Uergil
Posts:
433
Registered:
6/11/11
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Re:WM's Matheology
Posted:
Jun 23, 2012 3:31 PM
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In article
<5e457dde-997f-41cd-a9e8-4f2d8355799b@s9g2000vbg.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> Matheology § 047
>
>
> Does mathematics require axioms?
According to most mathematicians, axiom systems are incredibly useful.
Without them, how can one ever tell what one can argue from or not argue
from.
Such things as group theory, ring theory, field theory, etc., are based
on definitions and rules of deduction, which are essentially sets of
'axioms' for what constitutes a group, ring, field, or whatever.
Without them mathematicians would not have ben able to generate the sort
of mathematics that physicists need.
But mathematics, as usual, has gone far beyond far beyond mere physics,
and is essential to areas totally outside of and irreleevant to physics,
as well as developing mathematics for which ther is as yet no apparent
use. The kind that G.H. Hardy was so fond of.
--
"Ignorance is preferable to error, and he is less
remote from the- truth who believes nothing than
he who believes what is wrong.
Thomas Jefferson
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