I like this answer. Been reading “Gödel’s Proof” and for a demonstration where the definition of “tautology” in the main text makes use of the concepts of True and False, there is an appendix explaining that you can arrive at the same result without those concepts, just by treating things as belonging to one class vs another (there is a one to one correspondence with True and False but the meaning is arbitrary)
"An engineer, a physicist and a mathematician have to build a fence around a flock of sheep, using as little material as possible.
The engineer forms the flock into a tight circular shape and constructs a fence around it.
The physicist builds a fence with an infinite diameter and pulls it together until it fits around the flock.
The mathematician thinks for a while, then builds a fence around himself and defines himself as being outside.”
