Every good mathematician knows that any formal proof is based on axioms.
These axioms can not be reduced any further. They are just the "obvious
truths", like ~Ex.(x>x) or Ax.[Ea.(x=a)]. I'm thinking about how the people
who founded non-Euclidean geometry got to it by refuting one of the axioms,
to be more specific, the parral postulate (please pardon my spelling). You
could take any system and think up another system by refuting one or more
of it's axioms. For example, suppose you said, "What if there did exist a
number x in which x>x?". You could make a new system based on that. And
just like non-Euclidean geometry, it may have a basis in reality. Maybe
inside black holes x>x. I don't know.
z = z + c
n + 1 n