The Liar's Non-Paradox

[Chose]

How do you demonstrate the sentence "Perfection is a sexy beast" is true under your system?

Sure. So my claim is that "Perfection is a sexy beast" is logically equivalent to "It is true that Perfection is a sexy beast", where 'it' is referring to "Perfection is a sexy beast". So the claim "It is true" is true if the truth predicate of "Perfection is a sexy beast" is true. So I would need to demonstrate that Perfection meets the criteria of being a sexy beast, then we would know "It is true" is correct and we would show the entire statement is true.

For the Liar's Paradox we have "It is true that this sentence is false." Where the "It" is referring to the truth predicate of "This sentence is false." However, "This sentence is false" is also referring to the exact same truth predicate, but it is claiming it is false. So in the case, contrary to the above case, we have the two parts of the overall statement making two directly contrary claims about the same piece of information.

 

[warpus]

I have no opinion on this.

That's like saying

"Ghnekh is a word!"

"In which language?"

"In whichever language it is a word in, pick one"

 

[Borachio]

Ghnekhtian

 

[TheMeInTeam]

Sure. So my claim is that "Perfection is a sexy beast" is logically equivalent to "It is true that Perfection is a sexy beast", where 'it' is referring to "Perfection is a sexy beast". So the claim "It is true" is true if the truth predicate of "Perfection is a sexy beast" is true. So I would need to demonstrate that Perfection meets the criteria of being a sexy beast, then we would know "It is true" is correct and we would show the entire statement is true.

For the Liar's Paradox we have "It is true that this sentence is false." Where the "It" is referring to the truth predicate of "This sentence is false." However, "This sentence is false" is also referring to the exact same truth predicate, but it is claiming it is false. So in the case, contrary to the above case, we have the two parts of the overall statement making two directly contrary claims about the same piece of information.

You're still using the wording to assign truth value to something with no testable consequences/evidence. That's a pretty big perversion of the concept of something being "true".

Again, if I say "It is true that this sentence is permufulgatory", What does that mean? If you claim it means nothing, you need to explain why using "false" instead of "permufulgatory" carries any meaning, when true/false as concepts are constructed to reflect a verifiable state of reality. In a scenario where there is no verifiable state of reality, why should we prefer one meaningless term to another?

 

[Chose]

That's like saying

"Ghnekh is a word!"

"In which language?"

"In whichever language it is a word in, pick one"

I don't think so. We are talking about the fundamental laws of logic come prior to any formal logical system. These fundamental intuitions are what must inform and describe any logical system. My point is that the Liar's Paradox is creating two premises that contradict themselves. Any logical system will tell you this is false. I was able to discuss and show the flaw in the sentence just fine using natural language. You had a good point about the alternate version still being self-referential, I was happy to grant that.

If you are so inclined, like I said the Standford entry I linked in my previous reply has a nice entry on this topic, and shows a generic formal version of the paradox.

If A is a sentence, ┌A┐is the name of the sentence, and Tr is the truth predicate. The 'capture' and 'release' are A implies Tr(┌A┐) and Tr(┌A┐) implies A.:
Tr(┌A┐)↔A

So the Liar's Paradox is constructing sentence P such that it implies ¬Tr(┌P┐). So right away you see that the sentence is contradicting the fundamentals of the language. How could a sentence P imply ¬Tr(┌P┐) if all sentences A imply Tr(┌A┐)? This is my point, sentences are implying they are true by their very nature. So if a sentence states that it's own fundamental truth predicate is false, it's contradicting itself.

Of course Godel created a similar paradox using mathematical logic, but from what I have heard it is more like "This sentence is not provable."

You're still using the wording to assign truth value to something with no testable consequences/evidence. That's a pretty big perversion of the concept of something being "true".

Again, if I say "It is true that this sentence is permufulgatory", What does that mean? If you claim it means nothing, you need to explain why using "false" instead of "permufulgatory" carries any meaning, when true/false as concepts are constructed to reflect a verifiable state of reality. In a scenario where there is no verifiable state of reality, why should we prefer one meaningless term to another?

The argument is that if you say "This sentence is permufulgatory and not permufulgatory." we know it is false. I don't even need to know what permufulgatory means, the sentence must be false because it's contradicting itself. This is not completely analogous because I know what true and false mean. So a better example to express your point would be "This sentence is true.", to answer the question of whether is it true or false, I have no problem saying I don't know, but the point is that when we analyze the two cases, either if it is true, or not true, we don't get a contradiction. That is the uniqueness of the Liar's Paradox.

If you think the sentence has no truth value, that is another argument that can be made.

 

[Lexicus]

This thread is your brain on analytic philosophy

 

[warpus]

There are no "fundamental laws of logic". Logic only exists in whatever formal context you first set up. That's why it's important to first establish the framework in which this discussion takes place. Most people would assume this to be first-order logic. If it's something else, you've got to point out what it is.

 

[Chose]

There are no "fundamental laws of logic". Logic only exists in whatever formal context you first set up. That's why it's important to first establish the framework in which this discussion takes place. Most people would assume this to be first-order logic. If it's something else, you've got to point out what it is.

No, logic exists outside formal contexts, do you really think that? How could we be having this discussion if there are not valid rules of inference outside of formal contexts?

If to reject something, or to make a claim, as you have been repeated doing, is to mean anything at all, you must have already accepted the law of non-contradiction. How could you set up a formal context of logic without already assuming that the law of non-contradiction holds? You can't.

 

[TheMeInTeam]

The argument is that if you say "This sentence is permufulgatory and not permufulgatory." we know it is false.

You do not know that any more than you know "this sentence is false and not false" is false.

I don't even need to know what permufulgatory means, the sentence must be false because it's contradicting itself.

By this logic, "sentence is false and not false" is necessarily false, because it's contradicting itself.

This is not completely analogous because I know what true and false mean.

Apparently not, since you don't seem to affix any value of reality/evidence/testable consequences to the concept of true and false. However, true/false depend on those to have actual meaning > permufulgatory.

By extension, if I say "it is permufulgatory that Usain Bolt is the fastest 100M sprinter", that doesn't have meaning. If I claim it's true instead of using "permufulgatory", then I am referencing something in reality which has evidence to support it...a core requirement for something to be "true".

It is false that D&D black dragons exist in reality beyond the game concept level (with about as high a certainty as normally possible), but that does not give the statement "black dragons are false" utility. Falseness is not an inherent property of the black dragon concept despite that the proposition that they exist as living creatures in reality should be considered false.

Working off established definitions is important. If you just decide to define something as paradoxical, logical reasoning doesn't matter.

 

[warpus]

How could we be having this discussion if there are not valid rules of inference outside of formal contexts?

How could there be rules of logic if you haven't defined them?

Assuming these rules exist, what are they? Where do they come from?

If no context is specified, most people assume first-order logic. If that's not the context you want us to use, then you gotta say which one.

 

[Chose]

By this logic, "sentence is false and not false" is necessarily false, because it's contradicting itself.

Correct.

It is false that D&D black dragons exist in reality beyond the game concept level (with about as high a certainty as normally possible), but that does not give the statement "black dragons are false" utility. Falseness is not an inherent property of the black dragon concept despite that the proposition that they exist as living creatures in reality should be considered false.

Yes.

Working off established definitions is important. If you just decide to define something as paradoxical, logical reasoning doesn't matter.

I'm not sure what you are getting at. I didn't define the Liar's paradox as paradoxical, others have. I am trying to argue that it is actually not a paradox, since it simply creates two contradictory premises.

How could there be rules of logic if you haven't defined them?

Assuming these rules exist, what are they? Where do they come from?

If no context is specified, most people assume first-order logic. If that's not the context you want us to use, then you gotta say which one.

This is a separate philosophical question. The rules of logic exist by necessity, it is impossible to reject them because in doing so you would be assuming them. They are the assumptions you must accept in order to define something. As for the claim that most people assume first-order logic, that surely isn't true. Most people have an understanding of the fundamental logical inferences of natural language without any knowledge of formal logical systems.

 

[warpus]

They exist by necessity how? Where do they come from? Can you write them out for me?

 

[Chose]

They exist by necessity how? Where do they come from? Can you write them out for me?

I already mentioned one, the law of non-contradiction. Why is it necessary? Because if you reject the law of non-contradiction, you defeat that very position, because if two contradictory things can be true, you can show anything to be true, including that you accept the law of non-contradiction.

https://en.wikipedia.org/wiki/Law_o..._identity,_non-contradiction,_excluded_middle

Have you read the Standford entry yet for the Liar's Paradox? It would do you good. It explains what rules are accepted when constructing the paradox:

"In formal languages, self-reference is also very easy to come by. Any language capable of expressing some basic syntax can generate self-referential sentences via so-called diagonalization (or more properly, any language together with an appropriate theory of syntax or arithmetic).[5] A language containing a truth predicate and this basic syntax will thus have a sentence L implies ¬Tr(┌L┐) and vice versa:

L⊣⊢¬Tr(┌L┐)

Other conspicuous ingredients in common Liar paradoxes concern logical behavior of basic connectives or features of implication. A few of the relevant principles are:

• Excluded middle (LEM):>⊢A∨¬A
• Explosion (EFQ): A,¬A⊢B
• Disjunction principle (DP):if A⊢C and B⊢C then A∨B⊢C
• Adjunction: If A⊢B and A⊢C then A⊢B∧C."

This is how it is expressed in first order logic: L: ¬Tr(<L>). Is that what you wanted?

 

[warpus]

The law of non-contradiction can only exist in an already defined logical system. First-order logic is an example of a logical system.

Without a logical system in place you lack the building blocks with which to define things like the law of non-contradiction.

 

[Hygro]

3rd Edition had mostly weak dragon art but the black dragon was dope

 

[Chose]

The law of non-contradiction can only exist in an already defined logical system. First-order logic is an example of a logical system.

Without a logical system in place you lack the building blocks with which to define things like the law of non-contradiction.

No, what you said is completely backwards. The law of con-contradiction is something true about the world, which we then describe in a logical system. If humans or any other creatures were never around to create logical systems, the fact that something cannot be A and not A at the same time in the same way would remain.

 

[warpus]

The law of con-contradiction is something true about the world

The law of non-contradiction is a concept that only makes sense in the context of classical logic.

It's not something that just exists, it's a concept that makes sense in a logical framework that is defined in a certain way.

Whether there are real-world parallels to the concept or not

 

[Birdjaguar]

This sentence is true: Fifty would have enjoyed this thread.