On 10/05/2016 06:37 AM, xorcist@sigaint.org wrote: "'conjecture' or 'hypothesis', both of which connote apparently true but not self-evident statements." That's what you get for using dictionaries. English language dictionaries also conflate "Want" with "Need". Apparently that 'disease... that dumbing down of the English language, has spread to technical dictionaries as well. No wonder modern industrial output is half-baked shiny-and-soon-to-the-trashheap junk. Conjecture or Hypothesis ALWAY MEANT the person making the statement believes it so. "Conjecture" is quaintly referred to on the intertubz as "IMHO". Hypothesis would have SOME facts to back it... Usually single-sided to suit the hypothesizer] awaiting it's 'graduation' to 'theory, where it's tested against other facts. Rr
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.