"This
statement is
false."
You might be tempted to alleviate the paradox by claiming that the statement has no truth value at all (is neither true nor false). But consider this statement:
"This statement is false or it has no truth value."
If it is true, we have a contradiction.
If it is false, then it is true.
And if it has no truth value, it is also true.
There you have it. Math is inconsistent.
Gritchka:
A = C false
B = C hasnotruthvalue
C = A v B
So,
C true => A false & B false => (A v B) false => C false =><=
C false => A true & B false => (A v B) true => C true =><=
C hasnotruthvalue => A false & B true => (A v B) true => C true =><=
I don't see how A has to be N. Perhaps you are confusing A to be "A is false"?
I think the problem here, instead, is not the misuse of the hasnotruthvalue predicate, but that our notion of "true" is not well-defined.