classical formal languages (for example Starski)

Impossibility to solve the problem within the frame of formal logic show just one thing that philosophers don't understand the way how the formal logic works (another paradox).

I have read the part of your article relating to the Liar Paradox, and it has certain similarities to my own solution of that paradox. Mine begins from the position that "This statement is not true" is meaningless in the first place and hence not-true, but therefore true in the second place, not-true in the third place, and so on ad infinitum.

So you would say that it is both true and not true?

I would say that it has logically sequential elements of truth and non-truth. The things about which it is true and not-true are different. For example, it is true that it is not-true in the first place; not-true that it is not-true in the second place; true that it is not-true in the third place; and so on. Thus there is no real contradiction.

If you want a simpler answer, you could say it is partly true and partly not-true - but, as I say, these 'parts' are not simultaneous, but sequential.

I'm not sure that's coherent. Propositions can have truth values, but what you've done here is essentially an ad hoc maneuver to avoid a contradiction.

Plus, if the "truth value" goes
(1) true, (2) not true, (3) true ...
You could just as easily start at
(1) not true, (2) true, (3) not true ...
And you're back at a contradiction.

Most propositions are straightforwardly true or not true, but there is no reason why this should apply to all propositions. "This statement is not true" is a special kind of proposition, with an irreducible logical complexity. If the law of non-contradiction is to be preserved, it cannot be simply true or not-true.



At the start of the analysis, the statement is empty of meaning, since it does not relate to any independent fact. So in the first place it is meaningless, and hence not-true. So the sequence goes:

(1) not true, (2) true, (3) not true ...

and not the other way round. Therefore, no contradiction.

If you break it down, we have two separate propositions. The first proposition is to tell the reader that what they are reading is not true. The second proposition is inherant to the sentence itself. There is an implied assumption that this message is meant to introduce a fact. The validity of the fact depends on outside evidence, but the proposition itself logically represents itself as a truth. When these two propositions contradict each other, we can only logically conclude that they cannot both be true. The nature of statement "This statement is false" implies that the second proposition is actually not meant to represent a true fact. Therefore, we can say that this proposition is actually "false". This would mean that the first proposition, which was to tell the reader that what they are reading is untrue, is actually true. By saying "This statement is false" It is not saying that the facts are wrong. It is saying that the representation of the statement is false because it does not follow the implied assumption of representing a truth.