The Liar

Concern for logical problems of self-reference originated with the Liar Riddle (pseudomenos) of the Greek dialectician Eubulides of Megara (ca. 440–ca. 380 BC), who included it in his register of seven paradoxes. In his telling, it posed the puzzle: “Does the person who says ‘I am lying’ actually lie?” (Or again: “Does the witness who declares ‘I am perjuring myself’ thereby perjure himself?”) The problem that arises here can be posed via the following dilemma:

Accordingly, what we have in this ancient puzzle is an untenable contention that involves an inherent conflict of truth-claims.

The situation is paradoxical because individually plausible theses are collectively inconsistent here. And this situation can be set in train by a single proposition, as per the Liar’s:

L: This statement is false.

For it now emerges that we have both

• (1) L is true

• and

• (2) L is false.

Here, (2) is simply what L itself affirms. And (1) follows because (2) is exactly what (1) itself maintains. L is accordingly paradoxical in that it creates this conf lict of affirmation among the various claims it plausibly authorizes.

As logicians address it, the Liar Paradox pivots on the puzzling truth-status of statements that affirm their own falsity (be it directly or obliquely), and thereby will apparently be true when false, and false when true. This situation arises not only with the Liar but also with such contentions as:

(A) Statement (B) is false.

(B) Statement (A) is true.

Here, if (A) is true, then (B) is false, so (A) is not true. And if (A) is false, then (B) is not false, so (A) is true.

Such contentions have puzzled theorists since classical antiquity when Greek philosophers approached the problem via the ancient story of Epimendes the Cretan, who is supposed to have said that “All Cretans are liars”—with “liar” being understood in the sense of a “congenital liar,” someone incapable of telling the truth.