A theory about the real world may be perfectly formal, it just won’t have a perfectly formal applicability proof. On the other hand, if you can show that a theory is applicable with probability of 1-2^{-10000}, it’s as good as formally proven to apply.
I disagree that it’s correct terminology to call a theory informal, just because it’s can’t be formally proven to apply to the real world.
It’s not the lack of a proof that makes it informal, it’s that the elements themselves of the theory aren’t precisely, formally, mathematically defined. A valid proposition in measure-theoretic probability is a subset of the measure space. nothingelse will do. Propositions in Bayseian probability are written in natural language, about events in the real world.
I’m using the word “formal” in the sense that it is used in mathematics. If you’re going to say that propositions written in natural language, about events in the real world are “formal” in that sense, then you’re just refusing to communicate.
A theory about the real world may be perfectly formal, it just won’t have a perfectly formal applicability proof. On the other hand, if you can show that a theory is applicable with probability of 1-2^{-10000}, it’s as good as formally proven to apply.
I disagree that it’s correct terminology to call a theory informal, just because it’s can’t be formally proven to apply to the real world.
It’s not the lack of a proof that makes it informal, it’s that the elements themselves of the theory aren’t precisely, formally, mathematically defined. A valid proposition in measure-theoretic probability is a subset of the measure space. nothing else will do. Propositions in Bayseian probability are written in natural language, about events in the real world.
I’m using the word “formal” in the sense that it is used in mathematics. If you’re going to say that propositions written in natural language, about events in the real world are “formal” in that sense, then you’re just refusing to communicate.