From: gordon brown <Gordon.Brown@Colorado.EDU>

Date: Thu Oct 09 2008 - 15:31:18 EDT

Date: Thu Oct 09 2008 - 15:31:18 EDT

On Wed, 8 Oct 2008, D. F. Siemens, Jr. wrote:

*> As to proof in mathematics, note that it depends absolutely on the axioms
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*> assumed. Some of these are so commonsensical that we do not usually
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*> recognize that they cannot be proved except by reiteration.
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*> Dave (ASA)
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*>
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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)

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Received on Thu Oct 9 15:32:14 2008

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