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

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Suppose y = sin(cos(x)). Which (sin or cos) would you say is inside, and which outside?

Quine was presumably referring to the stratification of types originally proposed by Russell, which ensures that the a map between type universes resides in a universe that is higher than both of the input and output universes. We might recall the fact that each universe contains a subclass that is isomorphic to the previous universe, as represented by the quotation marks in the liar sentence. So if we start with the highest level universe that we say contains everything we regard to be true, and use it to build in stepwise fashion an infinitely descending chain of so-called object languages that are each the meta-language of their predecessor, the liar sentence can be interpreted as stream of fluctuating truth values with respect to isomorphic, but non-identical terms of different types.

By contrast, both Sin and Cos are maps of type Real --> Real, i.e maps between terms of Reals, where the type Real --> Real resides in the same universe as the type Real, as does any function of functions of ... functions of reals; for they all reside in the universe definable in terms of second order logic. Following their example, we could alternatively interpret the liar sentence as directly referring to a stream of fluctuating values, where the stream and its values all exist in the same universe as a binary approximation to those trigonometric functions.
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Oh dear. The cos and sin question was my attempt to help someone grok Quine's (perfectly standard) usage of "inside sentence" vs "outside sentence". Nothing more.

Quine was presumably referring to the stratification of types originally proposed by Russell,sime

Yes. That may be relevant to clarification of his drift.

Yes, he's saying there may be a hierarchy of references. That may be relevant to clarification of his drift.

But that drift has nothing to do with cos and sin, and definitely has to do with the relation of inner to outer sentence.

I'm not quite sure what kind of objection [to the liar sentence] is being sustained? If any. And who had raised it, and where?

@sime Grateful for advice on that, but you would need to be more specific, at least.
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If you would read what I posted

I did. It is appearing, more or more credibly, that you're not really doing the same, as there is clarity from comment one of this exchange and several attempts to end the clear horseshit going on here.

"Why did it take nine pages" is very, very clear indicator, if you're actually paying attention, that I assent to RussellA's position. And, our subsequent exchange made that explicitly, painfully clear directly to you.

If you still have questions, perhaps aim them elsewhere as I have answered anything relevant several times now - and that's ignoring hte spoon-feeding required being a problem.
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Are you sure?

Yes. Quine clearly says that the whole outside sentence is what refers to something other than itself, and he clearly doesn't say that the inside sentence is what refers to something other than itself. And any competent reader sees that "this sentence is false" is the inside sentence.

So your comments aren't helping you or @RussellA to understand the passage.
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So your comments aren't helping you or RussellA to understand the passage.

Given ""This sentence is false" is false"

So which sentence is attributing falsity no longer to itself but merely to something other than itself?

This topic is mentioned Yannis Stephanou in his book A Theory of Truth in chapter 1, Aspects of Paradox.

One line of reasoning that leads to contradiction relies on the schema (T)
S is true iff p.

Some versions of the liar involve falsity rather than truth.
Take the sentence (6)
(6) is false.
This sentence attributes falsity to itself.
By (T), (6) is true iff (6) is false.

From Quine, ""This sentence is false" is false"
From Stephanou, (6) is false
Therefore (6) is "This sentence is false"

From Stephanou, the sentence (6) attributes falsity to itself
Therefore, ""this sentence is false" attributes falsity to itself

From Quine, The Ways of Paradox and Other Essays
"the whole outside sentence here attributes falsity no longer to itself but merely to something other than itself".

Therefore, "this sentence is false" is the outside sentence.

This is what I read both Quine and Stephanou to be saying.
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So which sentence is attributing falsity no longer to itself but merely to something other than itself?

Can you possibly see how answering this (again) might be considered "feeding the trolls"?
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Can you possibly see how answering this (again) might be considered "feeding the trolls"?

I am making a case that your previous statement was factually wrong, and am backing my case up with additional evidence from Yannis Stephanou's book A Theory of Truth

If you think that this is being inflammatory and provocative, then I'm sorry.

I won't bother you again.
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Late to the party, and I haven't read any responses yet. I'm going to agree that it is not a valid statement. The statement isn't about anything that can be declared true or false. It's truth/falsehood in a vacuum. I understand how it's used, and the paradox it's supposed to embody. But it's meaningless.
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I think you have to differentiate between pure logic and linguistic logic. The liar paradox is a linguistic construct - nothing more.
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If you would read what I posted — TonesInDeepFreeze

I did.

So I underestimated AmadeusD's willingness to not understand plain words.

For his remedial benefit, a review is in order. So let's take a gentle stroll back through recent memory lane:

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.

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.

At the point that AmadeusD posted the above, he had not posted in this thread except much earlier to ask me something about the incompleteness theorem. So "Why did it take 9 pages", at that point, could have meant different things.

I replied that the answer to his question is psychological. RussellA had been stubbornly sticking to arguments that had been demonstrated to be terribly confused, illogical and ignorant.

AmadeusD replied that he thinks RussellA is correct, as "it is not a paradox".

I pointed out that we had been talking about "This sentence has fifty words", which no one had claimed is a paradox, as the question was instead whether it is meaningful.

AmadeusD replied that it is not meaningful. At least credit AmadeusD for recovering by addressing the question of meaningfulness rather than that of paradoxicalness that was not at issue.

I replied that AmadeusD was merely asserting that "This sentence has fifty words" is not meaningful, and that counterarguments had been given that had not been refuted.

AmadeusD replied, "LOL, well fair enough!"

I don't know what what AmadeusD thought was laughable, and I didn't know whether "well fair enough" was sarcastic. I moved on to refute RussellA's latest posts.

* He claimed that "This sentence has fifty words" does not literally mean that "This sentence has fifty words" on account of "in the structure of the sentence. As has been pointed out". But there has been no rebuttal by RussellA that does not hinge on some combination of illogic, confusion and falsehood, so nothing that legitimately lays claim to "pointing out". Indeed, RussellA's arguments depend on his willfully not understanding the contextual nature of pronouns as he makes outlandish claims about them such as that "This sentence" could, in the context, just as well be referring to the city of Paris (or whatever his arbitrary example was).

* He argued again by mere assertion: "On it's face, it is plainly meaningless." Not even that is meaningless, but that it "plainly" meaningless, and not only that it is plainly meaningless but that "on its face" it is plainly meaningless.

* I pointed out that RussellA tried to slip around a refutation by changing the context from "This sentence has five words" to "This sentence is false". AmadeusD replied that I "added" meaning to the sentence discussed, but without addressing the careful detail I put into the question of meaning. And "adding" meaning doesn't address that RussellA tried to slip around a refutation by changing the context from "This sentence has five words" to "This sentence is false".

* He said, "whether or not the sentence is referring literally 'to itself' [...]" thus missing that that was not at issue but rather at issue is what "This sentence" refers to. The issue was not what a particular sentence refers to but rather to what a particular noun phrase refers to, as RussellA has the ridiculous notion that we might as well ignore the context in which the pronoun 'this' occurs.

Later, after posts not involving AmadeusD, he posted immediately following two posts by me, in entirety, "I can only laugh".

I took that to mean that he was scoffing at my posts. He then claimed that not referring to me. So, in good faith, I took him at his word for that. He said, "I assessed the page of the thread" and " I didn't tag you, or anyone. Clear indicator I am not talking to you". But a few posts later, he said, "I was intending there to point out that "I can only laugh" was in response to about eight posts, none of which were at or about me best I can tell - it was discussion between yourself and RussellA." So it was not just general, but about RussellA and me, and he had been defending RussellA's position and arguments against mine, and he decried what he calls my "distasteful approach". So, I can't take seriously that "I can only laugh" was directed at both RussellA and me, not at me in particular.

Then AmadeusD falsely claimed that I've attempted to dismiss RussellA on an ad hominem basis. I replied:

I have not dismissed any interlocutor on an ad hominem basis. Rather, I have engaged virtually every point he's tried to make, every claim, every argument - in detail and with thoroughness, and repeatedly in pace with his repetitiveness. And for a long time I made no personal comment about him. Meanwhile, his mode has to been to skip the rebuttals given him and shift his claims (but as if he has not) and spread a trail of red herrings . Then, in addition to my responding on point, I have also discussed that he is indeed ignorant on even basics and highly irrational in his arguments - and not just as free-floating characterizations, but in exact reference to the very specific points and arguments of his, as I have engaged virtually all of them.

Then a bunch more garbage from AmadeusD including such juvenility as "your ego".

Eventually, AmadeusD goes into "No Mas"stuff while he's still punching. ["No Mas" not a quote of AmadeusD]

I have never been able to imagine what is in the mind of posters when they keep saying that they consider the dust-up over, or that they want it to be over, while they are still continuing the dust-up. "You're an idiot, a waste of my time, and a bad speller too! Okay, we're cool, time for us to get off the personal attacks; we can just move on now. But, as I was saying, "You don't know anything about Habermas; you should get your money back from that correspondence school junior college you flunked out of; you're the stupidest person I've ever talked to on the Internet; you're twenty tons of idiocy in a four ounce can, you raging ignoranceaholic. All right, now we don't need more insults; we can respect each other as posters, you braindead wad of scum."

AmadeusD has the prerogative to diss me as he likes, and I have the prerogative to show how his disses are off-base and that he's dishonest to claim he wasn't dissing me with lameisms such as, just for starters, "I can only laugh".
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the clear horseshit going on here.

Always good to hear it straight from the horse's mouth.
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The passages from Quine:

"'This sentence is false'. Here we seem to have the irreducible essence of antinomy: a sentence that is true if and only if it is false.

In an effort to clear up this antinomy it has been protested that the phrase 'This sentence', so used, refers to nothing. This is claimed on the ground that you cannot get rid of the phrase by supplying a sentence that is referred to. For what sentence does the phrase refer to? The sentence 'This sentence is false'. If, accordingly, we supplant the phrase 'This sentence' by a quotation of the sentence referred to, we get: ''This sentence is false' is false'. But the whole outside sentence here attributes falsity no longer to itself but merely to something other than itself, thereby engendering no paradox." - Quine

There's no paradox because, as Quine says, "this sentence is false" is referring to something other than itself.

(1) As best I can tell Quine is relating an argument given by some people that I would unpack as:

If we regard "this sentence" as referring to "This sentence is false", then there is no paradox. Therefore, if there is a paradox, then "this sentence" does not refer to "This sentence is false" and therefore "this sentence" refers to nothing.

If my interpretation is correct, Quine doesn't say there is no paradox. Rather he relates an argument that if there is a paradox then "This sentence" does not refer.

I don't understand that argument.

Suppose "This sentence" refers to "This sentence is false". Then "This sentence is false" means that "This sentence is false" is false.

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

But it seems Quine disagrees, so I don't know what I'm missing.

Quine also says that ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is paradoxical:

"If, however, in our perversity we are still bent on constructing a sentence that does attribute falsity unequivocally to itself, we can do so thus: ''Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation'. This sentence specifies a string of nine words and says of this string that if you put it down twice, with quotation marks around the first of the two occurrences, the result is false. But that result is the very sentence that is doing the telling. The sentence is true if and only if it is false, and we have our antinomy." - Quine

Doesn't he mean 'prepended' rather than 'appended'? [Edited with strikethrough here and replacements made below without indication.]

I would unpack the argument this way:

Left to right:

If ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true, then ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false, as follows:

""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true if and only if "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

Suppose ""Yields a falsehood when appended to its own quotation" yields a falsehood when its own quotation" is true.

So, "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

But the result of appending "Yields a falsehood when appended to its own quotation" to its own quotation is ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation".

So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" yields a falsehood.

So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false.

Right to left:

If ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false, then ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true, as follows:

""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false if and only if "Yields a falsehood when appended to its own quotation" does not yield a falsehood when appended to its own quotation.

Suppose ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false.

So, "Yields a falsehood when appended to its own quotation" does not yield a falsehood when appended to its own quotation.

But the result of appending "Yields a falsehood when appended to its own quotation" with its own quotation is ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation".

So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" does not yield a falsehood.

So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true (if it were false it would yield a falsehood, viz. itself).

Notice that that argument makes use of the pronoun 'it'. But if we were to follow RussellA's disregard for the contextual basis of pronouns, the pronoun 'it' in this context could refer to the Taj Mahal. Good thing we are not bound by RussellA's ridiculous views. But RussellA cites Quine's other passages. So I wonder what RussellA would have to say about Quine's use of a pronoun in Quine's own formulation of the paradox.

(2) Clearly the inside sentence is "This sentence if false" since it is inside ""This sentence if false" is false", which is the outside sentence.

It makes no sense to say that a sentence that is literally inside another sentence is the outside sentence. And especially when Quine himself refers to the outside sentence as the one that "attributes falsity no longer to itself but merely to something other than itself", as that is ""This sentence is false" is false". RussellA is again nutso.
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And I may stipulate that in the context of my post, "This sentence" refers to "This sentence has five words"...On what basis is it claime[d] "This sentence has five words" [is] not meaningful? — TonesInDeepFreeze

On the basis of infinite recursion.

You should say that it's on the basis that your "infinite recursion" argument had been refuted at least three times but you choose to ignore the refutation.
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As you have said many times on this thread, something in the world cannot be an expression in language.

What?! Not only have I not said that many times, I've not said it even once. On the other hand, I have said many times that an expression is in the world. Your claim about what I've said is the complete opposite of what I've said. That is yet another instance of your bizarre mentation and illogic.

The Pentastring may be named as "this sentence has five words"

You have it reversed again! "This sentence has five words" is named "The Pentastring". The Pentastring is not named "This sentence has five words"!

the Pentastring isn't "this sentence has five words".

What you should say is "I choose to ignore the repeated explanations as to why the Pentastring is "This sentence has five words", so I'll just go ahead to claim that the Pentastring is not "This sentence has five words".

A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas.

The prop comedian Scott Thompson was named "Carrot Top". Carrot Top is the prop comedian Scott Thompson.

"Thou shall not steal" was named "The Eighth Commandment". The Eighth Commandment is "Thou shall not steal".

"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words".

Just because the name of the Pentastring has five words, it doesn't follow that the Pentastring itself has five words.

No one said that any name of the Pentastring has five words. Rather, "The Pentastring" is a name of "This string has five words".

Just because a name for the Eiffel Tower has two words, it doesn't follow that the Eiffel Tower itself has two words.

Of course. And no one said anything contrary by analogy. Again, for the 100th time in this thread: "The Pentastring" is a name for "This sentence has five words". The Pentastring is "This sentence has five words". The Pentastring is NOT a name for "This sentence has five words".

"The Pentastring has five words" is not how "the Pentastring" has been defined.

Of course that's right.

"The Pentastring" is defined so that it refers to "This string has five words".

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

For the sake of argument, using sentence instead of string

You started going back to 'sentence' rather than 'string', so for ease, I have been going along with that and allowing the "The Pentastring" to stand for "This sentence has five words" rather than for "This string has five words", especially since my point about "The Pentastring" is not affected by whether we use 'string' or 'sentence'.

Then "the Pentastring is this sentence has five words"

That doesn't even make sense. There are two quotation errors there:

(1) Maybe you mean that the Pentastring is this sentence has five words.

(2) But (1) makes no sense, so it should be:

The Pentastring is "This sentence has five words".

Therefore, "the Pentastring is this sentence has five words" is true IFF the Pentastring is this sentence has five words.

No. But these are right:

"The Pentastring has five words" is true if and only if the Pentastring has five words.

"The Pentastring has five words" is true if and only if "This sentence has five words" has five words.

"the Pentastring has five words" is true IFF the Pentastring has five words

Right! (A rarity for you.)

the Pentastring is this sentence has five words is not the same as the Pentastring has five words.

That's gibberish on account of the fact that you still don't know how to use quote marks.

Therefore, "the Pentastring has five words" is not how "the Pentastring" has been defined.

"The Pentastring" refers to "This sentence has five words". That is how "The Pentastring" was defined.

"The Pentastring" is a name for "This sentence has five words".

The Pentastring is "This sentences has five words".

Those stand, no matter that you bungle them by not knowing how to use quote marks and no matter that you REVERSED the definition.
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This topic is mentioned Yannis Stephanou in his book A Theory of Truth in chapter 1, Aspects of Paradox.

One line of reasoning that leads to contradiction relies on the schema (T)
S is true iff p.

Some versions of the liar involve falsity rather than truth.
Take the sentence (6)
(6) is false.
This sentence attributes falsity to itself.
By (T), (6) is true iff (6) is false.

None of that supports your confused mixing up which is the inner and which is the outer sentence.

From Quine, ""This sentence is false" is false"
From Stephanou, (6) is false
Therefore (6) is "This sentence is false"

First, Quine didn't assert that "This sentence is false" is false. Rather, he mentioned that some people regard ""This sentence is false" is false" to be an equivalent of "This sentence is false".

Second, at least in the passage you quoted, Stephanou didn't assert that (6) is false. He merely set it up so that (6) is "(6) is false", so that "(6)" stands for "(6) is false". (Similar to the Pentastring is "This sentence has five words", so that "The Pentastring" stands for "This sentence has five words".)

Third:

X has property P
Y has property P
Therefore, X is Y.

Obviously fallacious.

Moreover:

(6) is "(6) is false".

"(6) is false" has the word '(6)', but "This sentence is false" does not have the word '(6)'.

"This sentence is false" has the words 'this' and 'sentence', but "(6) is false" does not have the words 'this' and 'sentence'.

So, clearly "(6) is false" is not "This sentence is false".

"the whole outside sentence here attributes falsity no longer to itself but merely to something other than itself".

Therefore, "this sentence is false" is the outside sentence.

This is what I read both Quine and Stephanou to be saying.

First, Stephanou says nothing about that. Second, it is bizarre to take Quine as saying "This sentence is false" is outside ""This sentence is false" is false" when literally "This sentence is false" is inside ""This sentence is false" is false".

I am baffled as to why RussellA keeps going on and on making bizarrely illogical claims in a thread like this.

As you have said many times on this thread, something in the world cannot be an expression in language.

What?! Not only have I not said that many times, I've not said it even once. On the other hand, I have said many times that an expression is in the world. Your claim about what I've said is the complete opposite of what I've said. That is yet another instance of your bizarre imagination and illogic.
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It should IMO be handled differently in logic than a normal statement as it has an in-built truth value.

No, it doesn't have an in-built truth value, it's actually an ordinary statement, in a position where it has the illusion of seeming to be more than it really is. Words are like mirrors, they don't contain meaning, but they reflect it, the true source of meaning existing elsewhere. Take for example, "The sky is blue", this meaning can be found from a person's subjective experience of the sky being blue, not in the statement or words.

In the case of the liar's paradox, "This statement is false", the meaning can be found from a person's subjective experience of reading that statement, not in the statement or words itself. The illusion comes into play when we think that the statement actually contains meaning more than our subjective understanding. This causes us to see words and the statement not as mirrors, but as windows (in the sense of how if you don't know a mirror is a mirror, you might think it's a window showing another person who looks just like you). But this creates an issue because they are mirrors,

Normally when you read a statement, it reflects outwards to some type of subjective meaning, but when it reflects inwards, the only thing it shows a reflection of is another mirror (or a collection of mirrors, I guess you could say). When mirrors face mirrors, what happens? It creates an illusion of infinity if there's enough light, and in the case of the liar's paradox, the light would be our own thoughts, and the image in between the mirrors would be the ordinary statement value, thus creating an illusion of infinity, of "this statement is false" being more than a normal statement (in other words, it's all about positioning the "mirrors" that creates this paradox.

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"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words".

I have no problem with "this sentence has five words" being named "The Pentastring". In other words, "The Pentastring is this sentence has five words".

My fundamental problem is that it is logically impossible to go from knowledge about the content of an expression, such as "The Pentastring is this sentence has five words", to knowledge about something that may or may not exist in the world, such as The Pentastring.

It is logically impossible to go from knowing that "unicorns are grey in colour" to knowing whether unicorns do or not exist in the world.

There is no logical connection between "This sentence has five words" was named "The Pentastring" and The Pentastring is "this sentence has five words".

As you said:
"London" is a city. (false - "London" is a word, not a city)
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Doesn't he mean 'prepended' rather than 'appended'?

appended to = prepended by?
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You're right. My silly mistake. I made a note of the edits in my post. Thanks.
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I have no problem with "this sentence has five words" being named "The Pentastring". In other words, "The Pentastring is this sentence has five words".

No, only in your own ridiculous words.

Consider:

The Pentastring is this sentence has five words

That's gibberish.

Consider:

"The Pentastring is this sentence has five words"

That's quote marks around gibberish.

Consider:

The Pentastring is "This sentence has five words".

That's a sensical statement.

Consider

"The Pentastring is "This sentence has five words""

That's quote marks around a sensical statement.
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If I were you, I would get therapy.
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I would get therapy.

Your put-downs are lame-o-rama. If I were you, I'd get someone to help me write better insults.
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My fundamental problem is that it is logically impossible to go from knowledge about the content of an expression, such as "The Pentastring is this sentence has five words", to knowledge about something that may or may not exist in the world, such as The Pentastring.

"The Pentastring is this sentence has five words"

No one has anything to say about any "content" of that other than that it's gibberish.

These are all in world. They are not merely in the mind of one person:

""The Pentastring" refers to "This sentence has five words"" (stipulated by definition)

"The Pentastring is "This sentence has five words"" (true)

"This sentence has five words" (true, as far as I can tell)

"The Pentastring has five words" (true)

""This sentence has five words" has five words" (true)

"New York City has five boroughs" (true)

""New York City has five boroughs" has five words" (false)

"This guy is in love with you" (true when sung by Herb Alpert about Lani Hall, or by anyone about someone they love)

""This guy is in love with you" has five words" (false)

"The Pentastring is this sentence has five words" (gibberish)

It is logically impossible to go from knowing that "unicorns are grey in colour" to knowing whether unicorns do or not exist in the world.

(1) If we interpret as "All unicorns are grey" then usually, we do not infer "There exists a unicorn". (2) but the analogy is irrelevant. I didn't propose a predicate such as 'is a unicorn' and then infer that there is something of which that predicate is true.

Rather, merely, there does exist the expression "This sentence has five words". And I named that expression. I named it "The Pentastring". The expression "I shall return" exists. I can name it "Mac'sPromise" or whatever I want to name it.

There is no logical connection between "This sentence has five words" was named "The Pentastring" and The Pentastring is "this sentence has five words".

When we give the name "Y" to X, we then say such things as "Y is X". When you give the name "Buppy" to your dog, you then write "Bubby is my dog". When I give the name "The Pentastring" to "This sentence has five words" I then write "The Pentastring is "This sentence has five words"".

You SKIP the examples:

A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas.

The prop comedian Scott Thompson was named "Carrot Top". Carrot Top is the prop comedian Scott Thompson.

"Thou shall not steal" was named "The Eighth Commandment". The Eighth Commandment is "Thou shall not steal".

"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words".

As you said:
"London" is a city. (false - "London" is a word, not a city)
— TonesInDeepFreeze

Yes.

"This sentence has five words" is an expression. "The Pentastring" is an expression that is a name of the expression "This sentence has five words". The Pentastring is "This sentence has five words".

"All men are created equal" is an expression. "Jeffy'sBigCredo" is an expression that I now use to name the expression "All men are created equal". Jeffy'sBigCredo is "All men are created equal". I could name it "Flookimims" if I wanted to. Flookimins is "All men are created equal". The silliness of that is just to impress the point that names are stipulative and that when we give the name "Y" to X, we then say "Y is X". And contrary to an argument that you revive now, but that had been refuted many many posts ago, such naming does not cause us to assert that certain things have certain predicates other than, of course, they then have the predicate of being named a certain way.

I can anticipate an objection: But if you name your goldfish "Winston Churchill" then you would say "Winston Churchill is my goldfish", which is not true since Winston Churchill was a person, not a goldfish. But that merely reflects that natural languages have ambiguity. Sally Jones is a lab researcher. Another Sally Jones is not a lab researcher. We don't protest that "Sally Jones is a lab researcher" and "Sally Jones is not a lab researcher" is a contradiction, as we recognize that in natural languages names may have different referents. Even in formal languages. The symbol "+" might name standard addition of natural numbers or it might name modular addition for a given modulus. So we recognize that denotation is per an interpretation of a language and that truth is relative to such interpretations.
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When we give the name "Y" to X, we then say such things as "Y is X". When you give the name "Buppy" to your dog, you then write "Bubby is my dog". When I give the name "The Pentastring" to "This sentence has five words" I then write "The Pentastring is "This sentence has five words"".
You SKIP the examples:
A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas.

I agree that when we give the name "Y" to X, we can then say "Y is X"

For example, when we give the name "Noorbicks" to the puppy born in Smalltown, Kansas, we can then say "Noorbicks is the puppy born in Smalltown, Kansas"

But this is not what you are doing. You are giving the name "The Pentastring" to "this sentence has five words". You are not giving the name "The Pentastring" to this sentence has five words.

Knowing that "The Pentastring is this sentence has five words" gives me no knowledge about the existence or not in the world of the Pentastring, meaning that I cannot say anything about The Pentastring in the world.

This includes being able to say that The Pentastring is "this sentence has five words".
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Many posts ago I addressed the fact that I am naming an expression and so the definiens is in quotes.

You are giving the name "The Pentastring" to "this sentence has five words". You are not giving the name "The Pentastring" to this sentence has five words.

For about the 20th time, as you skip each time, and you still don't get use-mention:

Consider:

The Pentastring is this sentence has five words.

That does not parse because, in this case, the words after "is" form a sentence itself and must be mentioned not used.

[noun] is this sentence has five words

makes no sense.

[noun] is "this sentence has five words"

makes sense.

These are correct:

"The Pentastring" refers to "This sentence has five words"

The Pentastring is "This sentence has five words"

These are obviously gibberish:

"The Pentatsring" refers to this sentence has five words.

The Pentastring is this sentence has five words.

You've been making that mistake, and using it in your phony arguments, for a long long time in this thread.
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that was not an insult my friend.
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I can only laugh.
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