Re: [asa] David S Wilson

From: D. F. Siemens, Jr. <>
Date: Thu May 10 2007 - 00:02:36 EDT

On Wed, 9 May 2007 23:21:49 -0400 "Alexanian, Moorad"
<> writes:
> One really does not need God to develop a logical system that
> connects axioms to theorems. For instance, we do not need to invoke
> God in Euclidian geometry. The latter, essentially, is what
> mathematical models of Nature are. However, if one wants to explain
> Euclid or the existence of the objects to which Euclidian geometry
> is applied to, then that is a different problem where God needs to
> be invoked since one is dealing with ontological questions.
> Moorad
You're missing the point that the Euclidean geometry is arbitrary. Euclid
himself did not present 5 axioms for his system: it was 5 postulates. His
separate axioms were matters like "equals added to equals are equal." One
may drop the parallel postulate and have absolute geometry, or add any
one of three parallel postulates and have Euclidean, Lobachevskian or
Riemannian geometries. None of these can be proved consistent, but only
that if any of them is consistent the others are also.

If you want to insist on Euclidean geometry, you're going to have a
problem with relativity. But those who think they can do away with
consistency will face /consequentia mirabilis/.

As to calling in the deity, I am persuaded that, involving Riemannian
notions, one can deal very well with relativity without need of that

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Received on Thu May 10 00:06:50 2007

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