That Russell & Norvig quote doesn’t appear to be a very good response to the objection it’s addressing. De Finetti’s argument is supposed to be a pragmatic argument for probabilism. In response to someone asking “Why should my beliefs obey the probability calculus?”, de Finetti says “If you don’t, you’ll end up getting screwed (by being susceptible to dutch books).”
The response to de Finetti that Russell & Norvig are considering is “There are ways to get around susceptibility to dutch books other than accepting probabilism. For instance, I could formulate a policy of refusing to accept bets. Why is probabilism the right way to deal with susceptibility to dutch books?” Russell & Norvig are saying “Well, this is a thought experiment situation in which you are forced to bet.”
OK, but that completely ruins the pragmatic appeal of de Finetti’s theorem. I can feel the attraction of probabilism if it’s the only way I’m protected against being screwed in reality. But not if it’s the only way I’m protected against being screwed in an abstract model that doesn’t match reality. Why should I care about getting screwed in a thought experiment?
That Russell & Norvig quote doesn’t appear to be a very good response to the objection it’s addressing. De Finetti’s argument is supposed to be a pragmatic argument for probabilism. In response to someone asking “Why should my beliefs obey the probability calculus?”, de Finetti says “If you don’t, you’ll end up getting screwed (by being susceptible to dutch books).”
The response to de Finetti that Russell & Norvig are considering is “There are ways to get around susceptibility to dutch books other than accepting probabilism. For instance, I could formulate a policy of refusing to accept bets. Why is probabilism the right way to deal with susceptibility to dutch books?” Russell & Norvig are saying “Well, this is a thought experiment situation in which you are forced to bet.”
OK, but that completely ruins the pragmatic appeal of de Finetti’s theorem. I can feel the attraction of probabilism if it’s the only way I’m protected against being screwed in reality. But not if it’s the only way I’m protected against being screwed in an abstract model that doesn’t match reality. Why should I care about getting screwed in a thought experiment?