The liar

Suppose someone tells you “I am lying.” If what she tells you is true, then she is lying, in which case what she tells you is false. On the other hand, if what she tells you is false, then she is not lying, in which case what she tells you is true. In short: if “I am lying” is true then it is false, and if it is false then it is true. The paradox arises for any sentence that says or implies of itself that it is false (the simplest example being “This sentence is false”). It is attributed to the ancient Greek seer Epimenides (fl. c. 6th century BCE), an inhabitant of Crete, who famously declared that “All Cretans are liars” (consider what follows if the declaration is true). The paradox is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.