A couple of important distinctions between axioms and beliefs: 1) axioms are assumed to be logically consistent with each other, at least when the word "axiom"

A couple of important distinctions between axioms and beliefs: 1) axioms are assumed to be logically consistent with each other, at least when the word "axiom" is understood strictly; it's possible that someone may believe two things that are inconsistent with each other 2) belief is an involuntary mental acceptance that a particular claim is true. You can't make yourself believe something that you know to be false