The fallacy of strengthened liar's paradox.

Let P be the sentence "This sentence is meaningless." Is it true or
false? It should not be difficult to answer. Tractatus Logico-
Philosophicus says: "In order to tell whether a picture is true or
false we compare it with reality." [2.223] When we attempt to compare
"This sentence is meaningless" with reality we find that it is not
comparable with anything. It is not a picture of a fact; it is
meaningless.

We can analyze the situation further:
Case A: P is true.
If P is true. Then it is the case that it is meaningless. But then it
cannot be true. This is a contradiction. Therefore P is not true.

Case B: P is false.
If P is false then it is not the case that it is meaningless. It is
the opposite of what it claims. This is a contradiction. Therefore P
is not false.

Case C: P is meaningless.
If P is meaningless then nothing is the case. There is no
contradiction. In a three valued logic (T, F, M) we conclude that P is
meaningless.

It is not correct to say that if the sentence is meaningless than what
it SAYS is true. This argument assumes that it becomes TRUE half way
through the argument and then it IS THE CASE that it is meaningless.
Thus the sentence confirms our initial assumption that it was
meaningless. But if it stays meaningless all the time it confirms
nothing.

Clearly, if the sentence does not have any meaning then it does not
have the meaning that it is meaningless.

This gives us the basic insight that all self-referential, paradoxical
sentences, including possibly Goedel's sentence, are probably
meaningless.
.

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