5. When one is thinking about the more basic form of the Liar Paradox, called the Simple Liar—“This sentence is false”—one might think that the contradiction can be avoided by saying that the sentence is “neither true nor false.” The problem is that, when one tries to apply this solution to the version of the Liar Paradox called the Strengthened Liar—“This sentence is not true”—it generates a contradiction. How?
a. It just does.
b. If the sentence “this sentence is not true” is neither true nor false, then it’s not true, which is what it says of itself, and if what it says of itself is right, it’s true. Thus, if it’s neither true nor false, it’s both true and not true.
c. If you say that it is neither true nor false, the corner of the page on which it is written begins to smolder and burn, and deep, ominous laughter can be heard in the background.