> Again, truth is NOT a matter of agreement. And axioms are not > to be 'agreed' upon. Also, axioms can be proven. If axioms > couldn't be proven then any statement based on them would > be...unproven, meaningless, useless, et cetera.
>From the CRC Encyclopedia of Mathematics: "AXIOM: A proposition regarded as self-evidently true, without proof. The word "axiom" is a slightly archaic synonym for 'postulate'. Compare 'conjecture' or 'hypothesis', both of which connote apparently true but not self-evident statements." >From the Wiki: An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. ... Within the system they define, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems.
