[FoRK] Anything to be learned from religion?
Fri Aug 12 07:04:23 PDT 2005
A set of axioms and rules of derivation DEFINE a
mathematical system. The mathmematical system defines
a set of theoroms which are provable in that system.
In a sense those theoroms are TRUE in that system.
They are true by virtue of the nature of the
--- "J. Andrew Rogers" <andrew at ceruleansystems.com>
> On 8/11/05 7:04 PM, "Albert Scherbinsky"
> <albert at softwarepress.com> wrote:
> > To the extent that "truth" exists at all, there
> > different kinds of "truth". Math is "true" by
> > definition. It is an invention of the human mind.
> Eh? Math is not true by definition, it is 'true' by
> convention. It is
> based on an arbitrary set of axioms, and what
> constitutes that set is not
> even constant (the Axiom of Choice being the
> textbook example of this). We
> treat math as a pseudo-truth -- and it is
> astonishingly effective with the
> axioms we do typically assume -- but if you look too
> closely it may fray at
> the edges. There is not one math, there are as many
> maths as there are sets
> of axioms.
> While asserting axioms is bad science, it has one
> extremely valuable
> property if axioms are chosen carefully: It allows
> us to make consistent
> predictions about things we lack the ability to
> measure empirically. If the
> set of axioms used in a math are good, it will allow
> remarkably detailed
> predictions of things we've never seen and can
> barely imagine via a
> mechanical process from those axioms. That is so
> valuable when it works out
> that it is worth overlooking the fact that there is
> no intrinsic truth to
> the assumptions used, and we mitigate the potential
> danger by using as few
> axioms as possible.
> J. Andrew Rogers
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