What is false?? the statement inside your phrase or the whole statement??

If it's the first one, is false, as you are declaring it is false.
If it's the second, it's true, as affirmatively, the statement is false.

Its the statement inside the prase.
But if its false, then the statement is true.. :S

(Who was it again who "invented this?)

yes, it is

This is a quite funny logic game

Bertrand Russell

Ahh yes Thanks!

Something similar, albeit way more practical:

I never lie.

It's simply illogical...

"This red ball is blue"
"This dog is a cat"

And why is this in the Religion section? IMO it should be in General Discussion.

Extreme Coder

What comes after the "and"?
(Strictly speaking, that should be an "or", however. Ubuntu-geek should change that.)

I believe you mean to say:
"I always lie."

Someone who does indeed never lie can truthfully say "I never lie."

Either work - this board contains both Religion and Philosophy. It doesn't refer to every thread in the board.

Keep in mind, I am the type of person who wishes "xor" were commonly used in the English language. "Threads for religion and philosophy" damn well should include both.

Well, if you always lied, you could still say that you never lie, you'd only be lying

If you never lie, on the other hand, you couldn't say that you always lie, because then you'd be lying. But of course someone who never lies can sincerely say that he never lies, so you really couldn't tell if someone is a liar or not, even if he'd 'truthfully'* say that (s)he never lies.


* By truthfully I here mean something like 'being consistent with one's values', or something like that.

More on it can be found on the Wikipedia page of the 'liar paradox': Liar paradox - Wikipedia, the free encyclopedia

By the way: I surely consider things like this to be logical 'problems', and I surely consider logic to be a branch of philosophy; so I don't think this thread is out of place here.

On my computer, it's called "Religion & Philosophy" and the guy who first came up with this conundrum (Bertrand Russell) was a renowned Philosopher.

I would argue that the statement 'This statement is false' really is false.

For example, the typical chain of reasoning is:

1. assume the statement is true
2. then, by inference, the statement is false
3. assume the statement is false
4. then, by inference the statement is true.

However, I argue the jump from 3 to 4 is invalid. If the statement is false, interpreting the statement (assuming it's true) creates circular reasoning.

Furthermore, a statement can be false in more ways than one. For example, if

"The golden mountain is made of cheese" is false,

it doesn't follow that

"The golden mountain is *NOT* made of cheese." is true

as the statement may be false in virtue of having no referent. The *NOT* operator can be inserted in multiple places, each having a different meaning.

The statement 'This statement is false' actually has two components to it. Namely:

f(x) = 1 - x (an inverter function)
f(1) == f(0) (an assertion about identity)

Which is negated?

So... if we assume it's true, we can infer than it is false (reductio ad aburdum). If we assume it's false, no inference about it's truth can be made. Therefore, it's false.

I can explain further if anyone's interested.