Paradoxfrom Merriam-Webster Online:
This sentence is false.
The quintessential paradox. Any paradox is essentially the same: a statement that can neither be true nor false. If the sentence is true, then it's false, so it's not true. If the sentence is false, then it's true, so it's not false. Confused yet?
If you're familiar with the movie Labyrinth, one of the puzzles Sarah faces is a paradox. She faces two doors, one of which leads to death and the other to the castle:
SARAH: WHAT AM I SUPPOSED TO DO? JIM: TRY ONE OF THESE DOORS. TIM: ONE OF THEM LEADS TO THE CASTLE, TIM: AND THE OTHER ONE LEADS TO-- RALPH: BA BA BA BUM! TIM: CERTAIN DEATH! GUARDS: OOH! OOH! SARAH: WHICH ONE IS WHICH? JIM: WE CAN'T TELL YOU. SARAH: WHY NOT? JIM: UH... I, UH... JIM: WE DON'T KNOW. TIM: BUT THEY DO. SARAH: OH. THEN I'LL ASK THEM. ALPH: UH... ALPH: YOU CAN ONLY ASK ONE OF US. RALPH: IT'S IN THE RULES. RALPH: ONE OF US ALWAYS TELLS THE TRUTH, RALPH: AND ONE OF US ALWAYS LIES. RALPH: HE ALWAYS LIES. ALPH: I DO NOT! I TELL THE TRUTH! RALPH: OH, WHAT A LIE! TIM: HA HA HA! ALPH: HE'S THE LIAR!
The answer lies in a paradox:
SARAH: ALL RIGHT. ANSWER YES OR NO. SARAH: WOULD HE TELL ME SARAH: THAT THIS DOOR LEADS TO THE CASTLE? ALPH: UH... ALPH: WHAT DO YOU THINK? ALPH: REALLY? ALPH: YES. SARAH: THEN THE OTHER DOOR LEADS TO THE CASTLE, SARAH: AND THIS DOOR LEADS TO CERTAIN DEATH.
ALPH: HE COULD BE TELLING THE TRUTH. SARAH: BUT THEN YOU WOULDN'T BE, SARAH: SO IF YOU SAID HE SAID YES, SARAH: THE ANSWER IS NO. ALPH: I COULD BE TELLING THE TRUTH. SARAH: THEN HE'D BE LYING. SARAH: THE ANSWER WOULD STILL BE NO. ALPH: IS THAT RIGHT? RALPH: I DON'T KNOW. I'VE NEVER UNDERSTOOD IT. SARAH: NO, IT'S RIGHT. I'VE FIGURED IT OUT.
It's the same idea as my quintessential sentence, only since there's two people, it actually works.
Don't ask me why I'm writing this. I don't call it "random thoughts" for nothing.
For explanations of other pronunciation symbols -- see Guide To Pronunciation.