[medstrom]

What? You contradict yourself several times. Does accepting the axioms obligate you to accept the conclusion or not? First you say it does, then you say it doesn't. And proving something is of course quite literally "determining the truth", you can't just dribble it away like that. This comment looks like word salad intended to let the reader believe whatever they want.

[whatshisface]

Proving that some axioms imply a conclusion does not prove the truth of the conclusion, when the axioms themselves remain unproven. For example:

Axiom 1) All comments by whatshisface are right.

Theorem 1) This comment is right.

Proof: Whatshisface wrote this comment.

That's a proof in the mathematical sense and there's nothing wrong with it in that way, but that it has nothing to do with the truth of the theorem.

[medstrom]

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.