Incompleteness in foundations is not exactly analogous to your game.
The proposition MyTheoremsAreEnumerable is true but unprovable.
Adding MyTheoremsAreEnumerable to a foundational theory
makes the theory inconsistent.
The proposition MyTheoremsAreEnumerable is true but unprovable.
Adding MyTheoremsAreEnumerable to a foundational theory
makes the theory inconsistent.
Yes, I know as I already mentioned. That's why I wish somebody smarter than me can do it more accurately by putting the concepts such as "MytheoreumsAreEnumerable" into a better ELI5 way.