[par1970]

Does “self-evident” just mean that anyone who knows the sentence’s meaning can determine that it is true without any need to gather empirical data?

eg, All bachelors are unmarried.

eg, If X is a triangle, then X has three sides.

eg, the world is round or it is not the case that the world is round.

And does “universally recognized” just mean that most people believe the proposition is true?

[lionkor]

In this context an axiom is a nonlogical axiom, in other words an assumption, one that is not to be questioned or discussed

[par1970]

Okay. So, in your original comment are you asserting that teachers are mostly telling students to believe propositions without giving any epistemic justification for those propositions?

[lionkor]

Yes, as part of teaching one topic, teachers have to tell students to "not worry about" some other related topic and just take it as given fact, even when that's not technically true