Axioms can exist only in formal logic (and mathematics), laws between men – and conversely theories provide explanatory power about the universe.
An axiom in formal logic is declared the equivalent of true, and therefore we assume it’s no longer contingent or externally correspondent for our purposes of further (subsequent) construction and deduction.
So in that sense we can use axioms for ‘what if’ scenarios in logic, and the interpretation of moral norms, and legislation and law, and textual analysis including scripture – which is where all this form of verbal reasoning comes from: non correspondence with reality, only internal consistency.
Whereas we can only use hypotheses theories and laws when we are making a contingent truth claim about the existential rather than the verbal and ideal. Hypotheses theories and laws originated in the description of correspondence with reality.
As such the use of axioms helps us test logical internal consistency, and the use of theories helps us test external correspondence – since nature is always internally consistent: it can’t help it. That’s what determinism *means*. As such Axioms and Theories are polar opposites.
And using one in the place of the other is generally either a matter of ignorance or attributing the correspondence and consistency of that which is deterministic under logical declaration to that which is underdeterministic under physical description.
I don’t find this very difficult because in math we use axioms, in science we use laws, and only sophists in philosophy seem to attempt to either conflate the two, or to attribute the properties of axioms to that of theories and laws – and that means there are a lot of sophists (like Mises and Rothbard, not to mention Hoppe and every marxist that ever lived). And as I’ve said, as far as I know math survives, but formal logic was a dead end, the grammars replace them, and philosophy is reduced to the preferable and good not the true. And what we call science (due diligence) and law (testimony) determine truth.
So, at present, In my understanding – which I have serious doubts that I’ll ever be refuted – the word axiom is archaic and has no use outside of mathematics and symbolic logic that seeks to imitate mathematics through conversion of reality (operations) to ideals (sets). Axiom = Arbitrary, and Theory = Existential.
WTH is wrong with you? An axiom is a declaration – an ideal. A theory is a contingent explanation – a real. Logical and ideal axioms. Descriptive and real theories. They are not synonyms.