The opposite of "truth" is "deception". The opposite of a lie is the truth.
1+1=2 isn't truth, it is "correct" in that it adheres to the system of mathematics. All logical systems are either "correct" or "incorrect" ONLY in relation to the initial statement, which (always and absolutely) is an ASSUMPTION. The initial statement of a logical argument is ASSUMED to be true, but what if it is actually a deception, a lie?
The initial assumption (axiom) is presented by the disembodied voice within consciousness, and confirmed as "true" by the same voice. The entire logical process is then based upon this assumption. There is no way to prove that the initial axiom is correct. Correct in relation to what? The correctness of the rest of the argument is based upon the FAITH and BELIEF that the initial assumption is true. Again, what if this is actually a deception/lie?
In this way it is possible for a system of logic to appear to be self-referentially correct within, and yet be a complete lie as a whole.
"Correct" and "incorrect" have been mistaken to mean "truth" and "falsity". "Falsity" is a deception, it isn't "incorrectness." There is intent, and therefore subjectivity behind a deception whereas an incorrectness is simply an objective, mechanical result of the cause-effect nature of the system. Logic has nothing to do with truth and everything to do with correctness and incorrectness, which are relative and relevant only to the system itself. It is possible for a system of logic to be self-referentially correct, while at the same time being a lie/deception.
The statement: "This statement is false" is the equivalent of stating: "1+1=false". It's nonsensical, just as stating: "1+1=true" is nonsensical. Therefore, the question should be worded "This statement is a lie." If the statement is a lie, then there is a specific intent to deceive via the statement. The statement itself is the deception. Therefore the course of action is to disregard it completely, as there is no truth at all to the statement. It's a lie. If a paradox is produced while interacting with the statement, that lie has been accepted as truth.
All statements are a lie perpetrated by Maya to try to convince that the voice in your head is not lying to you. "This statement is false" is this slight-of-hand explicitly revealed.
Logic has nothing to do with Truth. Logic itself is a deception. It is Maya trying to divert attention away from Self and onto the voice in your head.