Jamesian Philosophy Refreshed

Last time I started out talking about this, I was sidetracked. I'll try again. You are on a game show. There are three doors. Behind two of the doors one would find a worthless gag gift. A pile of shaving cream or whatever. Behind the third door, a big check for a million dollars. You pick door 1, aware that the probability of getting the $1 million by virtue of this choice is 1/3. The game show host ("Monty Hall" for us oldsters), says, "Ah, that might be right or might be wrong. I'm gonna give you a clue and open door number 2." Door 2 opens. You see a pile of shaving cream. Everyone laughs because by convention the sight of a useless 'gift' is funny. Monty renews the choice. Now narrowed down a bit. You can stick with your initial decision, Door 1, or you can go with Door 3. What do you do and why? The striking answer is that if you are a rational being you will switch to door number 3 at this point. Your odds of being right wit...

An old paradox, named after a game show host, the emcee of "Let's Make a Deal" continuously from 1963 to 1976, and intermittently as revived thereafter. Monty Hall presented contestants with three curtains, often labeled A,B, and C, and asked them to make a choice. They would get whatever gift was behind the curtain they chose. In the story/paradox, Monty tells you that behind one of the curtains is a magnificent new car, the car of your dreams. Behind the other two curtains, not-so-desirable gifts. You tell him: "I pick A, Monty." Monty: "Not so fast! I will now reveal what is behind curtain C." The curtain opens, and there is some worthless gag gift, say a pile of shaving cream. Monty: "Now, you can stay with your choice of A, or you can switch to B." What should you do? The usual first response, and for many people a very powerful intuitive response, is that it doesn't matter what you do. You now have just two curtai...