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 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).