Philosophical, not logical. The actual axiom is still 'god exists."
Defining what god must be, rather than defining what would qualify as a god, assumes there is such a thing as god.
Example: The cat god is a being that is a better cat than any other imaginable cat.
Compared to: A god would be all-powerful. This being, x, is all-powerful. Therefore, x is a god.
Compared to: There exists a cat better than any other cat. This cat, being greater than all others must be the god of cats. (Does this qualify as an omnipotent 'god'? No, but at least the cat is provable.
Defining what’s good is good.
Adam and Eve were canonically cast from heaven for being able to define good and evil.