I'm still waiting for you to indicate the sentence that is false.

the alternative reading of the sentence is much clearer "Santa Claus exists, or this sentence is false"

if the sentence is false, then there are two possibilities, SC exists AND the sentence is false, or SC doesn't exist AND the sentence is true.

but from assuming the sentence is false we can remove the later possibility, and hence again come to the conclusion that SC exists.

That is assuming an exclusive xOR.

I may also be seen as an inclusive OR thusly - Santa Calus does not exist AND this sentence is false.

"Don't go into the water until you learn to swim." and "If you can read this, you're blind." are not paradoxes, just somewhat silly things to say. Although, arguably, some one could learn how to swim in theory (i.e. explained in a classroom) before going into water.

"Everything I say is a lie." and "All sentences are not true." are not paradoxes either. They are simply false statements, since the reality in each case could be that "somethings I say are not lies" and "some sentences are true" which makes the original sentences false but does not cause a paradoxical self-contradiction. The opposite of "all THINGS has PROPERTY" is "some THINGS does not have PROPERTY".

@orathic, logically speaking, it is inclusive OR

i didn't think it was clear which OR was being used.

The Santa Claus statement is called "Curry's Paradox" (http://en.wikipedia.org/wiki/Curry%27s_paradox). It is ONLY a paradox in NAIVE logic theory (i.e. when people have no idea what they are talking about).

The following are NOT logical paradoxes

I am dead. (probably just a false statement, but maybe you are dead by the time someone reads it.)
I always lie. (false statement, does not mean "I always tell the truth" just means that "I sometimes lie, but not always")
Do not read this. (just an instruction that is impossible to follow)
Absolutes do not exist. (either a false statement or somewhat ambiguous as "absolute" is not well-defined)
There is always an exception to any rule. (just another false statement, since "there is sometimes but not always an exception to any rule.")
This page left intentionally blank. (just a somewhat silly thing to put on a piece of paper)

"This sentence is false"
(see http://en.wikipedia.org/wiki/Godel%27s_incompleteness_theorem#First_incompleteness_theorem)

Basically, any system of a logic cannot be both Complete and Self-Consistent. Loosely speaking, completeness of a logic system means being able to determine if any constructible statement is true or false.

Thanks, yebellz, for explaining what I seemed to be failing to get through to some of them (*cough dave bishop*cough*).

yebellz +1

"I think the idea of the santa claus paradox is you just IMAGINE the sentence is true."

Erm..why?

As yebelz points out, it isn't a solid logical paradox, but a NAIZE logic paradox, which means strict logic rules don't apply. As such, it isn't a real paradox as it can be easily solved by saying the sentence is, in fact, false. It is an if/then statement without an else.

Think of it this way...

if ((1==0)==true)
{
SantaClaus.exists = true;
}

Clearly the result is it falls out of the if statement having never set the property for SantaClaus.

The Babel Fish is actually a paradox. Because if God doesn't exist, as it "proves" then the fish would have to have evolved naturally, which means it would be possible that God did not exist, which means you still have to have faith.
I think this is a paradox anyway. But it still proves that Douglas Adams didn't think it all the way through.

@Draugnar
well... maybe... i don't know what naive logic theory is.

i still don't think you can claim the sentence is false without claiming that IF the sentence was true, SC wouldn't exist- which is clearly wrong.

Thucydides is intelligent. Thucydides is a Texan.

Uh oh. :)

@Dave - my turn to try.
The point people are making is the first section has two forks.
Now, one of these is paradoxial.
However, the other evaluates, and doesn't reach a contradiction.

No, if the babel fish proves God's existance, and thus his non-existance and thus the babel fish evolved then the original proof of God's existance was flawed.

thus not a paradox at all, just a false claim to begin with.

haha fuck you friendly :P

@ if((1==0)==true) is incorrect

i think it should be written if((1==x)==true)
where x = the truth value of the sentence.

and since if() always* returns true then x is true.

*I think, '()' may be false or true, whereas 'if()' evaluates as true, unless it fails to evaluate at all. (which usually generates a compile time error)

@orathaic - I should have said:

if (evaluation==true)

I used the 1==0, which is clearly false, to demonstrate that there is the alternative of the sentence being false as if is not a declaration, but an evaluation and I wanted to show how "this sentence" in the quote could actually be false thereby negating the perceived paradox.

yeah, not a paradox is the sentence is false.

but i don't know how to evaluate the truth value of the sentence.

Wait wait wait wait wait what about this one. I spent all night coming up with it:


This paradox is a sentence.

so it's is a sentence so it is true, but it's not a paradox because it is simply true, so it is false, so it is a paradox, so it's not false, so it ...

@Orathaic - I would say by virtue that Santa doesn't exist (if any part is flase, the esentence is false), except you can't prove something doesn't exist. But that is just additional proof that it isn't a paradox.

@Thucy - explain please...

Here's mine.

I went back in time and killed my past self just to see what would happen.

I saw a girl with 'Rape me' on her shirt.
Now, if someone is wondering if they can rape her or not, this is a paradox.

edit: just seen it in a different way and as such it's not a paradox, just an impossible request.

Draugnar, your sentence is only self-defeating if we look at all time as a sort of line. Time travel by the multiple worlds theory causes no paradox - you travelling back in time would create a new timeline (or you would enter an existing one) in which you kill your younger self. This timeline is completely inviolate from the one you came from.