## The Liar Paradox - Is it even a valid statement?

• 1.6k
In your post you present eight complex linguistic and logical problems, each requiring the time it deserves, meaning that I only have the time to answer them one by one.

Wrong. It's referring to the sentence "this sentence has ten words", which is to say that it is referring to "this sentence has ten words".

On my screen I see a set of marks which I recognize as a set of words having meaning.

For convenience, I name the sentence "this sentence has ten words" as A.

I can see that sentence A has five words.

I can then write on the same screen sentence B. I can either explicitly write "sentence A has five words", or I can implicitly write "A (being a sentence) has five words".

In the first case, the predicate "has five words" is referring to the subject "sentence A". In other words the subject is "the sentence "this sentence has ten words""

In the second case, the predicate "has five words" is referring to the subject "A (being a sentence)". In other words the subject is ""this sentence has ten words" (being a sentence)".

Either way, whether explicit or implicit, the subject is "the sentence "this sentence has ten words"".
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You skipped my argument, for the second time (as now revised to use 'stirng' instead of 'sentence'): Suppose we define 'the Pentastring' as the "This string has five words". So, we have a subject from the world, viz. the Pentastring. So, "The Pentastring has five words" is meaningful.

We can define "the Pentastring" as "this string has five words".

Both "the Pentastring" and "this string has five words" exist in the world on my screen. I can see that the expression "the Pentastring" has two words, and the expression "this string has five words" has five words.

Given the expression "The Pentastring has five words", as "The Pentastring" has been defined as "This string has five words", we can replace "The Pentastring" by "This string has five words".

This gives us the expression "This string has five words has five words". But this is an ungrammatical expression.
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The glaring sophistry in that video is the claim that "this sentence" equals "this sentence is false."

"A cat" may be defined as "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

"A cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice". Although the two expressions are not linguistically equal (one is two words long and the other is fourteen words long), they are semantically equal, meaning that one expression can be replaced by the other.

Possibility three

In the expression "this sentence is false", "this sentence" refers to "this sentence is false".

As "a cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice", the expressions are interchangeable.

Rather than say "I saw a cat", I could equally say "I saw a carnivorous mammal long domesticated as a pet and for catching rats and mice". The meanings are equal.

Therefore, as "this sentence" refers to "this sentence is false", the expression "this sentence" can equally be replaced by the expression "this sentence is false"

IE, ""this sentence is false" is false"

Continuing, """this sentence is false" is false" is false"

This goes on ad infinitum.

If in the expression "this sentence is false", "this sentence" refers to "this sentence is false", its self-referential nature means that no meaning can be determined within a finite time, meaning that it becomes meaningless.
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The physical inscription on the blackboard is made of chalk. The physical inscription in the notebook is made of pencil lead. There are two inscriptions. But there is only one sentence involved.

Agree
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The ball is in your court to support that claim

I wrote: Possibility 2) If "this string" is referring to itself, then it is an empty reference, and the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.

If "this string" referred to "a sequence of code units", then it would mean something, as it is referring to something outside itself.

But if "this string" refers to itself, then it is impossible to know what it means, and if no-one knows what it means, then it becomes part of a meaningless set of words.
• 3.2k
In your post you present eight complex linguistic and logical problems, each requiring the time it deserves, meaning that I only have the time to answer them one by one.

My arguments are straightforward. I am explicit in the steps so that they can be understood exactly or so that they can be corrected exactly.

Meanwhile, you have time to write your arguments, and repeat them, while I have read each one of them carefully and answered virtually every detail in all of them. If you feel you are not caught up to mine, then I suggest you go back to my first reply to you and read carefully starting there, rather than thoughtlessly quoting as mere fodder for your non-responsive replies.

And now I see that you have a serious misunderstanding of how quotation marks work. Just as with the video that is you inspiration, you don't understand use-mention as you flagrantly fail to use quotation marks correctly. You mangle the enquiry that way.

Addressing your A and B:

"A" denotes "This sentence has ten words".

A is "This sentence has ten words".

"A" is not "This sentence has ten words".

"This sentence has ten words" does not have ten words.

"This sentence has ten words" is false.

A is false.

"B" denotes "A has five words".

B is "A has five words".

"B" is not "A has five words".

"A has five words" has five words.

"A has five words" is true.

B is true.

There is no problem in any of that.

the predicate "has five words" is referring to the subject "sentence A".

Wrong. Right there you mangled it.

"has five words" is true of A, not of "A".

You can't put quote marks around the letter 'A' like that.

A is a sentence.

"A" is not a sentence. Rather "A" denotes a sentence.

the subject is "the sentence "this sentence has ten words""

That's your same mistake.

You fail to understand the difference between the Pentastring and "the Pentastring".

"the Pentastring" denotes "this string has five words". We don't say that "the Pentastring" is "this string has five words". That would be ridiculous since "the Pentastring" is not "This string has five words"

When we define, we say one thing denotes another or is a name of another; we don't say one thing is another.

"the Pentastring" denotes (is a name of) "the string "this string has five words".

The Pentastring is "this string has five words".

But "the Pentastring" is not "this string has five words".

"Big Ben" (is a name of) the famous clock tower in London.

Big Ben is the famous clock tower in London.

But it is not the case that "Big Ben" is the famous clock tower in London!

"Einstein's famous formula'" (is a name of) "E=MC^2".

Einstein's famous formula is "E=MC^2".

But it is not the case that "Einstein's famous formula" is "E=MC^2"!
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• 3.2k
The glaring sophistry in that video is the claim that "this sentence" equals "this sentence is false."
— TonesInDeepFreeze

"A cat" may be defined as "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

The video you suggested said that:

"this sentence" equals "this sentence is false".

That is plainly a falsehood. It would help if you not skip that point.

And the video's argument is based on that falsehood.

"Big Ben" denotes the famous clock tower in London.

"Big Ben" is not the famous clock tower in London.

"The famous clock tower in London" denotes the famous clock tower in London.

"Big Ben" and "the famous clock tower in London" are (extensionally) interchangeable.

"Big Ben" and the famous clock tower in London are not interchangeable, since the former is a name and the latter is a clock tower.

"This sentence" denotes "This sentence has five words".

"This sentence" is not "This sentence has five words".

""This sentence has five words"" denotes "This sentence has five words".

/

"cat" is a word.

A cat is an animal

"cat" denotes the animal.

"cat" is not "the animal".

"A cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

No, "A cat" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice. "A cat" does not denote "a carnivorous mammal long domesticated as a pet and for catching rats and mice."

"Big Ben" denotes the famous clock tower in London.

"Big Ben" does not denote "the famous clock tower in London".

Your arguments rely upon the fact that you are not careful to distinguish between, for example,

"a carnivorous mammal long domesticated as a pet and for catching rats and mice" and a carnivorous mammal long domesticated as a pet and for catching rats and mice.

the two expressions are not linguistically equal (one is two words long and the other is fourteen words long) [...]

Yes, that is the point I made earlier.

(1) "a cat"
and
"a carnivorous mammal long domesticated as a pet and for catching rats and mice"
may be substituted for one another (in an extensional context).

(2) "a cat"
and
a carnivorous mammal long domesticated as a pet and for catching rats and mice
may not be substituted for one another.

(3) a cat
and
"a carnivorous mammal long domesticated as a pet and for catching rats and mice"
may not be substituted for one another.

The mistakes you made earlier are violations of the nature of (2) and (3)

[...] they are semantically equal, meaning that one expression can be replaced by the other.

"a cat" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice.

"a carnivorous mammal long domesticated as a pet and for catching rats and mice" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice.

So, yes, the two are interchangeable (in extensional contexts; I'll leave that qualification tacit from now on).

I suggest sticking with 'This string has five words' for now.

Just to be clear:

"This string" denotes "This string has five words".

Of course, that is contextual.

In "This string has ten words", "this string" does not denote "This string has five words".

"This string has five words" is true.

""This string has five words" is true" is true.

ad infinitum

There's no problem with that.

"Einstein's famous formula has five symbols" is true.

""Einstein's famous formula has five symbols" is true" is true.

ad infinitum.

There's no problem with that, and if there is, then it's a problem with nearly any sentence, not just self-referential sentences.

"This string" denotes "This string has five words".

"This string" is "This string".

"This string" is not "This string has five words".

"This string" does not denote "This string".

"Big Ben" denotes Big Ben.

"Big Ben" is "Big Ben".

"Big Ben" is not Big Ben.

"Big Ben" does not denote "Big Ben".

If in the expression "this sentence is false", "this sentence" refers to "this sentence is false", its self-referential nature means that no meaning can be determined within a finite time, meaning that it becomes meaningless.

That assertion comes from the fact that you that you improperly use quote marks.
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The ball is in your court to support that claim
— TonesInDeepFreeze

I wrote: Possibility 2) If "this string" is referring to itself, then it is an empty reference, and the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.

Like I said, the ball the ball is in your court to demonstrate that claim.
But if "this string" refers to itself, then it is impossible to know what it means, and if no-one knows what it means, then it becomes part of a meaningless set of words.

Your argument for that, as with the video, is shot down at the git-go by mentioning that the argument relies on the false equation: "This string" equals "This string has five words", mutatis mutandis in the video.
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This stands, at least so far:

Suppose we define 'the Pentastring' as the "This string has five words".

So, we have a subject from the world, viz. the Pentastring.

So, "The Pentastring has five words" is meaningful.

To determine whether the Pentastring is true, we determine whether the Pentastring has five words.

Put this way:

In "This string has five words", 'this string' refers to the Pentastring, which is in the world. And "This string has five words" is equivalent with "The Pentastring has five words", in the sense that each is true if and only if the Pentastring has five words. So, "This string has five words" is meaningful.

To determine whether "The Pentastring has five words" is true, we determine whether the Pentastring has five words, which is to determine whether "This string has five words" has five words. To determine whether "This string has five words" is true, we determine whether "This string has five words" has five words. The determination of the truth value of the Pentastring is exactly the determination of the truth value of "This string has five words".
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This stands and is central:

The predicate "has five words" is referring to "the sentence "this sentence has ten words""
— RussellA

Wrong. It's referring to the sentence "this sentence has ten words", which is to say that it is referring to "this sentence has ten words".

The sentence "this sentence has ten words" is "this sentence has ten words".

The sentence "this sentence has ten words" is not "The sentence "this sentence has ten words"".

And if your argument is supposed to be addressing mine, then no matter anyway, since I didn't use a construction "the sentence "this sentence has five words", and even if I had, your argument would be wrong since:

The sentence "this sentence has five words" has five words
is not saying
"The sentence "this sentence has five words"" has five words
— TonesInDeepFreeze
• 1.6k
And now I see that you have a serious misunderstanding of how quotation marks work. Just as with the video that is you inspiration, you don't understand use-mention as you flagrantly fail to use quotation marks correctly.

As @Lionino suggests, I will spend some time and go through the thread ""This sentence is false" - impossible premise" to see what I can learn from what others were saying about the Liar Paradox.

As quotation marks are critical to the problem of the Liar Paradox, I will also spend some time ensuring that I am using them correctly before making any other comments.
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You were right when you said:

"a cat" and "a carnivorous mammal long domesticated as a pet and for catching rats and mice" are interchangeable.

You were wrong when you said:

"a cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

This is right:

"a cat" refers to a carnivorous mammal long domesticated as a pet and for catching rats and mice.

"a cat" does not refer to "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

That is, "a cat" refers to the animal that is a carnivorous mammal long domesticated as a pet and for catching rats and mice", but "a cat" does not refer to the phrase "a carnivorous mammal long domesticated as a pet and for catching rats and mice".

"Big Ben" refers to the famous clock tower in London.

"Big Ben" does not refer to "the famous clock tower in London".

That is, "Big Ben" refers to the object that is the famous clock tower in London, but "Big Ben" does not refer to the phrase "the famous clock tower in London".

The use-mention distinction can get into some technicalities, but for ordinary discussions in logic, it's pretty simple:

Use:
Big Ben is the famous clock tower in London. (True)

Mention:
"Big Ben" has six letters. (True)

Mention:
"Big Ben" refers to the famous clock tower in London. (True)

Mistake:
"Big Ben" is the famous clock tower in London. (False)

Mistake:
Big Ben has six letters. (False)

Mistake:
Big Ben refers to the famous clock tower in London. (False)

Mistake:
Big Ben refers to "the famous clock tower in London". (False)

In this discussion there is a bit of a wrinkle that might (?) be throwing you off:

"This string" refers to "This string has five words".

In that example, the thing referred to is itself a phrase, so unlike with the "a cat" or "Big Ben" examples, there are quote marks on the right side not just the left side.

Another example of that:

Einstein's famous formula is "E=MC^2".

"Einstein's famous formula" refers to "E=MC^2".

So, the right side may itself be a phrase.

"This string" has two words. (True)

"This string" refers to "This string has five words". (True)

"This string" is "This string has five words". (False)

"This string" and "This string has five words" are interchangeable. (False)

"Einstein's famous formula" has three words. (True)

"Einstein's famous formula" refers to "E=MC^2". (True)

Einstein's famous formula is "E=MC^2". (True)

"Einstein's famous formula" is "E=MC^2". (False)

"Einstein's famous formula" and "E=MC^2" are interchangeable. (False)
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Returning to the OP: "this statement is false"

The sentence "this sentence is false" is not a paradox as it is meaningless.

In the sentence "this sentence is false", what does "this sentence" refer to?

It could refer to the sentence "the cat is grey in colour".

In which case the sentence "this sentence is false" means that the sentence "the cat is grey in colour" is false.

Or it could refer to the sentence "this sentence is false".

In which case the sentence "this sentence is false" means that the sentence "this sentence is false" is false.

But we know that the sentence "this sentence is false" means that the sentence "this sentence is false" is false.

This means that the sentence ""the sentence "this sentence is false" is false" is false

This goes on ad infinitum.
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The use-mention distinction

As regards use, Big Ben is the bell inside the clock tower.
As regards mention, "Big Ben" is "the bell inside the clock tower"
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"This string" and "This string has five words" are interchangeable. (False)

I agree that "this sentence" is not interchangeable with "this sentence is false"

However, this is not what is interchangeable.

It is the expression "this sentence" that is interchangeable with the sentence "this sentence is false"

On the one hand there is i) "this sentence" and on the other hand there is ii) the expression "this sentence". These are different things.

This should negate your doubts regarding interchangeability.
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the sentence "a carnivorous mammal long domesticated as a pet"

That is not a sentence though.
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That is not a sentence though.

True. I could say "a cat" is "a carnivorous mammal that has been long domesticated as a pet"
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"a carnivorous mammal that has been long domesticated as a pet"

That is also not a sentence. :confused:
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That is also not a sentence

Again true. I've edited my post. Hopefully it works this time.
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I was under the impression that you were going to take a moment to understand use-mention, but still you haven't, as you make the same mistake yet again, despite the fact that I gave you multiple examples from which one could easily understand the point, which you've skipped. You are incorrigibly irrational.

regards use, Big Ben is the bell inside the clock tower.

Right.

regards mention, "Big Ben" is "the bell inside the clock tower"

Wrong. Very wrong.

"Big Ben" has two words.

"the bell inside the clock tower" has six words.

So "Big Ben" is not "the bell inside the clock tower".

One more time:

Big Ben is the bell inside the clock tower.

"Big Ben" refers to the bell inside the clock tower.

"Big Ben" refers to Big Ben.

"the bell inside the clock tower" refers to the bell inside the clock tower.

"the bell inside the clock tower" refers to Big Ben.

"Big Ben" is not the bell inside the clock tower.

"Big Ben" is not "the bell inside the clock tower."

Big Ben is not "Big Ben".

Big Ben is not "the bell inside the clock tower".

One more time:

Big Ben is a physical object.

"Big Ben" is an expression.

"the bell inside the clock tower" is an expression.

"Big Ben" and "the bell inside the clock tower" refer to the same physical object.

"Big Ben" and "the bell inside the clock tower" are not the same expression.

Do you understand now?

it is the expression "this sentence" that is interchangeable with the sentence "this sentence is false"

"this sentence" is not "this sentence if false".

(in context) "this sentence" refers to "this sentence is false".

"this sentence" and "this sentence is false" are not interchangeable":

"this sentence" has exactly two words. (true)

"this sentence is false" has exactly two words. (false)

"this sentence" has exactly four words. (false)

"this sentence is false" has exactly four words. (true)

So, you see that "this sentence" and "this sentence is false" are not interchangeable.

"Mark Twain" and "Samuel Clemens" refer to the same person.

"Mark Twain" and "Samuel Clemens" are not interchangeable*:

"Mark Twain" has exactly nine letters (true)

"Samuel Clemens" has exactly nine letters (false)

"Mark Twain" has exactly thirteen letters (false)

"Samuel Clemens" has exactly thirteen letters (true)

So, you see that, in a context such as this, "Mark Twain" and "Samuel Clemens" are not interchageable.*

*In an extensional context, what is inside the quote marks of "Mark Twain" and "Samuel Clemens" are interchangeable, but the whole units including the quote marks are not interchangeable. For example:

Mark Twain was friends with Nikola Tesla
is interchangeable with
Samuel Clemens was friends with Nikola Tesla

"Mark Twain" has exactly nine letters
is not interchangeable with
"Samuel Clemens" has exactly nine letters

Yes, Mark Twain is Samuel Clemens. So, (in an extensional context) every statement true of Mark Twain is true of Samuel Clemens and vice versa. But it is not the case that every statement true of "Mark Twain" is true of"Samuel Clemens" and it is not the case that every statement true of "Samuel Clemens" is true of "Mark Twain".

the one hand there is i) "this sentence" and on the other hand there is ii) the expression "this sentence". These are different things.

Wrong.

"this sentence" is "this sentence".

the expression "this sentence" is "this sentence".

"this sentence" is the expression "this sentence".

the expression "this sentence" is the expression "this sentence".

should negate your doubts regarding interchangeability.

It affirms my knowledge that you haven't bothered to understand use-mention.

/

In the sentence "this sentence is false", what does "this sentence" refer to?

It could refer to the sentence "the cat is grey in colour".

But it doesn't.

Or it could refer to the sentence "this sentence is false".

That's better.

In which case the sentence "this sentence is false" means that the sentence "this sentence is false" is false.

I think so.

Yes, the sentence "this sentence is false" means: the sentence "this sentence is false" is false.

we know that the sentence "this sentence is false" means that the sentence "this sentence is false" is false.

That's merely a tautology from the previous. You're just saying again what you said:

the sentence "this sentence is false" means: the sentence "this sentence is false" is false.

This

What does 'This' refer to? I guess it refers to: the sentence "this sentence is false" is false.

means that the sentence ""the sentence "this sentence is false" is false" is false

""the sentence "this sentence is false" is false"

has an odd number of quote marks.

Maybe you mean:

"the sentence "this sentence is false" is false" means: the sentence "the sentence "this sentence is false" is false" is false.

So:

"this sentence is false"
means
the sentence "this sentence is false" is false.

"the sentence "this sentence is false" is false"
means
the sentence "the sentence "this sentence is false" is false" is false.

"the sentence "the sentence "this sentence is false" is false" is false"
means:
the sentence "the sentence "the sentence "this sentence is false" is false" is false" is false.

ad infinitum

"the sentence "Paris is a city" is true"
means
the sentence "the sentence "Paris is a city" is true" is true.

"the sentence "the sentence "Paris is a city" is true" is true"
means
the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true.

"the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true"
means
the sentence "the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true" is true.

ad infinitum

/

You've skipped the point we were discussing. You claimed that self-referential sentences are meaningless.

I mentioned "This sentence has five words". Then, to accommodate any objection that saying "sentence" there is question begging, I provided, "This string has five words". Perhaps "This string has five words"doesn't withstand scrutiny for meaningfulness after all. But at least prima facie it is meaningful. It has a subject "this string" that refers to "this string has five letters" and a predicate "has five words" that refers to the property of having five words. And it is true if and only if "this string has five words" has five words. And "this string has five words" has five words. So, "this string has five words" is true.

Then, to obviate any objections about the use of the pronoun 'this', I provided:

Suppose we define 'the Pentastring' as the "This string has five words".

So, we have a subject from the world, viz. the Pentastring.

So, "The Pentastring has five words" is meaningful.

To determine whether the Pentastring is true, we determine whether the Pentastring has five words.

Put this way:

In "This string has five words", 'this string' refers to the Pentastring, which is in the world. And "This string has five words" is equivalent with "The Pentastring has five words", in the sense that each is true if and only if the Pentastring has five words. So, "This string has five words" is meaningful.

To determine whether "The Pentastring has five words" is true, we determine whether the Pentastring has five words, which is to determine whether "This string has five words" has five words. To determine whether "This string has five words" is true, we determine whether "This string has five words" has five words. The determination of the truth value of the Pentastring is exactly the determination of the truth value of "This string has five words".

If your reply to that is yet more of your use-mention confusion, then my guess is that there's little hope you'd ever think about it enough to understand it, though it doesn't take a lot of thinking.
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"Big Ben" has two words. "the bell inside the clock tower" has six words. So "Big Ben" is not "the bell inside the clock tower".

Examples of "mention"

Consider "Big Ben" has two words.
As the expression "has two words" refers to the expression "Big Ben", not to Big Ben as a thing in the world, this is an example of "mention"

Consider "the bell inside the clock tower" has six words
As the expression "has six words" refers to the expression "the bell inside the clock tower", not to the bell inside the clock tower as a thing in the world, this is an example of "mention"

Consider "Big Ben" is "the bell inside the clock tower"
As the expression "the bell inside the clock tower" refers to the expression "Big Ben", not to Big Ben as a thing in the world, this is an example of "mention"
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"Big Ben" and "the bell inside the clock tower" are not the same expression

The expression "Big Ben" is referring to the bell inside the clock tower existing in the world.

The expression "the bell inside the clock tower" is referring to the bell inside the clock tower existing in the world.

The forms of the expressions "Big Ben" and "the bell inside the clock tower" are different, in that the first has two words and the second has six words

The contents of the two expressions are the same, in that both are referring to the bell inside the clock tower existing in the world.

As you pointed out earlier, form is different to content

The teacher writes on the blackboard, "Caesar was a Roman emperor". A student writes in her notebook, "Caesar was a Roman emperor". The physical inscription on the blackboard is made of chalk. The physical inscription in the notebook is made of pencil lead. There are two inscriptions. But there is only one sentence involved.
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I think people can (almost) be forgiven for misunderstanding use and mention in this way. "Mention" in ordinary usage (!) strongly fits with "by the way" or "in passing" ... "Mentioned in dispatches" (... ones that referred more obviously to more central characters.)

And perhaps it's natural to think that any use of a word toward its main function, i.e. towards referring beyond its linguistic context, to actual cats and mats etc, should be understood also to refer in a smaller way, in passing, to the word itself and its linguistic context. And that this subsidiary reference (to syntactic features) might be what the distinction is acknowledging as "mention".

Whereas the distinction as I understand it is the other way round. It insists that we use a word (employ syntax) for the semantic purpose of mentioning, referring to, an object, subjecting it to this or that scrutiny or description. (Or, in less common usage of the same technical distinction, we use a sentence in order to mention a state of affairs.)

Which is slightly at odds with the usual connotation. When you say "scoundrel" do you mean to refer to the man in the dock? Fine. Do you mean to mention the man in the dock? In what oblique connection?? (In ordinary usage of "mention", I mean.)

No excuses. It's a technical distinction, and not rocket science. Just saying.
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Many modern historians consider Octavianus to be the first emperor, not Gaius :nerd:
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I would say just
mention
not
"mention"

As the expression "the bell inside the clock tower" refers to the expression "Big Ben", not to Big Ben as a thing in the world,

Wrong. Very wrong.

"the bell inside the clock tower" refers to Big Ben, not to "Big Ben".

Once you're clear about that, we can go back to this:

The video you suggested said that

"this sentence" equals "this sentence is false".

That is plainly a falsehood.

And the video's argument and your argument is based on that falsehood.
• 3.2k

There's more to it also:

There are these forms:

(1) [name] refers to [object]

"Big Ben" refers to the bell.

(2) [object] is [object]

Big Ben is the bell.

(3) [name] refers to [object that is itself an expression]

"Einstein's famous formula" refers to "E=MC^2".

(4) [object] is [object that is itself an expression]

Einstein's famous formula is "E=MC^2".

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The video and you conflate 'refer' with 'is' (or 'equals').

(5) "This sentence" refers to "This sentence is false".

but it is not the case that

(6) "This sentence" is (equals) "This sentence is false".
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I would say just mention not "mention"

I wrote "Examples of "mention""

The problem is, I want the word "examples" to refer to the word "mention", I don't want the word "mention" to refer to the word "examples".

For example, the expression "examples of importance" means "important examples", where the word "important" is being used as an adjective.

Similarly, "examples of mention" means "mentionable examples", where the word "mentionable" is being used as an adjective.

I want the word "mention" to be used as a noun, which is why I included it in quotation marks.

The use-mention distinction and the question of quotation marks is a highly complex topic, and the subject of numerous academic articles. I don't think we will be able to come to any definitive solution in a thread about the liar paradox.
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It's not rocket science.

We use a word to mention a thing.

We use a word in quote marks to mention the word.
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Or, if you want to be weird like me, use a word to mention a thing, use a word in single marks to mention the word itself (type), use a word in double marks to mention the word as used in a text (token), which is a quote.
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I guess you mean that the examples are instances where the word 'mention' applies to describe them.

Anyway, your argument that self-referring strings are not meaningful sentences failed.

And the argument in the video you endorsed about the liar paradox fails.
• 2.2k
It's not rocket science.

We use a word to mention a thing.

We use a word in quote marks to mention the word.

Yes, but for some there is a great deal to be gained by a misunderstanding.
• 54

Part 1: definitions

You can't define "mentions".

You are trying to assert a set of invariant linguistic rules. This is an impossible task.

Words are defined by their context. X is not(everything else).

I suspect you are somewhat aware of this. And yet here you are trying to browbeat into believing that your interpretation of words is the one and only true interpretation.

In case we do need to establish that you can't define anything objectively:

Me: I challenge you to define "Word".
You: Words.
Me: Define those words.
You: More Words.
Me: Define those words.
Etc.

You can choose infinite regression or circular definitions.

Part 2: Interpretations

There is no single correct interpretation.

Every single person who reads a sentence interprets it as they will.

You can't stop them interpreting it howsoever they choose.

The idea that your personal interpretation of, say, the Liar's paradox is correct and everyone else is wrong is a level of hubris even I don't aspire to.

I get that you are trying to establish a common ground for productive dialogue. But you can't do it.

The only person who interprets things identically to you - is an identical copy of you.

Each and every person has a unique response to every experience. Their response is their response. You cannot force them to respond the same way you do.

Part 3: Meaning

Meaning is relationships. Relationships change. Ergo, Meaning changes.

The meaning of words depends on context. Part of the context is the observer.

As you grow and change, your perception of meaning changes.

Mathematics chases after inherent meaning by stripping away relationships to find the essence of a thing.

Of course, in a world where meaning is contextual - the essence is the relationships.

All of which to say: meaning is in the eye of the beholder and changes as you change.

Coming on strong

It is possible you are deserving of more respect than I'm currently giving you... but for someone apparently sure of their position - you are peddling a whole lot of BS.

Your interpretation of the Liar's paradox is YOUR interpretation. RusselA's interpretation is his.

Can the paradox be interpreted in that way. Yes. Valid interpretation.

Right and wrong can get bent. Each interpretation exists.

Language is subjective.

I struggle to understand how anyone with the slightest awareness of linguistics can turn around and proclaim a given interpretation to be definitive. And yet here you are trying to tell RusserlA that his interpretation is wrong.

For shame.

Or do you genuinely believe that you can define... anything?
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Is there a reference you can point to for this approach? A manual or guide?
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You may do an Internet search on 'use-mention' for guidance. Meanwhile, the notion of use-mention is prevalent in the literature of logic, and is explained with examples in a lot of texts including these:

'Introduction To Mathematical Logic' - Alonzo Church, pg 61

By the way, the Introduction of this book is the best overview of starting considerations for logic that I have found.

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'Elementary Logic - 2nd ed' - Benson Mates, pg 21

By the way, this is one of the best intro books logic that I have found - rigorous, clear and concise.

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'Introduction To Logic' - Patrick Suppes, pq 121

By the way, this book has the best treatment on formal definitions that I have found.

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'Methods Of Logic - 4th ed' - W.V. Quine, pg 50

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'An Introduction To Formal Logic' - Peter Smith, pg 83

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'The Logic Of Book - 4th ed' - Merrie Bergman, James Moor, Jack Nelson, pg 67
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