I guess I don't see a paradox here. Sounds more like a lawyer with faulty reasoning.

I love paradoxes. Maybe its the mathematician in me.

Ah, the famous unexpected hanging paradox, it bugged me for weeks. (The envelope paradox, and Newcombs paradox bugged me even more.)
So the judge said
1: You will die this week
2: You won't expect it.

The lawyer makes the argument that if there is only one day left and he is still alive, because of statement #1, that must be the day he dies on. He surely would expect it then, but this would violate statement #2. So he cannot be executed on the last day, because it would be expected. However, here's the catch, once you suppose this you are no longer holding statement #1 to be true. Your argument is now invalid. In a sense, once you reason you cannot be executed on a day because it would be expected, you can then be executed on that day because it would be unexpected.

Lets simplify the problem. Suppose I have two boxes, #1 & #2. #1 must be opened before #2. One of them has $100 in it. The person who put the money in one of the boxes says that if you can open a box, knowing perfectly well it has the money in it before looking, that you can keep the money, otherwise he keeps it.
Well, would the person setting it up put the money in box #2? If it were in box #2 then you could open it knowing full well the money is in the box because it's the only one left, and you get the money instead of him. With the lawyers logic you would say that this means that the money cannot be in box #2, so it must be in #1, but then you use the same logic, and it can't be in box #1 either. But once you accept that it isn't in #2 or #1, then the person setting it up can put it in either box, and you would be suprised.

I guess it boils down to the concept of something being expected being ill-defined. The truth or falsity of the statements by the judge can both be true, because it is still possible to be hanged unexpectedly on the last day. Otherwise it would be a real paradox.

". . .the most famous is never get involved in a land war in Asia, but only slightly less well-known is this: never go in against a Sicilian when death is on the line!"

...anybody wanna peanut?

I often wondered what it meant in the Article of Faith when it says that the earth will receive its paradoxical glory... (hey, that one's for you Coco -- consider it as you would the Sock of Al Bundy...)

heh.. it's in Italian. I caught about half the words...

--Ray

My wife says I'm a treasure trove of useless information. And that movie was definitely useless information. So is it possible to be your own grandpa?

That was too complicated a Paradox. Now wondering if it is possible to be your own grandpa is something even a redneck with a third grade education can contemplate.

Pt314, I liked your explanation. The judge must have been counting on the lawyer explaining that the man was off scot-free so he wouldn't be expecting to die. If the lawyer had kept his mouth shut, maybe the convicted man wouldn't have figured it out!

I am confused by all this genealogy conversation.

Heres another one.

Suppose you are given envelopes, and you are told that one has twice as much money in it than the other one. You open one of the envelopes and are given the option to keep the money in that one, or to swich envelopes. Is it in you interest to switch?

If you open up the first envelope, and it has $100 in it, then the other envelope has either $50 or $200. The expected value of this is $125, which is better then $100 right? Or you can look at it as a 50% chance of losing $50, or a 50% chance of gaining $100. So it's in your interest to switch.

However you can make the same argument that it is better to switch, irregardless of how much money is in the envelope. If the envelope you opened has x in it, the other one has 2x or 0.5x in it. The expected value of switching is 1.25x.

But then why bother opening the envelope in the first place, if it is in your interest to always switch? But this doesn't make any sense, the two envelopes are on the same footing aren't they?

-- Edited by Pt314 at 08:32, 2007-10-18

-- Edited by Pt314 at 08:33, 2007-10-18

Oh yeah, like one envelope has 50 dollars and the other has a bill for $25?

The envelope choice between gaining or owing wouldn't work because if you open the envelope, you know immediately which one you have. Either you have the money and keep it, or you have a bill and your switch it.