[FoRK] Re: Anything to be learned from religion?
Russell Turpin
deafbox
Fri Aug 12 07:49:06 PDT 2005
J. Andrew Rogers:
>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.
That seems to me an odd way to put things. It seems
to remove from the field of math any issue of why some
axiom sets are more interesting than others, or even the
tie between axioms and result. In other words, you're
writing as if stating a result lies properly in math, or rather
properly within math-ZFC, but that stating "result x is
proved in ZFC" is not within the field of math. My
experience is that most mathematicians are able to
abstract back to where axioms also are objects, not
solely principles. ;-)
Nor would I call axioms are arbitrary. The set theories
we get are a result of the project to put analysis and
topology on rigorous basis, a fairly famous historical
project.
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