Why is the statement 'This sentence is false' so confusing?

Answer 1

In the logical sense, sentences must be either true or false and not both. "This sentence is false" cannot be true because that would mean that it is false, and it cannot be both. It also cannot be false because that would mean that it is true, and it cannot be both. Therefore, if it is true or false, then it is both true and false. Therefore it is either neither true nor false or both true and false; therefore, in the logical sense, it is not a sentence. However, it says it is a sentence; therefore, it is lying; therefore, it is false.