how do you avoid the problem of infinite recursion in a self-referential sentence? — RussellA
"This sentence contains five words". — RussellA
Non self-referential case
Let "this sentence" refer to the sentence "this sentence contains five words" — RussellA
Then, "this sentence, the sentence "this sentence contains five words", contains five words". This is meaningful. — RussellA
the sentence "this sentence contains five words" is not the same sentence as "this sentence contains five words", even though the wording is identical. These are two completely different sentences. — RussellA
the truth of the sentence "this sentence contains five words" is independent of the truth of the sentence "this sentence contains five words". — RussellA
Self-referential case
In the self-referential case, "this sentence, the sentence "this sentence contains five words", contains five words".
But we know that this sentence is the sentence "this sentence contains five words". — RussellA
Therefore, "this sentence, the sentence "the sentence "this sentence contains five words" contains five words", contains five words".
Ad infinitum. Infinite recursion. Therefore meaningless. — RussellA
Note that in the self-referential case, the sentence "this sentence contains five words" is the same sentence. — RussellA
If "this sentence contains five words" is referring to itself, then "this sentence contains five words" means that "this sentence contains five words". — RussellA
In other words, "X" means "X". — RussellA
the law of identity states that each thing is identical with itself. — RussellA
I agree that "X" means "X" — RussellA
how can "X" be described as a meaningful sentence? — RussellA
I totally agree that there is nothing problematic with the sentence "this sentence contains five words", and can indeed be a meaningful sentence.
As long as "this sentence contains five words" is not referring to itself. — RussellA
To say that "a horse is a horse" is true is saying no more than "a horse is a horse".
To say that "this sentence contains fifty words" is true is saying no more than "this sentence contains fifty words".
To say that "x" is true is saying no more than "x". — RussellA
Truth only enters when self-reference disappears — RussellA
Truth only enters when self-reference disappears — RussellA
how can any one say that "this sentence contains five words" is true if no one knows which sentence is being referred to? — RussellA
It is not correct to say that the sentence "this house is very tall" is true because it contains five words.
Similarly, it is not correct to say that the sentence "this sentence contains five words" is true because it contains five words. — RussellA
"This house is very tall" is true IFF this house is very tall, not because the sentence "this house is very tall" contains five words.
Similarly, "this sentence contains five words" is true IFF this sentence contains five words, not because the sentence "this sentence contains five words" contains five words. — RussellA
The subjective content of the sentence "this sentence contains five words" cannot determine the objective form of itself, ie, that it contains five words. — RussellA
All I'm trying to say is that an expression that self-refers cannot be grounded in the world, and if not grounded in the world cannot have a truth value. — RussellA
"This sentence contains fifty words" is true IFF this sentence contains fifty words. — RussellA
The word "truth" in the following would be redundant:
"This sentence contains fifty words" is true IFF "this sentence contains fifty words" — RussellA
"This sentence contains fifty words" is true IFF this sentence contains fifty words. — RussellA
In the sentence "this ferry contains fifty people", we don't normally think that "this ferry" is referring to the sentence "this ferry contains fifty people". We normally think that it is referring to a ferry in the world.
So why would we think that "this sentence" is referring to "this sentence contains fifty words". It seems more likely that "this sentence" is referring to another sentence. — RussellA
if I said "this sentence contains fifty words", the listener may infer that I meant that this sentence, ie the sentence "this sentence contains fifty words", contains fifty words. — RussellA
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. — RussellA
However, we are not discussing what the sentence "this sentence contains fifty words" is inferred to mean, we are discussing what it literally means. — RussellA
We infer what it literally means. — TonesInDeepFreeze
That is an important point. RussellA should not resort to trying to change the context from "This sentence has five words" to "This sentence is false". — TonesInDeepFreeze
If "this sentence" is referring to the sentence "The Eiffel Tower is a lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower from 1887 to 1889. Nicknamed "La dame de fer", it was constructed as the centrepiece of the 1889 World's Fair" then this sentence does have fifty words. — RussellA
So, whether or not the sentence is referring literally 'to itself' (this should answer your query about a sentence wanting to say something above) — AmadeusD
You can't simply read it in a way which is false, but meaningful by adding meaning to it, without sufficient reason. — AmadeusD
On it's face, it is plainly meaningless. — AmadeusD
it seems all you're wanting to do is have the sentence refer to itself — AmadeusD
The sentence is not paradoxical, but a lot of the ways in which this is the case, Russell has covered. — AmadeusD
Is that a joke? — TonesInDeepFreeze
Wrong. "This sentence has five words" is "This sentence has five words". They are the same linguistic object. As RussellA himself says, the wording is identical. So they are the same sentence. — TonesInDeepFreeze
But that's not fair to the inquiry, since the fact that one dialectically incompetent poster can't come up with a good argument for his claim should not be taken to entail that no one can. — TonesInDeepFreeze
In an effort to clear up this antinomy it has been protested that the phrase `This sentence', so used, refers to nothing. [Trolls explode with glee.] 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, The Ways of Paradox
what sentence does the phrase refer to? The sentence 'This sentence is false'.
here's Quine — bongo fury
But the whole outside sentence here attributes falsity no longer to itself but merely to something other than itself, thereby engendering no paradox. Quine
Mary in 1975 in New York said "This sentence has five words".
Rafael in 1923 in Rio de Janeiro said "This sentence has five words"
Just because the wording is identical, this doesn't mean that they are the same sentence, the same linguistic object. In part, because we don't know what sentence they are referring to. — RussellA
The professor looks at a Geography student's essay and says to the student: this sentence is false.
The student had written "Paris is in Germany". — RussellA
The paradox arises when "this sentence is false" is not referring to something other than itself. IE, when it is self-referential. — RussellA
There's no paradox because, as Quine says, "this sentence is false" is referring to something other than itself. — RussellA
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