"I am lying." True or False?

"I am lying." This single statement is considered a Liar Paradox.

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the following self-referential sentence:

(1) This sentence is false.

Experts in the field of philosophical logic have never agreed on the way out of the trouble despite 2,300 years of attention. Here is the trouble--a sketch of the Liar Argument that reveals the contradiction:

If (1) is true, then (1) is false. But we can also establish the converse, as follows. Assume (1) is false. Because the Liar Sentence is saying precisely that (namely that it is false), the Liar Sentence is true, so (1) is true.

We've now shown that (1) is true if and only if it is false. Since (1) is one or the other, it is both.

Thus for the case of "I am lying.",

If I am lying, then the statement is true. But if the statement is true, then I'm not really lying, am I? But if I'm not lying, then it must be false! It is unanswerable, a splendid paradox indeed.

More detailed analysis:

Person: I am lying right now.

Reply: To be lying you would have to be trying to get me to believe something that you do not believe by presenting yourself as though you believed it. Therefore, (a) if you are trying to get me to believe that you are lying and you do not believe that you are lying, then you are lying. Or, (b) if you are trying to get me to believe that you are lying and you do believe that you are lying, then you are not lying but simply confused about what 'lying' means. And, finally, (c) if you are not trying to get me to believe that you are lying then you are not lying whether you believe that you are lying or not.

In short, whether one lies or not is purely a matter of motive and not at all a matter of whether the normal meaning of what one says is true or false.

Sources: Yahoo!Answers

http://www.alanrhoda.net/blog/2006/09/how-to-respond-to-liar-paradox.html