Don Hubin's Puzzles and Paradoxes Page

Philosophical problems are often prompted by paradoxes and puzzles. Sometimes these puzzles and paradoxes prove remarkably rich in their implications. If you like puzzles and paradoxes, take a look at these.

The Isle of Noose
The Surprise Quiz Paradox
The Well-named/Ill-named Paradox

The Isle of Noose

On a certain island, let us call it 'The Isle of Noose', some married men engage in adulterous behavior. In this respect, the people of Noose are not so different from us. However, the men of Noose, being naturally incautious and boastful, promptly inform everyone on the island of their affairs-everyone, that is, except for their wives. There is a good reason for this exception. The women of Noose will not tolerate infidelity in their mates. When a woman of Noose learns that her husband has committed adultery, she hangs him that night at midnight from the public hanging tree in the middle of the village. This tree is placed where everyone will see it so hat those hanging from it may teach a last lesson to others who might be tempted to follow them on their sinful path.

A missionary comes to live with the people of Noose for some time. Finally, despairing of ever getting the husbands or the wives to change their ways, he decides to leave the island. He concludes his farewell speech, which all of the islanders attend, by saying (truthfully) that some of the husbands in the audience have been adulterous. All of the islanders know that the missionary is an honest man and he would not lie about such a thing. The husbands whisk their wives home before the wives can compare notes. Each wife is left to reason independently with only the information she had prior to the missionary's speech, that which she got from listening to the speech, and any she can pick up by watching what happens at the public hanging tree.

Question: How many husbands get hung? And when?

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The Surprise Quiz Paradox

I used to announce to all of my logic classes that there would be a surprise quiz given during the quarter. To the angry complaints of, "What do you mean, 'surprise quiz'?", I would reply (taking the objections as innocent requests for clarification), "I mean a quiz such that one cannot determine what day it will be given on in advance of the day it will actually be given."

I used to do this. I don't any more because a student proved to me that it was impossible for me to do what I promised (threatened). Here is how she proved it to me:

You can't wait until the last day of the term to give the surprise quiz. If you did, then we would know as we left class the second to the last day that the quiz would be on the last day. But, then, it wouldn't be a surprise. So, we all know from the outset that you can't give the surprise quiz on the last day of class.

third

fourth

Continuing to apply this reasoning, we can exclude every day of the course - all the way back to the first day - as possible dates for the so-called surprise quiz Now, I was very impressed by this reasoning and was inclined to give this student an 'A' in the course. Unfortunately, though, she failed the surprise quiz I gave the next day in class. She claims she didn't expect the quiz. But I reminded her that I had told her that there would be a surprise quiz.

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The 'Well-Named"/"Ill-Named" Paradox

Have you ever noticed that some people are very well named? Martin Short is, after all, rather short. I once met a realtor named 'Isolde Haus' and a preacher named 'Mike Pentacost'. Just recently, I received a letter from an evolutionary biologist named 'Steve Darwin'.

Let's call everyone else 'ill-named'. Some people who are ill-named are rather spectacularly ill-named. For example, Tiny Tim is really rather large. Most of us are ill-named in a less interesting way, though. In any case, let's just agree to call everyone who isn't well-named 'ill-named'.

I used to play a game of classifying everyone I met as well named if their name is, somehow, particularly appropriate for them and ill named if it is not. I quit playing this game when a new neighbor moved in next door. His name is John Ill-named. Is he well named, or ill named?

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