I am not certain that it’s the same A. If I say to you, here’s a book that proves that P=NP. You go and read it, and it’s full of Math, and you can’t fully process it. Later, you come back and read it again, this time you actually able to fully comprehend it. Even later you come back again, and not only comprehend it, but are able to prove some new facts, using no external sources, just your mind. Those are not all the same “A”. So, you may have some evidence for/against a sorcerer, but are not able to accurately estimate the probability. After some reflection, you derive new facts, and then update again. Upon further reflection, you derive more facts, and update. Why should this process stop?
I think we are talking about different things. I proved only that Bob cannot update his belief in Bright on the sole evidence “Bob believes in Bright”. This is a perfectly defined cognitive state, totally accessible to Bob, and unique. Therefore Bob cannot update on it. On the other hand, if from a belief Bob gathers new evidence, then this is clearly another cognitive state, well different from the previous, and so there’s no trouble in assigning different probabilities (provided that “Bob believes in Bright” doesn’t mean that he assigns to Bright probability 1).
I am not certain that it’s the same A. If I say to you, here’s a book that proves that P=NP. You go and read it, and it’s full of Math, and you can’t fully process it. Later, you come back and read it again, this time you actually able to fully comprehend it. Even later you come back again, and not only comprehend it, but are able to prove some new facts, using no external sources, just your mind. Those are not all the same “A”. So, you may have some evidence for/against a sorcerer, but are not able to accurately estimate the probability. After some reflection, you derive new facts, and then update again. Upon further reflection, you derive more facts, and update. Why should this process stop?
I think we are talking about different things.
I proved only that Bob cannot update his belief in Bright on the sole evidence “Bob believes in Bright”. This is a perfectly defined cognitive state, totally accessible to Bob, and unique. Therefore Bob cannot update on it.
On the other hand, if from a belief Bob gathers new evidence, then this is clearly another cognitive state, well different from the previous, and so there’s no trouble in assigning different probabilities (provided that “Bob believes in Bright” doesn’t mean that he assigns to Bright probability 1).