Logic and self referential statements

[Bomb#20]

Your example can be reduced to: <"X" X>. What I meant was that X is not a sentence. So, even preceded by itself it's still not a sentence.

Your reasoning sounds like the fallacy of composition. Why would X have to be a sentence in order for <"X" X> to be a sentence?

What is the subject of the second X in <"X" X>? Is it <X>, i.e. the X between the quotation marks, or is it <"X">, i.e. a string of characters that includes the two quotation marks? We just don't know (that's why I suggested earlier to put the "The phrase" before the quoted part to remove the ambiguity.

You're proceeding from a false premise. The second X in <"X" X> does not have a subject. As you said, X is not a sentence. X is a sentence fragment. Subjects are something sentences have. <"X" X> is a sentence; it has a subject, the <"X"> plus part of the <X>: up to but not including the main verb.

As far as the quotation marks are concerned, the object consisting of the quotation marks and the embedded text refers to the embedded text; quotation marks do not quote themselves.

My earlier link contained a link to this counterexample:

"is a sentence fragment." is a sentence fragment.​

It's different from your example in that it is self-explanatory. The second part explains properly how to take the quoted part, i.e. as a sentence fragment, which it is. So we have a way of understanding what the whole means, although it's also not a sentence (no capital letter).

I disagree. So does Wikipedia. The rule requiring capital letters at the front of sentences is orthography, not grammar. Besides, the rule should be suspended when a sentence starts with a quotation, in the interests of making it easier to unambiguously indicate whether the quoted material starts with a capital letter.

Be that as it may, fine, have it your way. I'll just change my counterexample to start with a capital letter.

"IS A SENTENCE FRAGMENT." IS A SENTENCE FRAGMENT.

However, the example also does not pretend to be a sentence (unlike in your own example). So, although it's not a sentence, it is still both understandable and true. Yet, still not a true sentence.

How do you figure something can be true without being a true sentence? By being Thomas the Rhymer? ("True Thomas lay on Huntlie bank; ...")

Also, unlike your example, there is not suggestion of this thing being self-referential. There's no logical issue here at all.

The logical issue isn't with the example per se; the issue is that it's a counterexample to the rule of inference you proposed. "What I meant was that X is not a sentence. So, even preceded by itself it's still not a sentence." That does not follow. You cannot correctly deduce that <"X" X> is not a sentence from the circumstance that X is not a sentence.

Here's an even simpler counterexample.

"contains three words." contains three words.​

This thing is true, although not a sentence. It's Ok since it doesn't pretend to be one and if nobody says it is one.

"CONTAINS THREE WORDS." CONTAINS THREE WORDS.

That doesn't pretend to be a sentence; that is a sentence.

 

[Bomb#20]

If that's acceptable to you, how about this?

"Pigs fly. The sentence immediately following the sentence immediately preceding is false."​

Sure it works but the statement is still not a self-referential statement. The second sentence is self-referential but you need the preceding sentence for it to work. But, Ok, I should have said there is no "stand-alone" self-referential statement.
EB

Hmm. How about this then?

If there is a sentence immediately preceding then the sentence immediately following the sentence immediately preceding is false; contrariwise, if there is no sentence immediately preceding then the first sentence is false.​

Now it doesn't need any preceding sentence.

Doesn't work. You example relies on assumptions you are implicitly asking readers to make. Without them, there is no formal interpretation making the sentence necessarily self-referential.

I put these assumptions in between <>:

If there is a sentence immediately preceding <this one> then the sentence immediately following the sentence immediately preceding is false; contrariwise, if there is no sentence immediately preceding <this one> then the first sentence is false.​

In other words, this sentence may be about any sentence, not just this one.

Your example is identical in its principle to the example <This sentence is false.>

Hey, all this was based on the premise "If that's acceptable to you". If you're going to read my sentence as containing implicit "this one"s, then the same goes for your proposal, "The sentence immediately following is false. The sentence immediately preceding is true.". That would have to implicitly mean "The sentence immediately following this one is false. The sentence immediately preceding this one is true.". If mine doesn't work then neither does yours.

 

[Speakpigeon]

Hey, all this was based on the premise "If that's acceptable to you". If you're going to read my sentence as containing implicit "this one"s, then the same goes for your proposal, "The sentence immediately following is false. The sentence immediately preceding is true.". That would have to implicitly mean "The sentence immediately following this one is false. The sentence immediately preceding this one is true.". If mine doesn't work then neither does yours.

I pointed out myself when I offered my example that it was not self-referential. I offered it as an example of good grammar compared to your earlier examples.

My criticism of your latest example is that although we are able to interpret it as self-referential it is not stand-alone self-referential. This is because there is ambiguity as to what it refers to and you need the cooperative assumptions of the reader to remove this ambiguity, something that is already the case for the statement "This sentence is false."
EB

 

[Speakpigeon]

Your example can be reduced to: <"X" X>. What I meant was that X is not a sentence. So, even preceded by itself it's still not a sentence.

Your reasoning sounds like the fallacy of composition. Why would X have to be a sentence in order for <"X" X> to be a sentence?

What is the subject of the second X in <"X" X>? Is it <X>, i.e. the X between the quotation marks, or is it <"X">, i.e. a string of characters that includes the two quotation marks? We just don't know (that's why I suggested earlier to put the "The phrase" before the quoted part to remove the ambiguity.

You're proceeding from a false premise. The second X in <"X" X> does not have a subject. As you said, X is not a sentence. X is a sentence fragment. Subjects are something sentences have. <"X" X> is a sentence; it has a subject, the <"X"> plus part of the <X>: up to but not including the main verb.

As far as the quotation marks are concerned, the object consisting of the quotation marks and the embedded text refers to the embedded text; quotation marks do not quote themselves.

Ok, you agree that X is not a sentence, so where is the sentence? What is the subject of the second "is an untrue sentence" in the phrase <"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.>?

The second <preceded by itself in quotation marks> is adjectival (or a "modifier" of the head noun). So we can simplify your example while keeping the same essential grammar: <"preceded by itself in quotation marks is an untrue sentence." is an untrue sentence.> My point is that the subject is a phrase, not a sentence, and therefore we don't know what <is an untrue sentence> refers to.


In a way, you have an other kind of paradox here. Predicates refer to the subject of the sentence. The predicate <is an untrue sentence> says it refers to a sentence (i.e. it describes its subject as a sentence). Yet, the subject in this case is not a sentence at all, so the predicate contradicts itself. Or rather, the semantic of the predicate is contradicted by its grammar.
EB

 

[Speakpigeon]

As far as the quotation marks are concerned, the object consisting of the quotation marks and the embedded text refers to the embedded text; quotation marks do not quote themselves.

My earlier link contained a link to this counterexample:

"is a sentence fragment." is a sentence fragment.​

It's different from your example in that it is self-explanatory. The second part explains properly how to take the quoted part, i.e. as a sentence fragment, which it is. So we have a way of understanding what the whole means, although it's also not a sentence (no capital letter).

I disagree. So does Wikipedia. The rule requiring capital letters at the front of sentences is orthography, not grammar. Besides, the rule should be suspended when a sentence starts with a quotation, in the interests of making it easier to unambiguously indicate whether the quoted material starts with a capital letter.

I still don't like it but I can't ask you to care about that.

The link to Wiki is interesting but it doesn't make the specific claim you suggest.

And I could claim that they contradict themselves with the 2nd sentence in 3rd paragraph:

The phrase "this sentence" refers directly to the sentence as a whole.

Here they did put <The phrase> to front <"this sentence">, which is exactly what I'm suggesting should be done.

Anyway, I would agree that it's a minor point.

A more interesting point here is that this is about "indirect" reference. I would argue that all their examples in this case are not at all self-referential (contrary to what they assert).

There are also aspects you could take a leaf out of. For example look at the use of "when" + "makes" and "yelds" + "when" in their example of quined sentences.
EB

 

[Speakpigeon]

My earlier link contained a link to this counterexample:

"is a sentence fragment." is a sentence fragment.

However, the example also does not pretend to be a sentence (unlike in your own example). So, although it's not a sentence, it is still both understandable and true. Yet, still not a true sentence.

How do you figure something can be true without being a true sentence? By being Thomas the Rhymer? ("True Thomas lay on Huntlie bank; ...")

Where did you get the idea that only sentences could possibly be true or false?

More general than sentences, you can think of representations. Sentences themselves can be considered to be representational in nature but obviously not all representations are sentences. I take any meaningful representation to be true or false.

Also, philosophers and logicians would rather talk of propositions rather than sentences and they take propositions to be something quite different from sentences. According to this view, sentences merely seem to stand for propositions. Sentences therefore are never true or false. It's the proposition they stand for which is true or false.

I was not myself talking about the proposition your example above may stand for, but something which can be understood to be representational in nature, and therefore either true or false if it is at all meaningful.
EB

 

[Speakpigeon]

Your example can be reduced to: <"X" X>. What I meant was that X is not a sentence. So, even preceded by itself it's still not a sentence.

Your reasoning sounds like the fallacy of composition. Why would X have to be a sentence in order for <"X" X> to be a sentence?

What is the subject of the second X in <"X" X>? Is it <X>, i.e. the X between the quotation marks, or is it <"X">, i.e. a string of characters that includes the two quotation marks? We just don't know (that's why I suggested earlier to put the "The phrase" before the quoted part to remove the ambiguity.

You're proceeding from a false premise. The second X in <"X" X> does not have a subject. As you said, X is not a sentence. X is a sentence fragment. Subjects are something sentences have. <"X" X> is a sentence; it has a subject, the <"X"> plus part of the <X>: up to but not including the main verb.

<snip>

The logical issue isn't with the example per se; the issue is that it's a counterexample to the rule of inference you proposed. "What I meant was that X is not a sentence. So, even preceded by itself it's still not a sentence." That does not follow. You cannot correctly deduce that <"X" X> is not a sentence from the circumstance that X is not a sentence.

I already conceeded that we could take your example as a sentence. But the "rule" as you present it here is not what I meant. If we accept <"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.> as a proper sentence then I take it to be syntaxically equivalent to <"is an untrue sentence." is an untrue sentence.>, i.e. <"X" X>. This is because the phrase <preceded by itself in quotation marks> is irrelevant as a modifier of the head noun which does not modify the reference. So, if what is in quotation marks is not a sentence then it is neither a true nor an untrue sentence.
EB

 

[Bomb#20]

As far as the quotation marks are concerned, the object consisting of the quotation marks and the embedded text refers to the embedded text; quotation marks do not quote themselves.

My earlier link contained a link to this counterexample:

"is a sentence fragment." is a sentence fragment.​

It's different from your example in that it is self-explanatory. The second part explains properly how to take the quoted part, i.e. as a sentence fragment, which it is. So we have a way of understanding what the whole means, although it's also not a sentence (no capital letter).

I disagree. So does Wikipedia. The rule requiring capital letters at the front of sentences is orthography, not grammar. Besides, the rule should be suspended when a sentence starts with a quotation, in the interests of making it easier to unambiguously indicate whether the quoted material starts with a capital letter.

I still don't like it but I can't ask you to care about that.

The link to Wiki is interesting but it doesn't make the specific claim you suggest.

Okay -- what it specifically says is it's a "true statement". The OED defines "sentence" as "A set of words that is complete in itself, typically containing a subject and predicate, conveying a statement, question, exclamation, or command, and consisting of a main clause and sometimes one or more subordinate clauses.", and the example consists of a main clause containing a subject and predicate, so I figure that's close enough. YMMV.

And I could claim that they contradict themselves with the 2nd sentence in 3rd paragraph:

The phrase "this sentence" refers directly to the sentence as a whole.

Here they did put <The phrase> to front <"this sentence">, which is exactly what I'm suggesting should be done.

Not seeing how that's a contradiction. They did it your way in one place and my way in the other. English offers options.

 

[Bomb#20]

I already conceeded that we could take your example as a sentence. But the "rule" as you present it here is not what I meant. If we accept <"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.> as a proper sentence then I take it to be syntaxically equivalent to <"is an untrue sentence." is an untrue sentence.>, i.e. <"X" X>. This is because the phrase <preceded by itself in quotation marks> is irrelevant as a modifier of the head noun which does not modify the reference. So, if what is in quotation marks is not a sentence then it is neither a true nor an untrue sentence.
EB

All your objections seem to amount to the insistence that a construction of the form <P Qed by R> sometimes equals the result of R Qing P and sometimes equals just P, depending on conditions understood by you but not by me. Fine, have it your way.

"preceded by a copy of itself in quotation marks results in a sentence that isn't true." preceded by a copy of itself in quotation marks results in a sentence that isn't true.

Oops, I guess we need one more change.

"preceded by a copy of itself in quotation marks results in a meaningful representation that isn't true." preceded by a copy of itself in quotation marks results in a meaningful representation that isn't true.

 

[Juma]

"preceded by a copy of itself in quotation marks results in a meaningful representation that isn't true." preceded by a copy of itself in quotation marks results in a meaningful representation that isn't true.

True in what sense? The problem is that our brain is hardwired to find meanings and thus goes berserk to force in meanings where there are none. To say "that sentence is true" is meaningless until the reference is resolved even if it feels like it should mean something.

When handling logical systems you have a matter at hand: a proposition that you want to know if it is inside or outside the system.
The proposition "this proposition is inside" is automatically outside since it doesnt refer to anything inside.

The truth value of that proposition is not the same type as the truthvalues of the proposiotions about the matter.

 

[Speakpigeon]

The post preceding this one is true. The post following it is true too.
EB

 

[Speakpigeon]

conditions understood by you but not by me.

I have long gathered as much.

Another, much simpler way to explain is as follow:

You version: X is true, therefore X preceded by "not" is false.

Which is wrong.

My version: X is true and therefore the negation of X is false. However, X preceded by "not" is not false since X preceded by "not" is still X. (Not X) is false, but X, preceded or not by "not", is true.
EB

 

[Bomb#20]

conditions understood by you but not by me.

I have long gathered as much.

Another, much simpler way to explain is as follow:

You version: X is true, therefore X preceded by "not" is false.

Which is wrong.

My version: X is true and therefore the negation of X is false. However, X preceded by "not" is not false since X preceded by "not" is still X. (Not X) is false, but X, preceded or not by "not", is true.
EB

That doesn't explain anything; it just generalizes your claim and asserts that "not X" is an example of <P modified by a modifier> referring to P rather than to the result of the modification. You haven't said a bloody thing about the criteria that determine when such constructions refer to the unmodified head and when they refer to the result, in the manner of "seven multiplied by two".

In any event, that whole issue shouldn't matter for my latest incarnation. Or are you going to argue that switching from "is" to "results in" doesn't make a difference, that even <X <verb>ed by Y results in Z.> still isn't talking about the result of Y <verb>ing X, and that such a sentence claims that <X results in Z .>?

 

[Speakpigeon]

I have long gathered as much.

Another, much simpler way to explain is as follow:

You version: X is true, therefore X preceded by "not" is false.

Which is wrong.

My version: X is true and therefore the negation of X is false. However, X preceded by "not" is not false since X preceded by "not" is still X. (Not X) is false, but X, preceded or not by "not", is true.
EB

That doesn't explain anything; it just generalizes your claim and asserts that "not X" is an example of <P modified by a modifier> referring to P rather than to the result of the modification. You haven't said a bloody thing about the criteria that determine when such constructions refer to the unmodified head and when they refer to the result, in the manner of "seven multiplied by two".

Seven multiplied by two multiplied by three is forty-two, yes? We agree on that because that's the standard way of interpreting such expressions with the word "multiplied" in them. This, however, doesn't work with the word "preceded". The word "pig" preceded by the word "cow" is still the word "pig", not the phrase "cow pig", and this even though fronting the word "pig" with the word "cow" results in the phrase "cow pig". So "X" preceded by itself in quotation marks is still "X", not <"X" X>. And "X" fronted by itself in quotation marks is still "X" so you would have to say something like that: fronting "X" with itself in quotation marks results in the sentence <"X" X>.

In any event, that whole issue shouldn't matter for my latest incarnation. Or are you going to argue that switching from "is" to "results in" doesn't make a difference, that even <X <verb>ed by Y results in Z.> still isn't talking about the result of Y <verb>ing X, and that such a sentence claims that <X results in Z .>?

Yes, I do, depending on the verb used. See above.

The verb "result" is much better than "is" in this context. But we still have the problem that "X preceded by K is blue" only implies that X is blue, not that the result of fronting X by K is blue.

And we still have the problem of the interpretation of the part starting and ending in a quotation mark. Is it a phrase or a just a sequence of letters and quotation marks.
EB

 

[Bomb#20]

Seven multiplied by two multiplied by three is forty-two, yes? We agree on that because that's the standard way of interpreting such expressions with the word "multiplied" in them. This, however, doesn't work with the word "preceded". The word "pig" preceded by the word "cow" is still the word "pig", not the phrase "cow pig", and this even though fronting the word "pig" with the word "cow" results in the phrase "cow pig".

Huh. I'd have said the word "pig" preceded by the word "cow" is the phrase "cow pig". I guess the only way of settling our conflicting linguistic intuitions on this point would be a poll of native English speakers.

Be that as it may, you appear to be suggesting that English's general rule requires the referent to be the word "pig", and the answer to your ultimate question is "forty-two" only because English has a special convention specifically for the interpretation of arithmetic expressions. Hmm. So does that mean you'd say copper alloyed with tin is still copper, rather than bronze?

In any event, that whole issue shouldn't matter for my latest incarnation. Or are you going to argue that switching from "is" to "results in" doesn't make a difference, that even <X <verb>ed by Y results in Z.> still isn't talking about the result of Y <verb>ing X, and that such a sentence claims that <X results in Z .>?

Yes, I do, depending on the verb used. See above.

The verb "result" is much better than "is" in this context. But we still have the problem that "X preceded by K is blue" only implies that X is blue, not that the result of fronting X by K is blue.

I'm not following why "X is blue" matters any more, since I said "results in" rather than "is". I'd think you'd need to show that "X preceded by K results in blue" only implies "X results in blue." But have it your way. I might as well work around that objection at the same time I'm working around this one:

And we still have the problem of the interpretation of the part starting and ending in a quotation mark. Is it a phrase or a just a sequence of letters and quotation marks.
EB

The result of inserting a copy of itself in quotation marks into the sentence "The result of inserting a copy of itself in quotation marks into the sentence between the fourteenth and fifteenth words is a sentence that isn't true." between the fourteenth and fifteenth words is a sentence that isn't true.

 

[Speakpigeon]

Huh. I'd have said the word "pig" preceded by the word "cow" is the phrase "cow pig".

More bad English (although that would be just as bad in Chinese).

I guess the only way of settling our conflicting linguistic intuitions on this point would be a poll of native English speakers.

Like, you mean, voting Obama or George W. Bush president? Both were Ok votes do you think?

Be that as it may, you appear to be suggesting that English's general rule requires the referent to be the word "pig", and the answer to your ultimate question is "forty-two" only because English has a special convention specifically for the interpretation of arithmetic expressions. Hmm. So does that mean you'd say copper alloyed with tin is still copper, rather than bronze?

Yes.

The alloy sure is bronze but the copper remains copper at least to the extent that we still want to talk about individual atoms of copper as copper. We apparently do but we don't really mean the same thing. In one case we mean the metal copper with its particular macroscopic properties such as conductivity and malleability, while in the other we talk about the element copper, with its microscopic properties such as atomic weight, number of electrons, etc. I will guess that we don't measure the conductivity of the copper present in the alloy and it's also not possible to say that it still has malleability (bronze does).
So in that sens the answer is yes but not quite.
EB

 

[Bomb#20]

Huh. I'd have said the word "pig" preceded by the word "cow" is the phrase "cow pig".

More bad English (although that would be just as bad in Chinese).

I guess the only way of settling our conflicting linguistic intuitions on this point would be a poll of native English speakers.

Like, you mean, voting Obama or George W. Bush president? Both were Ok votes do you think?

Well, the first GWB vote wasn't since the SCOTUS majority stole the election from the Florida voters; but the other three appear to have been okay votes. I take it what you're getting at is that linguistics questions aren't decided by vote. So what are they decided by? By you? There's no meaning fairy dispensing linguistic truth to a restive language community. Meaning is determined by use. Language constructions mean what fluent speakers use them to mean. You appear to be arguing that the word "pig" preceded by the word "cow" is the word "pig" rather than the phrase "cow pig", regardless of whether the majority of fluent speakers would understand it to be the word "pig", solely on the grounds that understanding it to be the word "pig" seems more logical to you. You might as well tell a Frenchman that "Je ne regrette rien." is a double negative and actually means "I don't regret nothing.", so he's saying he does regret something; and if he means he regrets nothing then he's using "bad French". Just as it's no more up to English speakers to define the correct interpretation of French than it's up to the Academie francaise; likewise the correct interpretation of English isn't up to any Academie anglaise.

 

[Speakpigeon]

Good French standardly relies on the construction "ne ... pas". For example, "Je ne regrette pas mes efforts". So the expression "je ne regrette rien" is just a particular case of the general rule. Second, if you polled the French about it, they would give you confused and contradictory answers because most of them never think about that sort of things. So you are going to have to rely on educated and proficient speakers, a biased procedure since these people will have received an extensive formal and informal education in French grammar and will essentially repeat what their family, relations, and teachers would have told them is the conventions in French grammar. These conventions are loosely based on usage. The official French language is a fiction to the extent that very few people would really be able to speak it properly (it's too complicated). Usage itself is not unified so again you'll have to favour a community of speech against others for each linguistic feature of the language. Nothing fair about that and largely conventional. And, of course, this is true of all languages.

Yes language is determined by use but as such it is essentially an unknown object and worse a fictional object. There is no book that describes English as it is used (vocabulary, grammar, phonetics, usage, expressions etc.). Any description can only be both incomplete and biased. Who decides who is a fluent speaker? Ah, yes, some committee of fluent speakers.

Now, it's also a fact there's no book that says that the word "pig" preceded by the word "cow" is anything else than the word "pig". That it is the word "pig" is not even in question. The question is, why the word "pig" could possibly be anything else than the word "pig". Sure it can be the subject of a predicat and you will find plenty of books which will allow you to draw this inference. It can be an object, a modifier, etc. All legit. Not so with "pig" suddenly becoming the phrase "cow pig" just because it is preceded by the word "cow".
EB