Question Details	Asked By	Asked On
Logic Can Be Fun - Or Can It?	Bradd	10/31/05
Read the following sentence. "This statement is a lie". Is the sentence a lie or not a lie? If it's a lie, then the sentence is not a lie. If it's not a lie, then the sentence is a lie. True or false, in place of lie, works too.
Clarification/Follow-up by Bradd on 10/31/05 6:28 pm: slight correction: for the quibblers - change "sentence" to "statement" - avoiding problems. Actually, either way is ok, but.........you know. Quibblers and all. Clarification/Follow-up by Jim.McGinness on 10/31/05 9:38 pm: There are people who consider this not to be a paradox, but it is commonly known as the Liar Paradox. http://en.wikipedia.org/wiki/Liar_paradox Clarification/Follow-up by Bradd on 11/04/05 3:10 pm: His example perfectly responded to Chou's comment. I guess you didn't have fun with this - sorry.
Answered By		Answered On
Jim.McGinness		10/31/05
Bertrand Russell developed a whole theory of categories to try to get around this and other similar paradoxes. Based on this, and on Gödel's Incompleteness Theorem, the turn-of-the-century programme to reduce all philosophical statements to mathematical logic came to a stumbling point. One way to resolve the problem is to say that self-contradictory statements, such as the one in your example, are neither true nor false. That's not really a solution, all by itself, because you can construct cycles or networks of statements that are individually not, in and of themselves, self-contradictory, yet the whole system contains contradictions.

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