Bayes for arguments: how do you quantify P(E|H) when E is an argument? E.g. I present you a strong argument supporting Hypothesis H, how can you put a number on that?
There’s not a principled way for informal arguments, but there are a few for formal arguments—ie proofs. The relevant search term here is logical induction.
I think P(E∣H) is close enough to 1 to be dropped here; the more interesting thing is P(E∣¬H) (how likely would they be to make such a convincing argument if the hypothesis is false?). We have:
Bayes for arguments: how do you quantify P(E|H) when E is an argument? E.g. I present you a strong argument supporting Hypothesis H, how can you put a number on that?
There’s not a principled way for informal arguments, but there are a few for formal arguments—ie proofs. The relevant search term here is logical induction.
I think P(E∣H) is close enough to 1 to be dropped here; the more interesting thing is P(E∣¬H) (how likely would they be to make such a convincing argument if the hypothesis is false?). We have:
P(E)=P(E∣H)P(H)+P(E∣¬H)(1−P(H))∼P(H)+P(E∣¬H)(1−P(H))
so Bayes rule becomes
P(H∣E)∼P(H)P(H)+P(E∣¬H)(1−P(H))
Edit: actually use likelihood ratios; it’s way simpler.