On Thu, 20 Jul 2006 11:39:47 EDT, "Dave L. Renfro" <firstname.lastname@example.org> wrote:
>Dave L. Renfro wrote: > >>> What do you mean by the truth of an axiom? > >Lester Zick wrote: > >> Whether an axiom is true or not. > >Axioms are true by definition.
Not quite. Axioms are true by assumption. That doesn't make them true. It is one of the quirks of moderm mathematics that the meaning of "definition" has been converted to "arbitrary assertion" or "fiat" solely in order to validate assumptions of truth without coming right out and saying so. Truth by definition and assumptions of truth are nothing more than revealed truth, divine truth and are purely faith based and undemonstrated intimations of intuition.
> 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.
Which is just another way of saying axioms can be false with a straight face.
>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.
Why would I want to argue with you? You haven't said anything worth arguing about.
>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. > >Dave L. Renfro