The important point to all this is that I routinely see people assert things which take our universe as axiomatic even when applied to concepts not strictly in our universe. This is a very slippery kind of bad reasoning, as most people have a hard time even thinking about things that don't use our universe as an axiom, and so most don't notice. One of the problems of living in this universe is that our pervasive immersion in it biases our thinking even when discussing things that are outside our universe.
A lot of people understand first-order logic as it is applied to our universe, but few understand the sense in which it exists and works when we are talking about universes that aren't strictly like ours.