What is the liar paradox?

In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that he or she is lying: for instance, declaring that "the following statement is true: I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "the following statement is true: this sentence is a lie" the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.  

Furthermore, if "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.

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