The Liar Paradox
The Liar Paradox is among the simplest of paradoxes. It can be traced back at least as far as Eubulides of Miletus, a fourth-century B.C. Greek philosopher.
Eubulides’ version of the paradox is this: A man says that he is lying; is what he says true or false?
However we answer this question, difficulties arise.
If we suggest that what the man says is true, then we end in contradiction: if the man’s claim that he is lying is true, then he is lying, in which case what he says is false.
If we suggest that what the man says is false, then we are no better off: if the man’s claim that he is lying is false, then he is not lying, in which case what he says is true.
Both answers give rise to logical contradictions; it cannot be the case either that what the man says is true or that what the man says is false.
The Liar Paradox is sometimes referred to as “Epimenides’ Paradox”, after the sixth-century B.C. Cretan who asserted that all Cretans are liars. The apostle Paul makes reference to Epimenides in Titus 1:12, writing, “It was one of them, their very own prophet who said, ‘Cretans are always liars, vicious brutes, lazy gluttons.’”
Epimenides’ statement alone does not give rise to a paradox. What he says can’t be true, for if Cretans are always liars, and he is a Cretan, then he must be lying, in which case his statement is false. His statement could be false however; it could be that Epimenides is dishonest but that not all Cretans are liars.
Paul, though, excludes this dissolution of the paradox, proceeding to say in the following verse, “This testimony is true.” This leaves Paul asserting that Epimenides truly said that he (and all other Cretans) are liars, which takes us back to Eubulides’ paradox above; Paul cannot be right.