The problem is when people decide that they believe / do not believe some proposition P, and then consider only the expected utility of the case where P is true / false.
Agree that this is widespread, and is faulty thinking. And my $.02, which you should feel free to ignore: your main post would be clearer, I think, if you focused more on the math of why this is so: find an example where different actions are appropriate based on the probability, and collapsing the probability into a 1 or 0 forces the choice of an inappropriate action; explain the example thoroughly; and only then name the concept with the labels believe/disbelieve. Hearing them right from the start put me on the wrong trail entirely.
I thought this was a post about language usage, but it’s actually a post about how not to do math with probabilities.
Agree that this is widespread, and is faulty thinking. And my $.02, which you should feel free to ignore: your main post would be clearer, I think, if you focused more on the math of why this is so: find an example where different actions are appropriate based on the probability, and collapsing the probability into a 1 or 0 forces the choice of an inappropriate action; explain the example thoroughly; and only then name the concept with the labels believe/disbelieve. Hearing them right from the start put me on the wrong trail entirely.
I thought this was a post about language usage, but it’s actually a post about how not to do math with probabilities.
Right. I’m not talking about the effect of saying “I believe X” vs. “X”.
It probably would have been clearer to use an example.