So that is the Bayesian view of things, and I would now like to point out a couple of classic brainteasers that derive their brain-teasing ability from the tendency to think of probabilities as inherent properties of objects.
Let’s take the old classic: You meet a mathematician on the street, and she happens to mention that she has given birth to two children on two separate occasions. You ask: “Is at least one of your children a boy?” The mathematician says, “Yes, he is.”
I think that this puzzle still has some brain-teasing ability left, even for the Bayesian.
After all, a proper Bayesian treatment would have to ask, “What was the prior probability that I would ask whether at least one of the children was a boy?” That is, you would have to ask yourself, “How do I condition on the fact that I’m the sort of person who asks whether one of the children is a boy, instead of asking whether one of the children is a girl?” Hence, the problem leads directly into anthropic considerations.
I think that this puzzle still has some brain-teasing ability left, even for the Bayesian.
After all, a proper Bayesian treatment would have to ask, “What was the prior probability that I would ask whether at least one of the children was a boy?” That is, you would have to ask yourself, “How do I condition on the fact that I’m the sort of person who asks whether one of the children is a boy, instead of asking whether one of the children is a girl?” Hence, the problem leads directly into anthropic considerations.