Axioms are true by definition. Of course, a certain axiom A for Theory T may be false in Theory T'. However, in any (consistent) theory for which A is an axiom, A will be true.
If you wish to argue with me further, please do so with specific references from specific mathematical logic and/or mathematical foundations texts that support what you're saying.
Dave L. Renfro wrote:
>> Not only that, but axioms can be proved >> quite easily. Here's an example I posted >> back on June 20: >> >> Axiom R: All right angles are congruent. >> >> Theorem: All right angles are congruent. >> >> Proof (2-column format): >> >> Statements Reasons >> >> 1. All right angles are congruent. 1. Axiom R.
Lester Zick wrote:
> You mean mathematikers can rely on circular > reasoning to demonstrate modern math theorems? > How nice. Certainly supports every speculative > conjecture I've made concerning the intellectual > content of modern math. Don't prove it; just > assume it; then claim you've proven it.
Mathematics is basically the study of various deductive structures. It appears that you think it's something else.
One *can* study structures generated from P ==> P for various statements P, but most people aren't going to be very interested.