P is a proposition, such as “all triangles have three sides.” ~P is “not P,” such as “Not all triangles have three sides.” ~~P is therefore “not not P.”
The very point of a reductio is to prove the starting premise true by demonstrating that assuming the opposite creates an absurdity and so the opposite must itself be false, thereby making the original statement true (if P and ~P exhaust all possibilities). That’s exactly what we’ve done here.
The point of me using this particular example in my first post is that it’s a truth that is known per se (in itself, once you grasp the terms) as opposed to per aliud (demonstrating it through something else), and that accusing a person making a per se proposition of begging the question is just absurd. (If the statement was per aliud, assuming it as a starting premise would beg the question). This is following Aristotle’s definition of the begging the question fallacy as opposed to more modern ones, which if followed would make statements like “all bachelors are unmarried because married men are not bachelors” fallacious arguments. Once you know what the terms mean, the proposition becomes self evident. A person can rightfully make such a statement without committing a fallacy, and if a person keeps asking “Why? Why? Why?”, it’s not unjust to just ignore them as a skeptic of all things and not worth arguing with, or mentally incompetent.
So God being eternal is not a per se proposition. To say, “if He wasn’t eternal he wouldn’t be God” as the full argument may be true, but it would beg the question. That has to be demonstrated through other things. However, if you establish that God is eternal, and then the challenger says “but why does that mean He always exists?” he is essentially asking “but how do you know that being eternal means existing at all times?” it is not a fallacy to retort “because if it wasn’t at all times it wouldn’t be eternal.” I mean, you could be more charitable and try to educate him on the terms so that he can grasp it, but it’s not a fallacy.
