On Fri, 14 Jul 2006 21:36:09 -0600, Virgil <firstname.lastname@example.org> wrote:
>In article <email@example.com>, > Lester Zick <DontBother@nowhere.net> wrote: > > >> > Can a piece of music be true? An >> > architect's plan for a building? A computer program? > >> Are any of these things constructed theoremetrically from >> demonstrably true assumptions? > >What does a "constructed theoremetrically" mean in English?
Probably exactly what it says.
>> > >> > I don't see any >> >sense in asserting that the axioms of Euclidean geometry or of group >> >theory are true or wrong. >> >> But you see plenty of sense in assuming the truth of what you can't >> demonstrate true or false? > >If one cannot assume anything without proofs or demonstrations, one >can never get started at all.
Getting started is way different from getting finished. What you're talking about is getting started; what I'm talking about is getting finished by demonstrating the truth of initial axiomatic assumptions. Conventional mathematical methodologies just get started and then assume everything is honky dorry for no better reason than they got started.
>> > And this does not mean that axioms of this kind are arbitrary >> > assumptions. There seem to be very few axiom systems that lead to >> > interesting theories. >> >> Arbitrary or not they're still assumptions. > > >Without any of which one has nothing to start with.
Once again getting started is not the same as getting finished. One gets finished with what one has started in formal terms when one demonstrates the necessary truth of what one has started.
>Unless, like Jefferson, et al, you take certain truths to be self >evident.
Exactly my point. Jefferson had his self evident truth and every dictator in history theirs. Hard to tell the chaff from the wheat without a scorecard.
>But then, again like Jefferson, et al, you must state what those self >evident truths are, so that we can know what we start with. > >I find that in matters mathematical there are no self evident truths. >One must assume something in order to get anywhere.
And if what one assumes is not true? This whole discussion is about whether contemporary mathematical set theory is true or false not whether it's assumed to be true.