I wasn’t making an analogy. I am surprised by that interpretation. I was providing a counterexample to the claim that it is absurd to prohibit accurate beliefs. One of my raffle-players has an accurate belief, but that player’s belief is nonetheless prohibited by the norms of rationality.
That’s not true for any reasonable definition of “belief,” least of all a Bayesian one. If all the raffle participants believed “I am likely to win,” or “I am certain to win,” then they are all holding irrational beliefs, regardless of which one of them wins. If all the raffle participants believed “I have a one in a billion chance to win,” then they are all holding rational beliefs, regardless of which one of them wins.
That’s not true for any reasonable definition of “belief,” least of all a Bayesian one. If all the raffle participants believed “I am likely to win,” or “I am certain to win,” then they are all wrong and they will all remain wrong after one of them wins. If all the raffle participants believed “I have a one in a billion chance to win,” then they are all correct and they will all remain correct.
???
Of course. But no English speaker would utter the phrase “I will win this raffle” as a gloss for “I have a one in a billion chance to win”.
I seem to have posed my scenario in a confusing way. To be more explicit: Each of my hypothetical players would assert “I will win this raffle” with the intention of accurately representing his or her beliefs about the world. That doesn’t imply literal 100% certainty under standard English usage. The amount of certainty implied is vague, but there’s no way it’s anywhere close to the rational amount of certainty. That is why the players’ beliefs are prohibited by the norms of rationality, even though one of them is making a true assertion when he or she says “I will win this raffle”.
ETA: Cata deleted his/her comment. I’m leaving my reply here because its clarification of the original scenario might still be necessary.
I don’t think that analogy holds up.
I wasn’t making an analogy. I am surprised by that interpretation. I was providing a counterexample to the claim that it is absurd to prohibit accurate beliefs. One of my raffle-players has an accurate belief, but that player’s belief is nonetheless prohibited by the norms of rationality.
That’s not true for any reasonable definition of “belief,” least of all a Bayesian one. If all the raffle participants believed “I am likely to win,” or “I am certain to win,” then they are all holding irrational beliefs, regardless of which one of them wins. If all the raffle participants believed “I have a one in a billion chance to win,” then they are all holding rational beliefs, regardless of which one of them wins.
???
Of course. But no English speaker would utter the phrase “I will win this raffle” as a gloss for “I have a one in a billion chance to win”.
I seem to have posed my scenario in a confusing way. To be more explicit: Each of my hypothetical players would assert “I will win this raffle” with the intention of accurately representing his or her beliefs about the world. That doesn’t imply literal 100% certainty under standard English usage. The amount of certainty implied is vague, but there’s no way it’s anywhere close to the rational amount of certainty. That is why the players’ beliefs are prohibited by the norms of rationality, even though one of them is making a true assertion when he or she says “I will win this raffle”.
ETA: Cata deleted his/her comment. I’m leaving my reply here because its clarification of the original scenario might still be necessary.
Yeah, I deleted it because I wasn’t doing a good job of distinguishing between “rational” and “correct”, so my criticism was muddled.