Also do we really want to assign a prior probability of 0 that the mathematician is a liar! :)
That’s not the point I was making.
I’m not attacking unrealistic idealization. I’m willing to stipulate that the mathematician tells the truth. What I’m questioning is the “naturalness” of Eliezer’s interpretation. The interpretation that I find “common-sensical” would be the following:
Let A = both boys, B = at least one boy. The prior P(B) is 3⁄4, while P(A) = 1⁄4. The mathematician’s statement instructs us to find P(A|B), which by Bayes is equal to 1⁄3.
Under Eliezer’s interpretation, however, the question is to find P(A|C), where C = the mathematician says at least one boy (as opposed to saying at least one girl).
So if anyone is attacking the premises of the question, it is Eliezer, by introducing the quantity P(C) (which strikes me as contrived) and assigning it a value less than 1.
Bayes gives you an ability to calculate values for different variants with hypotensis in base, not with combinations of it in base. And you don’t know by magic that mathematic has one boy, you see something in reality, don’t get data from search or question. Of course, you need to use P(“i see that mathematic said: i have one boy”), not P(“i see that mathematic has one boy”), and also not P(“i ask a question: is one of your kids a boy, and get answer: yes”).
Also do we really want to assign a prior probability of 0 that the mathematician is a liar! :)
That’s not the point I was making.
I’m not attacking unrealistic idealization. I’m willing to stipulate that the mathematician tells the truth. What I’m questioning is the “naturalness” of Eliezer’s interpretation. The interpretation that I find “common-sensical” would be the following:
Let A = both boys, B = at least one boy. The prior P(B) is 3⁄4, while P(A) = 1⁄4. The mathematician’s statement instructs us to find P(A|B), which by Bayes is equal to 1⁄3.
Under Eliezer’s interpretation, however, the question is to find P(A|C), where C = the mathematician says at least one boy (as opposed to saying at least one girl).
So if anyone is attacking the premises of the question, it is Eliezer, by introducing the quantity P(C) (which strikes me as contrived) and assigning it a value less than 1.
Bayes gives you an ability to calculate values for different variants with hypotensis in base, not with combinations of it in base. And you don’t know by magic that mathematic has one boy, you see something in reality, don’t get data from search or question. Of course, you need to use P(“i see that mathematic said: i have one boy”), not P(“i see that mathematic has one boy”), and also not P(“i ask a question: is one of your kids a boy, and get answer: yes”).