On Wed, 5 Oct 2016 13:37:50 -0000 xorcist@sigaint.org wrote:
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,
Axioms being self-evidently true means that if you choose to DENY them, you need to USE them in the denial process anyway, therefore proving that they ARE true. Try assuming that the so called identity principle is not 'true' and see where you get. I don't need to invoke internet authority or the sacred wikipedia scriptures xorcist. I can explain what an axiom in my own words. So no, truth and logic still are not a matter of agreement, and axioms are not arbitrary if that's what you are trying to suggest. And even going by that definition, if axioms are self-evidently TRUE, then people who don't 'agree' that they are true are self-evidently...troubled. (and by the way, your first source is about mathematics, not logic or philosophy in general)
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.