The Liar's paradox

[Tom Sawyer]

Yeah, I guess I have to broadly if only reluctantly agree with that, as long as you don't redefine our vocabulary all the time. The expressions "Real paradox" and "theoretical paradox" are not quite the thing but I grant you that it's the idea. If you can think of a better way to put it, I'd be interested.

Congratulation, it's not often that Speakpigeon grants a point!
EB

Ya, I don't like the terms "real paradox" and "theoretical paradox" either, but I couldn't think of better terms to sum up the distinction I was making. The main point was that if you come to a conclusion which points to something fundamentally contradictory about actual properties of the universe, that's either a WOW moment or an indication that one of your premises are wrong. If all you can do is assert contradictory premises and show that this leads to contradictory conclusions, that's a word game which may get you a quick chuckle as a party trick if there's a group of philosophy students at that party, but really has no additional value.

I 100% sign to this but I have to warn you that this is effectively disagreeing with nearly all mathematicians, nearly all computer scientists, and a good chunk of philosophers interested in logic as well as our in-house local expert in mathematical logic here, Angra Mainyu. Do you have a good life insurance?
EB

I don't know what they'd disagree with because it's pretty straightforward.

P1) X is true
P2) X is false
C) X is both true and false

Umm ... ok?

It's logically valid but doesn't tell you anything about anything and has absolutely zero applications towards anything, so it's just a complete waste of time. I guess the people who like it can hang out with the guys arguing about how many angels can dance on the head of a pin and have some fun talking in circles, but other than providing a cute word game there's not really any utility to it.

 

[Speakpigeon]

I 100% sign to this but I have to warn you that this is effectively disagreeing with nearly all mathematicians, nearly all computer scientists, and a good chunk of philosophers interested in logic as well as our in-house local expert in mathematical logic here, Angra Mainyu. Do you have a good life insurance?
EB

I don't know what they'd disagree with because it's pretty straightforward.

P1) X is true
P2) X is false
C) X is both true and false

Umm ... ok?

It's logically valid

Yes.

but doesn't tell you anything about anything and has absolutely zero applications towards anything, so it's just a complete waste of time. I guess the people who like it can hang out with the guys arguing about how many angels can dance on the head of a pin and have some fun talking in circles, but other than providing a cute word game there's not really any utility to it.

Well, it was first discussed in Ancient Greece and apparently it did help philosophers at the time to start formalising logical reasoning from scratch, and as I understand it, this is what ultimately led to Aristotle's theory of syllogisms. And there's no equivalent in the whole of human history. There's a bit of Chinese and Indian logic but nothing much. So, not really nonsense, no. It was people 2,500 years ago becoming aware of logical conundrums. Still, what may be ridiculous is the fact we still have to talk about it.

Anyway, thanks for a bit of common sense...
EB

 

[Tom Sawyer]

Well, it was first discussed in Ancient Greece and apparently it did help philosophers at the time to start formalising logical reasoning from scratch, and as I understand it, this is what ultimately led to Aristotle's theory of syllogisms. And there's no equivalent in the whole of human history. There's a bit of Chinese and Indian logic but nothing much. So, not really nonsense, no. It was people 2,500 years ago becoming aware of logical conundrums. Still, what may be ridiculous is the fact we still have to talk about it.

What's ridiculous about it is that it's a word game with zero applications. My 11 year old son loves these word games with logical contradictions and thinks that they're hilarious and they make him laugh. That's about the extent of their usefulness.

The whole point about Aristotle's syllogisms was that the logical models were not just word games but instead useful tools which could be applied to the real world outside of the model. If you know that Aristotle is a mortal and that Aristotle is a man, you now know that Aristotle is a mortal man. You were able to deduce something about a real person named Aristotle and therefore have more information after applying the model than you did before applying the model, hence its a useful model. With word games like "This sentence is false", you are not actually able to deduce anything outside of the model, so you have the exact same amount of information after applying the model as you did before applying the model and therefore it was not a useful model. It's a cute thing you can use for a chuckle, but that's it.

 

[untermensche]

A thing cannot be both true and false.

Being true means you are not false.

Being false means you are not true.

Saying A is both true and false is absolute nonsense.

 

[Torin]

Here's my solution to the paradox:

1. The meaning of a proposition derives from the evidence and reasoning in its support.
2. "This statement is false" has no evidence or reasoning in its support.
3. Therefore, "this is statement is false" is meaningless.

Some philosophers try to get around arguments like this by revising the Liar's Paradox sentence to say "this statement is either false or meaningless." The idea is that if you call this revised statement meaningless, that makes it true. The paradox then supposedly starts again at that point, because if the revised statement is true, then it is false or meaningless, which are mutually exclusive with truth.

My answer is: No. The statement "this statement is either false or meaningless" is meaningless, not true, because it still has no connection to evidence or reasoning. So the paradox does not start again.

So, that's my opinion on the Liar's Paradox. Thoughts?

 

[Tom Sawyer]

Saying A is both true and false is absolute nonsense.

Well, it both is and it isn't.

 

[Speakpigeon]

Here's my solution to the paradox:

1. The meaning of a proposition derives from the evidence and reasoning in its support.
2. "This statement is false" has no evidence or reasoning in its support.
3. Therefore, "this is statement is false" is meaningless.

Some philosophers try to get around arguments like this by revising the Liar's Paradox sentence to say "this statement is either false or meaningless." The idea is that if you call this revised statement meaningless, that makes it true. The paradox then supposedly starts again at that point, because if the revised statement is true, then it is false or meaningless, which are mutually exclusive with truth.

My answer is: No. The statement "this statement is either false or meaningless" is meaningless, not true, because it still has no connection to evidence or reasoning. So the paradox does not start again.

So, that's my opinion on the Liar's Paradox. Thoughts?

How could it be meaningless?

The sentence is in proper English. It is very simple and we all understand what it means, provided we are told we have to understand it as being about itself, and this isn't problematic at all.

The empirical evidence is the existence of sentence itself in the real world and our relation to it as we try to decide if it's true or false. It exists.

The connection to reasoning is that if you understand the sentence and try to determine whether it's true, you won't succeed, even though the evidence of the sentence itself is right there for you to look at and consider.

So, just claiming it is meaningless because it has no connection to evidence or reasoning is clearly wrong.
EB

 

[Speakpigeon]

Well, it was first discussed in Ancient Greece and apparently it did help philosophers at the time to start formalising logical reasoning from scratch, and as I understand it, this is what ultimately led to Aristotle's theory of syllogisms. And there's no equivalent in the whole of human history. There's a bit of Chinese and Indian logic but nothing much. So, not really nonsense, no. It was people 2,500 years ago becoming aware of logical conundrums. Still, what may be ridiculous is the fact we still have to talk about it.

What's ridiculous about it is that it's a word game with zero applications. My 11 year old son loves these word games with logical contradictions and thinks that they're hilarious and they make him laugh. That's about the extent of their usefulness.

The whole point about Aristotle's syllogisms was that the logical models were not just word games but instead useful tools which could be applied to the real world outside of the model. If you know that Aristotle is a mortal and that Aristotle is a man, you now know that Aristotle is a mortal man. You were able to deduce something about a real person named Aristotle and therefore have more information after applying the model than you did before applying the model, hence its a useful model. With word games like "This sentence is false", you are not actually able to deduce anything outside of the model, so you have the exact same amount of information after applying the model as you did before applying the model and therefore it was not a useful model. It's a cute thing you can use for a chuckle, but that's it.

Possibly but it remains that many different people, including philosophers and mathematicians, have given very different resolution of the paradox, including in modern times. If the issue was as simple as you say, we would nearly all agree. We don't.
EB

 

[Tom Sawyer]

So, just claiming it is meaningless because it has no connection to evidence or reasoning is clearly wrong.

The meaninglessness has to do with the application of it. It has none. A model which cannot apply to anything outside of the model is a useless and meaningless model, since it doesn't do the one and only thing you build models for.

 

[Tom Sawyer]

Possibly but it remains that many different people, including philosophers and mathematicians, have given very different resolution of the paradox, including in modern times. If the issue was as simple as you say, we would nearly all agree. We don't.

But none of those resolutions have any meaning at all. I agree that lots of philosophers and mathematicians like to waste their time with pointless navel gazing which provides no value at all, but that doesn't counter the claim that what they're doing is pointless and has no value at all.

 

[Speakpigeon]

Tarski, great mathematician, developed a theory of truth in 1935 saying that "Snow is white" is true if and only if snow is white.

So, "This sentence is false" is true if and only if this sentence is false.

Isn't it interesting?
EB

 

[Speakpigeon]

So, just claiming it is meaningless because it has no connection to evidence or reasoning is clearly wrong.

The meaninglessness has to do with the application of it. It has none. A model which cannot apply to anything outside of the model is a useless and meaningless model, since it doesn't do the one and only thing you build models for.

The application is the theory of logic. Apparently there's no theory of logic that solves the paradox. As such, this horse can still do some effective work.
EB

 

[Tom Sawyer]

So, just claiming it is meaningless because it has no connection to evidence or reasoning is clearly wrong.

The meaninglessness has to do with the application of it. It has none. A model which cannot apply to anything outside of the model is a useless and meaningless model, since it doesn't do the one and only thing you build models for.

The application is the theory of logic. Apparently there's no theory of logic that solves the paradox. As such, this horse can still do some effective work.
EB

Because it's a dumb word game made up to have no solution. That's not effective work. That's nothing. We can theorize things that aren't real - whoop-dee-fucking-shit. We can also make up knock-knock jokes and limericks. The difference is that you need to be a little bit clever to create an effective limerick and this thing doesn't rise up to that bar.

 

[untermensche]

Tarski, great mathematician, developed a theory of truth in 1935 saying that "Snow is white" is true if and only if snow is white.

So, "This sentence is false" is true if and only if this sentence is false.

Isn't it interesting?
EB

No.

To claim something is white requires there be a something.

To claim something is false requires a something that is false. A sentence is only true or false based on content. Not empty claims.

 

[Torin]

How could it be meaningless?

The sentence is in proper English. It is very simple and we all understand what it means, provided we are told we have to understand it as being about itself, and this isn't problematic at all.

A statement isn't necessarily meaningful just because it is grammatically correct. It has to have a relationship to observation. Otherwise "colorless green ideas sleep furiously" would be meaningful. To give another example, many Christian statements about the Trinity are grammatically correct and appear meaningful until analyzed (e.g., "the Son proceeds not from the Father alone, but from the Father and the Holy Spirit together").

The empirical evidence is the existence of sentence itself in the real world and our relation to it as we try to decide if it's true or false. It exists.

So does any meaningless statement. The evidence required is not evidence for the existence of the statement as a series of physical words, but evidence for the content of the statement.

The connection to reasoning is that if you understand the sentence and try to determine whether it's true, you won't succeed, even though the evidence of the sentence itself is right there for you to look at and consider.

The statement itself was just plopped down out of thin air, though, so it has no connection to reasoning.

 

[Speakpigeon]

A statement isn't necessarily meaningful just because it is grammatically correct.

Please provide convincing examples of a grammatically correct statement which is not meaningful.

It has to have a relationship to observation.

Who says?

If the universe was all in blue we would see life in blue. You don't understand this sentence?!

Otherwise "colorless green ideas sleep furiously" would be meaningful.

Wrong example.

Please explain why it is not meaningful.

To give another example, many Christian statements about the Trinity are grammatically correct and appear meaningful until analyzed (e.g., "the Son proceeds not from the Father alone, but from the Father and the Holy Spirit together").

Ah, yes, but what do they mean by "proceed", do you know? Religious communities are self-centred communities, they have a special vocabulary, you can't decide this sentence is meaningless until you know what they mean by "proceed", "Son, "Father", and "Holy Spirit".

I would assume the idea is that the Son is one aspect of the Trinity, and one that proceeds, or comes, from the two other aspects, the Father and Holy Spirit. What's not to be understood there?

So does any meaningless statement. The evidence required is not evidence for the existence of the statement as a series of physical words, but evidence for the content of the statement.

Sure, but a meaningless statement cannot be understood as referring to something because it cannot be understood to begin with.

The Liar sentence is meaningful and it obviously refers to something and to something which obviously exists since it is itself.

The connection to reasoning is that if you understand the sentence and try to determine whether it's true, you won't succeed, even though the evidence of the sentence itself is right there for you to look at and consider.

The statement itself was just plopped down out of thin air, though, so it has no connection to reasoning.

The connection to reasoning is that if you understand the sentence and try to determine whether it's true, you won't succeed, even though the evidence of the sentence itself is right there for you to look at and consider.
EB

 

[Speakpigeon]

The application is the theory of logic. Apparently there's no theory of logic that solves the paradox. As such, this horse can still do some effective work.
EB

Because it's a dumb word game made up to have no solution. That's not effective work. That's nothing. We can theorize things that aren't real - whoop-dee-fucking-shit. We can also make up knock-knock jokes and limericks. The difference is that you need to be a little bit clever to create an effective limerick and this thing doesn't rise up to that bar.

I guess i already explained my position so there's no need to repeat. Merely claiming something is dumb isn't good enough with me.
EB

 

[untermensche]

Otherwise "colorless green ideas sleep furiously" would be meaningful.

Wrong example.

Please explain why it is not meaningful.

The first two words are a contradiction so that in itself removes meaning from what they describe.

Ideas do not sleep so that is meaningless.

And they can't sleep furiously if they do not sleep.

It is words arranged grammatically with no meaningful idea expressed.

 

[Tom Sawyer]

The application is the theory of logic. Apparently there's no theory of logic that solves the paradox. As such, this horse can still do some effective work.
EB

Because it's a dumb word game made up to have no solution. That's not effective work. That's nothing. We can theorize things that aren't real - whoop-dee-fucking-shit. We can also make up knock-knock jokes and limericks. The difference is that you need to be a little bit clever to create an effective limerick and this thing doesn't rise up to that bar.

I guess i already explained my position so there's no need to repeat. Merely claiming something is dumb isn't good enough with me.
EB

Dumb, pointless, useless, however you want to term it. A logical model with no application is really nothing more than just a logical model with no application.

There's nothing profound about a word game.

 

[Speakpigeon]

Otherwise "colorless green ideas sleep furiously" would be meaningful.

Wrong example.

Please explain why it is not meaningful.

The first two words are a contradiction so that in itself removes meaning from what they describe.

Ideas do not sleep so that is meaningless.

And they can't sleep furiously if they do not sleep.

It is words arranged grammatically with no meaningful idea expressed.

Don't worry I won't congratulate you but I'm sorry to say you're absolutely right.

What did you have this morning for breakfast?! I want the same.
EB