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Originally Posted by Jasper84  @utabintarbo: Just said that about religion as a precaution. In your quote of a definition of an axiom:
I disagree, you can take axioms that need other axioms to define things, but cannot be proven from that. Also note that some axioms can either be taken as axiom, or as proof from other (stronger)axioms; and there is also equivilence. I would instead say "Axioms are not proven from anything to be valid", although sometimes internal consistentcy is not obvious. |
"Axioms" derived from other axioms fail the test of axioms in that they would no longer be irreducible primaries. This topic is about axioms.
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Originally Posted by Jasper84 An aspect of logic; A=> not A is a proof that A is false by self-contradiction. An axiom that self-contradicts isnt much use  . |
Precisely my point.