hi, Thats a beautiful one. --- Jim Choate <[EMAIL PROTECTED]> wrote: To assert that a theorem is > false means to deny > one or more of the axioms. However, to assert that a > theorem is true does > not necessarily mean to assert the truth of all > axioms.
yes-it only means its time to update our mathametical model for certain observations which does not agree with the model we made for it. > Some theorems > remain true even if some of the axioms of a > mathematical theory are > rejected. yes-our original model still works for the domain it still agrees with our observations. > > To accept the truth of the axioms is simply to agree > to assume them to be > true. yes-we will have to,other wise we won't have models which work. > However, the consistency of the axioms with > each other is sometimes > in question. Then its time to modify our axioms. > Then, if any two or more axioms of an > alleged mathematical > theory are found to be inconsistent with each other, > the whole theory > collapses." It will be a proposition then-won't be an axiom.If we find that the two axioms are inconsistent with each other-its time we update our axioms and they will become propositions and no more axioms.The theory as such doesn't collapse. Regards Sarath. __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
