Lester Zick <DontBother@nowhere.net> wrote: >> > >> >> On Mon, 17 Jul 2006 20:59:40 -0600, Virgil <firstname.lastname@example.org> wrote: >> >> >> >> >In article <email@example.com>, >> >> > Lester Zick <DontBother@nowhere.net> wrote: >> >> > >> >> >> The question I have is whether you or others believe in the >> >> >> possibility of universally exhaustively true mathematical axioms? >> >> > >> >> >What is "truth"? >> >> >> >> I approach the subject the other way around. I try to define "false" >> >> and determine "truth" to be what is not false. Of course the >> >> difficulty here is that there are many problematic claims whose >> >> falseness we cannot determine. So we have to find some method of >> >> reducing falseness unambiguously such that alternatives must be >> >> universally true. It' a pretty little problem but not intractable. >> > >> >Then "tract" if for me. Find me something other than logical tautologies >> >that can be unequivocally determined to be not false. >> >> Who says there is anything other than tautological alternatives which >> can be determined to be other than false (assuming I've read your >> string of double negatives with anything like verisimiltude). > > You have not read my reference to " logical tautologies" correctly. > >If, for example. "P and not P" would qualify as "false" does your >gobledegook require its negation, "P or not P", to be true?
"P and not P" is only universally false because it provides no mechanical basis for alternatives since any "not (P and not P)" converts into itself "not P and P". So there is no alternative in strict mechanical terms because "P or not P" is not always true if P itself contains a self contradiction because P and "not P" are the same.
This is the problem of the unexcluded middle for propostions in general like P. In order to avoid it we have to reduce P to "not" where the excluded middle applies in which case "not" is universally true because "not not" is universally self contradictory and hence necessarily false.
>That is also known as the law of the excluded middle is not accepted by >every mathematician as being true. > >So that alternative to "P and not P", even though a logical tautology, >does not qualify as unmabiguously true. > >You have yet to show that there is anything that is unambiguusly true.
See if the above impresses you even a little.
>> >> >I can deal with the tautologous logical truth of implications like "if P >> >> >then (P or Q)", but other than those, which include the more complex >> >> >logical deductions from a set of axioms, I know of no absolute truth. >> >> >> >> Ah but there is the mechanically reducible absolute falseness of self >> >> contradiction such that alternatives to self contradiction must be >> >> necessarily and universally true. >> > >> >Name one! >> >> I just did. > >You made an assertion which you cannot, or at least have not yet, >demonstrated to be true.
The general proposition is that something is universally true if its necessary alternatives are self contradictory and necessarily false. This claim is perfectly analyzable in its own right. I have avoided making this claim in other than general form so it can be analyzed on its own merits because seems like everyone has some idea of his own regarding what I have to mean by what I say. I make the idea specific above so now we have something else to argue about than the basic claim.