Originally Posted by

**Lyn**
Sure. An axiom, by definition, is a proposition that cannot conclusively be proven true or false. It is assumed to be true so that it can form the basis of other propositions. Sunshinewarrior mentioned Douglas Hofstadter's claim that any attempt to "prove" an axiom will result in an infinite regress, and Golkarian asked whether this infinite regress makes the axiom false. I'm pointing out that the question is misleading because "falseness" (and "truth") does not apply to axioms the same way it applies to other propositions. Axioms are the assumptions that allow us to create a system of truth and falseness in the first place, so applying that system to the axioms themselves leads to all sorts of paradoxes; but these paradoxes are not generally thought to undermine the validity of the axioms.