That being said, sure, sometimes you have to explain why you consider something to be an axiom.
But at the same time, if you where to explain your axioms all the time you wouldn't get very far. So, I guess the question here is: Is it reasonable to assume this axiom in this context?
And I would argue that it is reasonable, otherwise it would be an entierly different text, about a very different subject, and for me personally, it would be a less interesting article.