Proof by assertion is an informal fallacy in which a proposition is repeatedly restated regardless of contradiction and refutation. 1
Proof by assertion is very common in day-to-day conversation. At times, employing it serves its purpose by sparing us from endless cycles of debate. For instance, it’s far simpler for me to ask a bigot STFU than to engage in futile attempts at persuasion. Nonetheless, proof by assertion often arises when individuals fail to engage in critical thinking or, even worse, as a manipulative tactic.
This is very different from establishing initial axioms when building a mathematical or logical framework.
Extreme versions of this in politics can be seen as brainwashing or big lie.