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.
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d)
Larry D'Anna on Jaynes:
I found the first two chapters of PT:TLOS to be absolutely, wretchedly awful. It's full of technical mistakes, crazy mischaracterizations of other people's opinions, hidden assumptions and skipped steps (that he tries to justify with handwaving nonsense), and even a discussion of Godel's theorems that mixes meta levels and completly misses the point.
Not to mention the totally unnecessary and irrelevant screeds against mainstream pure mathematics in general, which can only serve to alienate potential converts in that discipline (they sure alienated the hell out of me).