> There in lies the whole problem.  Axioms have not been proven to be
> true and they cannot be proven, therefore I pose the question, "How
> can we create 'proofs' based on 'ideas' (axioms) that are said to be
> self-evident truths?".  Using this line of reasoning, couldn't I say
> that 'magic' is real since it appears to be 'self evident' and it is
> repeatable?

The proofs based on a set of axioms are valid in the space of the corpus
(or corpii or groups) where they are defined. Higher algebra explains
this. They 'fail' only people who try to apply them on some ill-defined
corpus instead.

Magic is very real if you believe in it. You know the saying 'sufficiently
advanced technology is indistinguishable from magic'. Perhaps this can be
extended to sufficiently primitive technology too.  As in DNA & co. There
is a philosophical idea about the knowledge horizon or volume of man being
a donut-shaped body in the space of knowledge (with as many dimensions
considered, as you please). Anything beyond that he should either not
comprehend, refute, ignore, or take as granted.

Peter

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