I just thought of this ‘cute’ question and not sure how to answer it.
The sample space of an empirical statement is True or False. Then, given an empirical statement, one would then assign a certain prior probability 0<p<1 to TRUE and one minus that to FALSE. One would not assign a p=1 or p=0 because it wouldn’t allow believe updating.
For example: Santa Claus is real.
I suppose most people in LW will assign a very small p to that statement, but not zero. Now my question is, what is the prior probability value for the following statement:
Actual numbers are never easy to come up with in situations like these, but some of the uncertainty is in whether or not priors of zero or one are bad, and some of it’s in the logical consequences of Bayes’ Theorem with priors of zero or one. The first component doesn’t seem especially different from other kinds of moral uncertainty, and the second component doesn’t seem especially different from other kinds of uncertainty about intuitively obvious mathematical facts, like that described in How to Convince Me That 2 + 2 = 3.
I just thought of this ‘cute’ question and not sure how to answer it.
The sample space of an empirical statement is True or False. Then, given an empirical statement, one would then assign a certain prior probability 0<p<1 to TRUE and one minus that to FALSE. One would not assign a p=1 or p=0 because it wouldn’t allow believe updating.
For example: Santa Claus is real.
I suppose most people in LW will assign a very small p to that statement, but not zero. Now my question is, what is the prior probability value for the following statement:
Prior probability cannot be set to 1.
Prior probability cannot be set to 1.is itself not an empiric statement. It’s a question about modelling.Actual numbers are never easy to come up with in situations like these, but some of the uncertainty is in whether or not priors of zero or one are bad, and some of it’s in the logical consequences of Bayes’ Theorem with priors of zero or one. The first component doesn’t seem especially different from other kinds of moral uncertainty, and the second component doesn’t seem especially different from other kinds of uncertainty about intuitively obvious mathematical facts, like that described in How to Convince Me That 2 + 2 = 3.