In article <firstname.lastname@example.org>, Lester Zick <DontBother@nowhere.net> wrote:
> On Fri, 14 Jul 2006 21:36:09 -0600, Virgil <email@example.com> wrote: > > >In article <firstname.lastname@example.org>, > > 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.
As I do not find any definition of "theoremetrically" anywhere, I assume that it means nothing at all. > > >> > > >> > 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.
How does one come up with the ur-truths on which to found one's initial axiomatic assumptions? You seem to suggest that one can bootstrap from nothing to something, ie, to demonstrate the truth of some set of initial axiomatic assumptions with no a priori assumtions of any sort about anything.
And I know of no way to do that.
I have always regarded something for nothing as pie in the sky.
> Conventional mathematical methodologies just get started and then > assume everything is honky dorry for no better reason than they got > started.
One has to start somewhere to gat anywhere. You seem to think it possible to get something from nothing. I do not. > > >> > 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.
When you claim to be able to justify an initial set of axioms as somehow being "true", I have to ask "How do you know they are true?"
Where does your truth come from?
> > >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?
That is precisely my point! By what criteria can one determine that?
What I say that there are no absolute a priori criteria.
> This whole discussion is about > whether contemporary mathematical set theory is true or false not > whether it's assumed to be true.
And I am asking once more, how one tells the difference.