Cat Dancer, I think by “no alternative,” he means the case of two girls.
Of course the mathematician could say something like “none are boys,” but the point is whether or not the two-girls case gets special treatment. If you ask “is at least one a boy?” then “no” means two girls and “yes” means anything else.
If the mathematician is just volunteering information, it’s not divided up that way. When she says “at least one is a boy,” she might be turning down a chance to say “at least one is a girl,” and that changes things.
At least, I think that’s what he’s saying. Most of probability seems as awkward to me as frequentism seems to Eliezer.
Cat Dancer, I think by “no alternative,” he means the case of two girls.
Of course the mathematician could say something like “none are boys,” but the point is whether or not the two-girls case gets special treatment. If you ask “is at least one a boy?” then “no” means two girls and “yes” means anything else.
If the mathematician is just volunteering information, it’s not divided up that way. When she says “at least one is a boy,” she might be turning down a chance to say “at least one is a girl,” and that changes things.
At least, I think that’s what he’s saying. Most of probability seems as awkward to me as frequentism seems to Eliezer.