Again, I am sorry for being direct, but this does not make sense. If a Venusian man is immortal, then the "axiom" (preposition) that all men are mortal is false

Again, I am sorry for being direct, but this does not make sense. If a Venusian man is immortal, then the "axiom" (preposition) that all men are mortal is false. In other words, the issue is not that the preposition "Socrates is Venusian" was missing but that the preposition "all men are mortal" is false. It is possible to develop significant mathematical theory without using some axioms. For example, mathematicians sometimes choose not to use the "axiom of choice" when working with Zermelo–Fraenkel set theory. That does not mean that mathematical theorems proven without using the axiom of choice are invalid, even if you later assume that this axiom is true (or false).