At 10am tomorrow, I can legitimately express my confidence in the proposition “the cable guy will arrive after noon” is different to what it was today.
There are two cases to consider:
The cable guy arrived before 10am (occurs with 25% probability). In this case, I expect that he has a close on zero probability of arriving after noon.
The cable guy is known not to have arrived before 10am (occurs with 75% probability). At this point, I calculate that the odds of the cable guy turning up after noon are two in three.
But none of this takes anything away from the original statement:
“There is no possible plan you can devise, no clever strategy, no cunning device, by which you can legitimately expect your confidence in a fixed proposition to be higher (on average) than before.”
This is because I am changing my probability estimate on the basis of new information received—it’s not a fixed proposition.
At 10am tomorrow, I can legitimately express my confidence in the proposition “the cable guy will arrive after noon” is different to what it was today.
There are two cases to consider:
The cable guy arrived before 10am (occurs with 25% probability). In this case, I expect that he has a close on zero probability of arriving after noon.
The cable guy is known not to have arrived before 10am (occurs with 75% probability). At this point, I calculate that the odds of the cable guy turning up after noon are two in three.
But none of this takes anything away from the original statement:
This is because I am changing my probability estimate on the basis of new information received—it’s not a fixed proposition.