At least you have middle age to look forward to. — RussellA

I would look forward to it everyday if I had dementia.

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.
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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.

"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.

"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?

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? — RussellA

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.

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"

All I'm trying to say is that an expression that self-refers cannot be grounded in the world — RussellA

Yes it can.

The self-referential sentence "this sentence contains five words" is true because it contains five words.

The self-referential sentence "this sentence contains fifty words" is false because it doesn't contain fifty words.

This is incredibly straightforward.

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.

Similarly, it is not correct to say that the sentence "this sentence contains five words" is true because it contains five words. — RussellA

Yes it is.

it is not correct to say that the sentence "this sentence contains five words" is true because it contains five words. — RussellA

"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. — RussellA

This sentence has five words. Not true? — TonesInDeepFreeze
Yes, true. — RussellA

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

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

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?

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

In context we do know.

If I hold out an apple and say "this apple is red" then it's obvious that I'm referring to the apple in my hand and not the apple on the table behind me, and so what I say is true iff the apple in my hand is red.

If you want to be explicit, then:

The self-referential sentence "this sentence contains five words" is true.
The self-referential sentence "this sentence contains fifty words" is false.

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 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.

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.

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

Just to repeat:

"this sentence contains five words" is true IFF this sentence contains five words — RussellA

This sentence has five words. Not true? — TonesInDeepFreeze
Yes, true. — RussellA — EricH

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

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.

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.

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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.

Barbers cannot shave themselves.

I maintain that barbers are people who shave people who are in the world.

If they must be shaved, the barbers must visit other barbers. Shaving involves a correspondence between an ideal of cleanliness and the state of affairs on an actual face. Therefore, if a barber tries to shave himself, there is an inherent contradiction.

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I hope this is clear?

I maintain that barbers are people who shave people who are in the world.......................Therefore, if a barber tries to shave himself, there is an inherent contradiction. — bongo fury

Makes sense to me. I've never understood any validity in the barber paradox.

The expression ‘secondary employment’, also commonly referred to as ‘double jobbing’, simply describes a situation where an employee takes on a second job.

During the day, someone works as an engineer in an engineering works. In order to pay their rent, during the evening they work in a cafe as a barista.

No one would call someone who serves you coffee an engineer.

No one would call someone welding machinery a barista.

As you say, being a barber is what someone does, not what they are.

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. — RussellA

It’s meaningful even when it’s referring to itself.

It’s meaningful even when it’s referring to itself. — Michael

From Wikipedia -Meaning (Philosophy)

In philosophy—more specifically, in its sub-fields semantics, semiotics, philosophy of language, metaphysics, and metasemantics—meaning "is a relationship between two sorts of things: signs and the kinds of things they intend, express, or signify".

If "this sentence contains five words" is referring to itself, then "this sentence contains five words" means that "this sentence contains five words".

In other words, "X" means "X".

In logic, the law of identity states that each thing is identical with itself.

I agree that "X" means "X", but how can "X" be described as a meaningful sentence?

What are you talking about?

It’s really simple; the self-referential sentence “this sentence contains five words” is meaningful. I understand what it means, you understand what it means, and everyone else understands what it means. It’s not some foreign language or random combination of words. And we can count the words in the sentence to determine that it’s true.

You’re trying to create a problem where there is none.

It’s really simple; the self-referential sentence “this sentence contains five words” is meaningful. I understand what it means, you understand what it means, and everyone else understands what it means. It’s not some foreign language or random combination of words. And we can count the words in the sentence to determine that it’s true. — Michael

Question: how do you avoid the problem of infinite recursion in a self-referential sentence?

"This sentence contains five words".

Non self-referential case
Let "this sentence" refer to the sentence "this sentence contains five words"

Then, "this sentence, the sentence "this sentence contains five words", contains five words". This is meaningful.

Note that the sentence "this sentence contains five words" is not the same sentence as "this sentence contains five words", even though the wording is identical. These are two completely different sentences.

Note that the truth of the sentence "this sentence contains five words" is independent of the truth of the sentence "this sentence contains five words".

Self-referential case
In the self-referential case, "this sentence, the sentence "this sentence contains five words", contains five words".
But we know that this sentence is the sentence "this sentence contains five words".
Therefore, "this sentence, the sentence "the sentence "this sentence contains five words" contains five words", contains five words".
Ad infinitum. Infinite recursion. Therefore meaningless.

Note that in the self-referential case, the sentence "this sentence contains five words" is the same sentence.

There is no problem. The self-referential sentence "this sentence contains five words" is both meaningful and true. The self-referential sentence "this sentence contains fifty words" is both meaningful and false. It's that simple.

Barbers cannot shave themselves.

I maintain that barbers are people who shave people who are in the world.

If they must be shaved, the barbers must visit other barbers. Shaving involves a correspondence between an ideal of cleanliness and the state of affairs on an actual face. Therefore, if a barber tries to shave himself, there is an inherent contradiction. — bongo fury

Is that a joke? To shave is to cut hair from the skin. There is no requirement of an ideal of cleanliness or that a face is involved.

A barber is someone who is in the business of cutting hair and shaving. There is no contradiction that a barber shaves himself of herself; surely some barbers do.

Moreover, the barber paradox is merely an illustration. The relation of 'x shaves y' could be any 2-place relation R:

(1) There is an x such that for all y, Rxy if and only if it is not the case that Ryy.

And (1) is logically false.

I maintain that barbers are people who shave people who are in the world.......................Therefore, if a barber tries to shave himself, there is an inherent contradiction. — bongo fury

Makes sense to me. I've never understood any validity in the barber paradox. — RussellA

The barber sentence is not just invalid, it is logically false.

The expression ‘secondary employment’, also commonly referred to as ‘double jobbing’, simply describes a situation where an employee takes on a second job.

During the day, someone works as an engineer in an engineering works. In order to pay their rent, during the evening they work in a cafe as a barista.

No one would call someone who serves you coffee an engineer.

No one would call someone welding machinery a barista.

As you say, being a barber is what someone does, not what they are. — RussellA

Wow! How can someone so ignorantly miss the point!

The barber paradox doesn't at all rely on claiming that someone is a barber. Mentioning someone who is a barber is merely incidental and does not at all bear upon the logic.

We could just as well not use the word 'barber' or even 'person':

There is an x such that for all y, x shaves y if and only if y does not shave y.

For that matter, we don't need 'shave', which is merely illustrative:

For any 2-place relation R:

(1) There is an x such that for all y, Rxy if and only if it is not the case that Ryy.

And (1) is logically false.

Wow. RussellA has such strong opinions on the subject but doesn't know what the subject even is.

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. — RussellA

Why did it take 9 pages.

Why has it taken nine pages for RussellA still to still stick with his refuted arguments for his claim:

"If "this sentence" is referring to "this sentence contains fifty words", it has no truth-value and is meaningless."

The answer is psychological.

He's correct, as far as I can tell and am concerned at this stage. It is not a paradox.

He's been refuted at every point in every detail.

"This sentence has fifty words" does not seem to be a paradox.

That's not what has been at issue.

Rather at issue has been whether sentences such as "This sentence has fifty words" are meaningful.