Suppose y = sin(cos(x)). Which (sin or cos) would you say is inside, and which outside? — bongo fury
Quine was presumably referring to the stratification of types originally proposed by Russell, — sime
Yes, he's saying there may be a hierarchy of references. That may be relevant to clarification of his drift. — bongo fury
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? — bongo fury
If you would read what I posted — TonesInDeepFreeze
Are you sure? — AmadeusD
So your comments aren't helping you or RussellA to understand the passage. — bongo fury
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.
"the whole outside sentence here attributes falsity no longer to itself but merely to something other than itself".
So which sentence is attributing falsity no longer to itself but merely to something other than itself? — RussellA
Can you possibly see how answering this (again) might be considered "feeding the trolls"? — bongo fury
If you would read what I posted — TonesInDeepFreeze
I did. — AmadeusD
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. — AmadeusD
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. — TonesInDeepFreeze
the clear horseshit going on here. — AmadeusD
There's no paradox because, as Quine says, "this sentence is false" is referring to something other than itself. — RussellA
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. — RussellA
As you have said many times on this thread, something in the world cannot be an expression in language. — RussellA
The Pentastring may be named as "this sentence has five words" — RussellA
the Pentastring isn't "this sentence has five words". — RussellA
Just because the name of the Pentastring has five words, it doesn't follow that the Pentastring itself has five words. — RussellA
Just because a name for the Eiffel Tower has two words, it doesn't follow that the Eiffel Tower itself has two words. — RussellA
"The Pentastring has five words" is not how "the Pentastring" has been defined. — RussellA
For the sake of argument, using sentence instead of string — RussellA
Then "the Pentastring is this sentence has five words" — RussellA
Therefore, "the Pentastring is this sentence has five words" is true IFF the Pentastring is this sentence has five words. — RussellA
"the Pentastring has five words" is true IFF the Pentastring has five words — RussellA
the Pentastring is this sentence has five words is not the same as the Pentastring has five words. — RussellA
Therefore, "the Pentastring has five words" is not how "the Pentastring" has been defined. — RussellA
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. — RussellA
From Quine, ""This sentence is false" is false"
From Stephanou, (6) is false
Therefore (6) is "This sentence is false" — RussellA
"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. — RussellA
As you have said many times on this thread, something in the world cannot be an expression in language. — RussellA
It should IMO be handled differently in logic than a normal statement as it has an in-built truth value. — Devans99
"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words". — TonesInDeepFreeze
"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze
Doesn't he mean 'prepended' rather than 'appended'? — TonesInDeepFreeze
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". — RussellA
I would get therapy. — AmadeusD
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. — RussellA
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. — RussellA
There is no logical connection between "This sentence has five words" was named "The Pentastring" and The Pentastring is "this sentence has five words". — RussellA
As you said:
"London" is a city. (false - "London" is a word, not a city)
— TonesInDeepFreeze — RussellA
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. — TonesInDeepFreeze
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. — RussellA
As for "this sentence is false" or 'this statement is false"... its essentially meaningless because it doesn't actually "state" anything ie stating something requires the subject of the statement to be separate from the statement itself — Benj96
It can also be resolved another way by changing the statement itself from "this statement is false" to something like "this statements grammar false is" in this way it remains self referential but justifies falsity by adding a variable to contextualise its falsity - namely erroneous structure. — Benj96
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