Interestingly enough, Mathematics and logic is what you get if you only allow 0 and 1 as probabilities for proof, rather than any intermediate scenario between 0 and 1. So Mathematical proof/logic standards are a special case of probability theory, when 0 or 1 are the only allowed values.
Credence in a proof can easily be fractional, it’s just usually extreme, as a fact of mathematical practice. The same as when you can actually look at a piece of paper and see what’s written on it with little doubt or cause to make less informed guesses. Or run a pure program to see what’s been computed, and what would therefore be computed if you ran it again.
Interestingly enough, Mathematics and logic is what you get if you only allow 0 and 1 as probabilities for proof, rather than any intermediate scenario between 0 and 1. So Mathematical proof/logic standards are a special case of probability theory, when 0 or 1 are the only allowed values.
Credence in a proof can easily be fractional, it’s just usually extreme, as a fact of mathematical practice. The same as when you can actually look at a piece of paper and see what’s written on it with little doubt or cause to make less informed guesses. Or run a pure program to see what’s been computed, and what would therefore be computed if you ran it again.