Self-reference paradoxes

[Speakpigeon]

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.

What's an English speaker?

Any proficient speaker of English would recognise that the use of the word "this" in these examples is non-standard. Words like "This" don't normally refer to the very sentence containing it. In fact, these words refer not to other words or to sentences, but to what other words and sentences refer to themselves. In "John is missing. We lost him during this morning's operation", "him" doesn't refer to the word "John" but to John. You seem to be unaware of the difference. If you want to refer to a sentence, you have to spell it out between quotation marks.

If you can't provide a formal version of the sentence you want to discuss then you are fooling yourself. Personally, when I read "This statement has five words", I think immediately that I don't know which statement is being referred to. I may take it for granted it's a statement but which one? The statement doesn't say. In "This object is green" you may accept that there is a green object but you may also decide that there isn't. That's because the statement doesn't actually tell you what is the object in question. As such it's not a logical proposition. That you are willing to entertain the idea that it is and then get into a muddle tells something about you (and about many logicians) and nothing about logic. It's not for nothing that people invented formal logic. If you insist you can do without it then it's just a case of doing it for fun: No serious point.
EB

 

[Speakpigeon]

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.

So, try to reword your examples relying on the word "this".
Try it on "This sentence has fifty words" for example: "Trump is my hero. The previous sentence has fifty words." Right. So, the sentence, "The previous sentence has fifty words", is just wrong.
So now modify the sentence "This sentence is false" by : "The following sentence is false. The following sentence is true." Which produces the same result, apparently. Yet, there is a solution: both statements are neither ture nor false so they are not logical so you can't infer anything from them, least of all take what they say at face value. They are effectively meaningless.

Now, compare to this:

"The following sentence is false: 'The previous sentence is true'."

It's meaningful, there's no paradox, and we accept that we don't know whether any of this two sentences are true or false, essentially because we are not told in the second sentence what is the previous sentence (that because there's not typographical rules for that), yet can still understand what is said pretty good, unlike your examples. But of course my example respect typographical rules.
EB

 

[lpetrich]

Any proficient speaker of English would recognise that the use of the word "this" in these examples is non-standard. Words like "This" don't normally refer to the very sentence containing it. ...

I don't agree with Speakpigeon's attempt to disallow self-referential sentences. They may not be commonly used, but I don't see how they are an impossibility.

So I think that self-referential sentences are valid in English -- and in any other natural language.

 

[Juma]

Any proficient speaker of English would recognise that the use of the word "this" in these examples is non-standard. Words like "This" don't normally refer to the very sentence containing it. ...

I don't agree with Speakpigeon's attempt to disallow self-referential sentences. They may not be commonly used, but I don't see how they are an impossibility.

So I think that self-referential sentences are valid in English -- and in any other natural language.

Then how do you create self referencing propositions using formal logic?


While pointing on a text on the wall saying "this sentence is false", Wilbur says "this sentence is self referencing"

While pointing on a text on the wall saying "this sentence is false", Tom says "this sentence is not self referencing"

 

[Juma]

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.

"Lieutenant Garcia" is a reference, a name, to something that is part of the reality referred to by the sentence. "Himself" doesnt refer to the name but what is referred to by that name.

 

[Juma]

Suppose not all natural numbers are interesting. Then there must be a smallest uninteresting number. What an interesting property! Therefore every natural number is interesting. But for what property is some arbitrary number N proven to be interesting, when we've just ruled out the existence of the very property we used in the proof?

That doesnt make sense at all. "Interesting" isnt well defined. It isnt a proprty of the number, it is the property of properties.

 

[Speakpigeon]

Any proficient speaker of English would recognise that the use of the word "this" in these examples is non-standard. Words like "This" don't normally refer to the very sentence containing it. ...

I don't agree with Speakpigeon's attempt to disallow self-referential sentences. They may not be commonly used, but I don't see how they are an impossibility.

You could invent a language where you could make self-referencing sentences. But there's no language on Earth containing words specifically used for this. That because people have better things to do than got their statements in a muddle. The so-called paradoxes contrived by philosophers are all couched in ordinary language, many are Ok but some are not acceptable. Those are never provided with the corresponding interpretation in formal logic (although Bertrand Russell may have tried it with "This sentence is false"). I'd like to hear of a computer language allowing self-referencing too. A paradoxe ultimately relies on your willingness to entertain the meaningfullness of the sentence proposed, only to discover that it is mind boggling. In the case of the sentence "This sentence is false", the assumption that it is true implies it is false and the assumption that it is false implies it is true. The only reasonable attitude is to say that it is neither true nor false. The consequence of that is that there is no longer any problem with the logic of the sentence and that it is not subject to formal logic since propositions have to be either true or false. Problem solved. You could argue it's still subject to logic but then it's your logic not mine so please explain now to me how you're going to find an exit wherever you happen to have trapped yourself.

So I think that self-referential sentences are valid in English -- and in any other natural language.

Doesn't make much sense. There's no rule saying self-referential sentences are valid. All you can say is the "This sentence is false" is grammaticaly correct. That's all and it's not enough to support your claim. There's no sentence that can be unambiguously regarded as self-referential. There are no words that are specifically used for constructing self-referential sentences. There are no grammars that explain how self-referential sentences are produced in English (or in any language). So it's entirely down to your personal willingness as a speaker of English to read a sentence as self-referential. Books presenting the paradox "This sentence is false" always direct the reader to take it as a case of self-reference. I say, well, let the reader decide on that without directing his interpretation and we'll see what the informed reader does.
EB

 

[Speakpigeon]

Some smarter ass pointed out that it's not self-reference which is the problem but self-comment, as when you say "What I'm saying now is really profound", which doesn't make sense (except jocularly). Self-comment leads to sentences having "undeterminate propositional depth", as when you can't stop at any particular proposition as being the meaning of the sentence, as in "What I'm saying now, namely that what I'm saying now, namely that etc. ... <infinite regress> ... is realy profound". If you can't stop then the sentence doesn't mean anything you could tell so it's not a meaningful sentence. "This sentence is false" is just a particular case of undeterminate propositional depth. That it is about truth and falsehood is not essential.

I'm not quite sure I entirely agree but there's something in there.
EB

 

[fromderinside]

Some smarter ass pointed out that it's not self-reference which is the problem but self-comment, as when you say "What I'm saying now is really profound", which doesn't make sense (except jocularly). Self-comment leads to sentences having "undeterminate propositional depth", as when you can't stop at any particular proposition as being the meaning of the sentence, as in "What I'm saying now, namely that what I'm saying now, namely that etc. ... <infinite regress> ... is realy profound". If you can't stop then the sentence doesn't mean anything you could tell so it's not a meaningful sentence. "This sentence is false" is just a particular case of undeterminate propositional depth. That it is about truth and falsehood is not essential.

I'm not quite sure I entirely agree but there's something in there.
EB

Now there are two of us. Better?

 

[Speakpigeon]

Any proficient speaker of English would recognise that the use of the word "this" in these examples is non-standard. Words like "This" don't normally refer to the very sentence containing it. ...

I don't agree with Speakpigeon's attempt to disallow self-referential sentences. They may not be commonly used, but I don't see how they are an impossibility.

So I think that self-referential sentences are valid in English -- and in any other natural language.

What do you mean "valid"? Valid like this: The blue time dispirited the small man of school cars? Somebody English might want to say that and we sort of understand what it means, yet we wouldn't say it makes much sense. When is something a sentence? I'd say when it means something to a speaker of the language, just as a string of letters is an English word when it means something to English speakers.

When I say, "The sentence I am typing now is self-referencing", it is still me commenting on the sentence. it is not the sentence commenting on itself, and so it is actually not self-referencing in any real sense. You always need somebody to interpret any sentence and people can disagree too and for many sentences, the context will affect the interpretation. Interpreting "This sentence is false" doesn't make any sense to me. So I guess we can say it's meaningless even though it does have a sort of bare-bones grammatical sense. Apparently, most logicians have come to accept that this particular paradox is good English but you still have a few others who agree to dismiss it as meaningless.
EB

 

[Lion IRC]

- - - Updated - - -

Spoken like a true philosopher.

 

[Lion IRC]

...and you would need to engage in philosophical analysis to determine whether philosophy was or wasn't useful in addressing existential 'why' questions. And you would be left asking Mr Hawking philosophical questions like 'why' he thinks philosophy is dead.

Christian apologist Ravi Zacharias uses a lovely rhetorical device to demolish post-modern, relativism. He presents an anecdote about how he and a Hindu are debating absolute truths and the superiority of Eastern religions which embrace many paths rather than a "Jesus Only" path.

Zacharias insists he is right. His opponent says no you're not. Zacharias sticks to his guns. His opponent becomes even more adamant. They continue at loggerheads. Then his opponent gradually starts to see why the "many paths" philosophy is self-refuting.

"...even a Hindu looks both ways before crossing the road."

 

[GenesisNemesis]

Zacharias insists he is right.

That's the "rhetorical device?" Everyone does that all the time.

 

[Lion IRC]

No they don't.

 

[Juma]

...and you would need to engage in philosophical analysis to determine whether philosophy was or wasn't useful in addressing existential 'why' questions. And you would be left asking Mr Hawking philosophical questions like 'why' he thinks philosophy is dead.

Christian apologist Ravi Zacharias uses a lovely rhetorical device to demolish post-modern, relativism. He presents an anecdote about how he and a Hindu are debating absolute truths and the superiority of Eastern religions which embrace many paths rather than a "Jesus Only" path.

Zacharias insists he is right. His opponent says no you're not. Zacharias sticks to his guns. His opponent becomes even more adamant. They continue at loggerheads. Then his opponent gradually starts to see why the "many paths" philosophy is self-refuting.

"...even a Hindu looks both ways before crossing the road."

This is so confused... Being stubborn is not a "lovely retorical device". It is just being stubborn. And in this case entirely "being an asshole".

 

[Lion IRC]

*sigh*
GenesisNemesis and Juma you are missing the point. Ravi Zacharias is using the (paradoxical) Eastern Religion's "many paths" concept to demonstrate how self-refuting it really is.
He is saying...
oh, you think all roads lead to God, but how do you answer someone who denies your religion?

How do you reject the Christian claim that there is no other way than Jesus if you think that all religion is true?

It's like the person who advocates tolerance and equality but who won't tolerate the opposite point of view.

 

[GenesisNemesis]

*sigh*
GenesisNemesis and Juma you are missing the point. Ravi Zacharias is using the (paradoxical) Eastern Religion's "many paths" concept to demonstrate how self-refuting it really is.
He is saying...
oh, you think all roads lead to God, but how do you answer someone who denies your religion?

How do you reject the Christian claim that there is no other way than Jesus if you think that all religion is true?

It's like the person who advocates tolerance and equality but who won't tolerate the opposite point of view.

I haven't seen anyone other than New Age mystics or Unitarian Universalists claim that "all religions are true". Which Eastern religion claims this?

 

[Lion IRC]

Taoism. Vedanta Hinduism. Zen Buddhism...

One day Chuang-tzu and a student were walking along a riverbank.
"How delightfully the fishes are enjoying themselves in the water!" Chuang-tzu exclaimed.
"How do you know whether or not the fishes are enjoying themselves? You are not a fish," his student said.
"And you are not me," Chuang-tzu said.

If you think you have a hard time getting fundy Christians to accept scientific empiricism, you should try debating with Siddhārtha.

 

[Speakpigeon]

*sigh*
GenesisNemesis and Juma you are missing the point. Ravi Zacharias is using the (paradoxical) Eastern Religion's "many paths" concept to demonstrate how self-refuting it really is.
He is saying...
oh, you think all roads lead to God, but how do you answer someone who denies your religion?

How do you reject the Christian claim that there is no other way than Jesus if you think that all religion is true?

It's like the person who advocates tolerance and equality but who won't tolerate the opposite point of view.

Bad logic. If you think all roads lead to God whatever other people think become just so many roads to God. If some Jesus fundy thinks Jesus is the only road so be it. Why would you argue with anybody who thinks there is just one road to Rome? Let him try it and if you really think all roads lead to Rome you should be confident the guy will get there. The point of the "many roads" perspective is precisely to stop you wasting your time arguing needlessly with the narrow-minded of this Earth. But maybe some advocates of this many-road perspective don't really get it. Or Ravi Zacharias, whoever that is, don't get it.
EB