The Mystery of Logical Paradoxes Solved

[IlyaStavinsky]

Introduction
(1.) In general all existing analyses of logical paradoxes show only their practical shortcomings: they are meaningless, contradictive in itself for different reason and so on. If we eliminate those disadvantages we will solve the problem. One does not have to be a philosopher to uncover these shortcomings in the logical paradoxes, it is enough for a person who has a common sense. The scientific (theoretical) approach in relation to logical paradoxes begins only then when philosopher successfully explains the reasons for the existence of these shortcomings by using categories and Laws of Formal Logic. And this can’t be done by an ordinary person but by philosopher who know and understand the Laws of Formal Logic. There was attemp to solve the problem from the point of view of Laws of formal logic but it was incomplete because they ignore the law of sufficient ground. See web "Are Mysteries of the Christian Faith Against Logic? pt. 2"
(2.) According to the opinion of many philosophers the cause of these shortcomings existing in logical paradoxes, could be the problem with formal logic or problem with our language (may be something else?). For these reasons the solution of logical paradoxes was transferred from the frame of Formal Logic to the frame of mathematical logic (for example Russell) and to the frame of classical formal languages (for example Starski). To look for the solution of that problem with help of mathematical logic or with help of classical formal languages is not logically at all, because they are both based on the Formal Logic and consequently both would inherited shortcomings of formal logic if the later had ones. (About the later I doubt very much). 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). Scientific explanation of existence of logical paradoxes must be done within the frame of Formal Logic and, for the first time, this is done in my article on Internet “The Mystery of Logical Paradoxes Solved”. ..

[ACB]

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.

[Zogg the Demon]

The statement "This statement is false" is obviously paradoxal. But what about the statement "This statement is false or paradoxal" ?

[leafy]

classical formal languages (for example Starski)

Do you mean Alfred Tarski?

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).

What are you talking about?

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?

[ACB]

Originally Posted by leafy

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.

[leafy]

Originally Posted by ACB

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.

[ACB]

Originally Posted by leafy

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.

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.

Originally Posted by leafy

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.

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.

[leafy]

Originally Posted by ACB

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.

You seem to be avoiding the contradiction by inventing out of whole cloth a system of proposition truth-value evaluation that only apply to liars (semantic paradoxes). Why not reject LNC?

[Emil]

Meaningfulness is not applicable to propositions. Meaningfulness is applicable to sentences. Truth and falseness is not applicable to sentences. Truth and falseness is applicable to propositions. Some sentence are meaningful. Some sentences are cognitively meaningful. All cognitively meaningful sentences express propositions.

Is the liar sentence cognitively meaningful? It seems so. I think we prima facie ought to accept that it does express a proposition. However since contradictions follow from doing this, I think the sentence is not cognitively meaningful.

I have yet to read Priest on paraconsistency.

[Kroni]

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.