[FoRK] Anything to be learned from religion?

Albert S. albert.scherbinsky
Fri Aug 12 07:06:29 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
DEFINITION.


--- "J. Andrew Rogers" <andrew at ceruleansystems.com>
wrote:

> On 8/11/05 7:04 PM, "Albert Scherbinsky"
> <albert at softwarepress.com> wrote:
> > To the extent that "truth" exists at all, there
> are
> > 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.
> 
> 
> Cheers,
> 
> J. Andrew Rogers
> 
> 
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