"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"

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.
===============================================================================

The use-mention distinction — TonesInDeepFreeze

As regards use, Big Ben is the bell inside the clock tower.
As regards mention, "Big Ben" is "the bell inside the clock tower"
===============================================================================

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

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.

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. — TonesInDeepFreeze

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.

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

Agree
===============================================================================

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.

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.

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".

"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.

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". — TonesInDeepFreeze

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. — TonesInDeepFreeze

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.

'This string has five words' Is that a sentence? — TonesInDeepFreeze

On my screen I see the set of words "This string has five words".

What is a sentence? Is the meaningless set of words "colourless green ideas sleep furiously" a sentence? According to the Merriam Webster Dictionary, a sentence is a group of words that expresses a complete thought and has a subject and a verb. I would therefore suggest that a meaningless set of words cannot be classed as a sentence.

I am making use of Steve Patterson's video "How to Resolve the Liar's Paradox"

The question is, is the set of words "This string has five words" a sentence or not.

The problem is in knowing what "this string" refers to.

Possibility 1) If "this string" is referring to a string of characters existing in the world, such as the characters on my keyboard, then the set of words "This string has five words" is meaningful, is a sentence, has a truth-value and can be either true or false.

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.

Possibility 3) If "this string" is referring to "This string has five words", then the expression "this string" can be replaced by "this string has five words".
We then get: ((this string has five words) has five words).
Continuing, we get: (((this string has five words) has five words) has five words).
But as this will go on ad infinitum, meaning that the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.

Whether the set of words "this string has five words" is a sentence or not depends on what "this string" is referring to.
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"This string has five words" asserts that "This string has five words" has five words. That seems meaningful. — TonesInDeepFreeze

If "This string has five words" did assert that "This string has five words" has five words
then "This string has ten words" would be asserting that "This string has ten words" has ten words, which is not the case.

Therefore, "This string has five words" cannot be asserting that "This string has five words" has five words.
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"This string has five words".................'has five words' corresponds with the property of a string having five words, which is something that I observe some strings to have. — TonesInDeepFreeze

I see on my screen the set of words "this string has five words", and I see that there are five words in this set of words.

I see on my screen the set of words "this string has ten words", and I see that there are five words in this set of words.

I see on my screen the set of words "Diese Zeichenfolge besteht aus fünf Wörtern", and I see that there are six words in this set of words.

I go into a shop and buy five apples and notice that the time is exactly five pm. There is no logical link between the fact that I bought five apples and the fact that the time is five pm. That both involve the number five is accidental.

Similarly, that the content of the set of words "this string has five words" and the form of the set of words involves five is also accidental.

There is a lot to work through in your post, and to do justice to the points you have made, I am working through them one by one.
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But is it the case that all self-referential sentences are meaningless? — TonesInDeepFreeze

There are sets of words, such as "colourless green ideas sleep furiously", that are meaningless, yet are not self-referential.

If I am correct in my belief that any set of words that is self-referential must be meaningless, then this set of words shouldn't be called a "sentence", as a sentence is a syntactic unit in language that does have a meaning.

From the Merriam Webster definition of "sentence"

a word, clause, or phrase or a group of clauses or phrases forming a syntactic unit which expresses an assertion, a question, a command, a wish, an exclamation, or the performance of an action, that in writing usually begins with a capital letter and concludes with appropriate end punctuation, and that in speaking is distinguished by characteristic patterns of stress, pitch, and pauses

The expression "self-referential sentence" is itself a paradoxical contradiction, in that if a set of words is self-referential then it cannot have meaning, and if cannot have meaning then cannot be a sentence.
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"This sentence has five words" has five words. The meaning of the sentence is that the predicate (has five words) holds for the subject ("This sentence has five words"); and its truth value is 'true'. — TonesInDeepFreeze

Difference between form and content
Suppose there are marks on a screen. The screen is in the world. Both an Italian speaker and English speaker in looking at these marks observe the same form, that of five distinct marks, but only the English speaker knows that the marks are words and the content of these words is "this sentence has ten words".

The content of these marks, that there are ten marks, is independent of the form of these marks, that there are five marks.

This means that the form of the words cannot be determined from the content of the words

The sentences "this sentence has ten words", "this sentence has five words" and "this sentence has fifty words" all have different contents, but are all five words.

The number of words in a sentence cannot be determined from the content of that sentence. IE, the content of a sentence does not refer to the form of that sentence.

The form of these marks exists in the world, whilst the content of these marks only exists in the mind of a sentient observer.

The sentence ""This sentence has five words" has five words" is ungrammatical, and therefore without truth-value.
On the screen I see the sentence "this sentence has ten words"

I can then write on the same screen "the sentence "this sentence has ten words" has five words"

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

The predicate "has five words" is not referring to "this sentence has ten words".

The sentence "the sentence "this sentence has ten words" has five words" has the truth-value of being true.

The sentence ""this sentence has ten words" has five words" is ungrammatical, and therefore meaningless, and therefore without any truth-value.
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It's not the case that in general self-reference using the pronoun 'this' is meaningless: "This Guy's In Love With You" — TonesInDeepFreeze

I agree that there is nothing ungrammatical about the sentences "this sentence has five words" and "this guy is in love with you".

However, as the pronoun "this" is external to both "the sentence" and "the guy", the pronoun isn't being self-referential.

The problem arises when the sentence is being self-referential, in the event that "this sentence has five words" is referring to itself and "this guy is in love with you" is referring to itself.
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It's not the case that a sentence referencing a sentence is meaningless: — TonesInDeepFreeze

True. The sentence "the sentence "this sentence has ten words" has five words" has the truth value of being true.
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So, why would "This sentence has five words" be meaningless? — TonesInDeepFreeze

It depends what "this sentence" refers to. If it refers to the sentence "this sentence has five words", then it has a truth-value, but if it refers to "this sentence has five words", then it has no truth-value.
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It would help to have an explanation of what you mean by 'the world'. — TonesInDeepFreeze

As an Indirect Realist, I perceive things through my five senses. My belief is that these perceptions have been caused by something outside me, and this something outside me I call "the world".
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it seems your argument should allow that sentences are in "the world". I surmise you would agree — TonesInDeepFreeze

I agree that marks exist in the world, but only a sentient being can attach a meaning to these marks. Only a sentient being knows when a set of marks is a part of a language. Only a sentient being knows when a set of marks is a sentence, meaning that sentences only exist in the mind.

Sets of marks exist in the world. Sentences exist in the mind.

There is quite a lot of stage setting that would occur to understand if such an individual had such a rule. — Richard B

True, the individual must have an extensive web of beliefs in order to believe that tomorrow the sun will rise in the east.

Referring back to the OP, all these beliefs make up a "form of life".

An individual may believe they are part of a community having a particular form of life. However, an individual can only get information about any world outside them through their five senses.

One question is, is what the individual perceives a copy of the cause of such perceptions (Direct Realism) or a representation of the cause of such perceptions (Indirect Realism).

Dependant on the answer to this question, an individuals knowledge of the form of life of a community is either a fact or a fiction.

I don't whole hog buy into your general view about language, but for the sake of argument, suppose these matters are observer dependent. May not another observer determine that it is a statement? — TonesInDeepFreeze

Yes. Every observer of a set of words interprets the same set of words differently, because it is the observer that gives the set of words meaning. It is not the "squiggles" that the observer sees on the screen that give the "squiggles" meaning.

So I don't trust that the very brief synopsis does justice to Kripke's view. — TonesInDeepFreeze

I agree, but we have to start somewhere.

Though my belief remains that the basic problem with the statement "this statement is false" is that it is not grounded in the world. In the same way, any set of words, such as the statement "a b c", is meaningless until grounded in the world.

The word "a" may be defined as "d e f"
The word "b"may be defined as "g h i"
The word "c" may be defined as "j k l"

Continuing, the word "d" may be defined as "m n o", etc

This may give us a coherent language, but will remain meaningless until sooner or later a word corresponds with something in the world.

IE, a language in order to be useful must correspond with the world in addition to being coherent. IE a useful language must be grounded in the world , which the statement "this statement is false" isn't.

Can I make a rule for myself, privately? Here "privately" means "not subject to enforcement by anything else (human or otherwise)". In other words, is it possible for the correct application of my rule to be solely determined by my application of it? In yet other words, if I make my rule and determine what is the correct application of it, is it meaningful to say that I am bound by it? — Ludwig V

An individual sees the sun rise in the east on 100 consecutive days. They become aware of the rule that the sun rises in the east, and then live by the rule that the sun rises in the east.

However, as Hume pointed out, perceived constant conjunction of events in the world may be as much accidental as a rule.

From the Wikipedia article on Constant conjunction

In An Enquiry concerning Human Understanding and A Treatise of Human Nature, Hume proposed that the origin of our knowledge of necessary connections arises out of observation of the constant conjunction of certain impressions across many instances, so that causation is merely constant conjunction—after observing the constant conjunction between two events A and B for a duration of time, we become convinced that A causes B. However, this position raises problems, as it seems that certain kinds of constant conjunction are merely accidental and cannot be equated with causation.

An individual only has knowledge about the world from what they perceive through their five senses.

If an individual lives by a rule, as Hume's principle of constant conjunction shows, they cannot have discovered it through their senses, meaning that it is a rule they must have made themselves. IE, a private rule.

If the individual has made the rule, then not only will they correctly apply it but may also decide to be bound by it.

Suppose Albert lives by himself on a desert island and Betty lives in a community of one million people. Both A and B only have knowledge about the world from what they perceive through their senses.

From before, if A lives by a rule, it must be a private rule.

Even if within the community that B lives in there are public rules, B will only know about them from what she perceives through her senses. But as before, what she perceives through her senses to be a rule may in fact be accidental, meaning that if she does live her life following a rule, she must have made it herself. IE, B also lives by private rules.

IE, if individuals live by rules, as Hume's principle of constant conjunction shows, the individual cannot have discovered them through their senses, but must have made them, and in this sense are private rules. If an individual has made the rule, then they must know how to correctly apply it. However, even if the individual has made the rule, they may or may not decide to be bound by it.

This sentence has five words. Not true? — TonesInDeepFreeze

Yes, true.

Language communicates

As not every animal is a cat, not every set of words is part of a "Language".

The Merriam Webster Dictionary describes "Language" as i) the words, their pronunciation, and the methods of combining them used and understood by a community ii) a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings iii) the means by which animals communicate

As the core feature of a "Language" is its ability to communicate, presumably a set of words that is not able to communicate is not a part of what can be called a "Language".

A computer could be programmed to collect together random words, but a set of words does not of necessity make a "Language".

The meaning of words is not fixed

As prose, the set of words "colourless green ideas sleep furiously" is a nonsensical proposition, and because it doesn't communicate any idea, cannot be considered as part of a proper language. However, the meaning of words is not fixed, and the same words could be interpreted in a poetic or metaphorical way. If that were the case, one could possibly gleam some sensible meaning out of this particular set of words.

But for the sake of this post, I am only considering a set of words as prose.

Not all expressions in Language have a truth-value

Some expressions in language can be true or false, such as the expression "the Eiffel Tower is 1,200m in height", but other expressions, such as the command "bring me a coffee" or the exclamation "ouch!" are neither true nor false.

The author of a set of words is irrelevant to the meaning of the set

I see five words on the screen in front of me, and the particular words are "this", "sentence", "has", "five" and "words". I see five crayons on my desk next to the computer screen, and the particular colours are red, green, blue, yellow and orange.

As five crayons don't of necessity make a language, five words don't of necessity make a language.

I don't know who or what has determined these five words. It could have been a person or a machine. In fact, I don't need to know as long as I can find my own meaning in the words. The observer determines any meaning in any set of words. The meaning is not determined by the words themselves. Only the observer is a conscious being. The words themselves are inanimate, neither aware of themselves not anything outside themselves.

The meaning of a set of words is determined by an outside observer of the words

That the five words on the screen include the words "this statement" is meaningless, as it is not the words that determine whether the five words forms a statement or not, but rather it is the observer who determines whether or not these five words are part of a language. The observer may in fact determine that these five words are not part of a language, in that they are not a statement.

Truth-values must be grounded in the world

Kripke proposed that a statement that refers to itself cannot have a truth-value as not grounded in the world, and only statements that are grounded in the world can have a truth value.

It is true that the set of five words on my screen are grounded in the world, as are the five crayons on my table, but as both the five words and the five crayons are inanimate, neither being conscious nor self-aware, neither the five words nor five crayons are able to refer. Only a conscious outside observer of the five words and five crayons is able to refer.

A set of words independent of any observer can never have any meaning. A set of inanimate words cannot give themselves meaning. Meaning cannot give itself meaning. Meaning is not self-referential, and as such can never give itself a truth-value.

A set of words can only have meaning when given a meaning by an outside observer, and in order for a set of words to be given meaning by an outside observer, this set of words must exist in the world.

Summary

In summary, I see a set of words on my screen. I see that there are five words, and this is true. The five words happen to be "this", "sentence", "has", "five" and "words". I, as the observer, recognize a meaning in the five words as "this sentence has five words". Words being inanimate cannot refer. Only a conscious observer outside the words can refer. In the mind of this conscious outside observer, the words "this sentence" refers to the statement "this sentence has five words", which is true.

I think the word ‘declarative’ is important; a statement declares a fact; it does not in addition instantiate that fact to a given truth value. — Devans99

Yes. I think Kripke's solution, as described in the Wikipedia article Liar Paradox, seems to be the most reasonable.

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.

A statement can only be true or false as it refers to the world. The statement "snow is white" is true IFF in the world snow is white.

As the statement "this statement is false" doesn't refer to the world, but only refers to itself, the words "this", "statement", "is" and "false" have no sense, as sense only comes from reference to the world, meaning that the statement "this statement is false" is senseless.

As the statement "colourless green ideas sleep furiously" expresses a nonsense proposition, then so does the statement "this statement is false".

As you say, a statement such as "this statement is false" may declare something without giving a truth-value to that something it has declared.

AC Grayling: "One need not take as one's target so radical a form of the thesis to show that cognitive relativism is unacceptable, however."

FORMS OF LIFE

As rules are private, a rule-based language must also be private

Suppose there is culture A with its own form of life, its own language, its own rules and its own truth and culture B with its own form of life, its own language, its own rules and its own truth.

The cognitive relativist says that because each culture has its own form of life it has its own truth, meaning that truth is relative between different cultures.

But AC Grayling argues that cognitive relativism is unacceptable, because its premise that there are different cultures each with its own form of life is an implicit acceptance of the fact that we can only recognize that cultures are different only if we understand what these differences are. If we understand these differences, then there is a common ground between different cultures, thereby negating the concept of cognitive relativism.

But cultures aren't Platonic entities, they are sets of individuals, whether one considers a single individual on a desert island or 6 billion individuals on planet Earth.

Each individual is an individual, receiving information about a world outside them through their five senses.

Knowledge is justified true belief.

The individual may have beliefs about a world existing outside them causing their perceptions, and may be able to justify their beliefs using logical reasoning, but cannot be said to have knowledge about any world existing outside them. Although the individual may be able to justify their beliefs about any outside world, they can never prove such beliefs.

For an individual, all the rules that they are aware of must be of their own invention, even if based on information received through their senses. As the tortoise said to Achilles, how can an individual discover just from the information received through their senses that a rule is a rule. Where is the rule that determines whether something is a rule or not, a problem of infinite regression.

As regards language, the individual perceives shapes, which are words, which are part of language, but as the rules of language cannot be included within the shapes themselves, the rules of language that the individual uses must have been created by the individual themselves. If language is rule-based, and these rules are private, then language must also be private, and must be a "private language".

An individual only gets information about any world outside them through their senses. There may or may not be different cultures in this world outside them. Dependent on what information the individual gets through their senses, some of these different cultures they may know about, and some they don't know about.

For those different cultures the individual is aware of, the individual creates the rules of that culture. The individual doesn't discover the rules of that culture in the information coming through their senses. As the form of life of a culture is dependent on the rules of that culture, the individual also creates the form of life of that culture. Therefore, if an individual is aware of different cultures, then not only has the individual created the rules of those cultures, but has also created the forms of life of those cultures. Of necessity, there is now common ground between these different cultures, and these cultures are not closed to each other. As Grayling says, the concept of cognitive relativism is negated. The important thing to note is that cognitive relativism is referring to the cognitive state of the individual who is aware of different cultures, not the cognitive states within these different cultures.

However, for those cultures the individual doesn't know about, the individual has no knowledge of either the rules or the forms of life of those unknown cultures. If the individual doesn't know about such cultures, they are obviously not able to recognize a different form of life. In this case, Grayling's assertion that cognitive relativism is unacceptable is clearly mistaken..

As rules are private, a rule based language and a rule based form of life must also be private. Grayling is correct when he says that cognitive relativism is unacceptable when an individual is able to recognize another form of life, but is turning a blind eye to those situations where the individual is not able to recognize another form of life, because the individual is not aware of them in the first place. An unknown remains an unknown.

For the aficionados, the javascript program: — Tarskian

Hey you got it! — flannel jesus

Not very elegantly, I'm afraid. Thanks for posting the logic problem.

So, whose door is White? And what medium does the Kenyan use for his art? — flannel jesus

The Brazilian's door is white. The Kenyan is a photographer.

Then I asked yesterday if A was ambiguous or just contradictory. The debate remains. — javi2541997

Suppose Person A says "the Tower Bridge is in London and the Taj Mahal is in Spain".

When he says "the Tower Bridge is in London", we describe them as a "Truth Teller", and when he says "the Taj Mahal is in Spain", we describe them as a "Liar".

Person A can only have two positions, either that of a "Truth Teller" or that of a "Liar", but only at different times, in that he cannot be a "Truth Teller" and "Liar" at the same time.

Similarly, that a train may be in Paris at one moment in time and in Lyon at another moment in time doesn't make the train either contradictory or ambiguous.

Is it possible to formulate it using first-order logic? — javi2541997

Person A claims person B always tells the truth.
Person B claims person B (himself) sometimes tells the truth.
Person C claims person B always lies.

Knowing that person A sometimes lies, person B always lies and person C never lies.

Perhaps in order to formulate in First Order logic, one should start with a set of statements, where each statement is either a lie or not a lie, and where the variable x stands for a statement.
∃x (Lie (x) ∨ ¬ Lie (x))

Perhaps one should also try to avoid the problem of Russell's Barber Paradox, where the person is named after their occupation. If someone always barbers, they can be called a "Barber". If someone never barbers, they can be called "Not a Barber". But if someone at one moment barbers and at a later moment doesn't barber, they can neither be called a "Barber" nor "Not a Barber"

Similarly, it seems that a problem with First Order Logic would arise if someone who always lies is called a "Liar" and someone who never lies is called "Not a Liar". Within the logic of First Order Logic, a "Liar" is not "Not a Liar". There is no middle ground to account for person A , who is neither a "Liar" nor "Not a Liar".

Therefore, given a set of statements, some of which are lies and some aren't:

Person A is someone whose statements are sometimes lies and sometimes not lies, not that person A makes every possible statement within the set that is a lie and every possible statement that is not a lie.
Person B is someone whose statements are always lies, not that person B makes every possible stalemate within the set that is a lie
Person C is someone whose statements are never lies, not that person C makes every possible statement within the set that is not a lie

How First Order Logic achieves this is beyond my pay grade.

Who is the liar? — javi2541997

I agree with @flannel jesus that A sometimes tells the truth, B always lies and C always tells the truth. (admittedly my solution is more convoluted).

Presumably, a person who always tells the truth is different to a person who sometimes tells the truth, and in this sense are mutually exclusive.

IF A always lies - B always tells the truth - C sometimes tells the truth
THEN B would not say of himself "B sometimes tells the truth"

IF A always lies - B sometimes tells the truth - C always tells the truth
THEN C would not say about B "B always lies"

IF A always tells the truth - B always lies - C sometimes tells the truth
THEN A would not say about B - "B always tells the truth"

IF A always tells the truth - B sometimes tells the truth - C always lies
THEN A would not say about B - "B always tells the truth"

IF A sometimes tells the truth - B always tells the truth - C always lies
THEN B would not say about himself - "B sometimes tells the truth"

The only remaining possibility is - A sometimes tells the truth - B always lies - C always tells the truth.

On the occasion that A was lying rather than telling the truth, A would say one of two things about B, either "B always tells the truth" or "B sometimes tells the truth"
B would say one of two things about himself, either "B always tells the truth" or "B sometimes tells the truth".
C would say of B, "B always lies"

The three statements work on the understanding that A happened to be lying rather than telling the truth.

Yes, the oracle may perfectly well know that thwarter will do the opposite of what he predicts, but he has committed to his prediction already. It will be too late already. — Tarskian

The Thwarter app has a source code which specifies how the Thwarter app performs a calculation when input information

The Thwarter app is given an input and performs a calculation to arrive at an answer.

It may be that the Oracle app knows that the answer is contained within the input information.

However, the Thwarter app would only know that the answer was contained in the input information after it had completed its calculation, and then it would be too late to change what type of calculation it had used.

IE, the calculation that the Thwarter app uses cannot be determined by an answer that is only known by the Thwarter app after it has completed its calculation.

In fact, there is no app that can tell minute by minute what even any other app will be doing. — Tarskian

Time is of the essence.

The Thwarter app is not aware (figuratively speaking) of the existence of the Oracle app. All the Thwarter app is aware of is input.

Therefore, we only need to consider the Thwarter app.

Feedback occurs when the output of the Thwarter app then becomes new input. This is a temporal process, in that its output happens at a later time than its input.

The source code of the Thwarter app determines the output from the input using the function F, where output = F (input).

For example, if the input is a set of numbers, such as 3, 5 and 7, the output could be the addition of this set of numbers, such as 15.

At time zero, let there be an input I (1). This input cannot include any subsequent output, as any output happens at a later time.

At time t + 1, the output O (1) can be predicted from the function F operating on input I (1).

At time t + 1, the new input I (2) includes output O (1).

At time t + 2, the new output O (2) can be predicted from the function F operating on input I (2).

At time t + 2, the new input I (3) includes output O (2).

Etc.

At each subsequent time, the output can be predicted from the input. The output is pre-determined by the input.

At any time t + x, the output has been pre-determined by the situation at time zero.

So in a way, negative self reference in my opinion is a very essential building block for logic. — ssu

Let p be "I can write anything". Let q be "I know everything".

Consider the statement "If I can write anything then I know everything"

"If I can write anything then I know everything" seems reasonably true.
"If I can write anything then I don't know everything" seems reasonably false.
"If I cannot write anything then I don't know everything" seems reasonable true'.

However, as regards logic using the Truth Tables, "if I cannot write anything then I know everything" is true, regardless of whether it initially seems unreasonable.

In logic, negative expressions are as important as positive expressions, but can lead to strange places.

Unfortunately, as away for a week, cannot give your post the time it deserves. The question remains, is the Tractarian atomic proposion "Is red (the patch)" or "Is red (x)"?

Witt clearly is offering this up as an example of an atomic proposition, not a proposition. He starts by saying that he believed that one needed to introduce numbers into atomic propositions, and that he would provide an example of what he means, which was the square example with [6-9, 3-8] R as the elementary proposition: — 013zen

I agree that [6-9, 3-8] R is an atomic proposition, aka elementary proposition.

Referring to Wittgenstein's Some Remarks on Logical Form, as he writes that any given proposition is the logical sum of simpler propositions, eventually arriving at the atomic proposition, this means that an atomic proposition is still a proposition.

He writes "the representation of a patch P by the expression [6-9, 3-8]

The numbers [6-9, 3-8] are introduced to represent the patch, which is the content.

He also writes "a proposition about it, e.g., P is red, by the symbol [6-9, 3-8] R"

So we have the proposition "the patch is red", which may also be written as either "Is red (the patch)" or [6-9, 3-8] R.

As [6-9, 3-8] R is an atomic proposition, then so is "the patch is red".

"Is red (the patch)" has both form and content, whereas "Is red (x)" has form only. The argument x being a variable is a Formal Concept.

He goes on to describe how one might analyze the proposition: "The square is red" into the elementary propsition: " [6-9, 3--8] R " — 013zen

If Witt truly thought that "X is red" was an elementary proposition, why would he attempt to construct an analysis into " [6-9, 3--8] R " in Some Remarks on Logical Form? — 013zen

As I understand it, the atomic proposition is of the form - Is red (the patch) - not - Is red (x).

In Wittgenstein's article Some Remarks on Logical Form, I take atomic proposition to be a synonym for elementary proposition.

Wittgenstein writes that "Every proposition has a content and form"

He also writes that any given proposition is the logical sum of simpler propositions, eventually arriving at the atomic proposition. It is in these atomic propositions that contain the material, the subject matter. IE, the content.

As every proposition has content and form, and as any given proposition is the sum of atomic propositions, atomic propositions must also have content and form.

As - Is red (x) - has form but no content, it cannot be an atomic proposition. However, as - Is red (the patch) - has both content and form, it may be an atomic proposition.

Wittgenstein writes that a proposition about the patch can be "P is red"

Wittgenstein represents this patch by [6-9, 3-8]

Therefore the expression - Is red (the patch) - may be replaced by - Is red [6-9, 3-8] - or as he writes [6-9, 3-8] R

Therefore the expression [6-9, 3-8] R is a proposition, and as he says, every proposition has content and form.

Wittgenstein replaces the proposition - Is red (the patch) - by [6-9, 3-8] R - where both are of the form of an atomic proposition.

(the colour exclusion problem)...........I've never heard the position that this supposed problem was one of if not the reason why Witt wrote the PI. — 013zen

The colour exclusion problem for the Tractatus
Ramsey's criticisms of the Tractatus is crucial in Wittgenstein's change from his early to late philosophy.

Ramsay argued that Wittgenstein's statement that it is logically impossible that a single point in the visual field can be two colours at the same time was contradictory to his statement that elementary propositions are logically independent, a pillar of the Tractatus, This is known as the colour-exclusion problem.

6.3751 For example, the simultaneous presence of two colours at the same place in the visual field is impossible, in fact logically impossible, since it is ruled out by the logical structure of colour.

4.211 It is a sign of a proposition's being elementary that there can be no elementary proposition contradicting it

It is the properties of space, time and matter that determine the non-logical impossibility that at the same place both the general propositions "this is red" and "this is green" can be true, not the logical necessity of the tautology or the logical impossibility of the contradiction.

On the one hand, the simple colour proposition "this is red" appears to be an elementary proposition because seemingly not a truth-function of other propositions, but on the other hand, the simple colour proposition "this is not green" logically follows from the simple colour proposition "this is red", meaning that such simple colour propositions cannot be independent.

Wittgenstein's abandoning logical atomism was in large part due to Ramsey's pointing out the colour-incompatibility problem in the Tractatus, and turned away from the Tractatus to that of a family resemblance approach in Philosophical Investigations, which does not use the logical necessity of the Tractatus to distinguish meaningful from senseless propositions.

What are elementary propositions.
Note that in Philosophical Grammar, Wittgenstein was treating the expression "this place is now red" as an elementary proposition, not the logical form of the proposition such as F(x) as the elementary proposition.

In addition, elementary propositions assert a states of affairs, where an elementary proposition is an arrangement of names and a state of affairs is an arrangement of objects. An elementary proposition is true or false dependant upon whether a state of affairs obtains or not. It is the case that the elementary proposition has the same logical form as the state of affairs it asserts, not that the elementary proposition is the logical form.

Sraffa’s Impact on Wittgenstein - Matthias Unterhuber, Salzburg, Austria

Ramsey’s criticism (1923) of the Tractatus (Wittgenstein 1922/1933) is essential for the change from Wittgenstein’s earlier to his later philosophy (Jacquette 1998). Ramsey’s influence on Wittgenstein is very easily traceable, as Ramsey (1923) published his criticism of the Tractatus and Wittgenstein modified the approach of the Tractatus to account for the criticism and published his response in Some Remarks on Logical Form (Wittgenstein, 1929). He, however, eventually noticed that his modified approach did not solve the problem suggested by Ramsey.

The criticism of Ramsey amounts to the fact that Wittgenstein could not explain a statement he accepted: that a “point in the visual field cannot be both red and blue” (Ramsey 1923, p. 473). According to the Tractatus “the only necessity is that of tautology, the only impossibility that of contradiction” (p. 473). The present contradiction, however, is attributable rather to properties of space, time and matter and is not accounted for by the general form of proposition which according to the Tractatus determines all and only genuine propositions. Wittgenstein eventually gave up the thesis that there is a general form of proposition and resumed a family resemblance approach which does not provide necessary and sufficient conditions for the distinction of meaningful and senseless propositions.

SEP - Frank Ramsey

Ramsey, as we saw in the previous section, was still an undergraduate when, aged 19, he completed a translation of the Tractatus Logico-Philosophicus (Wittgenstein 1922). Alas, C. K. Ogden got all the credit and it has been known since as the ‘Ogden translation’. Ramsey’s translation is usually considered to be superseded by the Pears-McGuinness translation (1961), but one should not lose sight of the fact that it was carefully scrutinized by Wittgenstein, who gave it his seal of approval. Ramsey then wrote a searching review of the Tractatus (1923) in which he raised many serious objections (Methven 2015, chapter 4) (Sullivan 2005). One such objections is the ‘colour-exclusion problem’ (1923, 473), against Wittgenstein’s claim in 6.3751 that it is “logically impossible” that a point in the visual field be both red and blue. This claim was linked to the requirement that elementary propositions be logically independent (otherwise, the analysis of the proposition would not be completed), a pillar of the Tractatus. Wittgenstein’s recognition in 1929 that he could not sustain his claim (Wittgenstein 1929), probably under pressure at that stage from discussions with Ramsey, was to provoke the downfall of the Tractatus.

Wittgenstein and the colour incompatibility problem - Dale Jacquette

What induced Wittgenstein to repudiate the logical atomism

I want to argue that Wittgenstein's abandonment of logical atomism and the development of his later philosophy was in large part the result of Ramsey's criticism of the Tractatus treatment of the color incompatibility problem, the problem of the apparent nonlogical impossibility of different colors occurring in a single place at the very same time.

Wittgenstein writes in Philosophical Grammar - "The proposition 'this place is now red' (or 'this circle is now red') can be called an elementary proposition if this means that it is neither a truth function of other propositions nor defined as such...But from 'a is now red' there follows 'a is now not green' and so elementary propositions in this sense aren't independent of each other like the elementary propositions in the calculus I once described - a calculus to which, misled as I was by a false notion of reduction, I thought that the whole use of propositions must be reducible".