Puzzles for Pleasure #1- The Prediction

I'm going to try something new for a while, I'm going to regularly post paradoxes, puzzles, and logical oddities just to entertain and stimulate! I hope you enjoy...

Can a fortune teller see the future in his crystal ball? 

Let's say a fortune teller, Genie, has a teenage daughter, call her Mary, whom he has promised to buy a car for when she graduates school. 

One day, Mary tells her father that he's a fake who can't tell the future, and challenges him to a test:

She writes something on a piece of paper and locks it into a box. She says, "I've written down an event that will either happen or not happen before sundown." She hands him a blank piece of paper, and says "If the event will happen, write "yes," if it will not, write "no." If you are wrong, buy me a car now, if you are right, don't buy me one at all."

Genie says it's a deal.

He writes something on the card, and at sundown Mary unlocks the box. Genie reads what she wrote:

"Before sundown, you will write NO on the card."

"You've tricked me!" declares Genie. "I wrote YES, so I was wrong, but if I'd written NO I'd be wrong too!"

Mary used her new sports car to drive across country and never went back to her crazy Dad's house.

The original version of this story is about a computer that can only respond "true" or "false" (which is exactly how computers work). We ask it to tell us whether it's next response will be "true," or "false." Since it is not possible for the prediction to be correct, the computer spends ten thousand years thinking and spits out "42," or something like that.

We can reduce this paradox to the question "Will the next word you speak be "no?" Please say "yes" or "no.""

This is a disguised version of the well known "liar" paradox. The liar paradox arises when one states "this sentence is false." It is what is known as a semantic, or truth-value, paradox.

The fun thing about semantic paradoxes is that they can all be rephrased as set theory paradoxes. The sentence, "this statement is false," for example, can be rephrased as "this assertion is a member of the set of all false assertions."

Every semantic paradox has a set theoretical analog and vice versa.

I hope you have enjoyed this first installment of "Puzzles for Pleasure."

Thanks for reading!