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panlives

Inner circle

2087 Posts
Posted: Nov 30, 2011 4:53pm

From Roberto Casati:

"All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false."

This array manages to be paradoxical without being circular.

The statements can’t all be false, because that would make the first one true, a contradiction.

But neither can any one of them be true, as a true statement would have to be followed by an infinity of false statements, and the falsity of any one of them implies the truth of some that follow.

“A paradox — but a rectilinear one.”

"Is there any point to which you would wish to draw my attention?"
"To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
"That was the curious incident," remarked Sherlock Holmes.
Scott Cram

Inner circle

2543 Posts
Posted: Dec 1, 2011 2:02am

I see you've discovered Futility Closet.

There are a lot of good puzzles and math facts there!

Grey Matters:Blog|Videos|Mental Gym|Presentation|Store
panlives

Inner circle

2087 Posts
Posted: Dec 1, 2011 8:28am

 Quote: On 2011-12-01 02:02, Scott Cram wrote: I see you've discovered Futility Closet. There are a lot of good puzzles and math facts there!

Yes, indeed!

Hundreds of pages, in fact...amazing resource.

Here is another from that great site:

"You and I are having an argument. Our wives have given us new neckties, and we’re arguing over which is more expensive.

Finally we agree to a wager. We’ll ask our wives for the prices, and whoever is wearing the more expensive tie has to give it to the other.

You think, “The odds are in my favor. If I lose the wager, I lose only the value of my tie. If I win the wager, I gain more than the value of my tie. On balance I come out ahead.”

The trouble is, I’m thinking the same thing. Are we both right?"

"Is there any point to which you would wish to draw my attention?"
"To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
"That was the curious incident," remarked Sherlock Holmes.
TomasB

Inner circle
Sweden
1121 Posts
Posted: Dec 2, 2011 5:25am

I'm not sure how to interpret the lowest "All the statements below this one are false." Is that one always false since there are no statements below it?

As for the tie thing, it's quite hard to pinpoint the error in the way the expected gain is calculated, which is what makes that such a great puzzle. If you calculate the expected value of your tie if the game is played you of course get 0.5 * [value of my tie] + 0.5 * [value of his tie] which tells you nothing since you do not know the value of his tie.

Anyone have a good way of explaining why it's wrong to calculate with the expected gain?

/Tomas
TomasB

Inner circle
Sweden
1121 Posts
Posted: Dec 8, 2011 3:15am

Let's see if I understand this:

The fifth statement is false since there are no statements below it.
The fourth statement says that it is false, which is true.
The third statement says that all below are false, which is false.
The second statement says that all below are false, which is false.
The top statement says that all below are false, which is false.

If I've misunderstood the fifth statement, let's say that it's true instead.
The fifth statement is true, since there are no statements below it.
The fourth statement will be false.
The third statement will be false.
The second statement will be false.
The first statement will be false.

Again no paradox, no matter how the fifth statement is interpreted.

/Tomas
Mr. Mystoffelees

Inner circle
I haven't changed anyone's opinion in
3477 Posts
Posted: Dec 12, 2011 8:09am

 Quote: On 2011-12-01 02:02, Scott Cram wrote: I see you've discovered Futility Closet. There are a lot of good puzzles and math facts there!

Oh, no! Scott, what have you done to me? Now I AM HOOKED! O, whoa is me...

Jim

Also known, when doing rope magic, as "Cordini"
scalito

New user

81 Posts
Posted: Dec 16, 2011 1:35pm

Here's a parody on a classic: If I make a statement. And my mother in law isn't there to here it. Am I still Wrong?!!!!
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