No one has searched all possible one page proofs of propositional logic to see if any of them prove false. Sure, you can prove that propositional logic is complete in a stronger theory, but you can prove large cardinality axioms from even larger cardinality axioms.
Why do you think that no proof of false, of length at most one page exists in propositional logic? Or do you think it might?
No one has searched all possible one page proofs of propositional logic to see if any of them prove false. Sure, you can prove that propositional logic is complete in a stronger theory, but you can prove large cardinality axioms from even larger cardinality axioms.
Why do you think that no proof of false, of length at most one page exists in propositional logic? Or do you think it might?