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? > > > > > 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. > > > 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.
Unless, like Jefferson, et al, you take certain truths to be self evident.
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.