This headline is (half) false

EPIMENIDES the Cretan, a philosopher of the 6th century BC, is said to have uttered the sentence, "All Cretans are liars". As he himself was a Cretan, this gave rise to a paradox--if he were telling the truth, then he would be a liar. Depending on how one defines a liar, the paradox is resolvable; he could have been a habitual liar who was telling the truth in this one instance. However, a stronger version of the paradox, known as the Liar paradox--"this sentence is false"--is not resolvable in conventional logic systems. Indeed, the circular loop that the sentence induces--if it is false, it must be true, and if true, false--has been used more than once in science-fiction movies to cause marauding computers to lose their sanity and explode.