The redundancy theory of truth usually applies to all sentences, whether it be "this sentence contains five words" or "it is raining". Seems strange to only apply it to self-referential sentences. — Michael

Not the case.

I did include the non self-referential example:

To say that "a horse is a horse" is true is saying no more than "a horse is a horse".

I also included Frege's 1918 comment:

It is worthy of notice that the sentence "I smell the scent of violets" has the same content as the sentence "it is true that I smell the scent of violets". So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth.

===============================================================================

But even then, there's still nothing problematic with the sentence "this sentence contains five words". It is meaningful, despite your protestations to the contrary. — Michael

I totally agree that there is nothing problematic with the sentence "this sentence contains five words", and can indeed be a meaningful sentence.

As long as "this sentence contains five words" is not referring to itself.

Which sentence were you referring to when you made these statements? — EricH

1) "this sentence contains five words" is true IFF this sentence contains five words

We don't know what "this sentence" is referring to, but, for example, it could be referring to the sentence "this house is grey in colour", "this book is important", "this animal is a cat" or "this sentence has five words".

Suppose it is referring to the sentence "this sentence has five words".

In language is the sentence "This sentence has five words"

I see on my screen the following shapes - This sentence has five words - which I recognize as the sentence "This sentence has five words".

2) This sentence has five words. Not true? Yes, true.

I am using the model of "snow is white" is true IFF snow is white.

Not being in quotation marks - this sentence has five words - is something that exists in the world, for example, on my screen, and is true in the sense that I can see it on my screen, rather than not see it on my screen.

In context we do know. — Michael

I agree that in the context of a thread on the Liar Paradox, the discussion is about can a self-referential sentence have any meaning.

If you want to be explicit, then: The self-referential sentence "this sentence contains five words" is true. — Michael

Truth depends on a correspondence between language and the world

To be even more explicit, if in the sentence "this sentence contains five words" the expression "this sentence" is referring to "this sentence contains five words", can the sentence "this sentence contains five words" have a truth-value, or is it meaningless.

You are arguing that "this sentence contains fifty words" has a truth-value.

I am arguing that any concept of truth in a self-referential expression is redundant.

My belief is that an expression in language can only have a truth-value if it corresponds with something in the world.

I accept Tarski's paradigm for defining truth, ie, Tarski's Semantic Theory of Truth:
"snow is white" is true IFF snow is white.

It can be argued what exactly this world is, but whatever the world is, it is external to a linguistic expression.

In the self-referential sentence, as the sentence is referring to itself, it cannot be referring to any world that exists outside of itself.

If a self-referential sentence is not referring to anything in the world, then it can have no truth-value.

In cases of linguistic self-reference, the concept of truth is redundant

1) "This sentence contains five words" is true IFF "this sentence contains five words".
The word true is redundant in that:
"This sentence contains five words" IFF "this sentence contains five words"

In the Wikipedia article Redundancy Theory of Truth

Gottlob Frege was probably the first philosophical logician to express something very close to the idea that the predicate "is true" does not express anything above and beyond the statement to which it is attributed. In 1892, he wrote:

One can, indeed, say: "The thought that 5 is a prime number is true." But closer examination shows that nothing more has been said than in the simple sentence "5 is a prime number." The truth claim arises in each case from the form of the declarative sentence, and when the latter lacks its usual force, e.g., in the mouth of an actor upon the stage, even the sentence "The thought that 5 is a prime number is true" contains only a thought, and indeed the same thought as the simple "5 is a prime number."[1]

In 1918, he argued:

It is worthy of notice that the sentence "I smell the scent of violets" has the same content as the sentence "it is true that I smell the scent of violets". So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth.[2][3]

To say that "a horse is a horse" is true is saying no more than "a horse is a horse".

To say that "this sentence contains fifty words" is true is saying no more than "this sentence contains fifty words".

To say that "x" is true is saying no more than "x".

Truth only enters when self-reference disappears and the world appears:
"x" is true IFF x

The words "has" and "contain" have identical meaning in the context of this discussion. — EricH

I agree.

Conclusion? "This sentence contains five words" is true. QED — EricH

No one would say that "this house contains five rooms" is true without first knowing which house is being referred to.

No one would say that "this book contains important knowledge" is true without first knowing
which book is being referred to.

Therefore, how can any one say that "this sentence contains five words" is true if no one knows which sentence is being referred to?

For example, so far, we have three sentences:

1) The sentence "this house contains five rooms", which happens to contain five words.
2) The sentence "this book contains important knowledge", which happens to contain five words
3) The sentence "this sentence contains five words", which happens to contain five words.

The sentence "this sentence contains five words" isn't telling us which sentence is being referred to.

Therefore, how do we know that it is true?

Do you think each of them is dependent on each other, or should we look at them individually? — javi2541997

Perhaps the following:

I know I see the colour red independently of any beliefs, thoughts or attitudes I may have towards sunsets.
I cannot have a belief about sunsets without having thoughts or attitudes towards them.
I cannot have a thought about sunsets without having an attitude towards them.
I cannot have an attitude towards sunsets without thinking about them, having beliefs about them or knowing about them.
I cannot have a thought about sunsets without having a belief in them or knowing about them.
I cannot have a belief about sunsets without knowing about them.

IE, I can know something like the colour red without having any beliefs, thoughts or attitudes towards it. But if I have a belief, thought or attitude towards something like a sunset, then I must know something about it.

The self-referential sentence "this sentence contains five words" is true because it contains five words.........................This is incredibly straightforward. — Michael

I wish it were.

"Snow is white" is true IFF snow is white.

The sentence "this house is very tall" contains five words.
The sentence "this sentence contains five words" also contains five words.

"This house is very tall" is true IFF this house is very tall, where this house is referring to, or pointing at, a particular house in the world.
Similarly, "this sentence contains five words" is true IFF this sentence contains five words, where this sentence is referring to, or pointing at, a particular sentence in the world.

It is not correct to say that the sentence "this house is very tall" is true because it contains five words.
Similarly, it is not correct to say that the sentence "this sentence contains five words" is true because it contains five words.

"This house is very tall" is true IFF this house is very tall, not because the sentence "this house is very tall" contains five words.
Similarly, "this sentence contains five words" is true IFF this sentence contains five words, not because the sentence "this sentence contains five words" contains five words.

The subjective content of the sentence "this sentence contains five words" cannot determine the objective form of itself, ie, that it contains five words.

What is a belief, and what is an attitude? — Noble Dust

There is also knowing. When looking at a sunset, I know that I see the colour red, I believe my seeing the colour red was caused by the sunset, I think that sunsets happen every day and I have a positive attitude towards them.

Knowing is more fundamental than believing, believing is more fundamental that thinking and thinking is more fundamental than having an attitude.

It's grounded in that we can count how many words are in the sentence "this sentence contains fifty words". There are five words, not fifty, and so the sentence is false. — Michael

Exactly. The sentence "this sentence contains fifty words" in order to have a truth value must be grounded in the world.

"This sentence contains fifty words" is true IFF this sentence contains fifty words.

The sentence "this sentence contains fifty words" in order to have a truth value cannot be grounded in itself. The expression "this sentence" within "this sentence contains fifty words" cannot be referring to itself, ie, it cannot be referring to "this sentence contains fifty words".

All I'm trying to say is that an expression that self-refers cannot be grounded in the world, and if not grounded in the world cannot have a truth value.

Form and content

I see on my computer screen the following shapes – this sentence contains fifty words.

I recognize these as words, part of a grammatical sentence, having the meaning "this sentence contains fifty words"

I can also see that on my computer screen that there are five words.

The subjective content of these words is "this sentence contains fifty words"

The objective form of these words is that there are five of them.

Subjective content and objective form are linked by:
"This sentence contains fifty words" is true IFF this sentence contains fifty words.

The word "truth" in the following would be redundant:
"This sentence contains fifty words" is true IFF "this sentence contains fifty words"

"this sentence contains five words" is grounded and is true.
"this sentence contains fifty words" is grounded and is false.
"this sentence is false" is ungrounded and is neither true nor false. — Michael

I agree with you that if the sentence "this sentence contains fifty words" is grounded in the world then it can have a truth value, and it is false.

For example:
"Snow is white" is true IFF snow is white
"This sentence contains fifty words" is true IFF this sentence contains fifty words.

Given the sentence "this sentence contains fifty words", whether it has a truth value or not all depends on what "this sentence" is referring to.

I have been trying to make the point that if "this sentence" refers to "this sentence has fifty words" then there is no grounding in the world and there can be no truth value.

I may be wrong, but you seemed to suggest that "this sentence" does refer to "this sentence has fifty words" when you said:

I do know that. It refers to itself, it contains five words, and so it doesn’t contain fifty words. — Michael

My question is, if the expression "this sentence" within "this sentence contains fifty words" is referring to itself, ie referring to "this sentence contains fifty words", then how can there be any grounding in the world?

I do know that. It refers to itself, it contains five words, and so it doesn’t contain fifty words. — Michael

In the sentence "this ferry contains fifty people", we don't normally think that "this ferry" is referring to the sentence "this ferry contains fifty people". We normally think that it is referring to a ferry in the world.

So why would we think that "this sentence" is referring to "this sentence contains fifty words". It seems more likely that "this sentence" is referring to another sentence.
===============================================================================

They are discussing the liar paradox. We are not discussing the liar paradox. We are discussing the sentences "this sentence contains five words" and "this sentence contains fifty words". — Michael

We are discussing self-referential expressions, of which the Liar Paradox is an example.

From the IEP article on Liar Paradox

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The Classical Liar Sentence is the self-referential sentence: This sentence is false.

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From the SEP article on self-reference:... self-reference is not a sufficient condition for paradoxicality. The truth-teller sentence “This sentence is true” is not paradoxical, and neither is the sentence “This sentence contains four words” (it is false, though) — Michael

In language is the sentence "this sentence contains fifty words".

In language is the sentence "X"

The only means of knowing the truth value of "X" is by comparing it to the world, ie, by grounding it in the world.

From the Wikipedia article on the Liar Paradox

Kripke proposes a solution in the following manner. If a statement's truth value is ultimately tied up in some evaluable fact about the world, that statement is "grounded". If not, that statement is "ungrounded". Ungrounded statements do not have a truth value. Liar statements and liar-like statements are ungrounded, and therefore have no truth value.

This is why "X" is true IFF X, where "X" is in language and X is in the world.

An expression in language that referred to another expression in language, such as "this sentence" referring to "this sentence has fifty words", cannot be grounded in the world, and if not grounded in the world, can have no truth value,

As regards the SEP article.

In language, meaning is often inferred. If I said "Paris is cool", the listener might infer that I meant "Paris is an excellent city to visit as a tourist".

Similarly, if I said "this sentence contains fifty words", the listener may infer that I meant that this sentence, ie the sentence "this sentence contains fifty words", contains fifty words.

I agree that if the sentence "this sentence contains fifty words" is inferred to mean that this sentence, ie the sentence "this sentence contains fifty words", contains fifty words, then this is not paradoxical and is false.

However, we are not discussing what the sentence "this sentence contains fifty words" is inferred to mean, we are discussing what it literally means.

And because not grounded in the world, if "this sentence" is referring to "this sentence contains fifty words", it has no truth-value and is meaningless.

It is quite possible you and Tones went through this exact point, but honestly if I read through all 8 pages I might develop dementia before I even hit middle age. — Lionino

At least you have middle age to look forward to.

But you weren't talking about the liar paradox. You were talking about the sentences "this sentence contains five words" and "this sentence contains fifty words". These two sentences are meaningful, with the first being true and the second being false. — Michael

You say that the sentence "this sentence contains fifty words" is false.

But you don't know that. It all depends on which sentence "this sentence" is referring to.

In the same way, we don't know whether the sentence "this ferry contains fifty people" is true or false, if we don't know which ferry is being referred to.

Similarly, we don't know whether the sentence "this idea contains fifty thoughts" is true or false, if we don't know which idea is being referred to.

If "this sentence" is referring to the sentence "The Eiffel Tower is a lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower from 1887 to 1889. Nicknamed "La dame de fer", it was constructed as the centrepiece of the 1889 World's Fair" then this sentence does have fifty words.

If "this sentence" is referring to the sentence "The Eiffel Tower is a lattice tower" then this sentence doesn't have fifty words.

If "this sentence" is referring to itself, ie, "this sentence contains fifty words", then both the SEP and IEP discuss the problems of self-referential expressions.

The SEP article on the Liar Paradox starts with the sentence "The first sentence in this essay is a lie"

The IEP article Liar Paradox talks about "this sentence is a lie"

But there is insufficient information within the sentence "this sentence contains fifty words" to know which sentence "this sentence" is referring to.

As we don't know which sentence "this sentence" is referring to, we cannot know whether the sentence "this sentence contains fifty words" is true, false or meaningless.

That you blatantly skip this point over and over is intellectual dishonesty. — TonesInDeepFreeze

Au revoir.

No it’s not. — Michael

That's why there is a SEP article on the Liar Paradox.
===============================================================================

No it doesn’t. It contains five words and so is false. — Michael

I agree that my statement was false. But is was meaningful, unlike the Liar Paradox, where a part of language refers to itself.

1. This sentence contains five words.
2. This sentence contains fifty words.
(1) is true and (2) is false. It's not complicated. I don't understand the problem you have. — Michael

The problem is, in 2) for example, what exactly is "this sentence" referring to?

If "this sentence" is referring to "this sentence contains fifty words", then this is a case of self-reference, and being a case of self-reference is meaningless.

In that event, this sentence, ie the sentence "this sentence contains fifty words", contains fifty words.

But we have been told that "this sentence" refers to "this sentence contains fifty words"

We therefore know that this sentence, ie the sentence "ie, the sentence "this sentence contains fifty words", contains fifty words", contains fifty words.

But we have been told that "this sentence" refers to "this sentence contains fifty words"

Ad infinitum.

That is my problem.
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1. It is raining.
2. "it is raining" is true iff it is raining.
(1) and (2) do not mean the same thing. (1) is true iff it is raining but (2) is true even if it isn't raining. — Michael

Agree, 1) and 2) don't mean the same thing.

1) It is raining is true IFF it is raining. The word "true" is redundant. If it is raining then it is raining. This is an example of the law of identity where something is equal to itself.

2) "It is raining" is true IFF it is raining. This is meaningful.

Yes? And the sentence would be false. — Michael

As regards the sentence "this sentence has fifty words" making the claim that "this sentence has fifty words" has fifty words:

No, it wouldn't be false, it would be meaningless, because self-referential.

"Snow is white" is making the claim that "snow is white" is true IFF snow is white.

"Jack is tall" is making the claim that "Jack is tall" is true IFF Jack is tall

"This sentence has fifty words" is making the claim that "this sentence has fifty words" is true IFF this sentence has fifty words.
In language is "this sentence has fifty words".
In the world is a set of words.
If in the world there is a set of fifty words, then "this sentence has fifty words" is true
If in the world is a set of words of which there are not fifty, then "this sentence has fifty words" is not true.
There is no problem here, as meaningful.

The problem arrives when "this sentence has fifty words" is making the claim that "this sentence has fifty words" is true IFF "this sentence has fifty words" has fifty words.

This is a problem of self-reference, because "this sentence has fifty words" is referring to itself.

For example, consider "unicorns are happy" is true IFF unicorns are happy. This is meaningful. Then consider "unicorns are happy" is true IFF "unicorns are happy". This is a tautology, an example of the law of identity where a thing is identical with itself.

This is why self-reference leads to a paradox, and why expressions that self-refer are meaningless.

"This sentence has fifty words" can meaningfully refer to a sentence having fifty words, but it cannot meaningfully refer to itself.

With the sentence "Jack is tall", the sentence makes the claim that Jack is tall...................With the sentence "This sentence has five words", the sentence makes the claim that "This sentence has five words" has five words. — TonesInDeepFreeze

The above is a key point of disagreement

"Snow is white" is true IFF snow is white
"Jack is tall" is true IFF Jack is tall
"This sentence has five words" is true IFF this sentence has five words

It is not the case that "this sentence has five words" is true IFF "this sentence has five words" has five words

It is true that the sentence "this sentence has five words" has five words, but this truth is independent of any meanings of the words within the sentence.

The meanings of the words within the sentence "this sentence has five words" play no part in the truth that the sentence "this sentence has five words" has five words.

The sentence "a b c d e" has five words, regardless of any meaning of the words "a b c d e".

The meanings of the words "a b c d e" play no part in the fact that the sentence "a b c d e" has five words

Similarly, the meanings of the words "this sentence has five words" play no part in the fact that the sentence "this sentence has five words" has five words.

As "Jack is tall" makes the claim that Jack is tall, then "this sentence has five words" makes the claim that this sentence has five words. It doesn't make the claim that "this sentence has five words" has five words.

Otherwise, the sentence "this sentence has fifty words" would be making the claim that "this sentence has fifty words" has fifty words.

"This sentence has five words" is the sentence in question. It is true if and only if "This sentence has five words" has five words. — TonesInDeepFreeze

Problematic.

I agree that
1) "snow is white" is true IFF snow is white
2) "New York is in France" is true IFF New York is in France
3) "This sentence has five words" is true IFF this sentence has five words

The meanings of 1) and 2) are straightforward.
The problem with 3) is what exactly are "this sentence" and (this sentence) referring to?
For clarity, using brackets to indicate the world

For example, in a non-self-referential case, "this sentence" could be referring to the sentence "New York is in France", and (this sentence) could be referring to (New York is in France).
The non self-referential case is meaningful.

However, in a self-referential case, "this sentence" could be referring to the sentence "this sentence has five words", and (this sentence) could be referring to (this sentence has five words).
The self-referential case is meaningless.

The problem with the self-referential case, is that the content of a sentence contains no information about the form of the sentence.

The content of the sentence "this sentence has five words" is that "this sentence has five words". The form of the sentence "this sentence has five words" is that the sentence "this sentence has five words" has five words.

The content of a sentence can say nothing about the form of the sentence. It cannot self-refer.

As the sentence "New York is in France" says nothing about how many words are in the sentence "New York is in Paris, the sentence "this sentence has five words" says nothing about how many words are in the sentence "this sentence has five words"

I agree when you say:

"New York is in France" makes no mention of the number of words in "New York is in France". — TonesInDeepFreeze

From the same logic, "this sentence has five words" makes no mention of the number of words in "this sentence has five words". It makes no mention of the fact that "this sentence has five words" has five words.

Any similarity in expression is purely accidental. Content cannot refer to its own form.

"This sentence has five words" is the sentence in question. It is true if and only if "This sentence has five words" has five words. — TonesInDeepFreeze

Tackling your points one by one.

1) "This sentence has five words" is true IFF "this sentence has five words" has five words.

If this were the case, then it would follow that:

"New York is in France" is true IFF "New York is in France" has five words.

So, the purpose of this thread is to submit memes, not to learn how to use 'postimages.org' — javi2541997

[img]http://

Almost. I fixed it for you. — Jamal

:100:

Gifs as well. A Pandora's box has been opened. :smile:

You think Mark Twain was someone other Samuel Clemens? — TonesInDeepFreeze

My problem is:

That baby was named "Samuel Langhorne Clemens" and was Samuel Clemens — TonesInDeepFreeze

Sense and reference
"Mark Twain" and "Samuel Clemens" both refer to the same thing in the world, although the names have a different senses, in that "Mark Twain" was an author whereas "Samuel Clemens" wasn't.

As regards reference, "Mark Twain" and "Samuel Clemens" are both referring to the same thing in the world. Let this something be both Mark Twain and Samuel Clemens. In this event, Mark Twain is Samuel Clemens.

As regards sense, "Mark Twain" is referring to something in the world that is an author. Let this be Mark Twain. "Samuel Clemens " is referring to something in the world that isn't an author. Let this be Samuel Clemens. In this event, Mark Twain cannot be Samuel Clemens, as Mark Twain is an author and Samuel Clemens isn't

Then what would it mean to say that Mark Twain is Samuel Clemens?

It would mean that names in language, such as "Mark Twain" have no sense, which would preclude any thoughts about him being an author and essayist, the father of American Literature and the greatest humourist the United States had produced.

Logical contradictions

That "Samuel Clemens" is Samuel Clemens would give rise to logical contradictions.

My assumption is, as with the expression "snow is white" is true IFF snow is white, that words in quotation marks refer to something in language and words not in quotation marks refer to something in the world.

I agree that "Samuel Clemens" born in Hannibal 1835 is "Mark Twain" who wrote "Roughing It" in 1872.

To say that when something in the world is named "Samuel Clemens" then that something in the world becomes Samuel Clemens leads to problems of logic.

1) If person A, born in Hannibal, is named "Samuel Clemens" then that person becomes Samuel Clemens. If person B, born in New York is also named "Samuel Clemens" than that person also becomes Samuel Clemens. In logic, the law of identity states that each thing is identical with itself, in this case, that Samuel Clemens is Samuel Clemens. But this means that person A born in Hannibal is person B born in New York. Something is wrong.

2) A group of Modernists name a painting "good", meaning that the painting is good. A group of Post-Modernists name the same painting "bad", meaning that the same painting is bad. But this means that good is bad, which breaks logic.

3) Someone sees something and names it "a cat", and someone else sees the same thing and names it "a dog", this means that a cat is a dog, which is not logical.

4) There is something in Paris. It has been named "a tower" meaning that it is a tower. It has been named "an eyesore" meaning that it is an eyesore. It has also been named "beautiful", meaning that it is beautiful. Therefore the same thing is both an eyesore and beautiful. But this gives rise to a logical contradiction, as something that is an eyesore cannot be beautiful.

One could argue that whether something in the world is an eyesore or beautiful depends on the particular observer. Exactly. "Eyesores" and "beauty" exist in the mind of the observer, not the world.

Similarly, "Mark Twain" and "Samuel Clemens" exist in the mind not the world. If there were no minds, then neither "Mark Twain" nor "Samuel Clemens" would exist.

A name cannot determine what exists in the world, because if a name did determine what exists in the world, then logical contradictions would arise.

"This string has five words" was named "The Pentastring", and "This string has five words" is the Pentastring. — TonesInDeepFreeze

My assumption is, as with the expression "snow is white" is true IFF snow is white, that words in quotation marks refer to something in language and words not in quotation marks refer to something in the world.

No problem that "this string has five words" was named "the Pentastring"

I agree when you say:

"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

Then how can "this string has five words" be the Pentastring?

In the expression "this sentence has five words", which sentence is "this" referring to?
Possibility 2
It could be referring to itself. In this case, the sentence "this sentence has five words" means that the expression "this sentence" has five words. Of course it's false, but per your reasoning it appears meaningful. — EricH

As I see it, in the self-referential case, where "this sentence" is referring to itself, this means that "this sentence" is referring to "this sentence".

Being self-referential, "this sentence" it is not referring to anything outside itself, which includes any words that happen to follow it, whether they are "has five words" or "is false". In fact, the expression could equally be "this sentence is on top of the mountain", "this sentence is extremely confusing" or "this sentence a b c", where a, b and c could be any words at all

Being self-referential, there is no semantic connection between "this sentence" and "a b c".

It initially seems that "this sentence", "the house" and "three mountains" are all meaningful parts of language. This is certainly the case when "the house" is referring to the house next to the river, and "three mountains" is referring to the Alps in Italy. But in the special case of self-reference where "this sentence" is referring to itself, "this sentence" may appear to be a part of language but in fact isn't. "This sentence" is just shapes on the screen.

In the self-referential case, that we see cognize a meaning in "this sentence" is accidental, in the same way that we see shapes in clouds or faces on Mars.

[img]http://

In the self-referential case, as "this sentence" is not a meaningful part of language, but just accidental shapes on the screen, it has no linguistic meaning.

You said previously that "This sentence has five words" is true. Do you still hold that position. Yes or no? — EricH

I agree that I could have been clearer in my reply.

My assumption is that if a set of words is in quotation marks, such as - "snow is white" -
then this means it is an expression in language, and if a set of words is not in quotation marks, such as - snow is white - then this is about something that exists in the world.

"Snow is white" is true IFF snow is white

Looking back, on page 2, the question was about the truth of the words - this sentence has five words.

The question was not about the truth of the words - "this sentence has five words".

As regards "this sentence has five words", it all depends on what "this sentence" is referring to. If it is self-referential, then it is meaningless, but if it is not self-referential and refers to something outside itself, then it is meaningful.

As regards - this sentence has five words - because not being in quotation marks, I took them as being something that exists in the world, such as on a computer screen.

I agree that something that exists in the world cannot be said to be either true or false, in that a mountain cannot be said to be either true or false, although it is true that the words - this sentence has five words - exist on the screen, otherwise I wouldn't be able to see them.

Whether "this sentence has five words" (which exists in language) is true or not depends on what "this sentence" refers to. The set of words - this sentence has five words - (which I take to exist in the world) cannot be said to be either true or false, although it is true that they exist in the world.

"Mark Twain" is a name for the person Samuel Clemens. — TonesInDeepFreeze

Function of quotation marks
My assumption has been that because "Mark Twain" is in quotation marks, this means that "Mark Twain" is an expression in language, and because Samuel Clemens is not in quotation marks, this means that Samuel Clemens is a person who exists in the world.

"Snow is white" is true IFF snow is white.

Mark Twain is Samuel Clemens. — TonesInDeepFreeze

Open to doubt.

The word "is" can have different meanings
In the predicate sense, "the apple is red"
In the identity sense, "the apple is a fruit"
In the existential sense, "there is an apple on the table"

Do apples exist in the world
It is said that "an apple" is the name in language of an apple in the world.
But do apples exist in the world?
There is something in the world that has been named "an apple"
For convenience, we say that in the world are apples, but this is shorthand for what we really mean, which is that there is something in the world that has been named "an apple"
In fact, as an Indirect Realist, I don't believe that apples exist in the world, but only exist in the mind as a concept.

Do Mark Twain and Samuel Clemens exist in the world?
I agree that "Mark Twain" is a name of something X in the world. Something X is referred to by the name "Mark Twain". I agree that "Samuel Clemens" is a name of the same something X in the world. The same something X is also referred to by the name "Samuel Clemens".

The question is, is this something X in the world Samuel Clemens, or has the something X in the world been named "Samuel Clemens"?

As naming something in the world "a cat" doesn't make that something a cat, in that I could name a horse "a cat", naming something in the world "Samuel Clemens" doesn't make that something Samuel Clemens.

My naming that tall tower in Paris in the 7th Arr of Champs de Mars "a kangaroo" doesn't make that something in the world a kangaroo.

Giving something in the world a name doesn't make that something into what has been named.

Just because something in the world has been named "Samuel Clemens", that doesn't mean that Samuel Clemens exists in the world. Just because something in the world has been named "Mark Twain", that doesn't mean that Mark Twain exists in the world.

Although "Samuel Clemens" and "Mark Twain" exist in language, as neither Samuel Clemens nor Mark Twain exist in the world, then it is not correct to to say that Mark Twain is Samuel Clemens.

"The Pentastring" is a name for the expression "This string has five words". — TonesInDeepFreeze

No problem, setting aside what "this string has five words" means, and treating it as a set of words such as "a b c d e", and ignoring any meaning that it may or may not have.

The Pentastring is "This string has words". — TonesInDeepFreeze

Open to doubt.

As before, my assumption has been that because "This string has five words" is in quotation marks, this means that "This string has five words" is an expression in language, and because the Pentastring is not in quotation marks, this means that the Pentastring is something that exists in the world.

The problem is, you are not saying that "this string has five words" is the name of the Pentastring, you are saying that "this string of five words" is the Pentastring.

If A is B then B is A. If "this string has five words" is the Pentastring, then the Pentastring is "this string has five words".

How can an expression in language be something in the world?

How can "London" be a city?

This is not a side issue, as crucial to your argument that a self-referencing expression can be meaningful.

When I first introduced the term "The Pentastring", I used it as a name not an adjective. — TonesInDeepFreeze

("The Pentastring" is a name for the expression "This string has five words".) — TonesInDeepFreeze

"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

OK so far.

I said that The Pentastring is "This string has five words". — TonesInDeepFreeze

This is critical to your argument, but this is where I get lost.

As we're not going to agree, I'm moving on.

Going back to your 3 possibilities, this is the form of your Possibility 3. So as I read this, you consider "This sentence has five words" to be true under your Possibility 3. Am I getting this right? — EricH

I see words on my screen, which happen to be the words - this - sentence - has - five - words.

I recognize a meaning in these words as 1) "this sentence has five words".

In addition, I have the thought that this sentence, ie the words on my screen, has five words, and say 2) "this sentence has five words".

It is a coincidence that 2) happens to be the same as 1).

1) has not determined 2).

This is not Possibility 3, as "this sentence" in 2) is referring to something outside itself, to something that physically exists in the word, ie, the words - this - sentence - has - five - words.

This is not a case of self-reference, as "this sentence" is neither referring to itself (possibility 2) nor to the sentence of which it is a part (possibility 3.)

"This sentence" in 2) is referring to something that exists outside itself.

As I understand it, an expression in language can only have a meaning if it refers to something outside itself.

For example "cat" in language has a meaning because it refers to a cat in the world.

Also, "cat" in language has a meaning because it can be defined as "a carnivorous mammal long domesticated as a pet and for catching rats and mice"

In both of these examples, the word "cat" has a meaning because it refers to something outside itself.

If I said "this sentence" is "this sentence". this would be meaningless.

If I said "this sentence has five words" is "this sentence has five words", this would also be meaningless.

As possibilities two and three are about the instances where an expression in language is self-referential, it would follow such self-referential expressions cannot have any meaning.

But are there any examples in language where a linguistic expression that refers to itself has a meaning?

To isolate the key point: — TonesInDeepFreeze

As you say, this is a key point, on which your other points depend.

1) "The Pentastring" exists in language, such that "The Pentastring is a string of five words". 2) The Pentastring exists in the world, such that the Pentastring is a string of five words.

As regards usage, as more than one Pentastring exists in the world, the expression "The Pentastring" is not referring to one particular Pentastring, but is being used to refer to a general class of objects.

On the other hand, as only one Eiffel Tower exists in the world, the expression "the Eiffel Tower" is referring to one particular Eiffel Tower, and not to a general class of objects.
===============================================================================

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

A Stanford article writes that the mass-energy equation, E = mc2, is one of the fundamental principles in physics, revealing that mass and energy are equivalent.

I would have thought that the formula E=MC^2 shouldn't be in quotation marks. For example, science is culturally important, and "science" has seven letters. Similarly, E=MC^2 is famous, and "E=MC^2" has six characters.
===============================================================================

The expression "The Pentastring" refers to the expression "This string has five words". — TonesInDeepFreeze

We agree that the Pentastring is a string of five words, but as there are many Pentastrings in the world, to say "The Pentastring is this string of five words" would be grammatically incorrect. It would be more grammatically correct to say either "this Pentastring is this string of five words" or "the Pentastring is a string of five words".

Otherwise, I would agree that the expression "The Pentastring" refers to the expression "a string of five words"
===============================================================================

The Pentastring is "This string has five words." — TonesInDeepFreeze

This is grammatically incorrect, as an object in the world is not an expression in language.

I agree when you wrote - "London" is a city. (false - "London" is a word, not a city).

"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

As a city is not "London", a Pentastring is not "this string has five words"

Notice that there you left out that the Pentastring is "This string has five words". — TonesInDeepFreeze

This conflicts with what you wrote on page 7.

"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

"This string has five words" is an expression, whilst the Pentastring is something that exists in the world.

The Pentastring is a string of five words - OK
This Pentastring is this string of five words - OK
"The Pentastring is a string of five words" - OK
"This Pentastring is this string of five words" - OK

The Pentastring is this string of five words - not OK
This Pentastring is the string of five words - not OK
"The Pentastring is this string of five words" - not OK
"This Pentastring is the string of five words" - not OK

Possibility two
It could be referring to itself. In this case, the sentence "this sentence is false" "this sentence has five words" means that the expression "this sentence"is false has five words. But this is meaningless, and is similar to saying "this house" is false.. This is meaningful but false ("this sentence" has two words.).........................So AFAICT the Pentastring is meaningful in all 3 of your possibilities. Yes this is a minor point, but I wanted to clear it up. — EricH

An expression that refers to itself can never have a meaning

An expression can only have a meaning if it refers to something outside itself.

We are given the expression "this sentence has five words", and are told that the expression "this sentence" refers to itself'.

I agree that the expressions "tall house", "grey cat", "that mountain" and "this sentence" have two words.

We are given the expression "this sentence has five words", yet we both agree that the expression "this sentence" has two words.

So how can the same expression have both two words and five words?

It can only be that the expression "this sentence" in the first instance of its use is not referring to the second instance of its use.

So, given the expression "this sentence has five words", where "this sentence" refers to itself, how do you get the knowledge that "this sentence" has two words?

Perhaps you were in a hurry when you responded, but I wasn't talking about the Liar Statement, I was talking about Tones' counter example "The sentence has five words." So in all 3 of your scenarios "This sentence has five words" appears to be meaningful. — EricH

I think that the sentences "this sentence has five words" and "this sentence is false"
can be treated in a similar way.

For both sentences, the question is, what does "this sentence" refer to?

Possibility one
It could be referring to the sentence "this cat is grey". In this case the sentence "this sentence has five words" means that the sentence "this cat is grey" has five words, which is meaningful, even if false.

Possibility two
It could be referring to itself. The sentence "the cat is grey" has a meaning because "the cat" is referring to something outside itself, ie a cat. However, if "this sentence" is referring to itself, the sentence "this sentence has five words" has no meaning, because "this sentence" is not referring to anything outside itself.

Possibility three
It could be referring to the sentence it is a part of, ie, "this sentence has five words". In this case, the sentence "this sentence has five words" means that the sentence "this sentence has five words has five words". But again, any meaning disappears.

Dependent on what "this sentence" is referring to, the sentence "this sentence has five words" may or may not be meaningless.
===============================================================================

Now if I'm following from your last reply to Tones you seem to be acknowledging this - but you are claiming that because "This sentence has five words" asserts a situation in the real world then it is no longer self referential. Am I following you correctly? — EricH

I think I am right in saying that @TonesInDeepFreeze wrote that he believed that there seems to be a self-referential sentence that is not meaningless, and gave the Pentastring example.

@TonesInDeepFreeze wrote on page 5:
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.

The sentence "the Pentastring has five words" is not self-referential, because we have been explicitly told that the Pentastring exists in the world, ie we have a subject from the world, viz. the Pentastring.

A self-referential expression cannot refer to something existing in the world.

If you skip my main argument, then we won't get anywhere. — TonesInDeepFreeze

I will set outside some of your other points for the moment, and try to get to the heart of the matter. Otherwise if you make five points, and I respond to each of your points with my own five points, and you then respond to each of my points with your own five points, this thread will end up longer than War and Peace.

I wrote that my belief is that self-referring expressions are meaningless. You wrote that your belief is that some self-referring expressions can be meaningful, and give the Pentastring example

I hope that I am not missing out anything crucial from your Pentastring argument.

The Pentastring argument is not a case of self-reference, as it is referring to something that exists in the world.

At least at first blush, "The string has five words" seems syntactic. A noun phrase, "This string" followed by a predicate, "has five words". — TonesInDeepFreeze

Agree, though it depends what "this" is referring to.

So you need to demonstrate that it is meaningless. But meanwhile, perhaps see if there is an error in the reasoning I gave for why we may take it to be meaningful. That reasoning could be wrong, but if it is, then I'd be interested to know how. — TonesInDeepFreeze

The sentence "this sentence is false" is not necessarily meaningless. The sentence is meaningful if the word "this" refers to the sentence "the cat is grey", for example.

"This string has five words" asserts that "This string has five words" has five words. That seems meaningful. — TonesInDeepFreeze

Why? If it did, then "this string has ten words" would assert that "this string has ten words" has ten words.

So it seems "This string has five words" is a sentence as it fulfills the two requirements: syntactical and meaningful. — TonesInDeepFreeze

Not necessarily. It depends what "this string" refers to. If it refers to either "this string" or "this string has five words", then it is self-referential and meaningless.

And "This string has five words" is true if "This string has five words" has five words, which it does; so "This string has five words" seems to be true. So, "This string has five words" seems to be true sentence. — TonesInDeepFreeze

Then it would follow that "the cat is grey" is true if "the cat is grey" has four words. That the sentence "the cat is grey" has four words doesn't make it true that the cat is grey.

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

No problem, let's define 'the Pentastring' as the "This string has five words". This sounds very similar to defining 'Big Ben' as "the bell inside the clock tower".

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

That we define 'a unicorn' as "a mythical, usually white animal generally depicted with the body and head of a horse........................" doesn't necessarily mean that unicorns exist in the world. But let us suppose that the Pentastring exists in the world alongside Big Ben.

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

But we know that "the Pentastring" has been defined as "This string has five words".
Therefore "The Pentastring has five words" means that "this string has five words has five words". But this doesn't seem grammatical, and if not grammatical, then meaningless

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

Suppose the Pentastring exists in the world, alongside the Big Ben. As objects existing in the world, such as Big Ben and the Pentastring have no truth value,they can be neither true not false. The sentence "the Pentastring has five words" has five words. It is not the Pentastring that has five words.

In "This string has five words", 'this string' refers to the Pentastring, which is in the world. — TonesInDeepFreeze

No problem. In the world exists the physical objects Big Ben, being a bell inside a clock tower, and a Pentastring, being a string of five adjacent words.

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. — TonesInDeepFreeze

We know that 'the Pentastring' has been defined as "This string has five words".

Therefore, the sentence "The Pentastring has five words" means that "this string has five words has five words"

Therefore, it is not the case that "This string has five words" is equivalent with "The string has five words has five words"

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

This is not an example of self-reference. A Pentastring is a string of five adjacent words existing in the world.

As "the cat" in the sentence "the cat is grey" is referring to the cat existing in the world, "the pentastring" in the sentence "the Pentastring has five words" is referring to the Pentastring existing in the world.

As the sentence "the cat is grey" is not an example of self-reference, then neither is the sentence "the Pentastring has five words"

which is to determine whether "This string has five words" has five words. — TonesInDeepFreeze

It is true that the sentence "this string has five words" has five words. It is also true that the sentence "the cat is grey" has four words.

The fact that the sentence "the cat is grey" has four words is irrelevant to whether the cat is grey. Similarly, the fact that the sentence "this string has five words" has five words is irrelevant to whether this string 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". — TonesInDeepFreeze

The sentence "the cat is grey" is true if the cat is grey. Similarly, the sentence "this string has five words" is true if this string has five words.

As a Pentastring is a string of five words, we can also say that the sentence "this string has five words" is true if this is a Pentastring.

But then again, this is not a case of self-reference, as "this string" is referring to something that exists in the world.

If I'm following this, you stated that all self referential statements are meaningless. Tones disagrees with that and offers the counter example "This sentence has five words". I could be mistaken (happens on a regular basis) but it seems that this is meaningful under all three of your possibilities. — EricH

It depends what the word "this" in the expression "this sentence is false" is referring to.

If it is referring, for example, to the sentence "this cat is grey", then the expression "this sentence is false" means that the sentence "this cat is grey" is false, which is meaningful.

But if it is referring to itself, then the expression "this sentence is false" means that the expression "this sentence" is false, which is like saying "this house" is false.

Surely in this instance, isn't it the case that both "this sentence" is false and "this house" is false are meaningless?

"London" has six letters. The word is spoken about. London is populous. The word is used to refer to the city not to the word. It should be easy to see: London is a city. (true).................."London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

The use-mention distinction

(Note, using brackets to try to make the expression clearer)

I agree that the expression ("London" has six letters) is an example of mention, in that the linguistic expression "London" is being spoken about. In this case that it has six letters.

I agree that the expression (London is a city) is an example of use, in that the linguistic expression "London" is being used to refer to something else, in this case a city.

I agree that expression ("London" is a city) is ungrammatical.

However, in the expression ("London" is "a city"), as the linguistic expression "London" is being spoken about, this is also an example of mention. In this case that it is "a city". Note that "a city" is just a set of words, and is not referring to anything that may or may not exist in the world.

Another example of meaning would be ("Big Ben" is "the bell inside the clock tower"), as the linguistic expression "Big Ben" is being spoken about. In this case that it is "the bell inside the clock tower". Note that "the bell inside the clock tower" is just a set of words, and is not referring to anything that may or may not exist in the world.

Norman Swatz in his article Use and Mention explains that dictionary definitions are examples of meaning.

The use/mention distinction (as it has come to be called) is of particular relevance in the theory of definitions. For when we give the definition of a term, we mention the term, we do not use it. For example, the term, "pain", is defined, but pain itself is not defined. We define only terms, never their referents.

As @Treatid correctly points out: 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.

In the Merriam Webster dictionary, "London" is defined as "a city and port on both sides of the Thames River in southeastern England............"

"Big Ben" is defined as "a large bell in the clock tower..............."

We use the dictionary to find out the meanings of words.

A word is defined by reference to another word, which is defined by reference to another word. Definitions never ground a word in the world. As Wittgenstein pointed out, there is a difference between a word being "said" as in a dictionary and a word being "shown" as in picturing something in the world.

The expression ("London" has six letters) is an example of mention, as the linguistic expression "London" is being spoken about, in that it has six letters.

Similarly, the expression ("London" is "a city") is also an example of mention, as the linguistic expression "London" is also being spoken about, in that it is "a city".
===============================================================================

The video that was mentioned argues erroneously by conflating "refers to" with "equals". — TonesInDeepFreeze

The Liar Paradox

That the paradoxical expression "this sentence is false" is meaningless doesn't depend on the word "equals". The argument in the video is about meaning.

I will repeat the argument, as this answers the OP.

In the expression "this sentence is false", which sentence is "this" referring to?

There are several possibilities.

Possibility one

It could be referring to the sentence "the cat is grey". In this case, the sentence "this sentence is false" means that the sentence "this cat is grey" is false, which is meaningful.

Possibility two
It could be referring to itself. In this case, the sentence "this sentence is false" means that the expression "this sentence" is false. But this is meaningless, and is similar to saying "this house" is false.

Possibility three
It could be referring to the sentence "this sentence is false". In this 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

Ad infinitum. Therefore meaningless.

I would say just mention not "mention" — TonesInDeepFreeze

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.

"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". — TonesInDeepFreeze

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"
===============================================================================

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

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. — TonesInDeepFreeze

That is also not a sentence — Lionino

Again true. I've edited my post. Hopefully it works this time.

That is not a sentence though. — Lionino

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