Self-reference paradoxes

[Bomb#20]

The text satisfies the criterion to be called "false", and it also satisfies the criterion to be called "true". What makes a paradox, if not this?

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

The text in question says that the text in question is not true. So the text says something that's perfectly meaningful when you say it. Why do you claim that when the text says it it's meaningless?

 

[Nexus]

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

No. First your Socrates line of reason is all positive and is logically consistent. That logic doesn't apply with negative assertions. If X≠Y and Z≠X it doesn't follow that Z=Y. Also I said meaningless text is neither true nor false. It exists outside of the paradigm of truth and false.

The text in question says that the text in question is not true.

That text while semantically correct doesn't say anything meaningful. Self referencing statements are nonsensical, neither true nor false.

So the text says something that's perfectly meaningful when you say it. Why do you claim that when the text says it it's meaningless?

Like I said its perfectly grammatical but that doesn't make it meaningful.

Here's an example of another meaningless statement.

Love is truth.

Some might argue hate is the opposite of love others might say indifference. Regardless the statements

Hate is false or indifference is false.

don't logically follow from the assertion that love is truth. Because the statement, while grammatically correct and with the appearance of meaning, is nonsensical and so is anything derived from it.

 

[Don2 (Don1 Revised)]

Here's one from PD:

Well, if I write an IOU and then I hand the IOU I wrote to myself, I created a liability but I have an asset too.

 

[Don2 (Don1 Revised)]

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

No. First your Socrates line of reason is all positive and is logically consistent. That logic doesn't apply with negative assertions. If X≠Y and Z≠X it doesn't follow that Z=Y. Also I said meaningless text is neither true nor false. It exists outside of the paradigm of truth and false.

The text in question says that the text in question is not true.

That text while semantically correct doesn't say anything meaningful. Self referencing statements are nonsensical, neither true nor false.

So the text says something that's perfectly meaningful when you say it. Why do you claim that when the text says it it's meaningless?

Like I said its perfectly grammatical but that doesn't make it meaningful.

Here's an example of another meaningless statement.

Love is truth.

Some might argue hate is the opposite of love others might say indifference. Regardless the statements

Hate is false or indifference is false.

don't logically follow from the assertion that love is truth. Because the statement, while grammatically correct and with the appearance of meaning, is nonsensical and so is anything derived from it.

I'm not trying to argue with you, but what do you mean by "meaningless?" How are you evaluating that?

Changing the example for a moment...would we say that lim sin(x) as x -> inf is meaningless just because we cannot get a numerical answer?

For the lying paradox, it's similar to say using f(x) = 1 if x = -1 and -1 if x = 1.
Then, the lying paradox is like lim f^n(1) as n goes to inf.

Does something whose limit is undefined have no meaning? If we relate it to a real world problem does it still have no meaning?

 

[Bomb#20]

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

No. First your Socrates line of reason is all positive and is logically consistent. That logic doesn't apply with negative assertions.

Sure it does. Socrates is a man; men are not gods; therefore Socrates is not a god.

If X≠Y and Z≠X it doesn't follow that Z=Y.

You made both premises negative but not the conclusion. I made the major premise and the conclusion negative, but not the minor premise.

Also I said meaningless text is neither true nor false. It exists outside of the paradigm of truth and false.

"Meaningless text is neither true nor false" means "Meaningless text is not true and meaningless text is not false." "P and Q" implies P. "X is not Y and X is not Z" implies "X is not Y." "Meaningless text is not true and meaningless text is not false" implies "Meaningless text is not true."

The text in question says that the text in question is not true.

That text while semantically correct doesn't say anything meaningful. Self referencing statements are nonsensical, neither true nor false.

Why do you believe self-referencing statements are nonsensical, neither true nor false?

This statement has five words.
This statement is a sentence in the English language.
This statement has fifty words.
This statement is a sentence in the Japanese language.

I expect any normal English speaker will understand all those statements and will easily recognize two of them as true and the other two as false.

 

[Juma]

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

No. First your Socrates line of reason is all positive and is logically consistent. That logic doesn't apply with negative assertions.

Sure it does. Socrates is a man; men are not gods; therefore Socrates is not a god.

If X≠Y and Z≠X it doesn't follow that Z=Y.

You made both premises negative but not the conclusion. I made the major premise and the conclusion negative, but not the minor premise.

Also I said meaningless text is neither true nor false. It exists outside of the paradigm of truth and false.

"Meaningless text is neither true nor false" means "Meaningless text is not true and meaningless text is not false." "P and Q" implies P. "X is not Y and X is not Z" implies "X is not Y." "Meaningless text is not true and meaningless text is not false" implies "Meaningless text is not true."

The text in question says that the text in question is not true.

That text while semantically correct doesn't say anything meaningful. Self referencing statements are nonsensical, neither true nor false.

Why do you believe self-referencing statements are nonsensical, neither true nor false?

This statement has five words.
This statement is a sentence in the English language.
This statement has fifty words.
This statement is a sentence in the Japanese language.

I expect any normal English speaker will understand all those statements and will easily recognize two of them as true and the other two as false.

Yes. But what is logical connection? How do you express "this" in only logical operators?

 

[Bomb#20]

Yes. But what is logical connection? How do you express "this" in only logical operators?

How do you express "statement" in only logical operators? How do you express "word" in only logical operators? To even apply logic in the first place to natural language speech rather than to mathematics requires that we accept that our listeners understand a lot of words without relying on definitions. I think it's reasonable to accept "this" as one of those words.

But that being said, people may legitimately disagree as to which words should be accepted as basic. I don't want to refight a whole thread from a year ago. I offered "This statement has five words." merely as a counterexample to the hypothesis that self-referencing statements are nonsensical, neither true nor false. I wasn't offering it as proof that the word "this" isn't problematical for analyses of the Liar Paradox. So to those who think "this" is problematical, my answer is the same as my answer to those who think "statement" is problematical: I'll say "Okay." And then I'll simply construct a new implementation of the paradox that avoids using the offending word.

 

[Juma]

Yes. But what is logical connection? How do you express "this" in only logical operators?

How do you express "statement" in only logical operators? How do you express "word" in only logical operators? To even apply logic in the first place to natural language speech rather than to mathematics requires that we accept that our listeners understand a lot of words without relying on definitions. I think it's reasonable to accept "this" as one of those words.

But that being said, people may legitimately disagree as to which words should be accepted as basic. I don't want to refight a whole thread from a year ago. I offered "This statement has five words." merely as a counterexample to the hypothesis that self-referencing statements are nonsensical, neither true nor false. I wasn't offering it as proof that the word "this" isn't problematical for analyses of the Liar Paradox. So to those who think "this" is problematical, my answer is the same as my answer to those who think "statement" is problematical: I'll say "Okay." And then I'll simply construct a new implementation of the paradox that avoids using the offending word.

My point is not with "this" but that any "self reference" is a beast of a very different kind than any logic construct/operator. The text != the meaning/interpretation and "self reference" builds on creating a false impression that the text is identical with the interpretation.

 

[Nexus]

Meaningless text is neither true nor false" means "Meaningless text is not true and meaningless text is not false." "P and Q" implies P. "X is not Y and X is not Z" implies "X is not Y." "Meaningless text is not true and meaningless text is not false" implies "Meaningless text is not true."

It also implies its not false. A statement that's both truth and false and neither true nor false is nonsensical. Perhaps its simply my raw assertion or axiom, but it seems self evident that if a word or sentence conveys everything and nothing its useless as a tool of communication ie nonsensical.

Why do you believe self-referencing statements are nonsensical, neither true nor false?

This statement has five words.
This statement is a sentence in the English language.
This statement has fifty words.
This statement is a sentence in the Japanese language.

I'll revise my assertion. Self-referencing statements regarding truth are nonsensical. The number of words, language or font used in a statement have a point of reference outside of the sentence ie shared language conventions, number theory and printing standards. This secondary point of reference is the necessary anchor to determine truth or false. In a way the statement

This statement is in Japanese.

Is actually not wholly self-referencing, rather its referencing a single smaller aspect of itself.

 

[Nexus]

I'm not trying to argue with you, but what do you mean by "meaningless?" How are you evaluating that?

By meaningless I mean the standard dictionary definition. Having no purpose or reason, synonyms: unintelligible, incomprehensible, incoherent. In natural language if a word or sentence can't convey a coherent message its meaningless. Which is why I think various statements about God are nonsensical since the word God has many different definitions to many people. The statement God is love sounds profound to a Christian whose reference to the word God is rooted in the concept of a loving God that sacrificed himself for them. To me it just sounds empty.

As far as your math analogy, We have to be careful analogizing math to natural language. Math can have rules that are useful for its goals which might not be applicable to natural language.

 

[Don2 (Don1 Revised)]

I'm not trying to argue with you, but what do you mean by "meaningless?" How are you evaluating that?

By meaningless I mean the standard dictionary definition. Having no purpose or reason, synonyms: unintelligible, incomprehensible, incoherent. In natural language if a word or sentence can't convey a coherent message its meaningless. Which is why I think various statements about God are nonsensical since the word God has many different definitions to many people. The statement God is love sounds profound to a Christian whose reference to the word God is rooted in the concept of a loving God that sacrificed himself for them. To me it just sounds empty.

As far as your math analogy, We have to be careful analogizing math to natural language. Math can have rules that are useful for its goals which might not be applicable to natural language.

I don't think your examples are meaningless. The first seems ambiguous, rather than meaningless. In natural language, that would mean there are multiple possible interpretations. The second seems contradictory to me, personally because of knowledge I obtained from reading about the alleged god. For you, perhaps the second is vague or incomplete. Is "incomplete" what you mean by meaningless?

In any case, I do think that the lying paradox is similar enough to math for it to be directly related to math. I will concede that Bomb#20's example isn't the same kind of paradox because it is self-referential in the scope of natural language, not the scope of logic or math. So I can understand why you would say it's meaningless in that sense.

 

[Bomb#20]

It also implies its not false.

Sure; but the sentence doesn't say it's false. The sentence says it's not true; and it appears you agree.

A statement that's both truth and false and neither true nor false is nonsensical.

How can it be nonsensical and yet say something you agree with? It seems to me "paradox" is exactly the right word for this sort of situation.

Perhaps its simply my raw assertion or axiom, but it seems self evident that if a word or sentence conveys everything and nothing its useless as a tool of communication ie nonsensical.

But the sentence doesn't convey everything and nothing. It doesn't say anything about the moon, or the Assyrian Empire, or the literary offenses of James Fenimore Cooper. But it appears to do an adequate job of conveying our collective puzzlement over the Liar Paradox.

I'll revise my assertion. Self-referencing statements regarding truth are nonsensical.

"Alito said Obama's statement wasn't true, and Alito was correct, and this statement says so."

Do you have any trouble telling what that sentence means?

The number of words, language or font used in a statement have a point of reference outside of the sentence ie shared language conventions, number theory and printing standards. This secondary point of reference is the necessary anchor to determine truth or false.

But the self-contradictory statement we're discussing from post #6 has that external point of reference in shared language conventions, number theory and printing standards too. It even explicitly talks about quotation marks and numbers of words.

In any event, why would things need points of reference outside themselves? "I have a headache." doesn't seem any more problematical to me than "You have a headache."; quite the reverse. To say a secondary point of reference is a necessary anchor smacks of Christian arguments that a human can't tell right from wrong without a moral frame of reference, which supposedly is their God; they never go on to explain how their God is able to tell right from wrong even though He doesn't have a tertiary point of reference outside Himself. Likewise, the universe manages to talk about itself without any external point of reference; so why shouldn't a little piece of the universe be able to do it?

In a way the statement

This statement is in Japanese.

Is actually not wholly self-referencing, rather its referencing a single smaller aspect of itself.

Well, my sentence's lack of truth is just a single smaller aspect of itself. The sentence doesn't say anything about whether it's false, or meaningless, or of fine literary quality, or in Japanese.

 

[Bomb#20]

My point is not with "this" but that any "self reference" is a beast of a very different kind than any logic construct/operator. The text != the meaning/interpretation and "self reference" builds on creating a false impression that the text is identical with the interpretation.

Okay.

The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true." between the eighteenth and nineteenth words is not a proposition that's true.

 

[Juma]

My point is not with "this" but that any "self reference" is a beast of a very different kind than any logic construct/operator. The text != the meaning/interpretation and "self reference" builds on creating a false impression that the text is identical with the interpretation.

Okay.

The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true." between the eighteenth and nineteenth words is not a proposition that's true.

Eh? What is "itself" supposed to refer to?

 

[Bomb#20]

Okay.

The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true." between the eighteenth and nineteenth words is not a proposition that's true.

Eh? What is "itself" supposed to refer to?

The first "itself" is a forward reference to the noun phrase:

the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true."​

The second "itself" is a forward reference to the noun phrase "the sentence".

(The version in post #6 used the same construction so I assumed you were okay with it. If you need me to redesign the whole thing to only use backward references, I'll give it a go, but I expect the result will be even clumsier.)

 

[Juma]

Eh? What is "itself" supposed to refer to?

The first "itself" is a forward reference to the noun phrase:

the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true."​

The second "itself" is a forward reference to the noun phrase "the sentence".

(The version in post #6 used the same construction so I assumed you were okay with it. If you need me to redesign the whole thing to only use backward references, I'll give it a go, but I expect the result will be even clumsier.)

Can it be more obvious that the text isnt "selfreferring"? The reference require external specification.

 

[Bomb#20]

The first "itself" is a forward reference to the noun phrase:

the sentence "The interpretation of the text resulting from inserting a copy of itself in quotation marks into the sentence between the eighteenth and nineteenth words is not a proposition that's true."​

The second "itself" is a forward reference to the noun phrase "the sentence".

(The version in post #6 used the same construction so I assumed you were okay with it. If you need me to redesign the whole thing to only use backward references, I'll give it a go, but I expect the result will be even clumsier.)

Can it be more obvious that the text isnt "selfreferring"? The reference require external specification.

You mean because you needed an explanation? A forward reference is a perfectly standard English construction. Throwing himself on the grenade was the only way Lieutenant Garcia could save his squad.

 

[Speakpigeon]

The text satisfies the criterion to be called "false", and it also satisfies the criterion to be called "true". What makes a paradox, if not this?

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

Yes, this is my position too.

The sentence "This sentence is false" is grammatically correct (not "semantically correct", as I don't think it means anything to say that a sentence is semantically correct). But it doesn't refer to anything we could think of. The phrase "this sentence" obviously refers to the sentence itself, so this part is ok (but not paradoxical in itself). This is the whole sentence, "This sentence is false", which does not refer, at least not to anything we could think of. This is the same as saying it's meaningless. As such it cannot be actually false or true.

The paradox, because I think there is one, is that our brain still tries to make sense of the sentence, just because it is grammatically (or formally) correct. To no avail. The actual paradox is that the sentence seems meaningful but is not.

Logicians have been fooled. The tend to forget they are human beings too and as such are still subject to illusions. They take the paradox to be a logical paradox but it's not. The various solutions they provided seem more pathetic than effective.

I'd be interested if anyone knows an exact, and strickly formal rendition of this example in formal logic. Every time people talk about it, it's given as an ordinary English sentence. I haven't seen any formal version of it. This is a suspicious circumstance. If there's a exact version in formal logic, I would be prepared to reconsider.
EB

 

[Speakpigeon]

I don't know whether Chomsky said this or someone else connected it to his work, but the text while semantically correct has no inherent meaning. A meaningless string of words is not true or false just like its neither an acid or base.

You're asserting that the text in question is meaningless? And you're asserting that meaningless text is not true. Together, those imply that the text in question is not true, by the "Socrates is a man; men are mortal; therefore Socrates is mortal" principle. Do you agree?

The text in question says that the text in question is not true. So the text says something that's perfectly meaningful when you say it.

You could have worked in Staline's thought police or in the Stasi. He didn't just say that the sentence isn't true, he also said, just as clearly (where were you?) that it wasn't false either. As you should remember, a sentence which is neither true nor false isn't a logical proposition at all and any attempt to treat it like one is a non sequitur (and a" lost proposition", ). You don't actually know that?! Whoa.

As to meaninglessness, I would have thought it's pretty obvious. If you try to treat it as a logical proposition, which are by definition either true or false, you are forced to infer that it is neither true nor false. QED.

I think you are mistaking grammaticality for meaningfullness, which is why I say logicians have been fooled. But sentences can be grammatical and meaningless. This one just seems to refer to itself, but as a false sentence, not just as any sentence. Since trying logic doesn't work, and the sentence cannot be understood as either true or false, the false sentence the sentence is apparently refering to in fact doesn't exist. Further, since the sentence seems to be refering to two very different things, a true sentence and a false one, it is clearly meaningless.

Do you happen to have a formulation of the sentence in formal logic? Because without that, any deduction of its truth value is pie in the sky. And usually it's a bit more complicated than meet the eye.
EB

 

[Speakpigeon]

That text while semantically correct doesn't say anything meaningful. Self referencing statements are nonsensical, neither true nor false.

I agree with you, all paradoxes based on self-referencing sentences, or even cross-referencing sentences, don't follow typographical rules, like how to use quote marks, or are otherwise defective. They are contrived, and visibly and painfuly so. The only lesson to be drawn from these examples is that they are confusing and effectively not used to make serious points. They can be fun, though.
EB