Logic and self referential statements

[Speakpigeon]

Gaah! Looking at the wrong sentence. Clearly senility is starting to set in. Sorry, let's try that again...

Reflect on what "itself" refers to.

The first "itself" doesn't refer to anything since it's mentioned rather than used. The second "itself" refers to the head of the subject of the sentence, just as any "itself" would in a sentence with the structure ( ed by itself ). The subject of the sentence is the following sentence fragment:

preceded by itself in quotation marks is an untrue sentence.
​

Reflecting on that hasn't produced any enlightenment. Care to help me out?

There are two instances of the same text. The "itself" refers to the one in citationmarks, not the other one. Thus a better version would be:
"followed by the same text results in a untrue sentence." followed by the same text results in a untrue sentence.

But then the question is: what sentence? To make it self refering we always must add extra information. The sentence itself is never enough.

The "this" is always there but even if it is explicitily added it is not enough.

So: no there are no self referring sentences. But there are self referring systems.

And a sentence is not true or false because it states that it is.

More on substance, nothing can precede itself.

Not even God could.
EB

 

[Speakpigeon]

What sentence?

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

One, there is a difference between a phrase and a sentence. What is between the quotation marks in your version is a phrase but not a sentence. So what would be "preceded by itself" would be a phrase but not a sentence. If it's not a sentence it could neither be a true nor a false sentence.

Two, nothing can precede itself.

So let's try to remedy these flaws:

The phrase "preceded by a phrase in quotation marks with an identical wording makes an untrue sentence." preceded by a phrase in quotation marks with an identical wording makes an untrue sentence.​

This is broadly the same idea as Juma's ""followed by the same text results in a untrue sentence." followed by the same text results in a untrue sentence" (assuming that using "followed" rather than "preceded" isn't crucial to his point).
EB

 

[fast]

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

One, there is a difference between a phrase and a sentence. What is between the quotation marks in your version is a phrase but not a sentence. So what would be "preceded by itself" would be a phrase but not a sentence. If it's not a sentence it could neither be a true nor a false sentence.

Two, nothing can precede itself.

So let's try to remedy these flaws:

The phrase "preceded by a phrase in quotation marks with an identical wording makes an untrue sentence." preceded by a phrase in quotation marks with an identical wording makes an untrue sentence.​

This is broadly the same idea as Juma's ""followed by the same text results in a untrue sentence." followed by the same text results in a untrue sentence" (assuming that using "followed" rather than "preceded" isn't crucial to his point).
EB

"untrue" is not a good substitute for "not true" in contexts where the distinction between "false" and "not true" is important.

 

[Speakpigeon]

"untrue" is not a good substitute for "not true" in contexts where the distinction between "false" and "not true" is important.

I agree that making the distinction between false and not true is essential.

However, I take "untrue" to be a synonym of "not true". In English, the prefix "un-" signifies "not", so "untrue" is synonymous with "not true". Do you disagree with that?

Maybe your point was that what Bomb#20 really meant was "false" rather than "not true"? Me, I wasn't concerned with the logic of his example, only with trying to make it effectively, or unambiguously (i.e. not ambiguously), self-referential. But I guess that "false" would indeed be better from his point of view than "untrue" or "not true".
EB

 

[Juma]

"untrue" is not a good substitute for "not true" in contexts where the distinction between "false" and "not true" is important.

I agree that making the distinction between false and not true is essential.

However, I take "untrue" to be a synonym of "not true". In English, the prefix "un-" signifies "not", so "untrue" is synonymous with "not true". Do you disagree with that?

Maybe your point was that what Bomb#20 really meant was "false" rather than "not true"? Me, I wasn't concerned with the logic of his example, only with trying to make it effectively, or unambiguously (i.e. not ambiguously), self-referential. But I guess that "false" would indeed be better from his point of view than "untrue" or "not true".
EB

I think fast means that we should blind assume valued logic. In tri-logic untrue is not necessarily equal to false.

 

[NobleSavage]

Has anyone ever here ever googled, "recursion"? Try it.

 

[fast]

However, I take "untrue" to be a synonym of "not true". In English, the prefix "un-" signifies "not", so "untrue" is synonymous with "not true". Do you disagree with that?

I don't disagree, but I don't think the truth of that defeats my reasoning. My seemingly endless pursuit of understanding the distinction between, "invalid" and "not valid" has led me to my view. The lexical meaning of a term is a function of how it's collectively used by fluent speakers of a language, and dictionaries report on that, and though I'm not arguing against the accuracy of what's reported, I believe there's a subtle difference not taken into account that is only often exposed through analysis.

Since you're using the prefix, "un," consider the difference between "happy" and "unhappy." Yes, in this instance, "un" signifies "not", and so "unhappy" is synonymous with "not happy", and this accords with collective usage as reported by authoritative sources, like dictionaries. The problem arises when when we use the term, "unhappy" and apply it to things that can neither be happy or unhappy, for instance a rock.

When we say something is unhappy, we're really saying more than we think we are. Sure, we're saying just what we would be saying if we said of it that it's not happy, but (and this is important), we're also saying that what we're speaking of is something that can be happy or unhappy. I deny that rocks are the kinds of things that can be happy or unhappy, and I hold the opinion that rocks are not happy, but saying "not happy" doesn't imply "unhappy" even though the inverse is true.

See, it's the cases where there's an underlying category error that reveals the need to be careful when looking to the authoritative sources. It's not to say the dictionaries are wrong, as it does report on correct usage. It's just that it doesn't delve into the times when such usages don't apply.

 

[Speakpigeon]

Ok, I agree with your analysis of happy/not happy/unhappy. Does it translate to true/not true/untrue (in logic). I suspect that your analysis of "happy" etc. is correct because happiness is a spectrum from happy to unhappy (i.e. sad etc.) with "not happy" originally in the middle (neither happy nor sad). Of course "not happy" can also mean sad. It seems to me each word can receive a special treatment(e.g. "un-" does not equal "not") on top of the generic treatment (e.g. "un-" equals "not"). So, although you're correct about "happy" etc., your analysis does not necessarily translate to "true" etc.

In ordinary linguistic exchanges, when we use "untrue" or "not true" it is normally to mean false. We wouldn't normally use "untrue" or "not true" to mean "neither true nor false". So, no ambiguity.

I also guess that most of us here assume logic to rule and assume logic to be classical logic, according to which statements may be either true, false or neither true nor false. And then logic does not consider the latter case. In this context "false", "not true" and "untrue" are synonymous and there's again no ambiguity.

So it's only in philosophy (and in trivalent logics), and the philosophy of logic, that the question arises of making the distinction you suggest. So, in this context, could you explain what "untrue" could mean if not "not true"? Is this that some statements are not true yet not untrue?
EB

 

[Bomb#20]

Has anyone ever here ever googled, "recursion"? Try it.

Well, I would, but first I'd have to google "google", and, well, you know where that leads...

 

[Bomb#20]

"untrue" is not a good substitute for "not true" in contexts where the distinction between "false" and "not true" is important.

Since you're using the prefix, "un," consider the difference between "happy" and "unhappy." Yes, in this instance, "un" signifies "not", and so "unhappy" is synonymous with "not happy", and this accords with collective usage as reported by authoritative sources, like dictionaries. The problem arises when when we use the term, "unhappy" and apply it to things that can neither be happy or unhappy, for instance a rock.

When we say something is unhappy, we're really saying more than we think we are. Sure, we're saying just what we would be saying if we said of it that it's not happy, but (and this is important), we're also saying that what we're speaking of is something that can be happy or unhappy. I deny that rocks are the kinds of things that can be happy or unhappy, and I hold the opinion that rocks are not happy, but saying "not happy" doesn't imply "unhappy" even though the inverse is true.

"preceded by itself in quotation marks is a sentence that isn't true." preceded by itself in quotation marks is a sentence that isn't true.

Happy?

More on substance, nothing can precede itself.

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

Happier? More not unhappy?

 

[fast]

So, in this context, could you explain what "untrue" could mean if not "not true"?

At first glance, I'd consider "untrue" to be more like "false" than "not true".

Is this that some statements are not true yet not untrue?

If we equate "untrue" to "false," then "not false" may either be "true" or "not true".

 

[fast]

Happy?

If you knew the women in my life, you wouldn't ask.

 

[Bomb#20]

Are you proposing to get out of the bind using an argument to the effect that the referent of "This" is ambiguous? "This" is inessential to the problem.

"preceded by itself in quotation marks is an untrue sentence." preceded by itself in quotation marks is an untrue sentence.

One, there is a difference between a phrase and a sentence. What is between the quotation marks in your version is a phrase but not a sentence. So what would be "preceded by itself" would be a phrase but not a sentence. If it's not a sentence it could neither be a true nor a false sentence.

True; but the full sentence doesn't claim the part in quotation marks is a sentence, or call it true or untrue. It only claims doing certain operations to the part in quotation marks gives you an untrue sentence.

So let's try to remedy these flaws:

The phrase "preceded by a phrase in quotation marks with an identical wording makes an untrue sentence." preceded by a phrase in quotation marks with an identical wording makes an untrue sentence.​

But that sentence doesn't describe an identical sentence. It describes something different, something that doesn't have the phrase "The phrase" on the front. If you think that part is necessary then you need to include it in the sentence's description of itself.

Incidentally, Doug Hofstadter made up a word for this business of writing a phrase twice with the first one in quotation marks. He called it

Show

", to quine a phrase.", to quine a phrase.

 

[Juma]

One, there is a difference between a phrase and a sentence. What is between the quotation marks in your version is a phrase but not a sentence. So what would be "preceded by itself" would be a phrase but not a sentence. If it's not a sentence it could neither be a true nor a false sentence.

True; but the full sentence doesn't claim the part in quotation marks is a sentence, or call it true or untrue. It only claims doing certain operations to the part in quotation marks gives you an untrue sentence.

So let's try to remedy these flaws:

The phrase "preceded by a phrase in quotation marks with an identical wording makes an untrue sentence." preceded by a phrase in quotation marks with an identical wording makes an untrue sentence.​

But that sentence doesn't describe an identical sentence. It describes something different, something that doesn't have the phrase "The phrase" on the front. If you think that part is necessary then you need to include it in the sentence's description of itself.

Incidentally, Doug Hofstadter made up a word for this business of writing a phrase twice with the first one in quotation marks. He called it

Show

", to quine a phrase.", to quine a phrase.

The thing is that normal everyday language is ho indistinct to be of any use in dicussions like this.
What does it mean that a sentence is true? What does it mean that a sentenwce refer somehhing? Can a sentence have a "itself" at all? Etc

 

[fast]

"preceded by a copy of itself in quotation marks is a sentence that isn't true." preceded by a copy of itself in quotation marks is a sentence that isn't true.
This doesn't make much sense. It's confounded even further by the fact it's a grammatically incorrect sentence containing a grammatically incorrect sentence, not to mention that the sentence minus the quote is identical to the quote. It's a mess!

 

[ontological_realist]

More on substance, nothing can precede itself.

Not even God could.
EB

"Nothing can precede itself"

Great!

 

[ontological_realist]

If I remember correctly, even before Russell, Gottlob Frege, a German mathematician and philosopher, showed that mathematics was a subset of logic and that logic as well as mathematics refer not to human thinking but to objective reality. This last part seems very interesting to me!

The last part seems wrong to me.
For me, maths are a tool. A very complex and fascinating tool, but their only connection with reality is when you choose a mathematical system whose axioms are modeling the scientific theories you want to expand on.

"logic as well as mathematics refer not to human thinking but to objective reality."

I do not know if that is true or not. But I am interested in exploring whether logic refers to reality or to human thinking.

By logic here I mean only:-

A is not ~ A , plus all that can be deduced from this.

Is the statement below true or untrue:-

"You do not have to know what it is to know that it is what it is."

--

 

[Speakpigeon]

At first glance, I'd consider "untrue" to be more like "false" than "not true".

Is this that some statements are not true yet not untrue?

If we equate "untrue" to "false," then "not false" may either be "true" or "not true".

Surely it depends on the context. Most teachers of logic would stick to classical logic, dismiss "untrue" as non-standard and equate "not true"with "false" and "not false" with "true", simply because classical logic does not consider statements that are neither true nor false.

If your argument is grounded on usage then you have to accept that different communities of speakers will use the same words differently and then, following your own prescription, you should adapt to their usage.

Unless your point is more metaphysical?
EB

 

[Speakpigeon]

One, there is a difference between a phrase and a sentence. What is between the quotation marks in your version is a phrase but not a sentence. So what would be "preceded by itself" would be a phrase but not a sentence. If it's not a sentence it could neither be a true nor a false sentence.

True; but the full sentence doesn't claim the part in quotation marks is a sentence, or call it true or untrue. It only claims doing certain operations to the part in quotation marks gives you an untrue sentence.

No it does not. The point was that your example is not a sentence at all. Therefore it is also not an untrue sentence.

There is also no "operations" at all (except to read the phrase and try to interpret it). So, it's just a phrase and then no amount of reading and interpretation will make it a sentence.

So let's try to remedy these flaws:

The phrase "preceded by a phrase in quotation marks with an identical wording makes an untrue sentence." preceded by a phrase in quotation marks with an identical wording makes an untrue sentence.​

But that sentence doesn't describe an identical sentence. It describes something different, something that doesn't have the phrase "The phrase" on the front. If you think that part is necessary then you need to include it in the sentence's description of itself.

Yes, that's true, and I suspect this is a fundamental limitation of language.

You tried to evade the problem by pretending your example was a proper sentence when it wasn't. I showed you what would be a proper sentence. I accept the example doesn't work but at least this is grammatically correct. Now you can try to make it work if you think that there should be a solution. Me I think there is no formal solution, i.e. something cannot refer to itself just by itself, i.e. only on the basis of formal rules (grammatical, logic, etc.).

The following example, I think already suggested, works:

"The sentence immediately following is false. The sentence immediately preceding is true."​

But it's not self-referential.
EB

 

[Kharakov]

The following example, I think already suggested, works:

"The sentence immediately following is false. The sentence immediately preceding is true."​

But it's not self-referential.
EB

A duplicitous statement is not true or false, it's both.

T= True= not duplicitous or false.
F1= False = not duplicitous and not true.
F2= False = duplicitous or not true.
D= Duplicitous= true and false and neither
N= No truth value= not T, F, or D

The paradox relies on incomplete definitions of true and false which don't contain the condition of duplicity.

The sentence immediately following is F2. The sentence immediately preceding is T.

Does order of evaluation matter?