Does this sound a little less indefensible, if I mention that PA trusts only proofs from the PA axioms, not proofs from every possible set of axioms?
This makes me wonder if something interesting might be said about a system that does trust proofs from every possible set of axioms. Or a system that consists of every possible axiom.
It would be inconsistent, obviously, but what else?
This makes me wonder if something interesting might be said about a system that does trust proofs from every possible set of axioms. Or a system that consists of every possible axiom.
It would be inconsistent, obviously, but what else?