Figure this out if you can.. Noone else can

[CnoteChris]

You're handed a paper napkin with side 'A' written with the following:

"The statement on the other side is TRUE!"

You turn over the napkin only to read the other side, 'B', assert:

"The statement on the other side is FALSE!"

The question is: Which is true or false? Is side 'A' true and 'B' false? Or vice versa? or, are both true or both false? Hmmm.

[Carl Berry]

Yes!

[Cabbage]

This post is false.

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[AuMatar]

The answer is both are neither true nor false. The easiest way to show this is whit boolean logic.


A=The statement on the other side is TRUE

so A=B

B=The statement on the other side is FALSE

so B=A' ' means not

so we get

A=A'

This is a mathematical impossibility. This means one of our assumptions is wrong. Meaning one side is wrong and the other is right (or possibly both are wrong, however that leaves us with the same mathematical impossibility). Which is which is undeterminable without more information.

[CnoteChris]

Aumatar- Are you saying that neither side is true? or neither is false?

[lvick]

42

[AuMatar]

Im not saying either. Im saying its an impossibility. This is the 3rd possibility in logic- a problem that ends up T->F.

Basically it means that the situation can never come up. The problem has no solution because some of our base assumptions are incorrect (either base assumption A or B).

[CnoteChris]

So what do you say to the guy that handed your the note?

Then again, maybe that argument could work with my girlfriend; "That question cannot be answered so I chose not to try"


Thanks,

[aseymayo]

Hey - isn't this from F. Scott Fitzgerald's This Side of Paradox?

[Cabbage]

Hey - isn't this from F. Scott Fitzgerald's This Side of Paradox?

I think you are correct. However, I believe it also occurs in Milton's "Paradox Lost" or "Paradox Regained" (sorry, I can't remember which) both of which predate it by a considerable amount.

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[bibliophage]

Originally posted by Cabbage:
I believe it also occurs in Milton's "Paradox Lost" or "Paradox Regained" (sorry, I can't remember which)



It's not easy to keep the two straight. All I know is that Milton got married and wrote Paradise Lost. Then his wife died and he wrote Paradise Regained.



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Work is the curse of the drinking classes. (Oscar Wilde)

[red_dragon60]

It's just like trying to solve the statement:
I always lie. The only possibility I can find in that is that someone lies some of the time, and they are lying to you right now. something to think about...

[Lumpy]

This is why on Star Trek, Kirk could always crash the evil A.I.s he kept running into. Whereas a human intelligence just says "Bullshit!"


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You say I'm blind, I say you're hallucinating.

[Chronos]

Both statements are exactly half true. Kinda makes ya feel all warm and fuzzy inside, doesn't it?

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"There are only two things that are infinite: The Universe, and human stupidity-- and I'm not sure about the Universe"
--A. Einstein

[qbert]

neither is true nor false.

since both the statements are posted on the same entity (being the napkin), it's a contradictory existence.

a contradictory existence that could only be resolved with a game of TWISTER.

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luke... i am your sperm donor.

[qbert]

you can't actually judge either side, it's a matter of opinion. had both the opinions been humans there would be a fight or something, who knows....

[chief]

i dont know, a million?

hehe, actually i think they are both wrong

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[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...

"What, you can't read?"

[billehunt]

Check out "Gödel, Escher, Bach" by Hofstadter. A classic book about lots of stuff, including Gödel's Incompleteness Theorem, which is intimately tied to the OP.

Also, check out "Infinity and the Mind" by Rucker.

[SPOOFE]

This is like the half-dead cat in the box. Each statement is half-accurate until you look at the opposite side, in which case the statement that you were previously looking at becomes half-innaccurate and the one you are currently looking at becomes half-accurate.

Neither will ever be completely accurate or innaccurate, for the second that the statement being viewed is switched, the accuracy of the other shifts to the other side of the accuracy spectrum. Like the glass being half-empty or half-full, or the aforementioned cat being half-dead or... well, the cat's always half-dead, but we're not talking about half-lives, we're talking about annoyingly paradoxical napkins.

Ultimately, it depends on your point of view. My favorite point of view is that both sides are complete bunk because the statement on either side is neither "TRUE" nor "FALSE" (not in terms of correctness... neither side reads "TRUE" or "FALSE", they read "The statement on the other side is etc. etc.") So just open a can of anality on anyone who presents this problem to you in the future... I, on the other hand, having never heard of this situation before, will immediately go about causing headaches for my friends.

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-SPOOFE

[funneefarmer]

Originally posted by Zor:
[B]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...
[B]

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.
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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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