Why are paradoxes considered profound?

@Cyracuz,

...nop ! is in the very plain english sentence that the paradox arises :

This sentence (valid) is false (valid)

PS - ...we have a problem between those two sets requiring dominance which is not explicit...
From a meta linguistic point of view a layer up it can be said regarding a layer down that such working sentence in that universe is false in the upper universe thus it is false although it works as a relative truth at the level down...it very much goes with what you believe regarding truth being provisional if it is the case that there are an Infinite number of universes...I debated that with Fresco long time ago concerning truth and infinity´s...don´t know if you remember that...

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@Cyracuz,

Cyracuz wrote:

If a person walks up to you and says "what I'm saying right now is false", and then just walks away again, did he say or do something logical?

Yes he did. He made a statement to which the laws of logic pertain. In that sense, it is logical.

Cyracuz wrote:

The sentence does not communicate anything of value or meaning.

That's just your opinion. A sentence doesn't have to be valuable to you or informative to you to qualify as logical.

Cyracuz wrote:

The only reason this sentence appears paradoxical is that the truth value isn't evident from the proposition itself, which is why it is not a logical proposition.

What if the man had said: "The following sentence is true. One plus one equals two". By your standards, would the first sentence be a logical proposition or not?

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@Fil Albuquerque,

(previous edited)

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@Fil Albuquerque,

"this sentence" is neither valid nor invalid. It lacks the information to decide either way.
"is false" suffers from the same problem.
Put them together, and you don't get any further. It is when you start assuming that it's either true of false that you get paradoxes.

Perhaps you will see it clearer if we ask another question:
If -"this sentence is false"- indeed is false, how is it false? What makes it false?
And if it's true, how is it true? What makes it true?

The answer is nothing does. It's when you assume it's either or you get a paradox...

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@Cyracuz,

The subject is what (or whom) the sentence is about, while the predicate tells something about the subject.

Thus:

The subject - This sentence (valid)

The predicate - is false (valid)

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@Cyracuz,

Cyracuz wrote:

If -"this sentence is false"- indeed is false, how is it false? What makes it false?
And if it's true, how is it true? What makes it true?

In standard Boolean logic, this question cannot be answered. In Fuzzy Logic, which extends the range of possible truth values to the whole interval [0 .. 1], the sentence "this sentence is false" if half-true---it has the truth value 0.5. So it's not as if the truth value of propositions like this cannot be computed in principle.

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@Thomas,

...there are several attempted solutions for it...I don´t actually know to which extent they are accepted by most logicians...

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@Thomas,

Quote:

Yes he did. He made a statement to which the laws of logic pertain. In that sense, it is logical.

There is simply not enough information in that sentence to apply the laws of logic. That's why you have to start assuming, which makes the paradox.

Quote:

That's just your opinion. A sentence doesn't have to be valuable to you or informative to you to qualify as logical.

A sentence does not have to be informative to qualify as grammatically sound, but that doesn't mean it qualifies as logical. If it did, applying logic to it would get you a logical outcome.

Quote:

What if the man had said: "The following sentence is true. One plus one equals two". By your standards, would the first sentence be a logical proposition or not?

Without the second sentence it would not be a logical proposition. With the second sentence it would.
But if, as in curry's paradox, you were to put something like "one plus one equals six" into the second sentence, the logical proposition would be false.

You could assume that the first part was true, in which case that would also validate the second part, but that would only be a repeat of what happened earlier. The validity of the sentence would no longer be decided by it's merits, but by an invalid axiom, which would be the cause of the paradox.

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@Thomas,

Quote:

In standard Boolean logic, this question cannot be answered.

Which is why you need the assumptions, the axioms. But no matter which axiom you chose, the sentence is nonsense.

There is, however a way to determine something about the sentence "this sentence is false". It contains the necessary grammatical components to qualify as a sentence, which makes it a true sentence that makes no sense.

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This sentence informs the subject is false informs the predicate... Rolling Eyes

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@Fil Albuquerque,

Yea, I heard you the first time. You don't seem to understand, though, that logic cannot be applied to something that is inherently illogical.
Just because it is grammatically correct doesn't make it worth something.

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@Cyracuz,

Thomas wrote:

What if the man had said: "The following sentence is true. One plus one equals two". By your standards, would the first sentence be a logical proposition or not?

Cyracuz wrote:

Without the second sentence it would not be a logical proposition. With the second sentence it would.

How about the following variant? "The following sentence is true. The preceding sentence is false."

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@Cyracuz,

That it is illogical we all know, that´s why it is a paradox... the thing is that you have to explain why and where according to rules is illogical...and propose a solution !

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@Thomas,

Quote:

How about the following variant? "The following sentence is true. The preceding sentence is false."

It is one logical proposition, and it's false. If you view them as two propositions, then neither are logical.

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@Fil Albuquerque,

Quote:

the thing is that you have to explain why and where according to rules is illogical

It doesn't communicate anything. That is why it is illogical. What information can you extract from "this sentence is false"?

The solution is simple. You have to consider the meaning of a proposition. If it is not a logical proposition, it is illogical to apply logic to it, which the occurrence of paradoxes clearly demonstrates. Actually, I suspect that these kinds of problems are only brought out to teach people that.

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@Cyracuz,

What you mean is that being false is not a property that something can have...from where it follows the famous saying whatever is the case to be true (actual) is true ! Whatever imply´s that we might not know...so regarding the true value of a PROPOSITION how do you solve it if is SOUND ?
That is the question !

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@Cyracuz,

There is no such thing as illogic to apply logic Cyr, that´s a contradiction again...if logic does n´t apply (yet) then it is neither logic nor illogic to apply the logic which does n´t apply...

You just gave an example on a not sound proposition !

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@Fil Albuquerque,

Quote:

so regarding the true value of a PROPOSITION how do you solve it ?

By collecting the information you need to determine it. If that information cannot be obtained, you create axioms or paradigms. And if your conclusions turn out to be something that don't add up, you know where the problem lies. Then you revise your axiom and keep on trucking until it breaks down again.

That is how scientific progress works. History is full of little paradigm shifts, and they follow in the wake of major breakthroughs where new information becomes available for study. There are always basic assumptions. Then they break down and are either replaced by new ones or with the information that couldn't be obtained at the time the first assumptions were made.
That way, the truth value of our propositions evolves in time with our understanding, one growing off the other.

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@Fil Albuquerque,

Quote:

There is no such thing as illogic to apply logic Cyr

Correct. Because "this sentence is false" has nothing to do with logic!

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@Cyracuz,

That is the damn challenge...that problem which is SOUND is old as Western Civilization is...nobody as solve it yet...give us your contribution.
Something clearly needs changing I gave you my 2 cents on it...

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Why are paradoxes considered profound?

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