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Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response

On Sun, 25 Jun 2006 01:25:16 +0200 Andreas Johansson <andreasj@gmail.com>
> On 6/23/06, Phil Bigelow <bigelowp@juno.com> wrote:

> The test of a scientific theory is if it agreess with observation. 
> The
> test of theorem is if it follows logically from the axioms.

While there is a difference, it appears to be rather minor. One is
physical, the other is mental.  Is a mental "test" itself an observation?

>From Webster's Dictionary:
Axiom:  a statement that needs no proof because its truth is obvious;

So, how do mathematicians canonize axioms?  In other words, what is the
process involved in determining that a mathematical concept is "obvious"
or "self-evident"?

If there *is* such a process, then I'll wager it probably involves some
form of testing.  Which is not that different than the testing of
scientific hypotheses and theories.