This is the problem which must be dealt with. Rather than assume an assumption must be correct, you must somehow show it will work even if you start from no assumptions.
Your universal propositional calculus might not be able to generate that proposition, but my calculus can easily prove: Yours won’t generate any propositions if it has no axioms.
Simple: The fact that we don’t see strange things happening is bayesian evidence that we don’t live in a world where that is possible.
As I already mentioned, it is probability itself which must be justified in the first place. How do you do that?
What assumptions am I granted? Can’t argue anythin’ from nuthin’. Even “I think” is an assumption if logic is.
This is the problem which must be dealt with. Rather than assume an assumption must be correct, you must somehow show it will work even if you start from no assumptions.
Your universal propositional calculus might not be able to generate that proposition, but my calculus can easily prove: Yours won’t generate any propositions if it has no axioms.
This is precisely the problem. I was posting in the hopes of finding some clever solution to this problem- a self-proving axiom, as it were.