IMHO, the difference between math and (modern) philosophy axioms is that the latter's are way higher level (e.g. "the world is material", "every humans deserves

IMHO, the difference between math and (modern) philosophy axioms is that the latter's are way higher level (e.g. "the world is material", "every humans deserves to live"...) while the former's are very low level and concern themselves with "simple" rules (refer to ZFC). Philosophers also make their arguments in natural language, while mathematicians use a formal language (ultimately also described in natural language). Your exemple is interesting, as it makes a bridge between philosophy and mathematics. It's basically Gödel's attempt to prove the existence of God with mathematical rigor. It's basically a form of the original ontological argument[1] with extra flair. You can still translate the axioms into natural language, like: "P(¬ᵠ)⇔¬P(ᵠ)" becomes "a property is bad if and only if the opposite property is good" or "P(G)" becomes "being God is good". Finally, mathematicians don't usually concern themselves with "universal truth seeking" and are often content to add axioms as it suit them, if it means they can do intersting things (e.g. the Axiom of Choice). [1] https://en.wikipedia.org/wiki/Ontological_argument https://en.wikipedia.org/wiki/Ontological_argument