Figure this out if you can.. Noone else can

[funneefarmer]

Originally posted by Zor:
**Since most paper napkins are folded, I’d just unfold the damn thing and throw it back in the face of the person who gave it to me…
**

I kind of like this answer. If you unfold the napkin aren’t both the statements on the same side of the napkin while the other side is blank ?

[EnochF]

Hmmm… okay, what you need to do is get a piece of tape.

Twist one end of the napkin 180 degrees and tape it to the opposite end, thus making the napkin into a makeshift Möbius strip. Now the napkin only has one side, and both statements are clearly false because there is no “other side.”

[Cervaise]

Some of the smart-ass peanut-gallery commentary aside, this quite well-known paradox goes all the way back to the Greek philosophers, who were famously attempting to work out all of the rules of nature by pure logic alone. (The “scientific method” came later.)

Anyway, for what it’s worth, this is technically known as, I believe, “Epimenides’ paradox.” (Kind of surprised our collection of usually well-informed 'Dopers haven’t already pointed this out.) It can also be stated in more concise form:

“This statement is false.”

As to its meaning, it really doesn’t have one. Consequently, though, it’s a basic element of several disciplines. Logicians use it to demonstrate the construction of a meaningless logical statement, linguists use it for similar purposes except specifically with reference to language (compare Chomsky’s “colorless green ideas sleep furiously”), and so on.

Don’t lose any sleep over it.

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[Scylla]

If you unfold the napkin, you have a total of 8 sides. If you find no additional statements on these sides Then one is left to ponder the the veracity or lacking of the void.

“when you stare into the void, the void stares back at you.”

Ultimately it is a question of self.

Are you true… or false…

This is the final lesson young Grasshopper. Now you are a man.

[moriah]

Or, to put it another way:

The truth-status of a statement depends on whether it is true or false in reality, and not on whether some other statement (or itself) declares it to be true or not.

When the reality of whether the statement is true or false depends on whether the statement is true or false, you then get self referential statements. The truth-status of the statement can be set up to be in contradiction to what the statement claims to be true. And there’s your paradox.

Peace.

Every odd statement above is false.

[Wissh3]

I have checked out Goedel, Escher, Bach…was lost as soon as I cracked the binding.

[Cabbage]

The statement “This statement is false” is known as the Eubulides paradox.

Epimenides paradox is “All Cretans are liars…One of their own poets has said so”.

Then there’s the Liar’s paradox, “I am lying”.

A brief analysis can be found here:
http://mathworld.wolfram.com/LiarsParadox.html

Such paradoxes are often analyzed be creating so-called “metalanguages” to separate statements into different levels on which truth and falsity can be assessed independently. For example, Bertrand Russell noted that, “The man who says, ‘I am telling a lie of order n’ is telling a lie, but a lie of order n+1” (Gardner 1984, p. 222).

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…ebius sig. This is a moebius sig. This is a mo…
(sig line courtesy of WallyM7)