Re: [asa] Science proves there's no need for God?

On Thu, 9 Oct 2008 13:31:18 -0600 (MDT) gordon brown
<Gordon.Brown@Colorado.EDU> writes:
> On Wed, 8 Oct 2008, D. F. Siemens, Jr. wrote:
>
> > As to proof in mathematics, note that it depends absolutely on the
> axioms
> > assumed. Some of these are so commonsensical that we do not
> usually
> > recognize that they cannot be proved except by reiteration.
> > Dave (ASA)
> >
>
> The modern attitude toward axioms in mathematics is different from
> the
> classical one. The key development in this change was the discovery
> that
> by changing the definition of certain terms in Euclidean geometry
> one
> could achieve a geometry in which Euclid's parallel postulate did
> not hold
> but would not lead to a contradiction unless Euclidean geometry did.
> Now
> rather than viewing axioms as being true commonsensical statements,
> the
> basic terms are taken as being undefined, and the question is not
> whether
> the axioms are true but rather whether they are consistent.
>
> Gordon Brown (ASA member)
>
I see a practical problem with this claim, for it means that all the
specific terms in the axioms are meaningless. As a consequence, any set
of consistent axioms, that is, empty terms with empty relations, would be
investigated. However, it seems that only a limited set of terms and
relations are worked with. Thus a plane is a two-dimensional structure,
with the earlier assumption that it is Euclidean restricted. What I can
draw on a sheet of paper fits Euclid's or Playfair's parallel axiom, with
the unexampled assumption that it be infinite. But it is equally possible
to deal with the surface of the earth as a Riemannian plane. Also, the
mathematical functions are essentially the same whether we deal with real
numbers, modular numbers or infinities, though there are different
consequences. So I hold that there are, despite claims to avoid
explanations, tacit assumptions about the underlying meanings.
Dave (ASA)
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Received on Thu Oct 9 17:31:50 2008