Axioms are not something you ever prove, as in, they're not provable even in principle. I would not call this an axiom, this is simply a premise. It can be determined. You'd trace this premise back up a chain of premise-based arguments, and if all are valid, you eventually reach some of the 5-10 (I forgot) core axioms that underlie all of logic. And those are not provable, but you'd generally be considered mad not to accept them.

I'm not sure what you want to achieve by focusing on this topic. You just saying you don't agree with the axioms in the article, right? So just say that.