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Paradoxes

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Graystripe77:
This statement is both true and false, and also neither.

Does anyone have any others?

timchen:
I am telling a lie.

Ozle:
The Unexpected Hanging Paradox.

Judge tells man he will be hanged one day next week, but that it will be a surprise.
Man goes away happy because he knows he cannot be hanged now

He reasons that he cannot be hung on friday, because if it gets to thursday evening and he is not hung, then the hanging must be on Friday, and this wouldnt be a surprise, so it cant be.
Once he has ruled out Friday for definite, he then also rules out Thursday. Because if it gets to wednesday night he will know he is be hanged on thursday, which wouldnt be a surprise.
Following this process rules out all the days left in the week. So he goes back to his cell happy he cannot be hung.

Judge hangs him on Wednesday which was a complete surprise to him!

jotheonah:
Is the set of sets which are not members of themselves a member of itself?

Or, put another way, a town has a barber who shaves all the men in town who don't shave themselves, and only the men in town who don't shave themselves. Does he shave himself?

O:

--- Quote from: jotheonah on April 22, 2012, 05:49:57 pm ---Is the set of sets which are not members of themselves a member of itself?

--- End quote ---

There is no such set. Mathematicians changed the definition of set as to avoid that issue.   ::)

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