Dude, that’s freaking me out. But when I think about it a second longer, i think it’s not THAT freaky. Because it’s quite clear: If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.
However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject the common beliefs about truth and falsity: the claim that every statement has to abide by the principle of bivalence, a concept related to the law of the excluded middle.