The Mathematics of Information Lecture 5 : Applications of Situation Theory

The Liar Paradox arises when a person stands up and says, “This assertion is false.” Is the speaker telling the truth or telling a lie? At first blush, it seems that the situation is paradoxical: if he is telling the truth, then he is not; if he is not telling the truth, then he is. In fact, that first blush lasted for almost two thousand years. First formulated by the ancient Greeks, the puzzle was not resolved until 1986, when Jon Barwise and John Etchemendy found an elegant solution using situation theory. As in the case of other famous paradoxes — such as Russell’s paradox in set theory — the heart of the problem was an unacknowledged context. And just as the solution to Russell’s paradox led to a better understanding of sets and to the formulation of suitable axioms of set theory, so too the solution to the Liar Paradox has lessons for us in terms of our understanding of language and communication.