A logical axiom is one of the Three Aristotelian First Principles of Thought. Those are considered self-evidently true, and they pass the Aristotelian test of Reductio Ad Absurdum. These, plus others such as coherence, grounding, valid form of deduction, are used in the generation of deductive truths - the only form of incorrigible truth.
A dialectical axiom is formed from observations of the material universe, where certain characteristics are found to be self-evidently true within the universe. This includes the three Aristotelian First Principles, as well as material determinism but not the principles of coherence, argument form, arithmetical axioms etc.
A Rhetorical Axiom is demanded by force, where opposition to the principle is demonized and demeaned by being muted due to fear - fear of rejection, fear of being falsely categorized, fear of being defamed, fear of other losses. Silencing is necessary when the axiom is not immutably self-evident as a universal truth or physical law which transcends criticism.
Evolution is a Rhetorical Axiom.
Here's how Jerry Coyne put it in his video, "Why Evolution is True":
If you dissent, then
"you are perverse; you are a moron; you simply can’t understand the nature of evidence; or you are blinded by religion."(3:27)There is no room for intelligent dissent, because you are placed into one of his Classes, his categories of Ad Hominem Abusive denigrations. Coyne thus is a Class Warrior, who protects his Rhetorical Axiom by placing any other concept into one of his classes of inferior beings. This is an axiom by force of fear of denigration, the common axiom of evolution.
"If you don't believe in evolution you are willfully ignorant."
"It is absolutely safe to say that if you meet somebody who claims not to believe in evolution, that person is ignorant, stupid or insane (or wicked, but I'd rather not consider that)."
John Maynard Smith:
"Natural selection is the only workable explanation for the beautiful and compelling illusion of 'design' that pervades every living body and every organ. Knowledge of evolution may not be strictly useful in everyday commerce. You can live some sort of life and die without ever hearing the name of Darwin. But if, before you die, you want to understand why you lived in the first place, Darwinism is the one subject that you must study."
The Rhetorical Axiom claims that a principle need not be self-evident to you; it is self-evident to me ("us", the constant if implicit Appeal to Authority), and that is sufficient to remove you from any class of principled, intelligent beings capable of valid thought, purely because you have some disagreement. Thus I need not recognize or address your point of disagreement, because of the source, which I declare non-valid and reprehensible.
In evolution, all criticism is blamed on stupidity, evil, religion, anti-science, insanity, morons and other pejoratives. Given that, there is the additional assumption of no need to address any criticisms, except by invoking "Creationism, stupidity, anti-science, insanity, etc." The Ad Hominem Abusive denigration accusation is seen as sufficient to silence the dissenter, and thus quell the dissent. It works well enough in university settings that jobs and careers have been lost due to dissent.
Further, the axiom of evolution is now protected by a friendly court. That is a protection which is not needed by any REAL science, those which have produced objective yet contingent knowledge to support their hypotheses (which necessary feat evolution cannot perform).
That is the Axiom of Evolution (and the Axiom of human caused global warming). Pure rhetorical Ad Hominem Abusives rather than disciplined, evidentiary, objective disproof of the dissent.