Objectivism does not accept any assumption as an axiom. It is the only system that does not. All other systems do. That is one of the primary differences between objectivism and all other philosophies and ideologies.
First, there must be an observation and identification of some fact of reality or our knowledge that is discovered to be both primary and irreducible. What determines which such observations are axioms or only derivative concepts is the law of non-contradiction. If the assertion of some discovered aspect of existence or knowledge cannot be denied without being self-contradictory it is an axiom.
For example. The mystic "axiom," "there is a god." To say, "there is no god" is not self-contradictory, and therefore not an axiom. The logical "axiom" "existence exists" (or there is existence). To say "existence does not exist" (or there is no existence) is self-contradictory, thus, "existence exists" is an axiom.
Hank
Really? When did it abandon the non-initiation of force principle?
No? How about "acting in one's self-interest is inherently rational"? Can you prove that, or do we just accept it to be true? After all, the denial, "acting in one's self-interest is not inherently rational" isn't self-contradictory, is it?
For example. The mystic "axiom," "there is a god." To say, "there is no god" is not self-contradictory, and therefore not an axiom. The logical "axiom" "existence exists" (or there is existence). To say "existence does not exist" (or there is no existence) is self-contradictory, thus, "existence exists" is an axiom.
No, actually it's not axiomatic - you just used the law of non-contradiction to logically prove that existence exists. Given that ~(P & ~P) is true, ~P being false logically implies that P is true. And if you can prove that something is true, there's no need to regard it as an axiom.
Hank
God told you His name, Hank: I AM THAT I AM