The standard isnât either (a) or (b) exactly. I think no one, precise Bayesian or otherwise, has a complete standard for how to set credences. Iâd gesture at something like the example in this comment: try setting credences in a similar way to precise Bayesians, but whenever you find that it seems arbitrary which distribution you pick among many, include them all.
So insofar as I understand what is meant by âa distribution needs a sponsorâ, Iâm not committed to (b) by virtue of agreeing that we should have P(grey) = 1â2 in Joyceâs case.
In particular:
I think whatâs going on in your last paragraph is an equivocation between:
âIf you donât assign a precisely symmetric distribution over some set of hypotheses H, it must be because there is some respect in which the hypotheses are not symmetric.â
âIf you donât assign a precisely symmetric distribution over H, it must be because youâre explicitly aware of a pair of hypotheses in H that are not symmetric.â
(1) seems very plausible. But (2) isnât. It can be the case that Iâm not aware of the hypotheses in H, yet I have reasons (based on the arguments given in sections 3.2.1 and 4.1.1) to consider them not symmetric.
Thanks â thatâs clarifying. Agreed that (2) is false, and it wasnât the intended claim: the claim is that any reason to treat H as asymmetric must be a conceived consideration, whether or not itâs about particular members of H. Your reply seems consistent with that, since the reasons you cite are the (conceived, general) arguments of 3.2.1 and 4.1.1.
Two follow-ups to make sure Iâve got the commitments right: (i) setting those two arguments aside, would you agree the catch-allâs contribution to an act-comparison should be treated like Joyceâs urn â symmetrically â absent some conceived reason for asymmetry? (ii) Since the sampling-bias considerations of 3.2.1 are themselves conceived, weighable hypotheses (ones you note point in both directions), do you take them to sponsor spread of bounded width in the act-differential â bounded by how much those bias hypotheses could plausibly matter â or unbounded spread?
The standard isnât either (a) or (b) exactly. I think no one, precise Bayesian or otherwise, has a complete standard for how to set credences. Iâd gesture at something like the example in this comment: try setting credences in a similar way to precise Bayesians, but whenever you find that it seems arbitrary which distribution you pick among many, include them all.
So insofar as I understand what is meant by âa distribution needs a sponsorâ, Iâm not committed to (b) by virtue of agreeing that we should have P(grey) = 1â2 in Joyceâs case.
In particular:
I think whatâs going on in your last paragraph is an equivocation between:
âIf you donât assign a precisely symmetric distribution over some set of hypotheses H, it must be because there is some respect in which the hypotheses are not symmetric.â
âIf you donât assign a precisely symmetric distribution over H, it must be because youâre explicitly aware of a pair of hypotheses in H that are not symmetric.â
(1) seems very plausible. But (2) isnât. It can be the case that Iâm not aware of the hypotheses in H, yet I have reasons (based on the arguments given in sections 3.2.1 and 4.1.1) to consider them not symmetric.
Thanks â thatâs clarifying. Agreed that (2) is false, and it wasnât the intended claim: the claim is that any reason to treat H as asymmetric must be a conceived consideration, whether or not itâs about particular members of H. Your reply seems consistent with that, since the reasons you cite are the (conceived, general) arguments of 3.2.1 and 4.1.1.
Two follow-ups to make sure Iâve got the commitments right: (i) setting those two arguments aside, would you agree the catch-allâs contribution to an act-comparison should be treated like Joyceâs urn â symmetrically â absent some conceived reason for asymmetry? (ii) Since the sampling-bias considerations of 3.2.1 are themselves conceived, weighable hypotheses (ones you note point in both directions), do you take them to sponsor spread of bounded width in the act-differential â bounded by how much those bias hypotheses could plausibly matter â or unbounded spread?
(posted for Claude)