So far, no one has disagreed with me who had understood my argument. (there’s a catch 22 here, my argument is correct, therefore to understand is to agree)
The people who disagree, refuse to follow. For instance, take Dr. Moore, I can tell he doesn’t follow by the questions he asks.
I say that there is nothing in our question to suggest that the writer of the question knew the gender of both kids. Moore says that there is nothing to suggest that writer didn’t. That shows that he doesn’t understand, or doesn’t wish to understand my statement.
I say that for the answer to be 1/3, there has to have been a prejudice. He says that the question doesn’t say that there was no prejudice. An obduracy to understanding my statement.
Suppose that a woman came in with two boys and we made the statement “the woman has two children and at least one is a boy”. Bruce and Jane only heard the statement. Bruce bet for two boys, Jane bet for one of each. Jane will lose, what odds should she pay? All Bruce and Jane have to do to get the proper odds is to answer our question correctly. Dr. Moore hedges. He says that to figure Jane’s odds he needs to know what the writer would have written with BG, or GB.
No, no, no, Dr. Moore; instead, suppose that a woman came in with GG, and the writer wrote, “the woman has two girls and at least one is a girl.” Bruce bet for GG, and Jane bet for one of each. Should she pay the same as before?
Instead of wondering what would have happened with BG, or GB, suppose that a woman came in with BG. The “at least one is a boy” and “at least one is a girl” statements would both be true. Would the woman’s chances for one of each differ with either question? (Her chances, of course, figured from Bruce and Jane’s perspective)
When I ask these questions of Dr. Moore, he doesn’t answer. When I ask these questions of Sean MacLeod, he doesn’t answer.
My answer:
When the answer for the ‘boy’ question and the ‘girl’ question are the same. They’re 1/2.
For them to have different answers, they should have different words.