For a quick description of the Liar, read this.
Some philosophers, including C.S. Peirce, have argued that the Liar is demonstrably false and not true. The argument is based on the premise that all statements implicitly assert their own truth.
At first glance, this seems plausible. If I tell someone, “I did your laundry,” it carries with it an implied “it is true that I did your laundry.” This would seem to hold for all assertions. So, Peirce argues, the Liar is really saying: “It is true that this sentence is false,” which essentially comes down to saying “this sentence is true and false.” This is no longer a paradox, but a plain contradiction, and so false. It is like saying, “I’m a cat owner that doesn’t own a cat.” That’s not a mystery, just a lie. What makes the Liar a paradox is that what it says is, on the surface of it, coherent. If it just asserts a flat-out contradiction, then it poses no problem.
That a proposition automatically asserts its own truth is an interesting notion, and it is not easy to say whether it is accurate or not. Peirce later in life argued that it was incorrect. Luckily, it is not necessary to determine whether it is accurate or not because, even if it is, it does not resolve the Liar.
It is not true that, if a proposition automatically asserts its own truth, then the Liar really says: “It is true that this sentence is false.” In that sentence, “this sentence” refers to that whole sentence.…