The Liar Paradox - Is it even a valid statement?
The liar paradox is that the statement: ‘This statement is false’ appears neither true nor false. If the statement is true, then it is false. If the statement is false, then it is true (and so on):
https://en.wikipedia.org/wiki/Liar_paradox
I’m going to argue that the paradox is due to the statement not being a valid statement. The definition of a statement:
https://en.wikipedia.org/wiki/Statement_(logic)
In our case, we take the first definition: ‘a meaningful declarative sentence that is true or false’.
I think the word ‘declarative’ is important; a statement declares a fact; it does not in addition instantiate that fact to a given truth value.
So a statement is associated with but distinct from a truth value. For example: ‘all cats are black’ is distinct from ‘false’.
Contrast this with ‘this statement is false’; the truth value is embedded in the ‘statement’. It is sufficiently different in structure to a normal statement as to be classed as not a statement. The truth value is also instantiated to false making the 'non-statement' both contradictory and redundant.
It should IMO be handled differently in logic than a normal statement as it has an in-built truth value.
So if statements including their own truth value where excluded from logic, then the liar paradox would not be a paradox. This would make logic self consistent again (I believe Godel's objections would go away though I need to look at that conjecture further).
https://en.wikipedia.org/wiki/Liar_paradox
I’m going to argue that the paradox is due to the statement not being a valid statement. The definition of a statement:
https://en.wikipedia.org/wiki/Statement_(logic)
In our case, we take the first definition: ‘a meaningful declarative sentence that is true or false’.
I think the word ‘declarative’ is important; a statement declares a fact; it does not in addition instantiate that fact to a given truth value.
So a statement is associated with but distinct from a truth value. For example: ‘all cats are black’ is distinct from ‘false’.
Contrast this with ‘this statement is false’; the truth value is embedded in the ‘statement’. It is sufficiently different in structure to a normal statement as to be classed as not a statement. The truth value is also instantiated to false making the 'non-statement' both contradictory and redundant.
It should IMO be handled differently in logic than a normal statement as it has an in-built truth value.
So if statements including their own truth value where excluded from logic, then the liar paradox would not be a paradox. This would make logic self consistent again (I believe Godel's objections would go away though I need to look at that conjecture further).
Comments (359)
1. this is a statement
2. and it is false
So 2 says 1 is false. IE it is not a statement.
Not all statements in a given language can be given a truth value, in that they don't refer to anything that allows to determine a truth value. Language is used to refer to things we observe, but in "This statement is false" we're never saying what we're referring to.
Quoting leo
If it can't be given a truth value, its not a statement would be a simple rule to adopt.
Yes I'm not disagreeing, I was just giving my point of view on the 'paradox'.
We can say things such as "This sound is purple" or "This smell is true", but they don't refer to anything in the range of what we experience, or at least I can't form a mental image of whatever these statements may refer to. Same goes with "This statement is false", not all statements that can be uttered in a language are meaningful, and I agree it's not much use to spend much time pondering about them or trying to fit them into some grand framework.
Like the paradoxes in the theory of relativity, they are a consequence of the postulates at the basis of the theory, we can choose to ignore them and just "shut up and calculate" and make predictions that fit somewhat with observations, or we can change the framework (change the theory, pick different postulates) so that the paradoxes disappear while making similar observable predictions, in the end it depends whether we're looking for mathematical 'elegance' with symmetries and so on or if we're looking for intuitive simplicity. I'm a bit like you on this, I prefer intuitive simplicity that can be grasped by many over mathematical elegance that leads to complexity, paradoxes and confusion.
I think that anything that is self contradictory or nonsensical should be classed as a non-statement - such statements disprove themselves if you see what I mean.
Quoting leo
Yes, just like infinity clouds and complicates set theory, the loose definition we have of statement greatly complicates logic.
It is complicated stuff that I admit I don't fully understand:
'The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such consistent formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.'
https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
These theorems place profound epistemological limitations on formal logic and mathematics. If we remove this class of malformed, contradictory statements then these limitations do not apply any more.
1) this is a statement
2) this is not provable
IE it is not provable if it is a statement. Also if you read the OP, it is syntactically different from a statement.
Right. The so-called "Liar's paradox" seems quite silly, akin to something a third grader thought up at recess.
Quoting leo
Me too. :up:
Knowing something about logic and the context helps to understand why the liar paradox is of interest.
Quoting Leontiskos
Good then that no one is forcing you to spend time on it. But meanwhile it is worth time to people who study logic.
Some statements do mention truth values.
Quoting Devans99
The incompleteness theorem is not at all disqualified by the liar sentence. And it's not a conjecture.
We can formulate the liar paradox without saying "is a statement".
That is not the Godel sentence.
Quoting Devans99
We do prove it is a sentence in the language of the theory at hand. And we don't the sentence in the theory.
For a formal language, per a given interpretation, every sentence has a truth value.
The incompleteness theorem does not rely on the liar sentence.
Regarding the liar sentence, what postulates?
The incompleteness theorem does not rely on any sentences that can't be formed in the language of arithmetic.
That is not the Godel sentence.
The Godel sentence is a sentence in the language of arithmetic. Given the standard interpretation of the language of arithmetic, the Godel sentence says something about natural numbers. But also, the Godel sentence is true in the standard interpretation if and only if it is not provable in the system (whichever system the incompleteness theorem is being proven about). In that sense, the Godel sentence says "I am not provable", but keep in mind that "I" is only our informal description; the language doesn't have such pronouns. And, the Godel sentence does not say "I am a sentence" nor mention "sentence". Rather, it is in the meta-theory that we show that the Godel sentence is indeed a sentence in the language of arithmetic and that, if the system is consistent, then the Godel sentence is not provable in the system, and the negation of the Godel sentence is not provable in the object theory, and that the Godel sentence is true in the standard model for the language. (Note that Godel did not specify formal models, as formal models were not explicated until later, and he proved for a different kind of system. Instead, he simply worked in ordinary mathematics regarding natural numbers without putting a fine point on that in terms of models and a standard interpretation.)
How is an unprovable proposition different from a postulate?
There are two different things:
(1) The incompleteness theorem. It's not a conjecture. It is proven. It is a theorem about certain kinds of object theories.
(2) The Godel sentence. In proving the incompleteness theorem, we prove that the Godel sentence is a sentence in the language of the object theory. And we prove that, if the object theory is consistent, then the Godel sentence is not provable in the object theory.
But to my point, if Godel proved there are limitless unprovable propositions and if these propositions can be used to make theorems then they are no more than postulates and we already knew that math had unprovable postulates on which the whole structure was built (you can't prove everything). So what exactly did Godel add to our body of knowledge?
You can perfectly know the construction logic of a system but that does still not allow you to know its complete truth. So, even if we manage to figure out the perfect theory of the physical universe, we will still not be able to predict most of its facts.
My point was that the incompleteness theorem is not a conjecture.
/
I take it that 'postulates' means axioms.
For every sentence, there is a system of which the sentence is an axiom.
A sentence is provable or not relative to a given system.
Every axiom is trivially provable in a system in which it is an axiom (by the trivial proof of putting the axiom itself as the only line in a proof).
For every sentence, trivially, there is a system in which the sentence is provable (by making the sentence an axiom).
So, the incompleteness theorem is not about what is provable simpliciter, but what is provable in certain kinds of systems.
The incompleteness theorem is: If a theory is formal, sufficient for a certain amount of arithmetic and consistent, then the theory is incomplete. That is highly informative: It tells us that there is no axiomatization of arithmetic such that every sentence of arithmetic is a theorem or its negation is a theorem. It tells us that there is no axiomatization that proves all the true sentences of arithmetic. It tells us that there is no algorithm to determine whether any given sentence of arithmetic is true. And the methods of the proof lead to profoundly informative results such as the unsolvability of the halting theorem and that there is no algorithm to determine whether a given Diophantine equation is solvable.
You seem to not be distinguishing between (1) For any given system, the axioms are not proven from previous theorems and (2) Given any consistent set of axioms sufficient for a certain amount of arithmetic, there are sentences of arithmetic such that neither the sentence not its negation is provable from the axioms, thus there are true sentences of arithmetic not provable from the axioms.
(1) is a trivial given. (2) is a remarkable result.
That is ridiculously overbroad and vague.
That is what Hawking has said on the matter:
Isn't it rather your own criticism that is ridiculous?
Unlike your post, that quote seems at least fairly clear and doesn't make an overbroad mischaracterization of incompleteness.
Noson Yanofsky writes:
What I wrote, is the combination of what Hawking and Yanofsky wrote on the matter. Why would that be an "overbroad mischaracterization"?
For a denumerable language, there are the same number of unprovable statements as provable ones, viz. denumerably many.
And he switched from 'statements' to 'facts', thus throwing off the count.
Quoting Tarskian
Too bad I'm not getting paid for correcting your stuff:
Quoting Tarskian
Incompleteness doesn't pertain to systems in general. Only to systems of a very certain kind.
"know its complete truth" is vague. What we could say is, "there are true sentences that are not provable". And no person can know individually infinitely many true sentences anyway.
"know the construction logic of". What is a "construction logic"? Maybe you mean the construction of the syntax? Better yet, just to say "the syntax rules".
You write slop. Though, that post is not your worst.
It was an answer to the relevance of Godel's theorem. Of course, it only applies to systems in which it is provable.
Quoting TonesInDeepFreeze
The system is a theory with a language. So, that is the "construction logic".
It emphasizes that you are in control of its true nature.
It's a bit like building a machine according to plan but you cannot predict everything it will be doing when it is running.
But you start out by mentioning logic in general, thus giving the impression that systems in general are incomplete, thus adding to the general confusion so prevalent on this point.
Quoting Tarskian
I usually take a (logistic) system to consist of a language, axioms and inference rules. And I take a theory to be a set of sentences closed under provability. A theory may be the set of theorems in a language and derivable from axioms with rules. So, with each system, there is the theory induced by that system.
It was an answer to "So what exactly did Godel add to our body of knowledge?".
My answer was a combination of what Hawking had said on the matter along with Yanofsky's take on the matter, without going into the nitty gritty details of when Godel's theorem is applicable because that was not the question to begin with.
No, though some argue something like that.
Thank you for making mention to Ramon Llull.
I hardly see references or allusions from my country's philosophers, thinkers, and mystics. I respect your cultural knowledge. Another significant Peninsular author is San Isidoro de Sevilla.
Right. A statement is about something, and, as a statement is separate from that something.
But “this statement is false” is about itself.
So it has no content to refer to other than the fact that it is a statement.
Quoting Devans99
Right. And there is nothing distinct from this statement to adjudge its truth value, to adjudge its content.
I agree it is not a statement, meaning it is not about anything. Not in the normal use of statements. It’s a fun logical puzzle, where the exercise of playing with it can yield some content about logic and language and truth. But if you don’t bring that content with you, it says nothing about anything, like saying “this statement is Fred”.
You don't have to go into details merely to avoid egregiously mischaracterizing the subject. I stated the theorem in just one sentence, and using only ordinary words. Plus the other dangling sloppiness in what you wrote.
A superb book that explains the theorem and discusses various reactions to it: 'Godel's Theorem' by Torkel Franzen.
The question was not about how to state the theorem. The question was about the value of the theorem.
In the context of the question "So what exactly did Godel add to our body of knowledge?", everything you say may be perfectly correct, but what answer does that give to the question at hand?
The "value of a theorem" is a philosophical question and not a technical one. It is not about giving precise technical details about what the terms "theorem", "theory" or "system" mean. The real answer will simply be lost amidst technical details that are irrelevant to the question at hand.
According to Stephen Hawking, Gödel's theorem is valuable because it shows us why positivism is futile. Yanofsky's work shows that Gödel's theorem is omnipresent. It is not an "overbroad mischaracterization" to state that Gödelian facts -- true but not provable -- are most likely omnipresent in our physical universe. Gödelian facts most likely massively outnumber predictable facts.
We most likely live in a Gödelian universe and not in a universe of Laplace's demon. That is the real metaphysical implication of Gödel's theorem.
The reason why Gödel's theorem has not yet been absorbed into modern metaphysics, almost a century after its discovery, is because of the incessant use of impenetrable language, meant to insist on irrelevant technical details, instead of dealing with the metaphysics that it implies.
Yes, it seems to me that this is just another case of "philosophers" confusing themselves.
However you slice it, the intent of the "liar" determines whether he is lying. He either is or he is not. There is no both-and. The same goes for someone who claims to be speaking falsely rather than lying. Either they intend to speak falsely or they do not. Many "philosophers" mistakenly hold that sentences have meaning apart from speakers, and when one reifies sentences in this way they have taken the first step towards this sort of self-confusion. They strangely believe that a sentence can self-negate itself because they have taken their eye off the ball: the speaker.
This is assuming lie as equivalent to some opposite forms.
How we interpret the sentence matters. Some will do so more literally than others and use their own methodology. If it is paradoxical then try to make it not so and see if any meaning can be established.
Yes. I think Kripke's solution, as described in the Wikipedia article Liar Paradox, seems to be the most reasonable.
A statement can only be true or false as it refers to the world. The statement "snow is white" is true IFF in the world snow is white.
As the statement "this statement is false" doesn't refer to the world, but only refers to itself, the words "this", "statement", "is" and "false" have no sense, as sense only comes from reference to the world, meaning that the statement "this statement is false" is senseless.
As the statement "colourless green ideas sleep furiously" expresses a nonsense proposition, then so does the statement "this statement is false".
As you say, a statement such as "this statement is false" may declare something without giving a truth-value to that something it has declared.
I'm not saying that Godel proved the mind is non-computational or that the brain is not solely a type of machine. The middle ground is to ask whether understanding Godel or having the capacity in the brain to think it proves the brain is not a computational machine. Yep
Your answer to the question includes a terribly misleading characterization of the theorem.
The question was:
Quoting Gregory
As far as "exact", I responded:
Quoting TonesInDeepFreeze
Those are exact and include the most salient implications of the theorem. Of course, a lot more came in the wake of the theorem, but a single post could not be exhaustive even as to mathematics. Also, in other threads I've commented on the matters of the incompleteness theorem in philosophy of mathematics. I don't have comments at this time on the incompleteness theorem in connection with science, epistemology, ontology and metaphysics. But I did recommend an excellent book as a starter kit. If that is not sufficient for you, then so be it; I'm not on retainer to answer all your questions.
The question didn't ask about the "value" of the theorem. It asked "what exactly did it add to our body of knowledge?" It added exact mathematical knowledge. Much of that is technical. But also, I answered in terms that are both technically accurate and also easily understandable if one took just a bit of time to understand the basic terms such as 'consistent', 'axiomatization', etc. Anyone is free to provide an even more informal explanation, but if the liberties taken in that endeavor lead to egregious mischaracterization, then that deserves be noted. And when the theorem is discussed in general, it is worthwhile to correct and clear up misconceptions about the theorem - both general and technical.
You are remarkable!
Quoting Tarskian
You gave your definition. So I responded with what I consider to be better a explanation. You felt a need to add your notion of 'system' in terms of 'language', but you fault me for providing better information. And you complain about "precise technical details" when my explanation was not even so technical:
Quoting TonesInDeepFreeze
language
axioms
inference rules
sentence
provability
closed under provability
theorem
theory
An understanding of those very basic rubrics is needed to even start discussing what the implications of the incompleteness theorem are. And if one doesn't know, then one can look in any introductory text or article on mathematical logic, or perhaps find one of many posts I've written that explains various terms, or even just ask me now about them, as given time, energy and interest, I'll respond.
You're continual insistence that discussion should be held only at the level of technicality and detail that you personally prefer is arrogant and irrational. Especially as often the subject does require being clear on certain technical matters, indeed as the subject concerns a technical subject, even if a particular discussion is centered on general, less technical ramifications of the technical mathematics. And especially as you often enough post your own technical formulations (often enough, they're botched).
You are really too much! How did you get so mixed up and unreasonable?
You arrogate to yourself what is "relevant" and what is the "question at hand". And you arrogate to yourself what level of technical detail should be mentioned.
Quoting Fire Ologist
Quoting RussellA
Yep. :up:
Or the so-called "Liar's paradox":
Such things as 'consistent', 'system', 'proof' are not "impenetrable". But sometimes more technical terminology needs to be mentioned - so that the incompleteness theorem is not incorrectly overgeneralized, misconstrued or misrepresented. If one is claiming implications in science and philosophy from the incompleteness theorem, then those claims should not be based on incorrect characterizations of what the theorem actually is.
There are formulations in which there is no speaker nor reference to "I' or things like that.
Quoting Leontiskos
This sentence has five words.
Not true?
It is true that we can treat sentences as objects of predication, but the difference is that the number of words that a sentence contains is a material property, not a formal property. So could say, "Colourless green ideas sleep furiously," has five words, but he could not say, "Colourless green ideas sleep furiously," is true (or meaningful). Counting words and affirming a truth value are two different things.
First, putting 'philosophers' in scare quotes is sophomoric.
Not every instance of a sentence needs to be considered dependent on a particular speaker.
For example, in a math book may appear sentences that were typed by an author but are not considered to be specific to any one person. For example, I can display the sentence, "Harry Truman was a president" and that sentence can be discussed no matter that its just typed by me.
Beyond that, one of the lessons of the liar paradox, due to Tarski, is that in certain interpreted languages, a liar sentence cannot be formulated
I asked whether the sentence is true.
Aside from the whether a sentence is part of "the world", obviously sentences are true or false when they refer to other sentences: "'Joe is cool' has three words" is true. "'This sentence has five words' has five words" is true.
But the other poster said that sentences have truth value only if they refer to "the world" and not themselves. But is that true? "This sentence has five words" has no truth value?
Count the words and decide whether or not the sentence is true, or don't decide.
There is always an implicit or implied speaker. When you consider a claim like that you are implying the linguistic intentions of the average English speaker in order to infer meaning. A nonsensical statement fails in all of this, insofar as there is no true speaker and there is no implicit speaker. The only people who pretend that such nonsensical statements have meaning are, again, "philosophers."
Quoting TonesInDeepFreeze
You continue your habit of falsely attributing quotes. He said nothing about the "material" world.
You are lying that I "continue". Among thousands of posts, not more than a handful of times, I've botched attribution, and I've corrected it immediately when I found out. And this time, I corrected the quote to take out 'material' before you posted (of course, I'm not blaming you for not seeing that before you posted, as obviously you were posting at the same time as I was editing).
Meanwhile, in another thread, I fulsomely documented your lies about what I posted, more than once. And your response was an obnoxious false attack on me while you didn't have the integrity to at least recognize that you had claimed I had said the opposite of what I said.
Quoting Leontiskos
Not for me. I can consider a sentence for consideration without assuming an implied speaker, and certainly not an implied speaker who asserts it to be true.
You are full of vapid nitpicking. But I am glad you corrected your mistake this time.
Quoting TonesInDeepFreeze
Sure you do. When someone considers the claim, "Colourless green ideas sleep furiously," you will inform them that the statement they are considering is nonsensical. We could say that to consider a possible utterance is to speak it secundum quid, and what is not able to be spoken is not able to be considered. The objection to such a consideration is always something like, "No one in their right mind would ever speak such a thing." To consider an utterance that has no possible speaker is to consider a nonsensical utterance.
Bringing this back, then, to the OP, we should ask whether the "sentences" in question—along with their attributed meaning—have any possible speaker. For example, is it possible for someone to speak, "I am lying," while simultaneously meaning that they are lying and that they are not-lying? No, it is not. There is no possible speaker in such cases, and hence the "sentences" are nonsensical (even in the additional cases where they are thought to have an extrinsic object).
Again, the true sentences are not provable in certain systems, but provable in others. We cannot prove the Godel sentence in, say, PA, but we can prove it in other systems. And, in other systems, we can prove that it is true in n other systems.*
* The distinction between (1) proving a sentence in a system and (2) proving that the sentence is true in an certain interpretation:
(1) In a system S, show a derivation of the sentence P. That is syntactical.
(2) For a given interpretation R of the language for S, show in another system T, a derivation of 'P is true per R'.
Talking about implied speakers, I do take it that there is a speaker behind "You continue your habit [...]" and that speaker chooses the words intentionally and for effect. And I refer now to that speaker as 'you'.
You wrote that I "continue a habit" of false attribution. But, again, (1) It is a light year away from a "habit". Again, over thousands and thousands of posts I've erred sometimes (as would just about any imperfect human). But anytime it's been pointed out to me or I've discovered it, I've acknowledge the error. And, in this case, I realized the error myself and immediately corrected in edit. (2) It is not vapid nor nitpicking to catch you claiming it is a continuation of a "habit". I take it that you wrote that it is a continuation of a habit to make a point that it is a continuation of habit and that you did that for effect.
You wrote a falsehood, and apparently for effect. Instead of owning your own words, you speciously turn it back on me, to fault me for catching your lie.
Meanwhile, still not acknowledgement of your lies about me elsewhere that actually were continued, and continued after I called you on them.
Quoting Leontiskos
You skipped my examples that are not of that kind.
But as to your example.
Just now, you referenced the sentence "colourless green ideas sleep furiously" without there being an implied speaker other than a hypothetical one. You were able to type the sentence, reference it, and still you are not the speaker of the sentence.
I'll do it again. Consider the following sentence that I am displaying but not asserting:
Colorless green ideas sleep furiously.
There is no implied speaker, especially not one asserting.
And previously:
Quoting TonesInDeepFreeze
Also, consider the following sentence that I am not asserting but merely displaying so that we can talk about it:
This sentence has five words.
Perhaps you have a habit that you are not aware of. Someone wrote a single post in the whole thread and you managed to misquote that single, short post. I submit that what is at play is the strawmanning that you are often engaged in, for your idiosyncratic interpretations always harm the legitimacy of your interlocutor's position.
Quoting TonesInDeepFreeze
There is a wonderful dovetailing between you and this thread with respect to conflating (purported) falsehoods with lies. But we've been over that already.
Quoting TonesInDeepFreeze
I addressed your example of word-counting.
Quoting TonesInDeepFreeze
Where have I said that the implied speaker cannot be hypothetical?
Quoting TonesInDeepFreeze
I addressed this in my reply to that post.
Quoting TonesInDeepFreeze
Again:
Quoting Leontiskos
"This sentence has five words," has a possible speaker, therefore it can be spoken, and therefore it can be spoken secundum quid (in the form of a consideration). When we consider a statement we say, "What would it be like to make a statement such as this? :chin:" When, "No one in their right mind would ever speak such a thing," then it cannot be legitimately considered.
Quoting Leontiskos
(1) Whatever your definitions of 'material property' and 'formal property', the question was:
Quoting TonesInDeepFreeze
(2) The comparison with "colorless green ideas" is not apt, since I am not asking about a sentence that has such problematic phrasing as that one.
The point was that the other poster said we should eschew self-referential sentences since they don't make claims about "the world".
But (a) Are sentence not part of the world? and (b) The sentence "This sentence is [s]false[/s] true" is self-referential, but is it not true? [corrected in edit]
Quoting Leontiskos
The matter I addressed whether self-referential sentences all must be disqualified, not whether the liar sentence in particular must be disqualified.
And we may consider sentences that are displayed without implication that they have an implied or even hypothetical speaker. There instances in which we may consider display of a sentence so that we may consider it in and of itself.
Quoting Leontiskos
At that point, that was about a self-referring sentence, not about implied speakers.
And the question does not reduce to counting words:
Later, I also gave examples about implied speakers.
Quoting Leontiskos
It's good that we agree that there may be hypothetical speakers.
Quoting Leontiskos
(1) "Perhaps" just about anything. Perhaps you don't know what you're talking about. Actually, you don't know what you're talking about. If it were a habit, then it would be more than a few instances. Moreover, if a few instances suffices to be a habit, and ones where the person refused to acknowledge, then you have a quite nasty habit.
(2) When I saw my post, I immediately recognized that 'material' was not correct. So I immediately corrected. That goes to my credibility not against it. When I see a newspaper that has a self-corrections section each day, then I credit that publication for that not discredit them for it. Rather than falsely say I have a habit of falsely attributing, true statements would be "TonesInDeepFreeze, has a long record of quite accurate posting, though, as with any imperfect human, he sometimes errs; but he as an exemplary record of correcting any error that he finds or is pointed out to him."
(3) You commit the fallacy of false sampling. For any given error by anyone, we could consider it in context of the few recent posts or in context of thousands and thousands of posts. Your fallacy is of the forrm "I went to Kansas City and got in a car accident the moment I got in a car. So Kansas City is a dangerous place to be in a car".
(4) But if we did adopt your false sampling speciousness. In a thread, you completely reversed what I said on the central topic. And you continued to lie in that way after I brought it your attention at least three time. So, by sampling in that thead alone, we may conclude that you lie habitually.
(5) It was not strawmanning. I mistakenly recalled what I read in his post, then immediately corrected. Moreover, my argument didn't even depend on whether the reference was to 'the world' or 'to the material world.
[added in edit] (5a) I am not dishonest to intentionally strawman. But even if I were (which I'm not), I'm not stupid to blatantly do it. If I had not corrected myself, but instead tried to get away with a strawman, then it very likely work directly against me.
(6) You accuse me of captiousness. But it is you who are captious in not recognizing that imperfect humans, such as I, err, and it is to their credit not discredit that they correct themselves when they see that they did.
Quoting Leontiskos
No conflation. And not merely purported. The first time you stated the falsehood, I corrected you. But you continued; then it becomes a lie. And it is in the record of the posts that at least a few times (probably at least five) I explicitly said the opposite of what you claimed I said, and that concerned not just some incidental matter but rather the central point in that thread.
What I am primarily interested in is the OP. I am sure Russell can speak for himself.
Quoting TonesInDeepFreeze
Despite the fact that these sentences of yours are not grammatically correct, you are of course welcome to try to defend your assertions.
Here is the central sort of question you are avoiding:
Quoting Leontiskos
It is eminently your prerogative to engage with whatever you like. But you did engage my points about the other poster. And you are now suggesting a wedge against me for not engaging more the original question. It is my prerogative to engage or not engage the original question or any other matters that arise.
The other poster addressed the original question with an argument that self-referring sentences are to be eschewed because they don't refer to "the world". So I followed up on that. That is eminently reasonble. And you followed up on my followup. And that is eminently reasonable.
And I did engage the original question. And I've given good background and information about it. And I addressed one of the questions about it. I don't propound a full explanation of the liar paradox and I don't propound a resolute position on it. That doesn't disqualify me from remarking on matters that arise about it or anything else in the discussion.
If you wish to continue to exercise your prerogative to speciously fault me as a poster, then I will exercise my prerogative to reply to that.
Quoting Leontiskos
Recently in another thread, another poster took exception to certain senses of 'grammatical'. So, you are welcome to define it yourself so that I can address your claim given your own definition. Otherwise, I'll just say that these are easily recognizable as well formed sentences, ordinary English:
Joe is cool.
Harry Truman was a president.
Also:
'This sentence is true' has five letters.
That is well formed in the sense that is has a subject (the string of words 'This sentence is true' and a predicate 'has five letters'), though it may be problematic depending on one's analysis. But note that the analysis does not require determining whether 'This sentence is true' is a legitimate sentence.
You <made some unfounded assertions> and then wrote 8 short non-committal replies with more unfounded assertions, all in response to posts that were written some five years ago. So no, I don't think you have.
Quoting TonesInDeepFreeze
See: Grammatically Correct (Collins). Here are the sentences in question:
Quoting TonesInDeepFreeze
The point here is that if you really think the cases that the OP has in mind, such as the "Liar's paradox," are coherent, then you are free to make such an argument. Thus far you have not done so, despite ample opportunity.
Oh, for Pete's sake! So you are not responding about the example sentences I gave regarding the subject of implied speakers. Instead, you're on about scrutinizing for strict proper construction in an informal, conversational post! Not even as to its substance but as to minor liberties it may take in conversational presentation! Talk about nits! Talk about veering from topic! And it is ubiquitous in posting forums that people take great liberties and often even carelessly type jumbles while, sometimes, we can still see what they're saying and honor that by replying to their intent, not to their typos, grammar mistakes or even their faltering with the language.
I'll say anytime: I don't even pretend that my prose is worthy of more formal publication. I make many typos. I take liberties with grammar. I sometimes make ignorant grammar mistakes. That is to say: Y kan be not so fulse you see!- metapiscics not untology true objects, yes?
Obviously 'There instances' is a typo of omission; 'implication' is terse for 'the implication'; 'display of' is terse, informal, for 'a display of'.
I don't bug other posters about things like that. However, sometimes when something is not clear to me because it was poorly written, I might point out that the lapse in the writing so that the poster can restate for more clarity. And that is distinct from people writing formulas or conveying a technical point so poorly that it is, or may be, false or misleading. Even then, unless the poster continually shows that he or she just doesn't care about being accurate, then I might comment on that. Also, sometimes, though certain formulations might not be incorrect, I suggest clearer or more elegant formulations.
But I definitely don't hassle people about examples such as you just gave!
We could spend 24 hours a day, 365 days a year raking over typos, grammar mistakes and spelling mistakes among all kinds of posters. How inane that you do so now!
Quoting Leontiskos
* Or that, "I am lying," represents an utterance that is simultaneously a lie and a non-lie.
Those are not unfounded. It is true that knowing the way many writers in logic have not found the subject silly helps to understand why it is of interest.
Argumentum ad populum, then? Such a weak response does not stand up to the arguments that are found in the OP and in this thread.
Wow, again, so much speciousness in just a few words.
(1) You skipped my point that posters are not required to take a position on any matter whatsoever, including the main subject of a thread.
(2) You skipped that I did happen to address crucial aspects of the subject.
(3) It is to my credit, not discredit, that I don't take a rash, polemical, tendentious approach to a complicated subject.
(3) You merely claim there are unfounded assertions.
(4) It doesn't matter how long ago posts were written. They still exist to be read, so they exist to be commented on.
Especially when the thread is brought back up, and so that people would naturally read the thread from its start.
And who brought the thread back up? Could it be .... you?
And you replied to a post from five years ago, while now you're suggesting that there's something askance in me doing that?
Moreover, I haven't just replied to posts five years ago, but to recent posts also.(Though, again, it would not be the least bit wrong to reply to old posts.)
Again, you are prosecuting the fact that I don't presume to have a full explanation of, and resolute position on, the liar paradox. You even skipped my remarks about that.
Quoting Leontiskos
If you want to know more about it, then you can find out by reading about it.I suggest starting with the undefinability theorem. And I suggest not a haphazard Wikipedia article. But a solid understanding does require understanding some technical material. If you don't wish to study the basics of mathematical logic, then of course that's your prerogative. But an answer to your comment "I have no idea what they purport to mean by this" is to suggest that you can find out.
And even in this thread I mentioned the undefinability theorem.
You have made it abundantly clear that you will continue to refuse to answer the question of the OP. :ok:
You persist to talk about me. So it is quite proper that I defend against your falsehoods about me and your inane pettiness about me.
And I've said a fair amount about the subject of the thread.
What alternate reality are you from?
Quoting Leontiskos
Yes, it is my job to clean the mirrors at the funhouse mirrors attraction at the amusement park down shore.
Meanwhile, I suggest you invest in a mirror. You bring up that I reply to old posts, when you started recently by replying to an old post. You fault me for talking about myself, when I am defending against your garbagy posting as you talk about me. You claim that I have a "habit" of false attribution when I don't, but you continued to falsely attribute to me. You faulted me for making several posts in a short time in another thread, but you do that pretty much all the time.
Too bad that alternate reality you're from is accessible to this one.,
No, it is not. My point went over your head. I didn't argue that the writers are right. Indeed, there are conflicting views about the liar sentence. I only said that you would find why it is of interest in logic, mathematics and philosophy, if you would read what some of those logicians, mathematicians and philosophers have written about it, and see why the subject is not silly to them. And noticed that I have not said that your position that the sentence is meaningless is incorrect due to what others have written, only that others don't find the matter to be silly and that one could find out why by reading about it.
What are you, The Philosophy Forum interrogation officer?
It is incumbent upon me to snap to right now for you with a reply to your position that the liar sentence is meaningless? If I don't do that, then any of my other comments are to be discounted?
Does you hold for posters in general that they are required to address a main subject directly, or is it just I that must do that?
(1) There is no question in the original post.
Your latest ridiculous comment deserves repeating some things I've said.
(2 People people are not required to declare a position on a subject in order to comment on it, comment on other comments about it, or to disagree with claims about it that come up in the course of conversation. It is not uncommon for people to engage aspects of a conversation beyond the initial subject or aspects of the conversation related to the initial subject, or even aspects of a conversation not related to the original subject but rather matters that come up incidentally or tangentially.
(3) I have addressed the main subject anyway, especially as I mentioned one of the most famous theorems about it.
(4) It is to a poster's credit, not discredit, if he or she presumes not to have achieved an adequate explanation to a philosophical problem and therefore declines to state a resolute position on it.
No, I'm just a guy wondering why I forgot to put you back on my ignore list when I reinstalled my browser. This has now been remedied.
I look forward to reading the posts of those who are interested in engaging the OP:
Quoting Leontiskos
That is a strawman.
If you understood what I'm saying, then you've chosen to misrepresent it.
I did not say that the writers are correct. Indeed, there is disagreement among them. I didn't even say in that remark, contrary to you, that the subject is not silly. I only said that one would find out why the subject is of interest by reading what writers have said about it.
Sorry to hear about your computer problems.
Consider "Phil is a fool".
or
Consider the sentence "Phil is a fool".
I did not assert the sentence "Phil is a fool". There is no implied actual speaker of the sentence. And there is no implied hypothetical speaker of the sentence. Merely, I mentioned the sentence for consideration. It is not the case that an occurrence of a sentence has an actual or implied speaker or relies on having a hypothetical speaker. Even without hypothesizing a speaker, I can consider the sentence in many ways, including whether it is true, how many words it has, etc.
Consider the sentence: "There is a baby Gila monster under the nearest rock that weighs more than three pounds and is closest to the northernmost gas station in the Mojave desert."
No actual nor implied speaker. And I don't need to hypothesize that there is a speaker merely to wonder whether the sentence is true or false. Even if no one said the sentence and even if I don't consider whether someone might say the sentence, I can still wonder whether it is true.
I make that point in response to an earlier question I asked, as the response claimed that any occurrence of a sentence has an actual or implied speaker.
And my earlier question was in response to an argument that self-referring sentences are to be eschewed because they don't refer to "the real world".
This sentence has five words.
Is that string true, false, neither, another truth value, meaningless, not a sentence?
I already addressed this in some detail:
Quoting Leontiskos
What is the difference between (1) and (2)? The relevant difference is simply that (1) has a possible (implicit or hypothetical) speaker whereas (2) does not. To merely assert that (1) has no hypothetical speaker is to ignore this difference between (1) and (2). The things that the OP is considering are like (2), not (1), ergo, "There is no possible speaker in such cases, and hence the "sentences" are nonsensical."
Quoting TonesInDeepFreeze
You brought this around full circle.
Again:
Quoting Leontiskos
Quoting Leontiskos
Of course "Colourless green ideas sleep furiously" can be spoken.
One could go out tomorrow with a bullhorn on the Spanish Steps to say a hundred times
"Colourless green ideas sleep furiously! Do you hear me people, colourless green ideas sleep furiously!"
And again, my point was to question the claim (not yours) that sentences may not refer to themselves.
And, I've answered the claim that there is always an implied speaker.
"This sentence has five words"
That sentence refers to itself. It has five words. My question is whether that sentence is true.
Still playing dumb, then. I've yet to find anyone online who intentionally misrepresents their interlocutor as often as you.
Quoting Leontiskos
In his 2002 lecture, "Gödel and the end of physics", Stephen Hawking made excellent comments on the connection with physics. He obviously left out technical details because those were irrelevant to the question at hand. People attending his lecture were simply not interested in the technical details. They just wanted to know what the value of Gödel's theorem is for physics. Hawking pointed out that positivism is simply futile. Laplace's demon is the wrong view on physics because it will never be possible.
Quoting Leontiskos
However, I grant that would be qualified by your earlier "in their right mind".
[An example where I was reading too fast, trying to keep up, but corrected myself immediately when it was made clear that I did not consider the full text. That is unlike Leontiskos who continues to deny that he lied about my view me regarding the main issue in a thread.]
My initial reply is that whether in right mind or not, it can be said. Moreover, my examples are not refuted by that example, as I argued.
Yes, good.
Quoting TonesInDeepFreeze
You were replying to my argument about speakers, and to disregard "whether in right mind or not" is to misrepresent my argument. It does little to help your case to note that someone who is not in their right mind might agree with you, and might say something that someone who is sane would not say.
Indeed, a reply to your argument should not have overlooked your qualification 'in their right mind', so when you noted that, I immediately recognized that you did qualify that way. Now, if you would only recognize that you were wrong to continue to claim I took a position, when I had posted at least a few times that I take the opposite of that position, and hopefully to desist from misrepresenting me that way. I pointed out to you that you misrepresented me, but I did not say you lied until you continued to misrepresent me even after I pointed it out to you.
Okay, I appreciate that.
Again, trying to get to the point:
(I am understating this given that a contradiction is more than merely nonsensical in the way of these other statements.)
Quoting TonesInDeepFreeze
What position is that?
The one in connection with the incident that you posted about in this thread earlier today, when you said that I conflate a mere falsehood with a lie! Wow, in this thread, you brought up the incident from another thread, and yet you don't even remember what it was about. Actually, not surprising.
In the other thread, I think about three times, you claimed that I conflate material implication with everyday use of "if then", or that I that I consider material implication to be the only correct understanding of "if then", or that I insist that "if then" can only be considered as material implication. Something to that effect.
But I had said probably at least three times that material implication does not represent many everyday senses of "if then", and not just everyday senses, but also material implication is not compatible with other approaches to "if then" in logic. And I said that I do not claim that material implication is the only way that "if then" should be understood.
And what makes your lies even more egregious is that they were not about mere interstitial points, but about the central subject in the thread.
(I added to my previous post in edit while you were posting your latest.)
Of course, one needs to leave out a lot of details in a talk like that or in a post. But again, as you keep skipping:
(1 Your post didn't just leave out details, but it mischaracterized the theorem terribly, and in a way that readers would think it says something it does not, and was even about something it is not about. And that is critical in that discussion, since overstatement of the theorem feeds to bad inferences about its implications.
(2) It requires only very easy and basic technical terms (such as 'consistent', 'axiomatization') to correctly state the theorem.
(3) You often enter technical details anyway.
(4) Your reply doesn't relate to what you quoted of me.
I'm probably missing some detail or atomization
This is the same conflation of falsehoods with lies that I brought up. You can have a habit without realizing it, and I can believe this to be true without lying. You may as well accuse a doctor of lying when he tells you that you have a tumor and you tell him that you do not.
Yes, but it seems to me that in this case we are considering the assertion, "I am a liar," or, "I always tell lies," rather than, "I am lying." To lie requires a statement about which to lie, whereas to be a liar does not (at least in the same proximate way). The OP tends to pivot on a statement that is supposed to simultaneously be a lie and a non-lie. Nevertheless...
If we know that someone is a liar then, as you say, their utterances are thrown into question. These utterances wouldn't be both true and false; they would merely be questionable.
Another basic thing to note is that knowledge of a lie or a falsehood is composite, not simple. There must be both the utterance that is false or a lie, and also the claim that it is false or a lie. Thus for such a thing to obtain there must be two things, or at least two aspects of the same thing. "This is a lie," or, "This is a falsehood," provides only one thing, not two. There can be no lie or falsehood without some claim that is apt to be lied about or to be understood as false.
That's not "e.g." since it is not what you said - it is clearly weaker.
And, if I recall, you didn't merely say that you "think" I have that position.
You're trying to ameliorate your lies.
And it's not even a matter of what one thinks. I explicitly stated my view, at least a few times, that is the opposite of what you what you claimed about me. And I stated it again at least a couple of timse after you misrepresented it, and then lied about it as you persisted after I pointed out to you. Explicitly and clearly. The posted record is there. And brought to your attention, but you continued.
Quoting Leontiskos
That is a stupid analogy.
I did not merely claim that I posted the opposite of your claim about me. It is posted record that I said the opposite of your lie about me.
If someone said, "Leontiskos says that JFK was a secret member of the Ku Klux Klan" then you would be quite right to say that you did not say that, and if the person persisted, you would be quite right to say they're lying.
You lied about me about then and you're trying to weasel out of it now.
It seems that you have no clear idea what I am supposed to have said:
Quoting TonesInDeepFreeze
Which is wonderful: you run around accusing people of lying and you have no idea what they are even supposed to have said. :roll:
Quoting TonesInDeepFreeze
It's not.
I didn't read the whole speech but Hawking said this about incompleteness:
"Godel's theorem is proved using statements that refer to themselves. Such statements can lead to paradoxes. An example is, this statement is false. If the statement is true, it is false. And if the statement is false, it is true. Another example is, the barber of Corfu shaves every man who does not shave himself. Who shaves the barber? If he shaves himself, then he doesn't, and if he doesn't, then he does. Godel went to great lengths to avoid such paradoxes by carefully distinguishing between mathematics, like 2+2 =4, and meta mathematics, or statements about mathematics, such as mathematics is cool, or mathematics is consistent. That is why his paper is so difficult to read. But the idea is quite simple. First Godel showed that each mathematical formula, like 2+2=4, can be given a unique number, the Godel number. The Godel number of 2+2=4, is * (sic). Second, the meta mathematical statement, the sequence of formulas A, is a proof of the formula B, can be expressed as an arithmetical relation between the Godel numbers for A- and B. Thus meta mathematics can be mapped into arithmetic, though I'm not sure how you translate the meta mathematical statement, 'mathematics is cool'. Third and last, consider the self referring Godel statement, G. This is, the statement G can not be demonstrated from the axioms of mathematics. Suppose that G could be demonstrated. Then the axioms must be inconsistent because one could both demonstrate G and show that it can not be demonstrated. On the other hand, if G can't be demonstrated, then G is true. By the mapping into numbers, it corresponds to a true relation between numbers, but one which can not be deduced from the axioms. Thus mathematics is either inconsistent or incomplete. The smart money is on incomplete."
(1) Contrary to your claim about the speech, Hawking does go into some technical details.
(2) "G can not be demonstrated from the axioms of mathematics."
That's really bad and it is the kind of thing that leads people (who don't know the theorem) to make unfortunate inferences about the theorem. Ordinarily, one would take 'the axioms of mathematics' to refer to ZFC*. But it is provable in ZFC that G is true. Moreover, it's important to note that it's not the case that there are sentences of mathematics that are unprovable; for any sentence, there is a theory in which the sentence is a theorem. What the theorem does say is that, for any theory of a certain kind, there is a true sentence (such as G) that is not provable in that theory. It's a matter of quantification: It's not "There is a true sentence such that for all theories, the sentence is unprovable". Rather, it's "For all theories (of a certain kind), there is a true sentence not provable in the theory".
That is important, since people take such claims as "mathematics does not prove" to argue incorrectly about incompleteness.
(3) "Suppose that G could be demonstrated. Then the axioms must be inconsistent because one could both demonstrate G and show that it can not be demonstrated."
We need to not miss the distinction between the meta-theory and object theory. Let's take the object theory PA for example. It is the object theory PA that does not prove G and does not prove ~G, and it is not the case that PA proves that PA does not prove G and that PA does not prove G. Rather, it is in the meta-theory that we prove that PA does not prove G and does not prove ~G.
* I am not claiming that ZFC is the only axiomatization or that it is the best one. Only that if there is an axiomatization considered to be "the axioms of mathematics', then ordinarily it would taken to be ZFC. And, of course, that refers to classical mathematics.
Call this person 'L'. L says "I am lying". Now it could be the case that L lies always, or it could be the case that L lies only sometimes. But the puzzle asks whether he is lying or telling the truth when he says "I am lying".
Quoting Gregory
It's an interesting question how unreliable one would regard. Every person is unreliable at least to some degree. And a person who says he never lies would be taken as unreliable immediately, since (at least virtually) every one tells some lies. But a person who says "I am lying" is setting up a puzzle at least. I'm not sure what I would make of his reliability otherwise.
Quoting Gregory
How do you draw that inference?
All we know is that he has made one very bizarre statement that we can't determine to be a lie or not a lie, while arguably it's neither as it is merely nonsense. How would you infer from that that he lies most of the time?
You are too much!
Here's what I wrote:
Quoting TonesInDeepFreeze
(1) Note that I did not put those in quotes, unlike when you quoted yourself - "you are under the spell of material implication" (an actual quote?) as if it represented the times you directly claimed that I had made a claim, even though I claimed the opposite. As if "you are under the spell of material implication" is really all you said.
(2) It is correct that you said things to the effect I mentioned. And I did not overstate about you, while you now understate about yourself.
(3) About three times in the thread, I directly addressed what you did say about me.
(4) The posts are there; even though have not quoted them verbatim here. But perhaps I should take even more of my time and energy to again clean up after you by again quoting you verbatim.
(5) 'people'. There are a few people I've found to lie. And when I comment that they do, I cite their specific instances, just as I did with you in the other thread.
(6) You remind me that not only did you lie about me, but you persistently tried to wedge an argument against me by painting me as a "truth functionalist" while I countered each time by explaining why that is so off-base.
Quoting Leontiskos
I said exactly why it is stupid.
I think we can work with any of these:
"I always lie"
"I am lying now"
"I am lying"
"This statement by me is a lie"
"This statement is a lie"
"This is a lie"
There are difference among them that might affect the analysis, but I think they are all worthy of the subject.
I took the poster at face value when he used "I am lying".
1. “This sentence has five words.” Or
2. “The sentence ’this sentence has five words’ has five words in it.”
Sentence number 2 is about something. Number one isn’t. The reader has to make 1 be about itself. In the sentence “This sentence has five words” you don’t know which sentence the speaker is taking about without being the speaker and pointing back to the sentence. Number 2 tells you what it is referencing, tells you what it is about.
Number 1 is a puzzle game, with missing pieces you have to bring with you to play; Number 2 is about counting words.
“This sentence is false” isn’t about anything that can be true or false. “Grammar is false” similarly isn’t about anything that can be true or false.
“Punctuation is true.”
What?
It's about the sentence.
Quoting Fire Ologist
First, there doesn't have to be a speaker. We can consider the sentence in and of itself.
Second, I do know which sentence is the subject of the sentence. The subject of the sentence is the sentence "This sentence has five words".
Quoting Fire Ologist
Yes, those don't make sense, since presumably what are true or false are sentences, and 'grammar' and 'punctuation' are not sentences. But "this sentence has five words" is a sentence, and 'this sentence' refers to it, as 'this sentence' is the subject of the sentence.
Does "this sentence has five words" have five words? Yes, it does. And does "this sentence has five words" claim that "this sentence has five words" has five words? Yes, it does. So does it not state a truth? So is it not true?
.
If a liar says he is lying, his utterance does need to be compared to the substance of the utterance, to the lying-ness of the speaker. The "claim" of the utterance relates to he who utters before it hits our ears. To the liar, he knows where he stands. To us, when he says "i always lie", we must understand the language "game" involved. Either he HAS always lied and he is owning up to it or he is lying that he always lies, wherein he must have at least once spoken the truth.. The latter seems to be where the trouble is
When L says he is lying, he hasn't specified what he is lying about. It's like the barber paradox. Not enough information is given so we must assume he grow his hair to hippie length. The liar may be lying that he lies about lying, but the reality of his truth or falsehoid falls somewhere. It seems different if we say "this sentence is false" because it necessarily is taken out of context and merely implies a spurious infinity and, hence, is a big fat Zero in terms of truth
Wouldn't you agree we must assume a liar to be a liar most of the time, or is redemption possible in this logic game?
Yes, true.
Language communicates
As not every animal is a cat, not every set of words is part of a "Language".
The Merriam Webster Dictionary describes "Language" as i) the words, their pronunciation, and the methods of combining them used and understood by a community ii) a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings iii) the means by which animals communicate
As the core feature of a "Language" is its ability to communicate, presumably a set of words that is not able to communicate is not a part of what can be called a "Language".
A computer could be programmed to collect together random words, but a set of words does not of necessity make a "Language".
The meaning of words is not fixed
As prose, the set of words "colourless green ideas sleep furiously" is a nonsensical proposition, and because it doesn't communicate any idea, cannot be considered as part of a proper language. However, the meaning of words is not fixed, and the same words could be interpreted in a poetic or metaphorical way. If that were the case, one could possibly gleam some sensible meaning out of this particular set of words.
But for the sake of this post, I am only considering a set of words as prose.
Not all expressions in Language have a truth-value
Some expressions in language can be true or false, such as the expression "the Eiffel Tower is 1,200m in height", but other expressions, such as the command "bring me a coffee" or the exclamation "ouch!" are neither true nor false.
The author of a set of words is irrelevant to the meaning of the set
I see five words on the screen in front of me, and the particular words are "this", "sentence", "has", "five" and "words". I see five crayons on my desk next to the computer screen, and the particular colours are red, green, blue, yellow and orange.
As five crayons don't of necessity make a language, five words don't of necessity make a language.
I don't know who or what has determined these five words. It could have been a person or a machine. In fact, I don't need to know as long as I can find my own meaning in the words. The observer determines any meaning in any set of words. The meaning is not determined by the words themselves. Only the observer is a conscious being. The words themselves are inanimate, neither aware of themselves not anything outside themselves.
The meaning of a set of words is determined by an outside observer of the words
That the five words on the screen include the words "this statement" is meaningless, as it is not the words that determine whether the five words forms a statement or not, but rather it is the observer who determines whether or not these five words are part of a language. The observer may in fact determine that these five words are not part of a language, in that they are not a statement.
Truth-values must be grounded in the world
Kripke proposed that a statement that refers to itself cannot have a truth-value as not grounded in the world, and only statements that are grounded in the world can have a truth value.
It is true that the set of five words on my screen are grounded in the world, as are the five crayons on my table, but as both the five words and the five crayons are inanimate, neither being conscious nor self-aware, neither the five words nor five crayons are able to refer. Only a conscious outside observer of the five words and five crayons is able to refer.
A set of words independent of any observer can never have any meaning. A set of inanimate words cannot give themselves meaning. Meaning cannot give itself meaning. Meaning is not self-referential, and as such can never give itself a truth-value.
A set of words can only have meaning when given a meaning by an outside observer, and in order for a set of words to be given meaning by an outside observer, this set of words must exist in the world.
Summary
In summary, I see a set of words on my screen. I see that there are five words, and this is true. The five words happen to be "this", "sentence", "has", "five" and "words". I, as the observer, recognize a meaning in the five words as "this sentence has five words". Words being inanimate cannot refer. Only a conscious observer outside the words can refer. In the mind of this conscious outside observer, the words "this sentence" refers to the statement "this sentence has five words", which is true.
What is the definition of 'is a liar' here?:
every statement is a lie?
some statements are lies?
many statements are lies?
more than half the statements are lies?
etc.
Quoting Gregory
If only the latter is problematic, then there's no paradox, as we just conclude that he has always lied previously but is telling the truth now.
But that's not the puzzle.
When he says "I always lie", we take that to mean not just that he is saying that he has always lied but also that he's lying now. If I say "I always breathe", then I mean that I have always breathed and that I am breathing now.
If he says "i always lie" and he is being untruthful because he had once told the truth then his lie is now and his truth was once. "This sentence is false" doesn't say what the sentence is about so it's spurious but maybe not in infinite regress. I don't see how these paradoxes can be made into necessary paradoxes, ones entailed by logic itself
Does he need to? If I say "I am speaking", I don't need to say what I'm speaking about.
Quoting Gregory
I take that to mean that no one shaves the barber.
The premise is that there is a person who shaves all and only those who shaves himself. That premise is inconsistent, so we may infer all of these:
said person shaves herself.
said person does not shave herself.
no one shaves said person.
someone shaves said person.
everyone shaves said person.
no one is shaved by anyone.
everyone is shaved by everyone.
some are shaved by someone
some are not shaved by anyone
etc.
The puzzle [we don't need to mention 'barber' or 'village']:
There is a person who shaves all and only those who do not shave themselves. Therefore, there is a person who both shaves herself and does not shave herself.
We can put it in purely abstract form, where 'S' stands for any 2-place relation:
There is an x such that, for all y, xSy if and only if it is not the case that ySy. Therefore there is an x such that both xSx and it is not the case that xSx.
Right, but is it possible that his self-same statement is both the truth and a lie? I say that it is not possible.
Someone may be telling the truth or lying, and this is not a paradox. The paradox requires something more. If I am right then it requires that there be no speaker at all, even implicit or hypothetical.
The paradox depends on the idea that there is a sentence with two different senses, and both senses are true at the same time. What the proponent of the "Liar's paradox" fails to understand is that the two senses they attribute to the same sentence are mutually exclusive, and it is impossible for a speaker to intend or mean them both. If someone is lying then they are not telling the truth. If someone is telling the truth then they are not lying. To say, "Wow, but what if he is lying and telling the truth at the same time!?," is to fall into incoherence while pretending to be sophisticated.
Depends on the definition of 'is a liar'.
Godel's incompleteness theorems use the same basic structure as The Liar's paradox. As such, it is worth understanding the principles of contradiction/paradox.
Part 1: There are no lies
It is impossible to definitively define what a lie is.
A lie is not the truth. The truth is not a lie.
All definitions are circular (A defines B and B defines A).
Part 2: Squiggles don't lie
Sentences do not have any inherent meaning.
All descriptions are of the form: X is not(Everything Else).
That is, The Liar's Paradox as a set of symbols with no connection to anything else has no inherent meaning.
When we read a sentence, we create meaning as part of the process of interpreting the symbols.
The perception of a lie doesn't exist in written words - it exists in your mind.
Silly
You are right that the Liar's paradox is a silly misattribution within which lies cannot be defined and meaning exists within the observer, not arbitrary symbols.
However, understanding exactly why the paradox is not very paradoxical illuminates the nature of understanding and has direct implications in our pursuit of knowledge.
It is true that a lie cannot be represented by formal logic, as it pertains to intention. Still, Augustine defined a lie 1500 years ago, "Locutio contra mentem."
Quoting Treatid
I would point out that a written word is not merely a set of squiggles.
Quoting Treatid
I'm not convinced that it does.
Quoting Treatid
I think it is worth understanding the concepts of contradiction and paradox, but I don't think the "Liar's paradox" is either one.
Some have argued that,
Edit: Why do I think that the "Liar's paradox" is silly? Primarily because it is not a paradox, and it is silly to call a non-paradox a paradox. In particular I have run into individuals on TPF who think the "Liar's paradox" is so impressive that it justifies them in rejecting the principle of non-contradiction. Apparently such people call themselves "dialetheists." This is what I see as silly, and I don't think it has much to do with Godel. Studying someone else's mistake can always lead to insight, but I don't see this mistake as particularly helpful or important.
I don't whole hog buy into your general view about language, but for the sake of argument, suppose these matters are observer dependent. May not another observer determine that it is a statement?
Quoting RussellA
With admittedly only a cursory search, mainly what I find about Kripke in this regard are: a Wikipedia article and paper by Kripke about direct self reference and proving incompleteness.
Kripke's work is highly technical and I am not versed in it. However, the paper about incompleteness seems clear enough that not only does Kripke approve "This sentence is not provable" but he discusses how he arrives at such a sentence more directly (in a technical sense) than Godel did.
I don't trust Wikipedia, especially in technical matters in logic. So I don't trust that the very brief synopsis does justice to Kripke's view. Also 'grounded' is a very technical notion with Kripke and I don't know that it is properly reduced to a colloquial sense of 'grounded'. Also, while the Wikipedia article mentions 'contingent facts', I don't know that implies a colloquial sense of 'the world'; moreover as "the world" is not even mentioned in the Wikipedia article, and as we should keep in mind that with Kripke, and with modal logic in general, the notion of worlds also is technical. However, the Wikipedia article does refer to a paper by Kripke as its source, though I have not read the paper. I'm not claiming that Kripke doesn't align with you view, but rather that one should be cautious in claiming that he does.
I don't know of any such requirement.
Quoting Leontiskos
I don't know what 'proponent of the liar's paradox' means, but usually discussants of the liar paradox quite understand that the liar sentence is a contradiction and that to assert the liar sentence is to assert a contradiction. That is at the heart of subject.
Quoting Leontiskos
I don't know who says something like that. I think the most common view (which abides by the law of non-contradiction) is that "I am lying" implies a contradiction. We wouldn't say that it can be the case that the statements "I am lying" and "I am telling the truth" can both be true. Rather that the liar sentence implies that they are both true, so the liar sentence is inconsistent.
Paraconsistent logicians may eschew non-contradiction. But ordinarily, discussion of the liar paradox is not aimed at rejecting non-contradiction.
Ah, but later you wrote:
Quoting Leontiskos
That does put your remarks in better perspective. You're talking about some posters in a forum such as this, not necessarily logicians who discuss the liar paradox not toward trying to deny non-contradiction?
Quoting Leontiskos
A connection with Godel is that paraconsistent logic does not yield the incompleteness theorem.
Quoting Leontiskos
At least one way in which discussion of the liar paradox has been productive is that it suggests methods in mathematics that are similar to the liar paradox but that don't engender the absurdity of the liar sentence.
But we must keep in mind that there are crucial differences between the liar sentence and the Godel sentence.
I'd like to know those arguments in context.
On the other hand, in reverse, of course it is often mentioned that consideration of the liar paradox helps understanding the incompleteness proof. But, again, the liar paradox is not used in the incompleteness proof, but rather a similar, but crucially different construction is used.
If the barber shaves those and only those and all those who do not shave themselves then he doesnt shave himself because of the "not shave themselves" part and this leaves others who do shave themselves who the barber doesn't shave because he doesn't shave those who shave themselves. Maybe nobody shaves the barber. Or someone or everyone shaves him. Surely someone is shaved because it's about a barber. I think you are making this a tar baby toward no genuine purpose
Yes, the supposition that he shaves all and only those who do not shave themselves implies that he does shave himself. But that supposition also implies that he doesn't shave himself.
Suppose B shaves all and only those who don't shave themselves.
If B shaves himself, then he doesn't shave himself, which is impossible (B can't both shave himself and not shave himself), so B doesn't shave himself.
If B doesn't shave himself, then he does shave himself, which is impossible (B can't both not shave himself and shave himself), so B shaves himself.
Therefore, the supposition "someone shaves all only those who do not shave themself" is absurd.
Quoting Gregory
I'm just explaining the barber paradox.
Your premise 1 is oddly stated. There is no "if he does.. then he doesn't". He just doesn't shave himself because he shaves only those who do NOT shave themselves. Premise 2 is just plain wrong
An absurdity arises when "they/them" includes the Barber. The commonsensical reading would say that the Barber is not included in the set "they/them."
If we include the Barber in the set and then replace they/them with "the Barber," we get:
You seem to be missing that it's not just that B shaves only those who do not shave themselves, but also that B shaves all those who do not shave themselves.
The premise is "B shaves all and only those who do not shave themselves".
The rest of the argument follows to show that the premise is absurd.
Premise: B shaves all and only those who do not shave themselves. So:
B shaves all those who don't shave themself. So, if B does not shave himself, then B shaves himself. But it is impossible that both B does not shave himself and B does shave himself. So, by modus tollens, B does shaves himself.
B shaves only those who don't shave themself. So, if B shaves himself, then B does not shave himself. But it is impossible that both B shaves himself and B does not shave himself. So, by modus tollens, B does not shave himself.
But it is impossible that B shaves himself and does not shave himself. So it is impossible that B shaves all and only those who do not shave themself.
Oh so youre including the barber in "all". So this is just Russell's paradox in a simple form.? All that is needed to solve it is more information it seems to me. Not enough is given to make anything out of it that is normal and helps us grow. It's too narrow of a puzzle then for me to find interesting. The right and left hemispheres or some crap get too equally balanced to see it clearly. I doubt anyone can see that clearly
Thanks for the clarification.
It's Russell's paradox illustrated anecdotally.
It's actually a theorem schema of first order logic, whether 'shaves', 'is an element of' or any other 2-place predicate:
For any 2-place predicate S:
~ExAy(Syx <-> ~Syy)
and
~ExAy(Sxy <-> ~Syy)
The remainder of the speech is mostly about research headaches in (advanced) theoretical physics, probably his pet peeves.
Quoting TonesInDeepFreeze
Hawking was talking to other physicists. For most of them, I guess that life is often simplified to just one elusive further unspecified set of axioms in mathematics that they do not even explicitly name, because that is irrelevant to what they are doing. In fact, even mathematicians may operate like that:
Of course. Meanwhile, it is crucial not to say, "G can not be demonstrated from the axioms of mathematics", since that is plainly false. And the lecture botches the key point that it's not that there is a true sentence such that for all theories, the sentence is unprovable", but rather, ifor all theories (of a certain kind), there is a true sentence not provable in the theory. That is not a mere "detail" and it is even more critical in context of what may be the scientific or philosophical gleanings from the theorem.
So what? The incompleteness theorem has nothing to do with that, since the incompleteness theorem regards formal theories in which the axioms are explicit and such that theorems are strictly from explicit axioms.
For Hawking's audience of physicists, the term "axioms of mathematics" refers to PA or ZFC.
A mathematical theory in which Gödel's incompleteness does not apply -- because it cannot even do arithmetic -- is probably not even in use anywhere in science.
Therefore, what Hawking said, may be technically false, but in all practical terms it will never lead to problems.
Quoting TonesInDeepFreeze
That is indeed the case from the standpoint of mathematical logic.
From the point of view of science and engineering, since they always operate in PA and/or ZFC, I am confident that practitioners of science or engineering are not even conscious about their implicit choice, if only, because it actually never matters to them.
Gödel always applies to the default context in their typical environment.
Yes. Every observer of a set of words interprets the same set of words differently, because it is the observer that gives the set of words meaning. It is not the "squiggles" that the observer sees on the screen that give the "squiggles" meaning.
Quoting TonesInDeepFreeze
I agree, but we have to start somewhere.
Though my belief remains that the basic problem with the statement "this statement is false" is that it is not grounded in the world. In the same way, any set of words, such as the statement "a b c", is meaningless until grounded in the world.
The word "a" may be defined as "d e f"
The word "b"may be defined as "g h i"
The word "c" may be defined as "j k l"
Continuing, the word "d" may be defined as "m n o", etc
This may give us a coherent language, but will remain meaningless until sooner or later a word corresponds with something in the world.
IE, a language in order to be useful must correspond with the world in addition to being coherent. IE a useful language must be grounded in the world , which the statement "this statement is false" isn't.
You regard that sentence as meaningless on the basis that self-reference is meaningless when applied to a sentence.
But is it the case that all self-referential sentences are meaningless? If they are not, then, if that sentence is deemed meaningless, there must be a basis other than that it's self-referential.
But there's another aspect to the sentence, which is negation. So I ask about a self-referential sentence that does not involve negation:
"This sentence has five words"
"This sentence has five words" has five words. The meaning of the sentence is that the predicate (has five words) holds for the subject ("This sentence has five words"); and its truth value is 'true'.
It's not the case that in general self-reference using the pronoun 'this' is meaningless:
"This Guy's In Love With You" [a song title]
It's not the case that a sentence referencing a sentence is meaningless:
""This sentence has five words" has five words" is meaningful and true.
So, why would "This sentence has five words" be meaningless?
If it's meaningless, then it's not because it's self-referential nor that its subject is a sentence, but rather that it's both self-referential and its subject is a sentence.
But why does being both self-referential and having a sentence as its subject make it meaningless?
As I understand, your argument is that the sentence does not pertain to "the world".
(1) It would help to have an explanation of what you mean by 'the world'.
(2) But no matter what you mean by 'the world', sentences may be subjects of sentences and be meaningful, so, it seems your argument should allow that sentences are in "the world". I surmise you would agree. But you draw the line at sentences that refer to themselves. But such sentences are in "the world". "This sentence has five words" is right in front of us in "the world". If one argued that it's not in "the world" because it refers to itself, then that would be petitio principii.
Quoting RussellA
I think the following is right:
Suppose we define 'the Magna Carta' as "the charter assented to by King John' and we define 'is old' as 'dates from the long past'.
So, we have a subject in the world, viz. the Magna Carta.
So, "The Magna Carta is old" is meaningful.
To determine whether "The Magna Carta is old" is true, we determine whether the charter assented to by King John dates from the long past.
Suppose we define the Witness Statement as "The Chevy ran a light".
So, we have a subject from the world, viz. the Witness Statement.
So, "The Witness Statement has five words" is meaningful.
To determine whether the "The Witness Statement has five words" is true, we determine whether the Witness Statement has five words.
Suppose we define 'the Minma Senta' as "This sentence has five words".
So, we have a subject from the world, viz. the Minma Senta.
So, "The Minma Senta has five words" is meaningful.
To determine whether the Minma Sentence is true, we determine whether the Minma Sentence has five words.
In "This sentence has five words", 'this sentence' refers to the Minma Senta, which is in the world. And "This sentence has five words" is equivalent with "The Minma Senta has five words", in the sense that each is true if and only if the Minma Senta has five words. So, "This sentence has five words" is meaningful.
To determine whether "The Minma Senta has five words" is true, we determine whether the Minma Senta has five words, which is to determine whether "This sentence has five words" has five words. To determine whether "This sentence has five words" is true, we determine whether "This sentence has five words" has five words. The determination of the truth value of the Minma Senta is exactly the determination of the truth value of "This sentence has five words".
(1) According to you, they are not versed in foundations of mathematics. So, by what basis do you claim that they take first order PA to be "the axioms of mathematics"? If one were not versed in foundations, then it's likely as not that they know of ZFC (since it is so often cited as the foundational theory) but know nothing or very little of PA (since PA does not axiomatize the mathematics for the sciences but only axiomatizes study of the natural numbers, which is subsumed by ZFC).
(2) As far as I know, "the axioms of mathematics" is ordinarily understood to mean ZFC as axioms sufficient for the mathematics for the sciences in the language of set theory in which analysis (calculus done right), topology, abstract algebra, etc. can be expressed, and not mere PA.
(3) By the way, Godel's own proof was not about PA nor ZFC but about a system P he formulated to simplify Whitehead and Russell's PM.
(4) Since G can be proven to be true in ZFC, "G can not be demonstrated from the axioms of mathematics" is horribly misleading, as it falsely suggests that ordinary mathematics cannot prove that G is true.
(5) Again, as you keep skipping this, saying "G can not be demonstrated from the axioms of mathematics" is not only horribly misleading, but it misses the crucial point that it is not the case that there is a sentence G that can't be proven in any theory, but that for any theory, there is a sentence such that neither it nor its negation are provable in that theory.
That is crucial to talking about scientific or philosophical implications of incompleteness. For example, some people argue that the human mind trumps computation because there are sentences that the mind sees to be true but for which there is no computation of their truth. But that argument is wrong, or at least need revision, since incompleteness very much does not show that there are such sentences, but rather that for any given consistent theory adequate for arithmetic, there are true sentences not provable in that theory. That is crucial to understand in order not to make wrong inferences about science or philosophy vis-a-vis incompleteness.
Quoting Tarskian
(6) I wouldn't rule out there being sub-theories without arithmetic that are useful.
(7) The claim you just made goes against your own argument. Indeed, if arithmetic weren't included then it wouldn't be in general adequate for science. But if the real numbers weren't included then that would not be adequate for the sciences. And the reals come from ZFC not PA. So PA is not an axiomatization of the mathematics for the sciences.
Quoting Tarskian
It is not merely "technically" false, it is both technically false and fundamentally false. Being fundamentally false and widely disseminated is a problem in and of itself. It terribly messes up the theorem in mathematics and is a welcome mat to misapplying the theorem in areas other than mathematics.
Quoting TonesInDeepFreeze
Quoting Tarskian
You miss the point again. I don't doubt that physicists don't care about tracking back to the mathematical axioms, but that's irrelevant to the subject Hawking is talking about when he is talking about what the axioms prove and don't prove. Yes, physicists don't bother with knowing how all the math was derived from ZFC or even what the ZFC axioms are. But their disinterest doesn't vitiate that the subject of incompleteness very much pertains to axioms and especially as in the lecture Hawking is directly talking about axioms.
Quoting Tarskian
Incompleteness applies to any consistent formal theory adequate for arithmetic. And the theorem is not that G is unprovable in ZFC. And the theorem is not that there is a sentence, such as G, that is not provable in any theory for a "default context" but rather that for any such theory, there is a sentence such that neither it nor its negation is provable in that theory.
You may not be interested in that point, but it is basic for understanding incompleteness, and avoidance of understanding it is an open door to bad misunderstanding of incompleteness vis-a-vis science and philosophy.
===============================================================================
Quoting TonesInDeepFreeze
There are sets of words, such as "colourless green ideas sleep furiously", that are meaningless, yet are not self-referential.
If I am correct in my belief that any set of words that is self-referential must be meaningless, then this set of words shouldn't be called a "sentence", as a sentence is a syntactic unit in language that does have a meaning.
From the Merriam Webster definition of "sentence"
The expression "self-referential sentence" is itself a paradoxical contradiction, in that if a set of words is self-referential then it cannot have meaning, and if cannot have meaning then cannot be a sentence.
===============================================================================
Quoting TonesInDeepFreeze
Difference between form and content
Suppose there are marks on a screen. The screen is in the world. Both an Italian speaker and English speaker in looking at these marks observe the same form, that of five distinct marks, but only the English speaker knows that the marks are words and the content of these words is "this sentence has ten words".
The content of these marks, that there are ten marks, is independent of the form of these marks, that there are five marks.
This means that the form of the words cannot be determined from the content of the words
The sentences "this sentence has ten words", "this sentence has five words" and "this sentence has fifty words" all have different contents, but are all five words.
The number of words in a sentence cannot be determined from the content of that sentence. IE, the content of a sentence does not refer to the form of that sentence.
The form of these marks exists in the world, whilst the content of these marks only exists in the mind of a sentient observer.
The sentence ""This sentence has five words" has five words" is ungrammatical, and therefore without truth-value.
On the screen I see the sentence "this sentence has ten words"
I can then write on the same screen "the sentence "this sentence has ten words" has five words"
The predicate "has five words" is referring to "the sentence "this sentence has ten words""
The predicate "has five words" is not referring to "this sentence has ten words".
The sentence "the sentence "this sentence has ten words" has five words" has the truth-value of being true.
The sentence ""this sentence has ten words" has five words" is ungrammatical, and therefore meaningless, and therefore without any truth-value.
===============================================================================
Quoting TonesInDeepFreeze
I agree that there is nothing ungrammatical about the sentences "this sentence has five words" and "this guy is in love with you".
However, as the pronoun "this" is external to both "the sentence" and "the guy", the pronoun isn't being self-referential.
The problem arises when the sentence is being self-referential, in the event that "this sentence has five words" is referring to itself and "this guy is in love with you" is referring to itself.
===============================================================================
Quoting TonesInDeepFreeze
True. The sentence "the sentence "this sentence has ten words" has five words" has the truth value of being true.
===============================================================================
Quoting TonesInDeepFreeze
It depends what "this sentence" refers to. If it refers to the sentence "this sentence has five words", then it has a truth-value, but if it refers to "this sentence has five words", then it has no truth-value.
===============================================================================
Quoting TonesInDeepFreeze
As an Indirect Realist, I perceive things through my five senses. My belief is that these perceptions have been caused by something outside me, and this something outside me I call "the world".
===============================================================================
Quoting TonesInDeepFreeze
I agree that marks exist in the world, but only a sentient being can attach a meaning to these marks. Only a sentient being knows when a set of marks is a part of a language. Only a sentient being knows when a set of marks is a sentence, meaning that sentences only exist in the mind.
Sets of marks exist in the world. Sentences exist in the mind.
Throughout my previous post, inside the strings, instead of 'sentence' we may say 'string' (and we could do that throughout :
'This string has five words'
Is that a sentence?
If you say it's not a sentence because it is self-referential, then you need to demonstrate the claim:
No string that is self-referential is a sentence.
You've argued for that claim, but my previous post is a response, and in the strings, we may use 'string' instead of 'sentence'.
Quoting RussellA
At least at first blush, "The string has five words" seems syntactic. A noun phrase, "This string" followed by a predicate, "has five words".
So you need to demonstrate that it is meaningless. But meanwhile, perhaps see if there is an error in the reasoning I gave for why we may take it to be meaningful. That reasoning could be wrong, but if it is, then I'd be interested to know how.
"This string has five words" asserts that "This string has five words" has five words. That seems meaningful. So it seems "This string has five words" is a sentence as it fulfills the two requirements: syntactical and meaningful. And "This string has five words" is true if "This string has five words" has five words, which it does; so "This string has five words" seems to be true. So, "This string has five words" seems to be true sentence.
Or:
Suppose we define 'the Pentastring' as the "This string has five words".
So, we have a subject from the world, viz. the Pentastring.
So, "The Pentastring has five words" is meaningful.
To determine whether the Pentastring is true, we determine whether the Pentastring has five words.
Put this way:
In "This string has five words", 'this string' refers to the Pentastring, which is in the world. And "This string has five words" is equivalent with "The Pentastring has five words", in the sense that each is true if and only if the Pentastring has five words. So, "This string has five words" is meaningful.
To determine whether "The Pentastring has five words" is true, we determine whether the Pentastring has five words, which is to determine whether "This string has five words" has five words. To determine whether "This string has five words" is true, we determine whether "This string has five words" has five words. The determination of the truth value of the Pentastring is exactly the determination of the truth value of "This string has five words".
Quoting RussellA
For sake of argument, let's say that is true. By what argument does it follow that the content of "This string has five words" is not meaningful? Do you claim that no observer can see it as contentful? An observer may reasonably and correctly say "I see it as contentful. The content is the claim that "This string has five words" has five words."
Quoting RussellA
Wrong. It's referring to the sentence "this sentence has ten words", which is to say that it is referring to "this sentence has ten words".
The sentence "this sentence has ten words" is "this sentence has ten words".
The sentence "this sentence has ten words" is not "The sentence "this sentence has ten words"".
And if your argument is supposed to be addressing mine, then no matter anyway, since I didn't use a construction "the sentence "this sentence has five words", and even if I had, your argument would be wrong since:
The sentence "this sentence has five words" has five words
is not saying
"The sentence "this sentence has five words"" has five words
Quoting RussellA
I don't know what you mean by 'external' there.
If by "referring to itself", then what is referring to "This sentence has five words" is 'this', in the sense that 'this' is referring to the sentence "This sentence has five words".
But with "This guy is in love with you", 'this' is referring to the guy who is the speaker of the sentence.
I mentioned "This guy's in love with you" only to put out of the way any objection that might come up to use of the pronoun 'this' to refer to the speaker of the sentence. Actually, it's not relevant here anyway.
Quoting RussellA
The sentence "this sentence has five words" is "this sentence has five words".
The tower Big Ben is Big Ben.
Quoting RussellA
Quoting RussellA
I don't see a good argument so far here that "This string has five words" cannot be only a set of marks and not exist in the mind.
You wrote:
Quoting RussellA
"This string has five words"
The words seem to me to correspond with things in the world.
'this string' corresponds with the string "This string has five words".
'has five words' corresponds with the property of a string having five words, which is something that I observe some strings to have.
And, as I mentioned, I see how "This string has five words" is meaningful, so that it is a sentence. And by the same reasoning, mutatis mutandis, "This sentence has five letters" is also a sentence.
On my screen I see the set of words "This string has five words".
What is a sentence? Is the meaningless set of words "colourless green ideas sleep furiously" a sentence? According to the Merriam Webster Dictionary, a sentence is a group of words that expresses a complete thought and has a subject and a verb. I would therefore suggest that a meaningless set of words cannot be classed as a sentence.
I am making use of Steve Patterson's video "How to Resolve the Liar's Paradox"
The question is, is the set of words "This string has five words" a sentence or not.
The problem is in knowing what "this string" refers to.
Possibility 1) If "this string" is referring to a string of characters existing in the world, such as the characters on my keyboard, then the set of words "This string has five words" is meaningful, is a sentence, has a truth-value and can be either true or false.
Possibility 2) If "this string" is referring to itself, then it is an empty reference, and the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.
Possibility 3) If "this string" is referring to "This string has five words", then the expression "this string" can be replaced by "this string has five words".
We then get: ((this string has five words) has five words).
Continuing, we get: (((this string has five words) has five words) has five words).
But as this will go on ad infinitum, meaning that the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.
Whether the set of words "this string has five words" is a sentence or not depends on what "this string" is referring to.
===============================================================================
Quoting TonesInDeepFreeze
If "This string has five words" did assert that "This string has five words" has five words
then "This string has ten words" would be asserting that "This string has ten words" has ten words, which is not the case.
Therefore, "This string has five words" cannot be asserting that "This string has five words" has five words.
===============================================================================
Quoting TonesInDeepFreeze
I see on my screen the set of words "this string has five words", and I see that there are five words in this set of words.
I see on my screen the set of words "this string has ten words", and I see that there are five words in this set of words.
I see on my screen the set of words "Diese Zeichenfolge besteht aus fünf Wörtern", and I see that there are six words in this set of words.
I go into a shop and buy five apples and notice that the time is exactly five pm. There is no logical link between the fact that I bought five apples and the fact that the time is five pm. That both involve the number five is accidental.
Similarly, that the content of the set of words "this string has five words" and the form of the set of words involves five is also accidental.
This is just to expand on RussellA ’s response. The underlying issue here is that there is no information in the 5 words which lets us know that it is self referential. The words “This string” (or “This sentence”) could be pointing to a different sentence, say, “Two plus two equals four”.
You say the the words seem to you to correspond with things in the world - and that may very well be the case - but in order to make that conclusion we need to rely on additional information NOT in those 5 words.
Suppose we did this:
A) “The sentence identified by the letter A in this post has thirteen words”
This works, but we need to rely on information not in the sentence.
Alternatively, I could hand you a piece of paper and on that piece of paper would be the words “The sentence on this piece of paper I just handed you has fourteen words”
That also works, but again we are relying on information in the world.
- - - - - - - - - - - -
I do have a slight different take than RussellA on what combination of words constitutes a sentence. Consider poetry:
“The quality of mercy is not strained”
“The moon was a ghostly galleon”
"Make a joyful noise unto the Lord"
etc
I consider these to be sentences. They are grammatically correct and they evoke images and/or emotions in my mind. However they do not take a truth value since they are not asserting anything specific about the world. Well OK - “The moon was a ghostly galleon” in theory makes a statement about the world, so literally interpreted it is false, but we all recognize that it is poetry and not to be taken literally.
So in this sense “This sentence has five words” is a legitimate sentence, it just does not take a truth value unless we make an assumption about the specific meaning of the first two words.
I hope this helps clarify things.
Quoting TonesInDeepFreeze
If you skip refutations, then we won't get anywhere.
You skipped my argument, for the second time (as now revised to use 'stirng' instead of 'sentence'):
Quoting TonesInDeepFreeze
If you skip my main argument, then we won't get anywhere.
/
The glaring sophistry in that video is the claim that "this sentence" equals "this sentence is false." No, "this sentence" refers to "this sentence is false" but they are not the same. One is a noun phrase, and the other is a noun phrase and a predicate. One has two words, the other has four words. One refers to the other but they are not the same, they are not equal to one another.
Quoting RussellA
I distinguish between physical inscriptions and sentences:
The teacher writes on the blackboard, "Caesar was a Roman emperor". A student writes in her notebook, "Caesar was a Roman emperor". The physical inscription on the blackboard is made of chalk. The physical inscription in the notebook is made of pencil lead. There are two inscriptions. But there is only one sentence involved.
Quoting RussellA
So you say. The ball is in your court to support that claim. Also, I've given an argument why it is a meaningful, true sentence. That argument could be wrong, but what do you claim is wrong with it? Mind you, any counter-argument you give cannot invoke the premise that self-reference is meaningless, since that would be petitio principii.
Quoting RussellA
Rule out that possibility. It's the specious argument that the video makes. "X refers to Y" doesn't entail "X can be replaced by Y".
Quoting RussellA
That's wrong.
It's not the case that "This string has ten words" has ten words; but it is the case that "This string has ten words" asserts that "This string has ten words" has ten words.
Quoting TonesInDeepFreeze
Quoting RussellA
Okay.
Quoting RussellA
I don't know what you mean by "the content of the set of words". But, yes, in form, "This string has five words" has five words. Anyway, I've made no argument that mentions "not accidental". I don't see how you infer that what I wrote is not correct:
Quoting TonesInDeepFreeze
Any pronoun could be referring to something different. "This ball is light" could be referring to any ball anywhere. But I don't think that way. It is by context that we regard the reference of a pronoun. There is no reason to arbitrarily think that 'this string' refers to "two plus two equals four" rather than "this string has five words" in which "this string" occurs. Or, if that's not good enough, we can stipulate that it does.
Quoting EricH
I said 'seem' because I am open to arguments to the contrary.
Quoting EricH
Denotations are not usually in words themselves. Rather, we stipulate denotations. It's not in the word 'ball' that it stands for the main objects in sports games.
Quoting EricH
Take a look at my argument with the Pentastring.
Quoting TonesInDeepFreeze
On my screen I see a set of marks which I recognize as a set of words having meaning.
For convenience, I name the sentence "this sentence has ten words" as A.
I can see that sentence A has five words.
I can then write on the same screen sentence B. I can either explicitly write "sentence A has five words", or I can implicitly write "A (being a sentence) has five words".
In the first case, the predicate "has five words" is referring to the subject "sentence A". In other words the subject is "the sentence "this sentence has ten words""
In the second case, the predicate "has five words" is referring to the subject "A (being a sentence)". In other words the subject is ""this sentence has ten words" (being a sentence)".
Either way, whether explicit or implicit, the subject is "the sentence "this sentence has ten words"".
===============================================================================
Quoting TonesInDeepFreeze
We can define "the Pentastring" as "this string has five words".
Both "the Pentastring" and "this string has five words" exist in the world on my screen. I can see that the expression "the Pentastring" has two words, and the expression "this string has five words" has five words.
Given the expression "The Pentastring has five words", as "The Pentastring" has been defined as "This string has five words", we can replace "The Pentastring" by "This string has five words".
This gives us the expression "This string has five words has five words". But this is an ungrammatical expression.
"A cat" may be defined as "a carnivorous mammal long domesticated as a pet and for catching rats and mice".
"A cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice". Although the two expressions are not linguistically equal (one is two words long and the other is fourteen words long), they are semantically equal, meaning that one expression can be replaced by the other.
Possibility three
In the expression "this sentence is false", "this sentence" refers to "this sentence is false".
As "a cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice", the expressions are interchangeable.
Rather than say "I saw a cat", I could equally say "I saw a carnivorous mammal long domesticated as a pet and for catching rats and mice". The meanings are equal.
Therefore, as "this sentence" refers to "this sentence is false", the expression "this sentence" can equally be replaced by the expression "this sentence is false"
IE, ""this sentence is false" is false"
Continuing, """this sentence is false" is false" is false"
This goes on ad infinitum.
If in the expression "this sentence is false", "this sentence" refers to "this sentence is false", its self-referential nature means that no meaning can be determined within a finite time, meaning that it becomes meaningless.
Agree
===============================================================================
Quoting TonesInDeepFreeze
I wrote: Possibility 2) If "this string" is referring to itself, then it is an empty reference, and the set of words "this string has five words" is meaningless, isn't a sentence and has no truth-value.
If "this string" referred to "a sequence of code units", then it would mean something, as it is referring to something outside itself.
But if "this string" refers to itself, then it is impossible to know what it means, and if no-one knows what it means, then it becomes part of a meaningless set of words.
My arguments are straightforward. I am explicit in the steps so that they can be understood exactly or so that they can be corrected exactly.
Meanwhile, you have time to write your arguments, and repeat them, while I have read each one of them carefully and answered virtually every detail in all of them. If you feel you are not caught up to mine, then I suggest you go back to my first reply to you and read carefully starting there, rather than thoughtlessly quoting as mere fodder for your non-responsive replies.
And now I see that you have a serious misunderstanding of how quotation marks work. Just as with the video that is you inspiration, you don't understand use-mention as you flagrantly fail to use quotation marks correctly. You mangle the enquiry that way.
Addressing your A and B:
"A" denotes "This sentence has ten words".
A is "This sentence has ten words".
"A" is not "This sentence has ten words".
"This sentence has ten words" does not have ten words.
"This sentence has ten words" is false.
A is false.
"B" denotes "A has five words".
B is "A has five words".
"B" is not "A has five words".
"A has five words" has five words.
"A has five words" is true.
B is true.
There is no problem in any of that.
Quoting RussellA
Wrong. Right there you mangled it.
"has five words" is true of A, not of "A".
You can't put quote marks around the letter 'A' like that.
A is a sentence.
"A" is not a sentence. Rather "A" denotes a sentence.
Quoting RussellA
That's your same mistake.
You fail to understand the difference between the Pentastring and "the Pentastring".
"the Pentastring" denotes "this string has five words". We don't say that "the Pentastring" is "this string has five words". That would be ridiculous since "the Pentastring" is not "This string has five words"
When we define, we say one thing denotes another or is a name of another; we don't say one thing is another.
"the Pentastring" denotes (is a name of) "the string "this string has five words".
The Pentastring is "this string has five words".
But "the Pentastring" is not "this string has five words".
"Big Ben" (is a name of) the famous clock tower in London.
Big Ben is the famous clock tower in London.
But it is not the case that "Big Ben" is the famous clock tower in London!
"Einstein's famous formula'" (is a name of) "E=MC^2".
Einstein's famous formula is "E=MC^2".
But it is not the case that "Einstein's famous formula" is "E=MC^2"!
The video you suggested said that:
"this sentence" equals "this sentence is false".
That is plainly a falsehood. It would help if you not skip that point.
And the video's argument is based on that falsehood.
"Big Ben" denotes the famous clock tower in London.
"Big Ben" is not the famous clock tower in London.
"The famous clock tower in London" denotes the famous clock tower in London.
"Big Ben" and "the famous clock tower in London" are (extensionally) interchangeable.
"Big Ben" and the famous clock tower in London are not interchangeable, since the former is a name and the latter is a clock tower.
"This sentence" denotes "This sentence has five words".
"This sentence" is not "This sentence has five words".
""This sentence has five words"" denotes "This sentence has five words".
/
"cat" is a word.
A cat is an animal
"cat" denotes the animal.
"cat" is not "the animal".
Quoting RussellA
No, "A cat" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice. "A cat" does not denote "a carnivorous mammal long domesticated as a pet and for catching rats and mice."
"Big Ben" denotes the famous clock tower in London.
"Big Ben" does not denote "the famous clock tower in London".
Your arguments rely upon the fact that you are not careful to distinguish between, for example,
"a carnivorous mammal long domesticated as a pet and for catching rats and mice" and a carnivorous mammal long domesticated as a pet and for catching rats and mice.
Quoting RussellA
Yes, that is the point I made earlier.
(1) "a cat"
and
"a carnivorous mammal long domesticated as a pet and for catching rats and mice"
may be substituted for one another (in an extensional context).
(2) "a cat"
and
a carnivorous mammal long domesticated as a pet and for catching rats and mice
may not be substituted for one another.
(3) a cat
and
"a carnivorous mammal long domesticated as a pet and for catching rats and mice"
may not be substituted for one another.
The mistakes you made earlier are violations of the nature of (2) and (3)
Quoting RussellA
"a cat" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice.
"a carnivorous mammal long domesticated as a pet and for catching rats and mice" denotes a carnivorous mammal long domesticated as a pet and for catching rats and mice.
So, yes, the two are interchangeable (in extensional contexts; I'll leave that qualification tacit from now on).
I suggest sticking with 'This string has five words' for now.
Just to be clear:
"This string" denotes "This string has five words".
Of course, that is contextual.
In "This string has ten words", "this string" does not denote "This string has five words".
"This string has five words" is true.
""This string has five words" is true" is true.
ad infinitum
There's no problem with that.
"Einstein's famous formula has five symbols" is true.
""Einstein's famous formula has five symbols" is true" is true.
ad infinitum.
There's no problem with that, and if there is, then it's a problem with nearly any sentence, not just self-referential sentences.
"This string" denotes "This string has five words".
"This string" is "This string".
"This string" is not "This string has five words".
"This string" does not denote "This string".
"Big Ben" denotes Big Ben.
"Big Ben" is "Big Ben".
"Big Ben" is not Big Ben.
"Big Ben" does not denote "Big Ben".
Quoting RussellA
That assertion comes from the fact that you that you improperly use quote marks.
Your argument for that, as with the video, is shot down at the git-go by mentioning that the argument relies on the false equation: "This string" equals "This string has five words", mutatis mutandis in the video.
Quoting TonesInDeepFreeze
Quoting TonesInDeepFreeze
As @Deleted user suggests, I will spend some time and go through the thread ""This sentence is false" - impossible premise" to see what I can learn from what others were saying about the Liar Paradox.
As quotation marks are critical to the problem of the Liar Paradox, I will also spend some time ensuring that I am using them correctly before making any other comments.
You were right when you said:
"a cat" and "a carnivorous mammal long domesticated as a pet and for catching rats and mice" are interchangeable.
You were wrong when you said:
"a cat" refers to "a carnivorous mammal long domesticated as a pet and for catching rats and mice".
This is right:
"a cat" refers to a carnivorous mammal long domesticated as a pet and for catching rats and mice.
"a cat" does not refer to "a carnivorous mammal long domesticated as a pet and for catching rats and mice".
That is, "a cat" refers to the animal that is a carnivorous mammal long domesticated as a pet and for catching rats and mice", but "a cat" does not refer to the phrase "a carnivorous mammal long domesticated as a pet and for catching rats and mice".
"Big Ben" refers to the famous clock tower in London.
"Big Ben" does not refer to "the famous clock tower in London".
That is, "Big Ben" refers to the object that is the famous clock tower in London, but "Big Ben" does not refer to the phrase "the famous clock tower in London".
The use-mention distinction can get into some technicalities, but for ordinary discussions in logic, it's pretty simple:
Use:
Big Ben is the famous clock tower in London. (True)
Mention:
"Big Ben" has six letters. (True)
Mention:
"Big Ben" refers to the famous clock tower in London. (True)
Mistake:
"Big Ben" is the famous clock tower in London. (False)
Mistake:
Big Ben has six letters. (False)
Mistake:
Big Ben refers to the famous clock tower in London. (False)
Mistake:
Big Ben refers to "the famous clock tower in London". (False)
In this discussion there is a bit of a wrinkle that might (?) be throwing you off:
"This string" refers to "This string has five words".
In that example, the thing referred to is itself a phrase, so unlike with the "a cat" or "Big Ben" examples, there are quote marks on the right side not just the left side.
Another example of that:
Einstein's famous formula is "E=MC^2".
"Einstein's famous formula" refers to "E=MC^2".
So, the right side may itself be a phrase.
"This string" has two words. (True)
"This string" refers to "This string has five words". (True)
"This string" is "This string has five words". (False)
"This string" and "This string has five words" are interchangeable. (False)
"Einstein's famous formula" has three words. (True)
"Einstein's famous formula" refers to "E=MC^2". (True)
Einstein's famous formula is "E=MC^2". (True)
"Einstein's famous formula" is "E=MC^2". (False)
"Einstein's famous formula" and "E=MC^2" are interchangeable. (False)
The sentence "this sentence is false" is not a paradox as it is meaningless.
In the sentence "this sentence is false", what does "this sentence" refer to?
It could refer to the sentence "the cat is grey in colour".
In which case the sentence "this sentence is false" means that the sentence "the cat is grey in colour" is false.
Or it could refer to the sentence "this sentence is false".
In which case the sentence "this sentence is false" means that the sentence "this sentence is false" is false.
But we know that the sentence "this sentence is false" means that the sentence "this sentence is false" is false.
This means that the sentence ""the sentence "this sentence is false" is false" is false
This goes on ad infinitum.
===============================================================================
Quoting TonesInDeepFreeze
As regards use, Big Ben is the bell inside the clock tower.
As regards mention, "Big Ben" is "the bell inside the clock tower"
===============================================================================
Quoting TonesInDeepFreeze
I agree that "this sentence" is not interchangeable with "this sentence is false"
However, this is not what is interchangeable.
It is the expression "this sentence" that is interchangeable with the sentence "this sentence is false"
On the one hand there is i) "this sentence" and on the other hand there is ii) the expression "this sentence". These are different things.
This should negate your doubts regarding interchangeability.
That is not a sentence though.
True. I could say "a cat" is "a carnivorous mammal that has been long domesticated as a pet"
That is also not a sentence. :confused:
Again true. I've edited my post. Hopefully it works this time.
Quoting RussellA
Right.
Quoting RussellA
Wrong. Very wrong.
"Big Ben" has two words.
"the bell inside the clock tower" has six words.
So "Big Ben" is not "the bell inside the clock tower".
One more time:
Big Ben is the bell inside the clock tower.
"Big Ben" refers to the bell inside the clock tower.
"Big Ben" refers to Big Ben.
"the bell inside the clock tower" refers to the bell inside the clock tower.
"the bell inside the clock tower" refers to Big Ben.
"Big Ben" is not the bell inside the clock tower.
"Big Ben" is not "the bell inside the clock tower."
Big Ben is not "Big Ben".
Big Ben is not "the bell inside the clock tower".
One more time:
Big Ben is a physical object.
"Big Ben" is an expression.
"the bell inside the clock tower" is an expression.
"Big Ben" and "the bell inside the clock tower" refer to the same physical object.
"Big Ben" and "the bell inside the clock tower" are not the same expression.
Do you understand now?
Quoting RussellA
"this sentence" is not "this sentence if false".
(in context) "this sentence" refers to "this sentence is false".
"this sentence" and "this sentence is false" are not interchangeable":
"this sentence" has exactly two words. (true)
"this sentence is false" has exactly two words. (false)
"this sentence" has exactly four words. (false)
"this sentence is false" has exactly four words. (true)
So, you see that "this sentence" and "this sentence is false" are not interchangeable.
"Mark Twain" and "Samuel Clemens" refer to the same person.
"Mark Twain" and "Samuel Clemens" are not interchangeable*:
"Mark Twain" has exactly nine letters (true)
"Samuel Clemens" has exactly nine letters (false)
"Mark Twain" has exactly thirteen letters (false)
"Samuel Clemens" has exactly thirteen letters (true)
So, you see that, in a context such as this, "Mark Twain" and "Samuel Clemens" are not interchageable.*
*In an extensional context, what is inside the quote marks of "Mark Twain" and "Samuel Clemens" are interchangeable, but the whole units including the quote marks are not interchangeable. For example:
Mark Twain was friends with Nikola Tesla
is interchangeable with
Samuel Clemens was friends with Nikola Tesla
"Mark Twain" has exactly nine letters
is not interchangeable with
"Samuel Clemens" has exactly nine letters
Yes, Mark Twain is Samuel Clemens. So, (in an extensional context) every statement true of Mark Twain is true of Samuel Clemens and vice versa. But it is not the case that every statement true of "Mark Twain" is true of"Samuel Clemens" and it is not the case that every statement true of "Samuel Clemens" is true of "Mark Twain".
Quoting RussellA
Wrong.
"this sentence" is "this sentence".
the expression "this sentence" is "this sentence".
"this sentence" is the expression "this sentence".
the expression "this sentence" is the expression "this sentence".
Quoting RussellA
It affirms my knowledge that you haven't bothered to understand use-mention.
/
Quoting RussellA
But it doesn't.
Quoting RussellA
That's better.
Quoting RussellA
I think so.
Yes, the sentence "this sentence is false" means: the sentence "this sentence is false" is false.
Quoting RussellA
That's merely a tautology from the previous. You're just saying again what you said:
the sentence "this sentence is false" means: the sentence "this sentence is false" is false.
Quoting RussellA
What does 'This' refer to? I guess it refers to: the sentence "this sentence is false" is false.
Quoting RussellA
""the sentence "this sentence is false" is false"
has an odd number of quote marks.
Maybe you mean:
"the sentence "this sentence is false" is false" means: the sentence "the sentence "this sentence is false" is false" is false.
So:
"this sentence is false"
means
the sentence "this sentence is false" is false.
"the sentence "this sentence is false" is false"
means
the sentence "the sentence "this sentence is false" is false" is false.
"the sentence "the sentence "this sentence is false" is false" is false"
means:
the sentence "the sentence "the sentence "this sentence is false" is false" is false" is false.
ad infinitum
"the sentence "Paris is a city" is true"
means
the sentence "the sentence "Paris is a city" is true" is true.
"the sentence "the sentence "Paris is a city" is true" is true"
means
the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true.
"the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true"
means
the sentence "the sentence "the sentence "the sentence "Paris is a city" is true" is true" is true" is true.
ad infinitum
/
You've skipped the point we were discussing. You claimed that self-referential sentences are meaningless.
I mentioned "This sentence has five words". Then, to accommodate any objection that saying "sentence" there is question begging, I provided, "This string has five words". Perhaps "This string has five words"doesn't withstand scrutiny for meaningfulness after all. But at least prima facie it is meaningful. It has a subject "this string" that refers to "this string has five letters" and a predicate "has five words" that refers to the property of having five words. And it is true if and only if "this string has five words" has five words. And "this string has five words" has five words. So, "this string has five words" is true.
Then, to obviate any objections about the use of the pronoun 'this', I provided:
Quoting TonesInDeepFreeze
If your reply to that is yet more of your use-mention confusion, then my guess is that there's little hope you'd ever think about it enough to understand it, though it doesn't take a lot of thinking.
Examples of "mention"
Consider "Big Ben" has two words.
As the expression "has two words" refers to the expression "Big Ben", not to Big Ben as a thing in the world, this is an example of "mention"
Consider "the bell inside the clock tower" has six words
As the expression "has six words" refers to the expression "the bell inside the clock tower", not to the bell inside the clock tower as a thing in the world, this is an example of "mention"
Consider "Big Ben" is "the bell inside the clock tower"
As the expression "the bell inside the clock tower" refers to the expression "Big Ben", not to Big Ben as a thing in the world, this is an example of "mention"
===============================================================================
Quoting TonesInDeepFreeze
The expression "Big Ben" is referring to the bell inside the clock tower existing in the world.
The expression "the bell inside the clock tower" is referring to the bell inside the clock tower existing in the world.
The forms of the expressions "Big Ben" and "the bell inside the clock tower" are different, in that the first has two words and the second has six words
The contents of the two expressions are the same, in that both are referring to the bell inside the clock tower existing in the world.
As you pointed out earlier, form is different to content
Quoting TonesInDeepFreeze
And perhaps it's natural to think that any use of a word toward its main function, i.e. towards referring beyond its linguistic context, to actual cats and mats etc, should be understood also to refer in a smaller way, in passing, to the word itself and its linguistic context. And that this subsidiary reference (to syntactic features) might be what the distinction is acknowledging as "mention".
Whereas the distinction as I understand it is the other way round. It insists that we use a word (employ syntax) for the semantic purpose of mentioning, referring to, an object, subjecting it to this or that scrutiny or description. (Or, in less common usage of the same technical distinction, we use a sentence in order to mention a state of affairs.)
Which is slightly at odds with the usual connotation. When you say "scoundrel" do you mean to refer to the man in the dock? Fine. Do you mean to mention the man in the dock? In what oblique connection?? (In ordinary usage of "mention", I mean.)
No excuses. It's a technical distinction, and not rocket science. Just saying.
I would say just
mention
not
"mention"
Quoting RussellA
Wrong. Very wrong.
"the bell inside the clock tower" refers to Big Ben, not to "Big Ben".
Once you're clear about that, we can go back to this:
The video you suggested said that
"this sentence" equals "this sentence is false".
That is plainly a falsehood.
And the video's argument and your argument is based on that falsehood.
There's more to it also:
There are these forms:
(1) [name] refers to [object]
"Big Ben" refers to the bell.
(2) [object] is [object]
Big Ben is the bell.
(3) [name] refers to [object that is itself an expression]
"Einstein's famous formula" refers to "E=MC^2".
(4) [object] is [object that is itself an expression]
Einstein's famous formula is "E=MC^2".
/
The video and you conflate 'refer' with 'is' (or 'equals').
(5) "This sentence" refers to "This sentence is false".
but it is not the case that
(6) "This sentence" is (equals) "This sentence is false".
I wrote "Examples of "mention""
The problem is, I want the word "examples" to refer to the word "mention", I don't want the word "mention" to refer to the word "examples".
For example, the expression "examples of importance" means "important examples", where the word "important" is being used as an adjective.
Similarly, "examples of mention" means "mentionable examples", where the word "mentionable" is being used as an adjective.
I want the word "mention" to be used as a noun, which is why I included it in quotation marks.
The use-mention distinction and the question of quotation marks is a highly complex topic, and the subject of numerous academic articles. I don't think we will be able to come to any definitive solution in a thread about the liar paradox.
We use a word to mention a thing.
We use a word in quote marks to mention the word.
I guess you mean that the examples are instances where the word 'mention' applies to describe them.
Anyway, your argument that self-referring strings are not meaningful sentences failed.
And the argument in the video you endorsed about the liar paradox fails.
Yes, but for some there is a great deal to be gained by a misunderstanding.
Part 1: definitions
You can't define "mentions".
You are trying to assert a set of invariant linguistic rules. This is an impossible task.
Words are defined by their context. X is not(everything else).
I suspect you are somewhat aware of this. And yet here you are trying to browbeat into believing that your interpretation of words is the one and only true interpretation.
In case we do need to establish that you can't define anything objectively:
Me: I challenge you to define "Word".
You: Words.
Me: Define those words.
You: More Words.
Me: Define those words.
Etc.
You can choose infinite regression or circular definitions.
Part 2: Interpretations
There is no single correct interpretation.
Every single person who reads a sentence interprets it as they will.
You can't stop them interpreting it howsoever they choose.
The idea that your personal interpretation of, say, the Liar's paradox is correct and everyone else is wrong is a level of hubris even I don't aspire to.
I get that you are trying to establish a common ground for productive dialogue. But you can't do it.
The only person who interprets things identically to you - is an identical copy of you.
Each and every person has a unique response to every experience. Their response is their response. You cannot force them to respond the same way you do.
Part 3: Meaning
Meaning is relationships. Relationships change. Ergo, Meaning changes.
The meaning of words depends on context. Part of the context is the observer.
As you grow and change, your perception of meaning changes.
Mathematics chases after inherent meaning by stripping away relationships to find the essence of a thing.
Of course, in a world where meaning is contextual - the essence is the relationships.
All of which to say: meaning is in the eye of the beholder and changes as you change.
Coming on strong
It is possible you are deserving of more respect than I'm currently giving you... but for someone apparently sure of their position - you are peddling a whole lot of BS.
Your interpretation of the Liar's paradox is YOUR interpretation. RusselA's interpretation is his.
Can the paradox be interpreted in that way. Yes. Valid interpretation.
Right and wrong can get bent. Each interpretation exists.
Language is subjective.
I struggle to understand how anyone with the slightest awareness of linguistics can turn around and proclaim a given interpretation to be definitive. And yet here you are trying to tell RusserlA that his interpretation is wrong.
For shame.
Or do you genuinely believe that you can define... anything?
You may do an Internet search on 'use-mention' for guidance. Meanwhile, the notion of use-mention is prevalent in the literature of logic, and is explained with examples in a lot of texts including these:
'Introduction To Mathematical Logic' - Alonzo Church, pg 61
By the way, the Introduction of this book is the best overview of starting considerations for logic that I have found.
/
'Elementary Logic - 2nd ed' - Benson Mates, pg 21
By the way, this is one of the best intro books logic that I have found - rigorous, clear and concise.
/
'Introduction To Logic' - Patrick Suppes, pq 121
By the way, this book has the best treatment on formal definitions that I have found.
/
'Methods Of Logic - 4th ed' - W.V. Quine, pg 50
/
'An Introduction To Formal Logic' - Peter Smith, pg 83
/
'The Logic Of Book - 4th ed' - Merrie Bergman, James Moor, Jack Nelson, pg 67
A nifty little editorial there, some about the subject, but a lot, pejoratively, about me.
Quoting Treatid
The sense in which 'mention' is used in context of the use-mention distinction:
To mention a word is to speak about the word.
On the other hand, a word may be used to refer to something else.
For example:
"London" has six letters.
The word is spoken about.
London is populous.
The word is used to refer to the city not to the word.
It should be easy to see:
London is a city. (true)
London is populous. (true)
London is a word. (false - London is a city, not a word)
London has exactly six letters. (false - London is not a word and does not have a number of letters)
"London" is a city. (false - "London" is a word, not a city)
"London" is populous. (false - "London" is not a city and does not have a population)
"London" is a word. (true)
"London" has exactly six letters. (true)
Quoting Treatid
I'm just observing that if we don't keep straight the difference between use and mention, then we get whacky results, and that some of the other poster's argument don't hold up on account of conflating a phrase itself with the thing the phrase refers to.
Quoting Treatid
I was interested in his argument and interested in what may be his reply to criticisms of it. I took a good amount of time to study his argument. Then I saw errors in it; and explained why they are errors. And I presented a counterargument that seems correct to me, though I was interested in what criticisms there might be to the counterargument. And I offered him information and explanation of a common and well known notion. I haven't tried to "browbeat" anyone into believing anything.
Quoting Treatid
True. And interesting that the other poster's view is that "This sentence has five words" can't be meaningfully understood. But it does seem understandable to me. Yet, I don't accuse the other person of trying to "browbeat" me to believe that is not understandable.
Quoting Treatid
Pretty much all I've said about the liar paradox is:
(1) To state what it is.
(2) To correct the the misunderstanding that results if we don't recognize that it stipulates "all and only" and not just "only".
(3) To point out that reading various writers on the subject informs us as to why it is a subject of interest in mathematics, logic and philosophy.
(4) The video that was mentioned argues erroneously by conflating "refers to" with "equals".
Quoting Treatid
Of course, there is never a perfect commonality among people. That doesn't entail that we cannot reach enough commonality in certain situations. We don't have to have perfect commonality just to have a productive exchange. Moreover, at least the other poster does know more about use-mention now, so that he can use it going forward, revise it for himself, or reject and ignore it if he likes.
Quoting Treatid
The only person who interprets identically to me is me. But identical understanding is not required. Meanwhile, the only person who interprets things identically to you is you. But I'm not disqualifying anything you say on that consideration.
Quoting Treatid
Actually, I explicitly stated that I am not sure of the argument I've given in favor of the view "This sentence has five words" is meaningful and true. I said it seems to me that my argument is correct but that I am interested in seeing how it might not be correct. On certain other matters though, yes, I'm pretty sure. I'm pretty sure that London is a city and not a word, and that "London" is a word and not a city. And that in the video "This sentence" refers to "This sentence is false", and that "This sentence" does not equal "This sentence is false". And that the other poster's argument about "This string has five words" suffers from a crucial use-mention error. And you've not shown that anything I've said is "BS".
Quoting Treatid
My remarks were about his claim that self-referring sentences are not meaningful. He gave an argument for his claim. I gave a plausibility counter-argument and showed errors in his own argument. And I carefully studied each line of his posts. I don't think that's shameful.
Quoting Treatid
I use many words in their ordinary sense, and some words in certain contexts in more academic senses. In some contexts, rigorous definitions may be provided, while in other contexts I would just point to an ordinary dictionary, and while recognizing that dictionaries are ultimately circular in that certain words are defined with other words whose definition circles back to the word being defined. And that certain words are just so basic that they are ultimately understood contextually or ostensively. And sometimes I use words idiosyncratically for effect, hoping that they'll be understood in context and by some tolerance of the reader. And sometimes I mistakenly misuse words.
Meanwhile, I guess you have your own notions about the way you use words, such as with the words you use in your fusillade against me.
The use-mention distinction
(Note, using brackets to try to make the expression clearer)
I agree that the expression ("London" has six letters) is an example of mention, in that the linguistic expression "London" is being spoken about. In this case that it has six letters.
I agree that the expression (London is a city) is an example of use, in that the linguistic expression "London" is being used to refer to something else, in this case a city.
I agree that expression ("London" is a city) is ungrammatical.
However, in the expression ("London" is "a city"), as the linguistic expression "London" is being spoken about, this is also an example of mention. In this case that it is "a city". Note that "a city" is just a set of words, and is not referring to anything that may or may not exist in the world.
Another example of meaning would be ("Big Ben" is "the bell inside the clock tower"), as the linguistic expression "Big Ben" is being spoken about. In this case that it is "the bell inside the clock tower". Note that "the bell inside the clock tower" is just a set of words, and is not referring to anything that may or may not exist in the world.
Norman Swatz in his article Use and Mention explains that dictionary definitions are examples of meaning.
As @Treatid correctly points out: Me: I challenge you to define "Word". You: Words. Me: Define those words. You: More Words. Me: Define those words. Etc. You can choose infinite regression or circular definitions.
In the Merriam Webster dictionary, "London" is defined as "a city and port on both sides of the Thames River in southeastern England............"
"Big Ben" is defined as "a large bell in the clock tower..............."
We use the dictionary to find out the meanings of words.
A word is defined by reference to another word, which is defined by reference to another word. Definitions never ground a word in the world. As Wittgenstein pointed out, there is a difference between a word being "said" as in a dictionary and a word being "shown" as in picturing something in the world.
The expression ("London" has six letters) is an example of mention, as the linguistic expression "London" is being spoken about, in that it has six letters.
Similarly, the expression ("London" is "a city") is also an example of mention, as the linguistic expression "London" is also being spoken about, in that it is "a city".
===============================================================================
Quoting TonesInDeepFreeze
The Liar Paradox
That the paradoxical expression "this sentence is false" is meaningless doesn't depend on the word "equals". The argument in the video is about meaning.
I will repeat the argument, as this answers the OP.
In the expression "this sentence is false", which sentence is "this" referring to?
There are several possibilities.
Possibility one
It could be referring to the sentence "the cat is grey". In this case, the sentence "this sentence is false" means that the sentence "this cat is grey" is false, which is meaningful.
Possibility two
It could be referring to itself. In this case, the sentence "this sentence is false" means that the expression "this sentence" is false. But this is meaningless, and is similar to saying "this house" is false.
Possibility three
It could be referring to the sentence "this sentence is false". In this case, the sentence "this sentence is false" means that the sentence "this sentence is false" is false.
But we know that the sentence "this sentence is false" means that the sentence "this sentence is false" is false.
This means that the sentence "the sentence "this sentence is false" is false" is false
Ad infinitum. Therefore meaningless.
Just to be clear: I haven't said that I deny that all self-referential sentences are meaningless. Rather, I only suspect that it is not the case that all self-referential sentences are meaningless, and I'm interested in what would be objections to an example I gave in which it seems there is a self-referential sentence that is not meaningless.
I said it is false; I didn't say it is ungrammatical.
Quoting RussellA
(1) Just to be clear, the example I gave was not:
"London" is "a city"
It was:
"London" is a city.
(2) "a city" refers to that two word phrase.
"London" is "a city"
assets that the "London" (which is one word) is "a city" (which is two words), which is false.
Quoting RussellA
(1) I never defined 'words'.
(2) It's not clear to me what his point is, but perhaps it's (a) We define 'word' by using words. So what? (b) Definitions are either circular or infinitely regressive (or some words are taken as undefined, i.e. primitive). So what? You and I are both using words and definitions. That doesn't disqualify either of our arguments.
/
Quoting RussellA
"This sentence" refers to "This sentence is false".
But "This sentence" is not "This sentence is false".
"This sentence" has two words. "This sentence is false" has four words. Clearly, "This sentence" is not "This sentence is false".
[He uses gray, white and black text to separate out phrases. But in certain instances I take it that he is indicating mention as opposed to use. I'll just use quote marks. And I'll use italics to indicate what he says orally or on screen.]
He says: "This sentence" has to reference the entire sentence.
Indeed, "This sentence" references "This sentence is false"'.
But then he conflates 'references' with 'equals':
He says: "This sentence" equals "This sentence if false".
That's false. "This sentence" references "This sentence is false". But "This sentence" does not equal "This sentence is false".
Then he says: If "This sentence" is "this sentence is false"
It's not. So we're done really. Same as with 'equals', "This sentence" references "This sentence is false". But "This sentence" is not "This sentence is false".
He continues: then what the liar's paradox is really saying is [on screen]"This sentence is false" is false[/on screen] but this is a problem, because if you substitute "This sentence" for itself, you're left with [on screen]""This sentence is false" is false" is false[/on screen]
But he didn't substitute "This sentence" for itself. He substituted "This sentence is false" for "This sentence", based on his false claim that "This sentence" doesn't just refer to "This sentence" but that "This sentence" is "This sentence is false".
Consider:
"This sentence was typed at noon"
And suppose "This sentence was typed at noon" is true.
There, "This sentence" refers to "This sentence was typed at noon" but it is not the case that "This sentence" is "This sentence was typed at noon".
"This sentence was typed at noon" was typed at noon. (True)
Substituting "This sentence was typed at noon" for "This sentence":
""This sentence was typed at noon" was typed at noon" was typed at noon. (False)
So substituting "This sentence was typed at noon" for "This sentence" is not legitimate.
Substituting "This sentence is false" for "This sentence" is not legitimate.
Quoting RussellA
Actually, you've introduced new arguments:
Quoting RussellA
One. "This" in "This sentence is false" doesn't refer to "the cat is grey".
Two. "This sentence is false" does not mean that the expression "this sentence" is false.
Three:
"This string has five words" is true.
""This string has five words" is true" is true.
ad infinitum
"Einstein's famous formula has five symbols" is true.
""Einstein's famous formula has five symbols" is true" is true.
ad infinitum.
Fermat's Last Theorem is true.
"Fermat's Last Theorem is true" is true.
ad infinitum
Even without self-reference, we can generate infinitely many sentences in the manner that you do.
I mentioned that a while ago, and you didn't address it.
And recall that your claim is not just that "This sentence is false" is meaningless but that all self-referential sentences are meaningless. So the ad infinitum argument doesn't work for you in that regard.
And what you and the video miss regarding "This sentence if false" is that the longer and longer sentences alternate ad infinitum between effectively claiming that "This sentence is false" is false and effectively claiming that "This sentence is false" is true. And that boils down to the paradox itself.
Also, he argues that "This sentence is false" is not defined. But what is the definition of any sentence? Usually we don't define a sentence. What is the definition of "The sky is dark"? Definitions of 'sky' and 'dark' sure. And we say such things as ""The sky is dark" is true if and only if the immediate atmosphere lacks light". But that's not a definition of "The sky is dark". Meanwhile, "This sentence is false" is true if and only if "This sentence is false" is false. That's the paradox, but not for failing to "define" "This sentence is false".
/
And you've still not addressed the Pentastring example. It doesn't lose effect just because you choose to ignore it.
It depends what the word "this" in the expression "this sentence is false" is referring to.
If it is referring, for example, to the sentence "this cat is grey", then the expression "this sentence is false" means that the sentence "this cat is grey" is false, which is meaningful.
But if it is referring to itself, then the expression "this sentence is false" means that the expression "this sentence" is false, which is like saying "this house" is false.
Surely in this instance, isn't it the case that both "this sentence" is false and "this house" is false are meaningless?
I will set outside some of your other points for the moment, and try to get to the heart of the matter. Otherwise if you make five points, and I respond to each of your points with my own five points, and you then respond to each of my points with your own five points, this thread will end up longer than War and Peace.
I wrote that my belief is that self-referring expressions are meaningless. You wrote that your belief is that some self-referring expressions can be meaningful, and give the Pentastring example
I hope that I am not missing out anything crucial from your Pentastring argument.
The Pentastring argument is not a case of self-reference, as it is referring to something that exists in the world.
Quoting TonesInDeepFreeze
Agree, though it depends what "this" is referring to.
Quoting TonesInDeepFreeze
The sentence "this sentence is false" is not necessarily meaningless. The sentence is meaningful if the word "this" refers to the sentence "the cat is grey", for example.
Quoting TonesInDeepFreeze
Why? If it did, then "this string has ten words" would assert that "this string has ten words" has ten words.
Quoting TonesInDeepFreeze
Not necessarily. It depends what "this string" refers to. If it refers to either "this string" or "this string has five words", then it is self-referential and meaningless.
Quoting TonesInDeepFreeze
Then it would follow that "the cat is grey" is true if "the cat is grey" has four words. That the sentence "the cat is grey" has four words doesn't make it true that the cat is grey.
Quoting TonesInDeepFreeze
No problem, let's define 'the Pentastring' as the "This string has five words". This sounds very similar to defining 'Big Ben' as "the bell inside the clock tower".
Quoting TonesInDeepFreeze
That we define 'a unicorn' as "a mythical, usually white animal generally depicted with the body and head of a horse........................" doesn't necessarily mean that unicorns exist in the world. But let us suppose that the Pentastring exists in the world alongside Big Ben.
Quoting TonesInDeepFreeze
But we know that "the Pentastring" has been defined as "This string has five words".
Therefore "The Pentastring has five words" means that "this string has five words has five words". But this doesn't seem grammatical, and if not grammatical, then meaningless
Quoting TonesInDeepFreeze
Suppose the Pentastring exists in the world, alongside the Big Ben. As objects existing in the world, such as Big Ben and the Pentastring have no truth value,they can be neither true not false. The sentence "the Pentastring has five words" has five words. It is not the Pentastring that has five words.
Quoting TonesInDeepFreeze
No problem. In the world exists the physical objects Big Ben, being a bell inside a clock tower, and a Pentastring, being a string of five adjacent words.
Quoting TonesInDeepFreeze
We know that 'the Pentastring' has been defined as "This string has five words".
Therefore, the sentence "The Pentastring has five words" means that "this string has five words has five words"
Therefore, it is not the case that "This string has five words" is equivalent with "The string has five words has five words"
Quoting TonesInDeepFreeze
This is not an example of self-reference. A Pentastring is a string of five adjacent words existing in the world.
As "the cat" in the sentence "the cat is grey" is referring to the cat existing in the world, "the pentastring" in the sentence "the Pentastring has five words" is referring to the Pentastring existing in the world.
As the sentence "the cat is grey" is not an example of self-reference, then neither is the sentence "the Pentastring has five words"
Quoting TonesInDeepFreeze
It is true that the sentence "this string has five words" has five words. It is also true that the sentence "the cat is grey" has four words.
The fact that the sentence "the cat is grey" has four words is irrelevant to whether the cat is grey. Similarly, the fact that the sentence "this string has five words" has five words is irrelevant to whether this string has five words.
Quoting TonesInDeepFreeze
The sentence "the cat is grey" is true if the cat is grey. Similarly, the sentence "this string has five words" is true if this string has five words.
As a Pentastring is a string of five words, we can also say that the sentence "this string has five words" is true if this is a Pentastring.
But then again, this is not a case of self-reference, as "this string" is referring to something that exists in the world.
Perhaps you were in a hurry when you responded, but I wasn't talking about the Liar Statement, I was talking about Tones' counter example "The sentence has five words." So in all 3 of your scenarios "This sentence has five words" appears to be meaningful.
Now if I'm following from your last reply to Tones you seem to be acknowledging this - but you are claiming that because "This sentence has five words" asserts a situation in the real world then it is no longer self referential. Am I following you correctly?
I think that the sentences "this sentence has five words" and "this sentence is false"
can be treated in a similar way.
For both sentences, the question is, what does "this sentence" refer to?
Possibility one
It could be referring to the sentence "this cat is grey". In this case the sentence "this sentence has five words" means that the sentence "this cat is grey" has five words, which is meaningful, even if false.
Possibility two
It could be referring to itself. The sentence "the cat is grey" has a meaning because "the cat" is referring to something outside itself, ie a cat. However, if "this sentence" is referring to itself, the sentence "this sentence has five words" has no meaning, because "this sentence" is not referring to anything outside itself.
Possibility three
It could be referring to the sentence it is a part of, ie, "this sentence has five words". In this case, the sentence "this sentence has five words" means that the sentence "this sentence has five words has five words". But again, any meaning disappears.
Dependent on what "this sentence" is referring to, the sentence "this sentence has five words" may or may not be meaningless.
===============================================================================
Quoting EricH
I think I am right in saying that @TonesInDeepFreeze wrote that he believed that there seems to be a self-referential sentence that is not meaningless, and gave the Pentastring example.
@TonesInDeepFreeze wrote on page 5:
Suppose we define 'the Pentastring' as the "This string has five words".
So, we have a subject from the world, viz. the Pentastring.
So, "The Pentastring has five words" is meaningful.
The sentence "the Pentastring has five words" is not self-referential, because we have been explicitly told that the Pentastring exists in the world, ie we have a subject from the world, viz. the Pentastring.
A self-referential expression cannot refer to something existing in the world.
In the expression [s]"this sentence is false"[/s] "this sentence has five words", which sentence is "this" referring to?
Possibility one
It could be referring to the sentence "the cat is grey". In this case, the sentence [s]"this sentence is false"[/s] "this sentence has five words" means that the sentence "this cat is grey" [s]is false[/s] has five words, which is meaningful but obviously false.
Possibility two
It could be referring to itself. In this case, the sentence [s]"this sentence is false"[/s] "this sentence has five words" means that the expression "this sentence" [s]is false[/s] has five words. [s]But this is meaningless, and is similar to saying "this house" is false.[/s]. This is meaningful but false ("this sentence" has two words.)
Possibility three
It could be referring to the sentence [s]"this sentence is false"[/s] "This sentence has five words". In this case, the sentence [s]"this sentence is false"[/s] "This sentence has five words" means that the sentence [s]"this sentence is false" is false[/s] "this sentence has five words" has five words. Meaningful and true.
So AFAICT the Pentastring is meaningful in all 3 of your possibilities. Yes this is a minor point, but I wanted to clear it up.
As to whether a sentence which is seemingly self referential but instead points to the world is truly self referential or not? I leave that to you and Tones. :grin:
Quoting TonesInDeepFreeze
Quoting RussellA
Notice that there you left out that the Pentastring is "This string has five words". So "This string has five words" exists (in the world, or whatever rubric du jour). Applying the name "The Pentastring" to "This sentence has five words" allowed you to determine that the Pentastring is meaningful. But the determination of the truth value of the Pentastring is exactly the determination of the truth value of "This string has five words".
So sayeth RussellA. Contrary to demonstration.
"The Pentastring has five words" doesn't have the word 'this' so perhaps it seems not self-referential in the way of "This string has five words". But keep in mind that the Pentastring is "This string has five words".
"This string has five words" is self-referential. But the Pentastring is "This string has five words", so the Pentastring is self-referential.
To determine whether the Pentastring is true is to determine whether "This string has five words" has five words.
To determine whether "This string has five words" is true is to determine whether "This string has five words" has five words.
The Pentastring is meaningful if and only if "This string has five words" is meaningful, because the Pentastring is "This string has five words".
An expression that refers to itself can never have a meaning
An expression can only have a meaning if it refers to something outside itself.
We are given the expression "this sentence has five words", and are told that the expression "this sentence" refers to itself'.
I agree that the expressions "tall house", "grey cat", "that mountain" and "this sentence" have two words.
We are given the expression "this sentence has five words", yet we both agree that the expression "this sentence" has two words.
So how can the same expression have both two words and five words?
It can only be that the expression "this sentence" in the first instance of its use is not referring to the second instance of its use.
So, given the expression "this sentence has five words", where "this sentence" refers to itself, how do you get the knowledge that "this sentence" has two words?
This conflicts with what you wrote on page 7.
Quoting TonesInDeepFreeze
"This string has five words" is an expression, whilst the Pentastring is something that exists in the world.
The Pentastring is a string of five words - OK
This Pentastring is this string of five words - OK
"The Pentastring is a string of five words" - OK
"This Pentastring is this string of five words" - OK
The Pentastring is this string of five words - not OK
This Pentastring is the string of five words - not OK
"The Pentastring is this string of five words" - not OK
"This Pentastring is the string of five words" - not OK
Quoting RussellA
Again, as I pointed out:
An expression, such as the expression "Big Ben" refers to the thing Big Ben.
But with other expressions, the thing an expression refers to may also be an expression.
Einstein's famous formula is "E=MC^2". The expression "Einstein's famous formula" refers to the expression "E=MC^2".
The Pentastring is "This string has five words." The expression "The Pentastring" refers to the expression "This string has five words".
Again, since the start, and as I have pointed out to you again, but now you ignore again:
I'll list the variations again so that, hopefully, you'll understand:
An expression refers to a thing:
Big Ben is the clock tower in London.
"Big Ben" refers to the clock tower in London.
"Big Ben" refers to Big Ben.
"Big Ben" is not "the clock tower in London".
"Big Ben" does not refer to "the clock tower in London".
"Big Ben" does not refer to "Big Ben".
Big Ben is not "the clock tower in London".
Big Ben is not "Big Ben".
An expression refers to a thing that is itself an expression:
Einstein's famous formula is "E=MC^2".
"Einstein's famous formula" refers to "E=M2^2".
"Einstein's famous formula" refers to Einstein's famous formula.
"Einstein's famous formula" is not "E=MC^2".
"Einstein's famous formula" does not refer to "Einstein's famous formula".
Einstein's famous formula is not "Einstein's famous formula".
An expression refers to a thing that is itself an expression:
The Pentastring is "This string has five words".
"The Pentastring" refers to "This string has five words".
"The Pentastring" refers to the Pentastring.
"The Pentastring" is not "This string has five words".
"The Pentastring" does not refer to "The Pentastring".
The Pentastring is not "The Pentastring".
Quoting RussellA
"This Pentastring is this string of five words" has more than five words, so it's false. Anyway, it's not something I ever wrote.
These are not something I wrote. I don't know the point of mentioning them:
Quoting RussellA
To isolate the key point:
The Pentastring is "This string has five words." The expression "The Pentastring" refers to the expression "This string has five words".
Just as:
Einstein's famous formula is "E=MC^2". The expression "Einstein's famous formula" refers to the expression "E=MC^2".
I said that it seems to me that there are self-referring expressions that are meaningful but that I'm open to be being convinced otherwise and that I'm interested in finding any flaws there might be with the Pentastring argument.
Cleaning up your mess:
Quoting RussellA
So what? "This string has ten words" is false. That doesn't make it meaningless. "London is in France" is false. That doesn't make it meaningless.
Why are you wasting our time on such points?
Quoting RussellA
That's just you again reasserting you claim! It's not an argument. You keep doing that: Responding to my argument by just reasserting you claim. Meet Mr. Ouroboros.
Quoting RussellA
What in the world? How in the world do you come up with such a bizarre non sequitur?
Quoting RussellA
There you ignore that I mentioned that an expression can refer to an expression.
Define "Einstein's famous formula" as "E=MC^2". So Einstein's famous formula is "E-MC^2".
Define "The EqualityClause" as "All men are created equal". The EqualityClause" is "All men are created equal".
Define "JFK's'IconicMaxim" as "Don't ask what your country can do for you. Ask what you can do for your country". JFK'sIconicUtterance is "Don't ask what your country can do for you. Ask what you can do for your country".
Quoting RussellA
No, "The Pentastring has five words" means "This string has five words" has five words.
You speciously (either from dishonesty or ignorance) dropped the quote marks.
I didn't say that the Pentastring is this string has five words. I said the Pentastring is "This string has five words"
How transparently specious or stupid to drop the quote marks!
Quoting RussellA
Big Ben is not a linguistic object. The Pentastring is a linguistic object. Just as TheEqualityClause is a linguistic object.
Quoting RussellA
Again, the Pentastring is "This string has five words". The Pentastring has five words, they are: 'this', 'sting', 'has', 'five' and 'words.
Just as the EqualityClause have five words.
Quoting RussellA
It's not enough for you to post that speciousness. You have to post it twice.
Quoting RussellA
Again, the Pentastring is "This string has five words".
Quoting RussellA
That is one of the most bizarrely irrelevant analogies I've ever read.
"The cat is grey" says nothing about number of words.
"This string has five words" does say something about number of words.
"The cat is grey" is true if and only if the cat is grey.
"This string has five words" if and only if "This string has five words" has five words.
Quoting RussellA
That's nonsense concocted by you by ignoring that pronouns are contextual.
Consider:
"This guy is in love with Lani" means this guy is in love with Lani.
That's false.
The first occurrence of 'this guy' refers to Herb Alpert. The second occurrence of 'this guy' refers to me. Herb Alpert is in love with Lani. I'm not in love with Lani.
"This guy is in love with Lani" in context is true if and only if Herb Alpert is in love with Lani. It's not the case that "This guy is in love with Lani" in that same context is true if and only if TonesInDeepFreeze is in love with Lani.
"This string has five words" in context is true if and only if "This string has five words" has five words. It's not the case that "This string has five words" is true if and only if this string has five words.
Quoting RussellA
No, I didn't define a predicate "is a Pentastring". Rather, I defined a name "The Pentastring".
That's your claim, which you try to support with arguments that have been shown to be specious.
Quoting RussellA
No expression can.
"This sentence" refers to "This sentence has five words".
"This sentence" is not "This sentence has five words".
Quoting RussellA
Consider:
This sentence has five words.
Recognize:
"This sentence" is not "This sentence has five words".
"This sentence" refers to "This sentence has five words".
"This sentence" doesn't refer to "This sentence".
As you say, this is a key point, on which your other points depend.
1) "The Pentastring" exists in language, such that "The Pentastring is a string of five words". 2) The Pentastring exists in the world, such that the Pentastring is a string of five words.
As regards usage, as more than one Pentastring exists in the world, the expression "The Pentastring" is not referring to one particular Pentastring, but is being used to refer to a general class of objects.
On the other hand, as only one Eiffel Tower exists in the world, the expression "the Eiffel Tower" is referring to one particular Eiffel Tower, and not to a general class of objects.
===============================================================================
Quoting TonesInDeepFreeze
A Stanford article writes that the mass-energy equation, E = mc2, is one of the fundamental principles in physics, revealing that mass and energy are equivalent.
I would have thought that the formula E=MC^2 shouldn't be in quotation marks. For example, science is culturally important, and "science" has seven letters. Similarly, E=MC^2 is famous, and "E=MC^2" has six characters.
===============================================================================
Quoting TonesInDeepFreeze
We agree that the Pentastring is a string of five words, but as there are many Pentastrings in the world, to say "The Pentastring is this string of five words" would be grammatically incorrect. It would be more grammatically correct to say either "this Pentastring is this string of five words" or "the Pentastring is a string of five words".
Otherwise, I would agree that the expression "The Pentastring" refers to the expression "a string of five words"
===============================================================================
Quoting TonesInDeepFreeze
This is grammatically incorrect, as an object in the world is not an expression in language.
I agree when you wrote - "London" is a city. (false - "London" is a word, not a city).
Quoting TonesInDeepFreeze
As a city is not "London", a Pentastring is not "this string has five words"
I thought I was understanding you, but now I'm confused. Here's what you said earlier:
Quoting RussellA
Quoting RussellA
Going back to your 3 possibilities, this is the form of your Possibility 3. So as I read this, you consider "This sentence has five words" to be true under your Possibility 3. Am I getting this right?
I see words on my screen, which happen to be the words - this - sentence - has - five - words.
I recognize a meaning in these words as 1) "this sentence has five words".
In addition, I have the thought that this sentence, ie the words on my screen, has five words, and say 2) "this sentence has five words".
It is a coincidence that 2) happens to be the same as 1).
1) has not determined 2).
This is not Possibility 3, as "this sentence" in 2) is referring to something outside itself, to something that physically exists in the word, ie, the words - this - sentence - has - five - words.
This is not a case of self-reference, as "this sentence" is neither referring to itself (possibility 2) nor to the sentence of which it is a part (possibility 3.)
"This sentence" in 2) is referring to something that exists outside itself.
As I understand it, an expression in language can only have a meaning if it refers to something outside itself.
For example "cat" in language has a meaning because it refers to a cat in the world.
Also, "cat" in language has a meaning because it can be defined as "a carnivorous mammal long domesticated as a pet and for catching rats and mice"
In both of these examples, the word "cat" has a meaning because it refers to something outside itself.
If I said "this sentence" is "this sentence". this would be meaningless.
If I said "this sentence has five words" is "this sentence has five words", this would also be meaningless.
As possibilities two and three are about the instances where an expression in language is self-referential, it would follow such self-referential expressions cannot have any meaning.
But are there any examples in language where a linguistic expression that refers to itself has a meaning?
Why do you ignore what is actually posted?
When I first introduced the term "The Pentastring", I used it as a name not an adjective.
I said that The Pentastring is "This string has five words". ("The Pentastring" is a name for the expression "This string has five words".)
I didn't say that a Pentrastring is a string with five words. (I didn't say "The Pentastring" is an adjective for the property: is a string with five words.)
And I recently wrote:
Quoting TonesInDeepFreeze
It is bizarre foolishness that you tried to falsely twist my naming a particular string into an adjective. Either you're hopelessly confused or hopelessly dishonest.
Said another way:
I could have used any phrase, whether "The Pentastring" or "ForumFinExample" or whatever to name the expression "This string has five words". That's not an adjective for the property of being a string with five words.
Quoting RussellA
Wrong. You still don't understand use-mention and quote marks.
I am referring to the literal string of symbols. The formula is a string of symbols. The string of symbols expresses a scientific principle, but the string of symbols is itself a linguistic entity.
Go back to the examples:
Define "Einstein's famous formula" as "E=MC^2". So Einstein's famous formula is "E-MC^2".
Define "The EqualityClause" as "All men are created equal". The EqualityClause" is "All men are created equal".
Define "JFK's'IconicMaxim" as "Don't ask what your country can do for you. Ask what you can do for your country". JFK'sIconicUtterance is "Don't ask what your country can do for you. Ask what you can do for your country".
Define "The Pentastring" as "This string has five words". The Pentastring is "This string has five words".
Quoting TonesInDeepFreeze
Expressions exist. The expression, "All men are created equal" exists.
Consider:
Jefferson's most famous quote is "All men are created equal".
"Jefferson's most famous quote" refers to "All men are created equal".
Those are grammatical.
/
Meanwhile, one after another of your arguments have been refuted. Your replies are yet more straw-grasping, foolishly specious, smoke blowing confusions that are refuted.
You don't understand use-mention, quote marks, pronouns, the difference between a name and an adjective. And you show that you don't read the posts to which you reply and that you don't know to refrain from obvious speciousness.
It's meaningful and true.
"this sentence" is a phrase. It is the same as itself.
Quoting RussellA
It's meaningful and true.
"this sentence has five words" is a phrase. It is the same as itself.
Quoting RussellA
Ding ding ding ding ding! RussellA gets the prize! RussellA gets the prize for the most times arguing by repetition of an assertion. Congratulations, RussellA! Enjoy your all expenses paid trip to the luxurious Rabbit Hole Hotel.
Quoting RussellA
The Pentastring?
Quoting TonesInDeepFreeze
Quoting TonesInDeepFreeze
OK so far.
Quoting TonesInDeepFreeze
This is critical to your argument, but this is where I get lost.
As we're not going to agree, I'm moving on.
You said that this is okay:
"The Pentastring" is a name for the expression "This string has five words"
You say you get lost at:
The Pentastring is "This string has five words"
Why are you lost?
Use-mention:
(1)
"Mark Twain" is a name for the person Samuel Clemens.
Mark Twain is Samuel Clemens.
Samuel Clemens is the person named by "Mark Twain".
Samuel Clemens is Mark Twain.
(2)
"Dangerfield's catchphrase" is a name for the expression "No respect".
Dangerfield's catchphrase is "No respect".
"No respect" is the expression named by "Dangerfield's catchphrase".
"No respect" is Dangerfield catchphrase.
(3)
"The Pentastring" is a name for the expression "This string has five words".
The Pentastring is "This string has words".
"This string has five words" is the expression named by "The Pentastring".
"This string has five words" is the Pentastring.
Function of quotation marks
My assumption has been that because "Mark Twain" is in quotation marks, this means that "Mark Twain" is an expression in language, and because Samuel Clemens is not in quotation marks, this means that Samuel Clemens is a person who exists in the world.
"Snow is white" is true IFF snow is white.
Quoting TonesInDeepFreeze
Open to doubt.
The word "is" can have different meanings
In the predicate sense, "the apple is red"
In the identity sense, "the apple is a fruit"
In the existential sense, "there is an apple on the table"
Do apples exist in the world
It is said that "an apple" is the name in language of an apple in the world.
But do apples exist in the world?
There is something in the world that has been named "an apple"
For convenience, we say that in the world are apples, but this is shorthand for what we really mean, which is that there is something in the world that has been named "an apple"
In fact, as an Indirect Realist, I don't believe that apples exist in the world, but only exist in the mind as a concept.
Do Mark Twain and Samuel Clemens exist in the world?
I agree that "Mark Twain" is a name of something X in the world. Something X is referred to by the name "Mark Twain". I agree that "Samuel Clemens" is a name of the same something X in the world. The same something X is also referred to by the name "Samuel Clemens".
The question is, is this something X in the world Samuel Clemens, or has the something X in the world been named "Samuel Clemens"?
As naming something in the world "a cat" doesn't make that something a cat, in that I could name a horse "a cat", naming something in the world "Samuel Clemens" doesn't make that something Samuel Clemens.
My naming that tall tower in Paris in the 7th Arr of Champs de Mars "a kangaroo" doesn't make that something in the world a kangaroo.
Giving something in the world a name doesn't make that something into what has been named.
Just because something in the world has been named "Samuel Clemens", that doesn't mean that Samuel Clemens exists in the world. Just because something in the world has been named "Mark Twain", that doesn't mean that Mark Twain exists in the world.
Although "Samuel Clemens" and "Mark Twain" exist in language, as neither Samuel Clemens nor Mark Twain exist in the world, then it is not correct to to say that Mark Twain is Samuel Clemens.
Quoting TonesInDeepFreeze
No problem, setting aside what "this string has five words" means, and treating it as a set of words such as "a b c d e", and ignoring any meaning that it may or may not have.
Quoting TonesInDeepFreeze
Open to doubt.
As before, my assumption has been that because "This string has five words" is in quotation marks, this means that "This string has five words" is an expression in language, and because the Pentastring is not in quotation marks, this means that the Pentastring is something that exists in the world.
The problem is, you are not saying that "this string has five words" is the name of the Pentastring, you are saying that "this string of five words" is the Pentastring.
If A is B then B is A. If "this string has five words" is the Pentastring, then the Pentastring is "this string has five words".
How can an expression in language be something in the world?
How can "London" be a city?
This is not a side issue, as crucial to your argument that a self-referencing expression can be meaningful.
I'm not following you. Please humor this bear of little brain and take this one step at a time. You said previously that "This sentence has five words" is true. Do you still hold that position. Yes or no?
I agree that I could have been clearer in my reply.
My assumption is that if a set of words is in quotation marks, such as - "snow is white" -
then this means it is an expression in language, and if a set of words is not in quotation marks, such as - snow is white - then this is about something that exists in the world.
"Snow is white" is true IFF snow is white
Looking back, on page 2, the question was about the truth of the words - this sentence has five words.
The question was not about the truth of the words - "this sentence has five words".
As regards "this sentence has five words", it all depends on what "this sentence" is referring to. If it is self-referential, then it is meaningless, but if it is not self-referential and refers to something outside itself, then it is meaningful.
As regards - this sentence has five words - because not being in quotation marks, I took them as being something that exists in the world, such as on a computer screen.
I agree that something that exists in the world cannot be said to be either true or false, in that a mountain cannot be said to be either true or false, although it is true that the words - this sentence has five words - exist on the screen, otherwise I wouldn't be able to see them.
Whether "this sentence has five words" (which exists in language) is true or not depends on what "this sentence" refers to. The set of words - this sentence has five words - (which I take to exist in the world) cannot be said to be either true or false, although it is true that they exist in the world.
OK. So now let's go back to your Possibility two
Quoting RussellA
So let's substitute "has five words" for "is false" but otherwise keep your reasoning word for word:
In the expression "this sentence has five words", which sentence is "this" referring to?
Possibility 2
It could be referring to itself. In this case, the sentence "this sentence has five words" means that the expression "this sentence" has five words. Of course it's false, but per your reasoning it appears meaningful.
As I see it, in the self-referential case, where "this sentence" is referring to itself, this means that "this sentence" is referring to "this sentence".
Being self-referential, "this sentence" it is not referring to anything outside itself, which includes any words that happen to follow it, whether they are "has five words" or "is false". In fact, the expression could equally be "this sentence is on top of the mountain", "this sentence is extremely confusing" or "this sentence a b c", where a, b and c could be any words at all
Being self-referential, there is no semantic connection between "this sentence" and "a b c".
It initially seems that "this sentence", "the house" and "three mountains" are all meaningful parts of language. This is certainly the case when "the house" is referring to the house next to the river, and "three mountains" is referring to the Alps in Italy. But in the special case of self-reference where "this sentence" is referring to itself, "this sentence" may appear to be a part of language but in fact isn't. "This sentence" is just shapes on the screen.
In the self-referential case, that we see cognize a meaning in "this sentence" is accidental, in the same way that we see shapes in clouds or faces on Mars.
In the self-referential case, as "this sentence" is not a meaningful part of language, but just accidental shapes on the screen, it has no linguistic meaning.
You think Mark Twain was someone other Samuel Clemens?
Quoting RussellA
Both.
"This string has five words" was named "The Pentastring", and "This string has five words" is the Pentastring.
Quoting RussellA
If you name something (other than the author of 'Roughing It') "Samuel Clemens" then, of course, that thing doesn't become the person who wrote 'Roughing It'. But "Samuel Clemens" may also refer to something other than the person who wrote 'Roughing It'. If someone today has the last name "Clemens" and names her baby "Samuel", then the name "Samuel Clemens" refers to her baby as well as, in other contexts, it refers to the author of 'Roughing It'.
Quoting RussellA
You're still mixed up. You ignore what has been pointed out to you. I didn't name "This string has five words" with "a Pentastring". And I didn't define a predicate "is a Pentastring". Rather, I made up the name "Pentastring" and used it to name "This string has five words".
Quoting RussellA
When the great trumpet player William Alonzo Anderson was nicknamed "Cat", of course, he didn't become a cat, but he is Cat.
Just for fun, some more in the menagerie of great jazz artists:
Hawk is Coleman Hawkins though he was not a hawk.
Bird is Charlie Parker though he was not a bird.
Rabbit is Johnny Hodges though he was not a rabbit.
Bunny is Roland Bernard Berigan though he was not a rabbit.
The Frog is Ben Webster though he was not frog.
Chick is William Henry Webb though he was not a chicken.
The Lion is William Henry Joseph Bonaparte Bertholf Smith though he was not a lion.
Pony is Norwood Poindexter though he was not a horse.
Quoting RussellA
The baby born on November 30, 1835 in Florida, Missouri existed no matter what his name would be. That baby was named "Samuel Langhorne Clemens" and was Samuel Clemens. If another person is named or nicknamed "Samuel Clemens" then that person too is Samuel Clemens though not the same Samuel Clemens who wrote 'Roughing It'.
Quoting RussellA
What? Samuel Clemens, who is Mark Twain, exists as a deceased person. You're really utterly captiously quibbling about this? Wow. But, to accommodate even your most ridiculous quibbles, we'll use an example of a living person:
Ben Kingsley is Krishna Pandit Bhanji.
"Ben Kingsley" and "Krishna Pandit Bhanji" are two names of the same person.
Quoting RussellA
I named the string itself. But then I also discussed meaning.
Quoting RussellA
Not reasonable doubt.
Quoting RussellA
If I recall, a while ago you agreed that expressions are things in the world.
And you've not shown any problem. (1) Of course I am not saying that "This string has five words" is a name of the Pentastring. I stipulated that "The Pentasting" is a name of "This string has five words". (2) The Pentastring is "this string has five words". You've only adduced your own confusions in trying to fight that.
Quoting RussellA
Indeed that is an instance of the symmetry of identity. But what's your point?
Quoting RussellA
If I recall, you said that it could. Moreover, you said "thing in the world" means [paraphrase:] "thing observed outside oneself". Well, I observe expressions outside myself. When someone says, "Today's soup special is split pea", I observe that there is the expression ""Today's soup special is split pea" and that it is outside myself.
Quoting RussellA
What? "London" is not a city. No one said it is.
Quoting RussellA
It's not any kind of issue, since no one says that "London" is a city. No, actually, it is an issue. The issue is why you would come to such a bizarre conclusion that it is an issue.
My assumption is, as with the expression "snow is white" is true IFF snow is white, that words in quotation marks refer to something in language and words not in quotation marks refer to something in the world.
No problem that "this string has five words" was named "the Pentastring"
I agree when you say:
Quoting TonesInDeepFreeze
Then how can "this string has five words" be the Pentastring?
My problem is:
Quoting TonesInDeepFreeze
Sense and reference
"Mark Twain" and "Samuel Clemens" both refer to the same thing in the world, although the names have a different senses, in that "Mark Twain" was an author whereas "Samuel Clemens" wasn't.
As regards reference, "Mark Twain" and "Samuel Clemens" are both referring to the same thing in the world. Let this something be both Mark Twain and Samuel Clemens. In this event, Mark Twain is Samuel Clemens.
As regards sense, "Mark Twain" is referring to something in the world that is an author. Let this be Mark Twain. "Samuel Clemens " is referring to something in the world that isn't an author. Let this be Samuel Clemens. In this event, Mark Twain cannot be Samuel Clemens, as Mark Twain is an author and Samuel Clemens isn't
Then what would it mean to say that Mark Twain is Samuel Clemens?
It would mean that names in language, such as "Mark Twain" have no sense, which would preclude any thoughts about him being an author and essayist, the father of American Literature and the greatest humourist the United States had produced.
Logical contradictions
That "Samuel Clemens" is Samuel Clemens would give rise to logical contradictions.
My assumption is, as with the expression "snow is white" is true IFF snow is white, that words in quotation marks refer to something in language and words not in quotation marks refer to something in the world.
I agree that "Samuel Clemens" born in Hannibal 1835 is "Mark Twain" who wrote "Roughing It" in 1872.
To say that when something in the world is named "Samuel Clemens" then that something in the world becomes Samuel Clemens leads to problems of logic.
1) If person A, born in Hannibal, is named "Samuel Clemens" then that person becomes Samuel Clemens. If person B, born in New York is also named "Samuel Clemens" than that person also becomes Samuel Clemens. In logic, the law of identity states that each thing is identical with itself, in this case, that Samuel Clemens is Samuel Clemens. But this means that person A born in Hannibal is person B born in New York. Something is wrong.
2) A group of Modernists name a painting "good", meaning that the painting is good. A group of Post-Modernists name the same painting "bad", meaning that the same painting is bad. But this means that good is bad, which breaks logic.
3) Someone sees something and names it "a cat", and someone else sees the same thing and names it "a dog", this means that a cat is a dog, which is not logical.
4) There is something in Paris. It has been named "a tower" meaning that it is a tower. It has been named "an eyesore" meaning that it is an eyesore. It has also been named "beautiful", meaning that it is beautiful. Therefore the same thing is both an eyesore and beautiful. But this gives rise to a logical contradiction, as something that is an eyesore cannot be beautiful.
One could argue that whether something in the world is an eyesore or beautiful depends on the particular observer. Exactly. "Eyesores" and "beauty" exist in the mind of the observer, not the world.
Similarly, "Mark Twain" and "Samuel Clemens" exist in the mind not the world. If there were no minds, then neither "Mark Twain" nor "Samuel Clemens" would exist.
A name cannot determine what exists in the world, because if a name did determine what exists in the world, then logical contradictions would arise.
"This sentence has five words" is the sentence in question. It is true if and only if "This sentence has five words" has five words.
Quoting RussellA
"This sentence" refers to "This sentence has five words".
Quoting RussellA
And we're full circle about the third time, as your support for your assertion comes down to you just reasserting the assertion.
__________
Quoting RussellA
Wrong. And it's been pointed out to you that it's wrong. "This sentence" refers to "This sentence has five words". "This sentence" and "This sentence has five words" are not the same expression.
__________
Quoting RussellA
Because I gave "this string has five words" the name "The Pentastring".
You might as well as how ask how Samuel Clemens can be Mark Twain. Samuel Clemens is Mark Twain because Samuel Clemens was given the name "Mark Twain". Or, suppose I give "All men are created equal" the name "JiffyJeff". Then "All men are created equal" is JiffyJeff.
__________
Quoting RussellA
Right.
Quoting RussellA
"Mark Twain" was not an author!
"Mark Twain" is the name of an author.
Mark Twain was an author.
You still don't understand use-mention.
Quoting RussellA
Now you're back to sanity.
Quoting RussellA
You just conflated sense and reference. What even does "regards sense, X is referring" mean?
"Mark Twain" refers to Mark Twain.
"Mark Twain" refers to Samuel Clemens.
"Samuel Clemens" refers to Samuel Clemens.
"Samuel Clemens" refers to Mark Twain.
Mark Twain is Samuel Clemens.
The denotation of "Mark Twain" is the denotation of "Samuel Clemens".
"Mark Twain" is not "Samuel Clemens".
The sense of "Mark Twain" is not the sense of "Samuel Clemens".
Not only do you not understand quotation marks, use-mention or pronouns, you don't understand sense-reference.
Back to the point, contrary to your claim, it is not in doubt that Mark Twain is Samuel Clemens.
Quoting RussellA
Of course "Samuel Clemens" is not Samuel Clemens.
Quoting RussellA
What is wrong is your failure to distinguish between formal logic and everyday usage.
In formal logic, given a particular interpretation of the language, a name refers to one and only one object. But in every day usage, sometimes names often have different referents. You didn't notice that there many thousands of people named "Jane Smith" and that all of them are Jane Smith, though they are different Jane Smiths?
Quoting RussellA
You did it again! You conflate a name with a predicate. You simply ignored that I already pointed out that error.
Naming a painting "Good" is very different from asserting that the predicate "is good" applies to the painting. If you make some squiggles and name that product "Good", of course it doesn't then follow that the squiggle drawing is good. If you named one of your posts "Reasoned Argument", of course it doesn't follow that your post is reasoned argument.
Quoting RussellA
You equivocate. First you say that expressions do exist in the world. And you agreed that expressions exist in the world not just as particular inscriptions. Now you say they don't exist in the world.
Still would like to know why you ask "How can "London" be a city?" when no one has said that "London" is a city.
Wait, I think I do know why. You still are confused about the distinction between use and mention.
Tackling your points one by one.
1) "This sentence has five words" is true IFF "this sentence has five words" has five words.
If this were the case, then it would follow that:
"New York is in France" is true IFF "New York is in France" has five words.
That is one of the most bizarre arguments I've ever heard.
"New York is in France" is true if and only if New York is in France.
"New York is in France" makes no mention of the number of words in "New York is in France".
From the fact that "This sentence has five words" is true if and only if "This sentence has five words" has five words it does not follow that "New York is in France" is true if and only if "New York is in France" has five words!
You are bizarre. It is amusingly disturbing about you that you are willing to enter increasingly outlandish arguments after each of your previous confused and outlandish claims is defeated.
You haven't "tackled" anything. You've fallen on your behind, dizzy from spinning while chasing yourself in circles of your own confusions.
Problematic.
I agree that
1) "snow is white" is true IFF snow is white
2) "New York is in France" is true IFF New York is in France
3) "This sentence has five words" is true IFF this sentence has five words
The meanings of 1) and 2) are straightforward.
The problem with 3) is what exactly are "this sentence" and (this sentence) referring to?
For clarity, using brackets to indicate the world
For example, in a non-self-referential case, "this sentence" could be referring to the sentence "New York is in France", and (this sentence) could be referring to (New York is in France).
The non self-referential case is meaningful.
However, in a self-referential case, "this sentence" could be referring to the sentence "this sentence has five words", and (this sentence) could be referring to (this sentence has five words).
The self-referential case is meaningless.
The problem with the self-referential case, is that the content of a sentence contains no information about the form of the sentence.
The content of the sentence "this sentence has five words" is that "this sentence has five words". The form of the sentence "this sentence has five words" is that the sentence "this sentence has five words" has five words.
The content of a sentence can say nothing about the form of the sentence. It cannot self-refer.
As the sentence "New York is in France" says nothing about how many words are in the sentence "New York is in Paris, the sentence "this sentence has five words" says nothing about how many words are in the sentence "this sentence has five words"
I agree when you say:
Quoting TonesInDeepFreeze
From the same logic, "this sentence has five words" makes no mention of the number of words in "this sentence has five words". It makes no mention of the fact that "this sentence has five words" has five words.
Any similarity in expression is purely accidental. Content cannot refer to its own form.
Quoting RussellA
Regarding (3): You agree with yourself. You don't agree with me.
"This sentence has five words" is true IFF this sentence has five words" is ridiculous. You skip my previous response in which it is pointed out to you that you are ignoring the way pronouns work.
Quoting RussellA
That's been answered. You skip my previous response.
Quoting RussellA
In "This sentence has five words", obviously "This sentence" does not refer to "New York is in France".
It is pointless for you to even offer that non-possibility.
That's been mentioned. You skip my previous response.
Quoting RussellA
Maybe what you mean is that "This sentence" refers to the claim that New York is in France.
Again, it doesn't.
It is pointless for you to even offer that non-possibility.
Quoting RussellA
"This sentence" refers to "This sentence has five words".
Quoting RussellA
The "content" of "This sentence has five words" is the claim that "This sentence has five words" has five words.
The "form" of "This sentence has five words" is that "This sentence has five words" is the string that is the sequence of the five words "this", "sentence", "has", "five" and "words".
Quoting RussellA
That's argument by mere assertion.
The "content" of "This sentence has five words" is the claim that "This sentence has five words" has five words. And having five words is an aspect of the form of "This sentence has five words".
Quoting RussellA
You repeat that bizarre and stupid analogy again!
Quoting RussellA
"This sentence" refers to the sentence "This sentence has five words" and makes the claim that that sentence has five words.
Quoting RussellA
Similarity between what and what? And what is meant by "accidental" in this context?
Quoting RussellA
Again, argument by mere assertion. And not even coherent. The content does not refer. The content is the claim that "This sentence has five words" has five words. That claim does not refer. With the sentence "Jack is tall", the sentence makes the claim that Jack is tall. What refers are the noun phrase "Jack", which refers to Jack, and the predicate "is tall", which refers to the property of being tall. With the sentence "This sentence has five words", the sentence makes the claim that "This sentence has five words" has five words. What refers is the noun phrase "This sentence", which refers to "This sentence has five words", and the predicate "has five words", which refers to the property of having five words.
"This sentence has five words" is true if and only if this sentence has five words.
But that is wrong and stupid. It is wrong and stupid as he is not distinguishing the two different contexts of 'this'.
In the first instance "This sentence" refers to "This sentence has five words".
In the second instance, "this sentence" refers to ""This sentence has five words" is true if and only if this sentence has five words."
It is foolishness to ignore that distinction.
"This guy is in love with Lani" is true if and only if Herb is in love with Lani.
It is not the case that "This guy is in love with Lani" is true if and only if this guy is in love with Lani.
In the first instance "This guy" refers to Herb.
In the second instance "this guy" refers to TonesInDeepFreeze.
Herb is in love with Lani. TonesInDeepFreeze is not in love with Lani.
"This sentence has five words" has five words.
""This sentence has five words" has five words" does not have five words. (where "has five words" is meant as "has exactly five words")
/
Suppose there is a billboard out on Highway 61 in Bobsville, Arizona that says:
This billboard has five words.
"This billboard" refers to the billboard out on Highway 61 in Bobsville, Arizona. That is, "This billboard" refers to itself.
"This billboard has five words" is true if and only if the billboard out on Highway 61 in Bobsville, Arizona has five words.
"The Pentastring" refers to "This string has five words".
The Pentastring is "This string has five words".
The Pentastring is true if and only if "This string has five words" has five words.
The Pentastring is true if and only if "This string has five words" is true. (where "this string" refers to the string "This string has five words")
"Einstein's famous formula" refers to "E=MC^2".
Einstein's famous formula is "E=MC^2".
Einstein's formula is true if and only if E=MC^2.
Einstein's formula is true if and only if "E=MC^2" is true.
"JiffyJeff" refers to "All men are created equal".
JiffyJeff is "All men are created equal".
JiffyJeff is true if and only if all men are created equal.
JiffyJeff is true if and only if "All men are created equal" is true.
"Herb'sVow" refers to "This guy is in love with Lani".
Herb'sVow is "This guy is in love with Lani".
Herb'sVow is true if and only if Herb is in love with Lani.
Herb'sVow is true if and only if "This guy is in love with Lani" is true. (where "this guy" refers to Herb)
"BobsvilleMessage" refers to "This billboard has five words".
BobsvilleMessage is "This billboard has five words".
BobsvilleMessage is true if and only if the billboard out on Highway 61 in Bobsville, Arizona has five words.
BobsvilleMessage is true if and only if "This billboard has five words" is true. (where "this billboard" refers to the billboard out on Highway 61 in Bobsville, Arizona)
It is not the case that "This billboard has five words" is true if and only if this billboard has five words. Especially since the second instance of "this billboard" does not even properly refer.
This is the song. It may be quite simple.
"This" refers to the song itself, which is the song that is titled "Your Song". "It" refers to the song itself, which is the song that is titled "Your Song".
Within the song, there is reference to the song. It seems to me that it is meaningful when the song says of itself that it may be quite simple.
"It may be quite simple" is true if and only if the song itself (which is titled "Your Song") may be quite simple.
Consider this botched version:
"It may be quite simple" is true if and only if it may be quite simple.
The first instance of "it" refers to the song.
The second instance of "it" refers to the sentence "It may be quite simple".
But the song is not the sentence "It may be quite simple".
We cannot sensibly ignore the context of pronouns as @RussellA so ignorantly does.
@RussellA offers three options for "This string has five words":
(1) "This string" refers to "This string".
(2) "This string" refers to some other unrelated string such as "The cat is black".
(3) "This string" refers to "This string has five words".
Each one:
(1) is false. "This string" doesn't refer to the string "This string" but rather to the string "This string has five words", which is the string that has five words.
(2) is false and ridiculous.
(3) is true. But he claims that then "This string has five words" is meaningless due to self-reference. But why does self-reference make it meaningless? His answer is that self-reference is meaningless because the would-be referrer doesn't refer to something in the world. But why is a string not something in the world? His answer is that because strings are in the mind not outside the mind. But then not just self-referring strings are in the mind not in the world. (Moreover, he agrees that strings are not mere inscriptions but that the same string may have more than one inscription.) So if strings are not things in the world, then the string "Caesar was a Roman emperor" is not in the world. So ""Caesar was a Roman emperor" has five words" must also be meaningless. But then his default is to merely reassert that it is self-referring strings that are meaningless. And around in circles it goes, back to him reasserting his three options.
Meanwhile, the Pentastring argument has not been refuted.
The above is a key point of disagreement
"Snow is white" is true IFF snow is white
"Jack is tall" is true IFF Jack is tall
"This sentence has five words" is true IFF this sentence has five words
It is not the case that "this sentence has five words" is true IFF "this sentence has five words" has five words
It is true that the sentence "this sentence has five words" has five words, but this truth is independent of any meanings of the words within the sentence.
The meanings of the words within the sentence "this sentence has five words" play no part in the truth that the sentence "this sentence has five words" has five words.
The sentence "a b c d e" has five words, regardless of any meaning of the words "a b c d e".
The meanings of the words "a b c d e" play no part in the fact that the sentence "a b c d e" has five words
Similarly, the meanings of the words "this sentence has five words" play no part in the fact that the sentence "this sentence has five words" has five words.
As "Jack is tall" makes the claim that Jack is tall, then "this sentence has five words" makes the claim that this sentence has five words. It doesn't make the claim that "this sentence has five words" has five words.
Otherwise, the sentence "this sentence has fifty words" would be making the claim that "this sentence has fifty words" has fifty words.
Yes? And the sentence would be false.
As regards the sentence "this sentence has fifty words" making the claim that "this sentence has fifty words" has fifty words:
No, it wouldn't be false, it would be meaningless, because self-referential.
"Snow is white" is making the claim that "snow is white" is true IFF snow is white.
"Jack is tall" is making the claim that "Jack is tall" is true IFF Jack is tall
"This sentence has fifty words" is making the claim that "this sentence has fifty words" is true IFF this sentence has fifty words.
In language is "this sentence has fifty words".
In the world is a set of words.
If in the world there is a set of fifty words, then "this sentence has fifty words" is true
If in the world is a set of words of which there are not fifty, then "this sentence has fifty words" is not true.
There is no problem here, as meaningful.
The problem arrives when "this sentence has fifty words" is making the claim that "this sentence has fifty words" is true IFF "this sentence has fifty words" has fifty words.
This is a problem of self-reference, because "this sentence has fifty words" is referring to itself.
For example, consider "unicorns are happy" is true IFF unicorns are happy. This is meaningful. Then consider "unicorns are happy" is true IFF "unicorns are happy". This is a tautology, an example of the law of identity where a thing is identical with itself.
This is why self-reference leads to a paradox, and why expressions that self-refer are meaningless.
"This sentence has fifty words" can meaningfully refer to a sentence having fifty words, but it cannot meaningfully refer to itself.
1. This sentence contains five words
2. This sentence contains fifty words
(1) is true and (2) is false. It's not complicated. I don't understand the problem you have.
It's not. Here are two propositions:
1. It is raining
2. "it is raining" is true iff it is raining
(1) and (2) do not mean the same thing. (1) is true iff it is raining but (2) is true even if it isn't raining.
The problem is, in 2) for example, what exactly is "this sentence" referring to?
If "this sentence" is referring to "this sentence contains fifty words", then this is a case of self-reference, and being a case of self-reference is meaningless.
In that event, this sentence, ie the sentence "this sentence contains fifty words", contains fifty words.
But we have been told that "this sentence" refers to "this sentence contains fifty words"
We therefore know that this sentence, ie the sentence "ie, the sentence "this sentence contains fifty words", contains fifty words", contains fifty words.
But we have been told that "this sentence" refers to "this sentence contains fifty words"
Ad infinitum.
That is my problem.
===============================================================================
Quoting Michael
Agree, 1) and 2) don't mean the same thing.
1) It is raining is true IFF it is raining. The word "true" is redundant. If it is raining then it is raining. This is an example of the law of identity where something is equal to itself.
2) "It is raining" is true IFF it is raining. This is meaningful.
No it’s not.
Quoting RussellA
No it doesn’t. It contains five words and so is false.
You should stop right there. You continue to blatantly assert the same confusion. You should go back and actually read the explanation that has been given you about this five times already.
For about the fifth time you have skipped the point that you are not taking into account that pronouns are contextual. So, again I suggest that you consider:
"This sentence has five words" is true IFF this sentence has five words.
The first occurrence of "This sentence" refers to the sentence "This sentence has five words"; but the second occurrence of "this sentence" refers to the sentence ""This sentence has five words" is true IFF this sentence has five words".
"This sentence has five words" has five words.
"This sentence has five words" is true IFF this sentence has five words" does not have five words.
Your argument that blatantly ignores the context of pronouns is blatantly fallacious.
Consider:
"This guy is in love with Lani" is true if and only if this guy is in love with Lani.
The first occurrence of "This guy" refers to Herb Alpert; but the second occurrence of "this guy" refers to TonesInDeepFreeze.
Herb Alpert is in love with Lani. TonesInDeepFreeze is not in love with Lani.
/
That you blatantly skip this point over and over is intellectual dishonesty.
/
The more you are corrected on each point, the more you continue to propagate both old and new speciousness.
That's why there is a SEP article on the Liar Paradox.
===============================================================================
Quoting Michael
I agree that my statement was false. But is was meaningful, unlike the Liar Paradox, where a part of language refers to itself.
Au revoir.
But you weren't talking about the liar paradox. You were talking about the sentences "this sentence contains five words" and "this sentence contains fifty words". These two sentences are meaningful, with the first being true and the second being false.
You say that the sentence "this sentence contains fifty words" is false.
But you don't know that. It all depends on which sentence "this sentence" is referring to.
In the same way, we don't know whether the sentence "this ferry contains fifty people" is true or false, if we don't know which ferry is being referred to.
Similarly, we don't know whether the sentence "this idea contains fifty thoughts" is true or false, if we don't know which idea is being referred to.
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.
If "this sentence" is referring to the sentence "The Eiffel Tower is a lattice tower" then this sentence doesn't have fifty words.
If "this sentence" is referring to itself, ie, "this sentence contains fifty words", then both the SEP and IEP discuss the problems of self-referential expressions.
The SEP article on the Liar Paradox starts with the sentence "The first sentence in this essay is a lie"
The IEP article Liar Paradox talks about "this sentence is a lie"
But there is insufficient information within the sentence "this sentence contains fifty words" to know which sentence "this sentence" is referring to.
As we don't know which sentence "this sentence" is referring to, we cannot know whether the sentence "this sentence contains fifty words" is true, false or meaningless.
I do know that. It refers to itself, it contains five words, and so it doesn’t contain fifty words.
Quoting RussellA
They are discussing the liar paradox. We are not discussing the liar paradox. We are discussing the sentences "this sentence contains five words" and "this sentence contains fifty words".
From the SEP article on self-reference:
Most people think otherwise, they know exactly what sentence it is referring to.
The syntagma 'this sentence' in 'This sentence has fifty words' refers to 'This sentence has fifty words'. Therefore it is false.
It is quite possible you and Tones went through this exact point, but honestly if I read through all 8 pages I might develop dementia before I even hit middle age.
At least you have middle age to look forward to.
I would look forward to it everyday if I had dementia.
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.
===============================================================================
Quoting Michael
We are discussing self-referential expressions, of which the Liar Paradox is an example.
From the IEP article on Liar Paradox
===============================================================================
Quoting Michael
In language is the sentence "this sentence contains fifty words".
In language is the sentence "X"
The only means of knowing the truth value of "X" is by comparing it to the world, ie, by grounding it in the world.
From the Wikipedia article on the Liar Paradox
This is why "X" is true IFF X, where "X" is in language and X is in the world.
An expression in language that referred to another expression in language, such as "this sentence" referring to "this sentence has fifty words", cannot be grounded in the world, and if not grounded in the world, can have no truth value,
As regards the SEP article.
In language, meaning is often inferred. If I said "Paris is cool", the listener might infer that I meant "Paris is an excellent city to visit as a tourist".
Similarly, 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.
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.
However, we are not discussing what the sentence "this sentence contains fifty words" is inferred to mean, we are discussing what it literally means.
And because not grounded in the world, if "this sentence" is referring to "this sentence contains fifty words", it has no truth-value and is meaningless.
"this sentence contains five words" is grounded and is true.
"this sentence contains fifty words" is grounded and is false.
"this sentence is false" is ungrounded and is neither true nor false.
I agree with you that if the sentence "this sentence contains fifty words" is grounded in the world then it can have a truth value, and it is false.
For example:
"Snow is white" is true IFF snow is white
"This sentence contains fifty words" is true IFF this sentence contains fifty words.
Given the sentence "this sentence contains fifty words", whether it has a truth value or not all depends on what "this sentence" is referring to.
I have been trying to make the point that if "this sentence" refers to "this sentence has fifty words" then there is no grounding in the world and there can be no truth value.
I may be wrong, but you seemed to suggest that "this sentence" does refer to "this sentence has fifty words" when you said:
Quoting Michael
My question is, if the expression "this sentence" within "this sentence contains fifty words" is referring to itself, ie referring to "this sentence contains fifty words", then how can there be any grounding in the world?
It's grounded in that we can count how many words are in the sentence "this sentence contains fifty words". There are five words, not fifty, and so the sentence is false.
Exactly. The sentence "this sentence contains fifty words" in order to have a truth value must be grounded in the world.
"This sentence contains fifty words" is true IFF this sentence contains fifty words.
The sentence "this sentence contains fifty words" in order to have a truth value cannot be grounded in itself. The expression "this sentence" within "this sentence contains fifty words" cannot be referring to itself, ie, it cannot be referring to "this sentence contains fifty words".
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.
Form and content
I see on my computer screen the following shapes – this sentence contains fifty words.
I recognize these as words, part of a grammatical sentence, having the meaning "this sentence contains fifty words"
I can also see that on my computer screen that there are five words.
The subjective content of these words is "this sentence contains fifty words"
The objective form of these words is that there are five of them.
Subjective content and objective form are linked by:
"This sentence contains fifty words" is true IFF this sentence contains fifty words.
The word "truth" in the following would be redundant:
"This sentence contains fifty words" is true IFF "this sentence contains fifty words"
Yes it can.
The self-referential sentence "this sentence contains five words" is true because it contains five words.
The self-referential sentence "this sentence contains fifty words" is false because it doesn't contain fifty words.
This is incredibly straightforward.
I wish it were.
"Snow is white" is true IFF snow is white.
The sentence "this house is very tall" contains five words.
The sentence "this sentence contains five words" also contains five words.
"This house is very tall" is true IFF this house is very tall, where this house is referring to, or pointing at, a particular house in the world.
Similarly, "this sentence contains five words" is true IFF this sentence contains five words, where this sentence is referring to, or pointing at, a particular sentence in the world.
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.
"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.
The subjective content of the sentence "this sentence contains five words" cannot determine the objective form of itself, ie, that it contains five words.
Yes it is.
Quoting RussellA
Quoting RussellA
The words "has" and "contain" have identical meaning in the context of this discussion.
Conclusion? "This sentence contains five words" is true. QED
I agree.
Quoting EricH
No one would say that "this house contains five rooms" is true without first knowing which house is being referred to.
No one would say that "this book contains important knowledge" is true without first knowing
which book is being referred to.
Therefore, how can any one say that "this sentence contains five words" is true if no one knows which sentence is being referred to?
For example, so far, we have three sentences:
1) The sentence "this house contains five rooms", which happens to contain five words.
2) The sentence "this book contains important knowledge", which happens to contain five words
3) The sentence "this sentence contains five words", which happens to contain five words.
The sentence "this sentence contains five words" isn't telling us which sentence is being referred to.
Therefore, how do we know that it is true?
In context we do know.
If I hold out an apple and say "this apple is red" then it's obvious that I'm referring to the apple in my hand and not the apple on the table behind me, and so what I say is true iff the apple in my hand is red.
If you want to be explicit, then:
The self-referential sentence "this sentence contains five words" is true.
The self-referential sentence "this sentence contains fifty words" is false.
I agree that in the context of a thread on the Liar Paradox, the discussion is about can a self-referential sentence have any meaning.
Quoting Michael
Truth depends on a correspondence between language and the world
To be even more explicit, if in the sentence "this sentence contains five words" the expression "this sentence" is referring to "this sentence contains five words", can the sentence "this sentence contains five words" have a truth-value, or is it meaningless.
You are arguing that "this sentence contains fifty words" has a truth-value.
I am arguing that any concept of truth in a self-referential expression is redundant.
My belief is that an expression in language can only have a truth-value if it corresponds with something in the world.
I accept Tarski's paradigm for defining truth, ie, Tarski's Semantic Theory of Truth:
"snow is white" is true IFF snow is white.
It can be argued what exactly this world is, but whatever the world is, it is external to a linguistic expression.
In the self-referential sentence, as the sentence is referring to itself, it cannot be referring to any world that exists outside of itself.
If a self-referential sentence is not referring to anything in the world, then it can have no truth-value.
In cases of linguistic self-reference, the concept of truth is redundant
1) "This sentence contains five words" is true IFF "this sentence contains five words".
The word true is redundant in that:
"This sentence contains five words" IFF "this sentence contains five words"
In the Wikipedia article Redundancy Theory of Truth
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".
Truth only enters when self-reference disappears and the world appears:
"x" is true IFF x
The redundancy theory of truth usually applies to all sentences, whether it be "this sentence contains five words" or "it is raining". Seems strange to only apply it to self-referential sentences.
But even then, there's still nothing problematic with the sentence "this sentence contains five words". It is meaningful, despite your protestations to the contrary.
Just to repeat:
Quoting EricH
Which sentence were you referring to when you made these statements?
1) "this sentence contains five words" is true IFF this sentence contains five words
We don't know what "this sentence" is referring to, but, for example, it could be referring to the sentence "this house is grey in colour", "this book is important", "this animal is a cat" or "this sentence has five words".
Suppose it is referring to the sentence "this sentence has five words".
In language is the sentence "This sentence has five words"
I see on my screen the following shapes - This sentence has five words - which I recognize as the sentence "This sentence has five words".
2) This sentence has five words. Not true? Yes, true.
I am using the model of "snow is white" is true IFF snow is white.
Not being in quotation marks - this sentence has five words - is something that exists in the world, for example, on my screen, and is true in the sense that I can see it on my screen, rather than not see it on my screen.
Not the case.
I did include the non self-referential example:
I also included Frege's 1918 comment:
===============================================================================
Quoting Michael
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.
I maintain that barbers are people who shave people who are in the world.
If they must be shaved, the barbers must visit other barbers. Shaving involves a correspondence between an ideal of cleanliness and the state of affairs on an actual face. Therefore, if a barber tries to shave himself, there is an inherent contradiction.
=========================================
I hope this is clear?
Makes sense to me. I've never understood any validity in the barber paradox.
The expression ‘secondary employment’, also commonly referred to as ‘double jobbing’, simply describes a situation where an employee takes on a second job.
During the day, someone works as an engineer in an engineering works. In order to pay their rent, during the evening they work in a cafe as a barista.
No one would call someone who serves you coffee an engineer.
No one would call someone welding machinery a barista.
As you say, being a barber is what someone does, not what they are.
It’s meaningful even when it’s referring to itself.
From Wikipedia -Meaning (Philosophy)
If "this sentence contains five words" is referring to itself, then "this sentence contains five words" means that "this sentence contains five words".
In other words, "X" means "X".
In logic, the law of identity states that each thing is identical with itself.
I agree that "X" means "X", but how can "X" be described as a meaningful sentence?
What are you talking about?
It’s really simple; the self-referential sentence “this sentence contains five words” is meaningful. I understand what it means, you understand what it means, and everyone else understands what it means. It’s not some foreign language or random combination of words. And we can count the words in the sentence to determine that it’s true.
You’re trying to create a problem where there is none.
Question: how do you avoid the problem of infinite recursion in a self-referential sentence?
"This sentence contains five words".
Non self-referential case
Let "this sentence" refer to the sentence "this sentence contains five words"
Then, "this sentence, the sentence "this sentence contains five words", contains five words". This is meaningful.
Note that 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.
Note that the truth of the sentence "this sentence contains five words" is independent of the truth of the sentence "this sentence contains five words".
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".
Therefore, "this sentence, the sentence "the sentence "this sentence contains five words" contains five words", contains five words".
Ad infinitum. Infinite recursion. Therefore meaningless.
Note that in the self-referential case, the sentence "this sentence contains five words" is the same sentence.
There is no problem. The self-referential sentence "this sentence contains five words" is both meaningful and true. The self-referential sentence "this sentence contains fifty words" is both meaningful and false. It's that simple.
Is that a joke? To shave is to cut hair from the skin. There is no requirement of an ideal of cleanliness or that a face is involved.
A barber is someone who is in the business of cutting hair and shaving. There is no contradiction that a barber shaves himself of herself; surely some barbers do.
Moreover, the barber paradox is merely an illustration. The relation of 'x shaves y' could be any 2-place relation R:
(1) There is an x such that for all y, Rxy if and only if it is not the case that Ryy.
And (1) is logically false.
The barber sentence is not just invalid, it is logically false.
Quoting RussellA
Wow! How can someone so ignorantly miss the point!
The barber paradox doesn't at all rely on claiming that someone is a barber. Mentioning someone who is a barber is merely incidental and does not at all bear upon the logic.
We could just as well not use the word 'barber' or even 'person':
There is an x such that for all y, x shaves y if and only if y does not shave y.
For that matter, we don't need 'shave', which is merely illustrative:
For any 2-place relation R:
(1) There is an x such that for all y, Rxy if and only if it is not the case that Ryy.
And (1) is logically false.
Wow. RussellA has such strong opinions on the subject but doesn't know what the subject even is.
Why did it take 9 pages.
Why has it taken nine pages for RussellA still to still stick with his refuted arguments for his claim:
"If "this sentence" is referring to "this sentence contains fifty words", it has no truth-value and is meaningless."
The answer is psychological.
He's been refuted at every point in every detail.
"This sentence has fifty words" does not seem to be a paradox.
That's not what has been at issue.
Rather at issue has been whether sentences such as "This sentence has fifty words" are meaningful.
Suffice it to say, it wants to say something it can't, and so contains no meaning.
So you assert.
Moreover, I don't know what you mean by a sentence "wanting" to say something.
Meanwhile, a counterargument has been given, and that counterargument has not been refuted.
No argument has been sustained that there is such a problem.
Quoting RussellA
For sake of continuity with the thread, I'll use:
This sentence has five words.
Quoting RussellA
Yes, please let it, since "This sentence" does refer to the sentence "this sentence has five words".
Quoting RussellA
Meaningful and false, since (1) "this sentence, the sentence "this sentence has five word", has five words" falsely claims that "this sentence, the sentence "this sentence has five word", has five words" is "this sentence has five words" and (2) "this sentence, the sentence "this sentence has five word", has five words" has twelve words not five.
Quoting RussellA
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.
RussellA has reduced himself to explicitly contradicting the law of identity.
Quoting RussellA
Since "this sentence has five words" is "this sentence has five words", the truth of "this sentence has five words" cannot possibly be independent of the truth of "this sentence has five words".
For any sentence S: S is true if and only if S is true; and S is false if and only if S is false.
RussellA has reduced himself to explicitly contradicting the the principle "P if and only if P".
Quoting RussellA
What does the first occurrence of "this sentence" refer to in the sentence immediately above?
Two choices:
(a) "this sentence" refers to "we know that this sentence is the sentence "this sentence has five words""
And (a) is false, since we do not know that "we know that this sentence is the sentence "this sentence has five words"" is the sentence "this sentence has five words"; but rather, we know that it is not the case that "We know that this sentence is the sentence "this sentence has five words"" is "this sentence has five words".
(b) "this sentence" refers to "this sentence, the sentence "this sentence contains five words", has five words".
And (b) is false, since we do not know that "this sentence, the sentence "this sentence contains five words", has five words" is "this sentence has five words"; but rather we know that it is not the case that "this sentence, the sentence "this sentence contains five words", contains five words" is "this sentence has five words".
Quoting RussellA
Non sequitur.
It is the case that:
"This sentence has five words" is true if and only if "This sentence has five words" has five words. (So, "This sentence has five words" is true.)
""This sentence has five words" is true" if and only if ""This sentence has five words" is true" is true. (So, ""This sentence has five words" is true" is true.)
ad infinitum - the value is true
But also:
"Florida is a state" is true if and only if Florida is a state. (So, "Florida is a state" is true.)
""Florida is a state" is true" is true if and only if ""Florida is a state" is true" is true.
ad infinitum - the value is true
That is different from the liar paradox:
"This sentence is false" is true if and only if "This sentence is false" is false, so "this sentence if false" is true.
""This sentence is false" is true" is true if and only if ""This sentence is false" is true" is true, so "this sentence is false" is false.
ad infinitum - the value alternates between true and false
These points - (a) it is not just self-referential sentences that provide "ad infinitum" and (b) mere self-reference doesn't provide paradox but rather the combination of self-reference and negation - have been pointed out to RusellA probably a half dozen times already
Quoting RussellA
Same sentence as what?
"This sentence" refers to "this sentence has five words". "This sentence" refers to the sentence in which "this sentence" is the noun. That is the nature of the self-reference in that case.
Quoting RussellA
"X" is true if and only if X.
But pronouns are contextual, so the above schema needs adjustment to the context of a pronoun's use.
So this does not work:
"This sentence has five words" is true if and only if this sentence has five words.
The first occurrence of "This sentence" refers to "This sentence has five words".
The second occurrence of "this sentence" refers to ""This sentence has five words" is true if and only if this sentence has five words".
Two ways to handle the context of pronouns:
(1) "This sentence has five words" is true if and only if the referent of "This sentence" in "This sentence has five words" has five words. That reduces to:
"This sentence has five words" is true if and only if "This sentence has five words" has five words.
(2) Let "The Pentastring" refer to "This sentence has five words". That is, "The Pentastring" is the referent of "This sentence" in "This sentence has five words". That is, the Pentastring is "This sentence has five words".
"This sentence has five words" is true if and only if the Pentastring has five words. That reduces to:
"This sentence has five words" is true if and only if "This sentence has five words" has five words.
RussellA keeps avoiding that pronouns are contextual. His central argument is based on blithely ignoring that pronouns need to be handled with context in mind.
Quoting RussellA
Indeed. So RussellA is ridiculous when he blatantly contradicts the law of identity when he says that "This sentence has five words" is not "This sentence has five words".
Quoting RussellA
RussellA agrees with whom, other than himself, about that?
"X" is "X". The meaning of "X" is not "X".
Quoting RussellA
Which "X"?
It has been shown about 100 times already the sense in which "This sentence has five words" is meaningful and true. There may be a reasonable argument that "This sentence has five words" is not meaningful, but RussellA has not produced such a reasonable argument. Confused and ignorant formulations, non sequitur, and avoidance of exact rebuttal is not reasonable argument.
"This sentence" refers to "This sentence has five words".
Quoting RussellA
RussellA pinions his claiims about his subject on Tarski's schema, but he gets even that wrong! (See a thread many months ago about Tarski and the correspondence theory. RussellA got it quite wrong there too and proceeded post after post with illogical arguments.)
The following is not an instance of the schema:
"This sentence has fifty words" is true if and only if "This sentence has fifty words".
That doesn't even make sense, since what occurs after the biconditional is not even a propostion but rather is a quote of a proposition.
And again, when we use pronouns that are contextual, the schema needs adjustment:
"This sentence has fifty words" is true if and only if the referent of "This sentence" in "This sentence has fifty words" has fifty words.
Since the referent of "This sentence" in "This sentence has fifty words" is "This sentence has fifty words", we have:
"This sentence has fifty words" is true if and only if "This sentence has fifty words" has fifty words.
Quoting RussellA
RussellA will keep asserting that over and over and over, no matter how many times he is shown that his arguments are both built on false premises and are illogical.
We infer that "This sentence" refers to "This sentence has five words" by observing that "This sentence" occurs within "This sentence has five words" and "This sentence has five words" is the only sentence spoken or displayed in the context. So the notion of "This sentence" referring to some other arbitrary sentence such as "The cat is black" is itself a gratuitously arbitrary notion.
When I hold an apple in my hand and say "this apple", unless there is additional context, we infer that "this apple" refers to the apple in my hand. When we have "This sentence is five words" as the only sentence at hand, we infer that "this sentence" refers to that sentence which is at hand, which is "This sentence has five words".
Moreover, we could just as well stipulate that "This sentence" refers to "This sentence has five words". Given that stipulation, the question still is whether "This sentences has five words" is meaningful.
What a nutty analogy!
"This house is tall" doesn't mention a number of words.
"This sentence has five word" does mention a number of words.
Quoting RussellA
RussellA will just not quit ignoring that pronouns have context.
Quoting RussellA
For example, no one claims that saying "This sentence has ten words" makes it that case that "This sentence has ten words" has ten words.
But "This sentence has five words" is true since "This sentence has five words" has five words.
RussellA presents yet another very silly and illogical argument.
We've been over the "grounded" argument about a dozen times already.
Whatever RusellA's definition of 'grounded' is, if sentences such as "The cat is black" are in the world, then RussellA must show why sentences such as "This sentence has five words" are not in the world. But each of his arguments for that claim have been refuted.
Quoting RussellA
About the 100th instance of RussellA ignoring that pronouns are contextual.
Quoting RussellA
"This sentence contains fifty words" is true IFF "this sentence contains fifty words"
That's not even coherent. Why does RussellA even mention it?
This is coherent:
"This sentence has fifty words" is true if and only if "this sentence has fifty words" has fifty words.
Oops, he did it again!
That is just so very nuts!
In "This ferry contains fifty people" we don't think this "this ferry" refers to the sentence "this very contains fifty people" since we infer that "this ferry" refers to a ferry and not to a sentence!
And why would it be more likely that "This sentence" in "This sentence has five words" refers to some other sentence not mentioned, not implied, not suggested, not even hinted at? Rather, we infer that "This sentence" refers to the sentence that is present, at hand, and in which "This sentence" itself occurs!
Moreover, we may just as well stipulate that "This sentence" refers to the sentence in which it occurs, which happens to be the only sentence around at the time.
Or we can use a name of "This sentence has five words" such as "The Pentastring".
"From the SEP article on self-reference:... self-reference is not a sufficient condition for paradoxicality. The truth-teller sentence “This sentence is true” is not paradoxical, and neither is the sentence “This sentence contains four words” (it is false, though)" — Michael
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".
Quoting RussellA
Close but still not right, as it is still not using pronouns correctly. It should be:
We infer that "This sentence has fifty words" is true if and only if "This sentence has fifty words" has fifty words.
Quoting RussellA
Close but still not right, as it is still not using pronouns correctly. It should be:
We infer that "this sentence has fifty words" is true if and only if "this sentence has fifty words" has fifty words, so "this sentence has fifty words" is not paradoxical and is false.
Quoting RussellA
We infer what it literally means. We infer by context that "this sentence" refers to "this sentence has fifty words", so, given the context, we infer that "this sentence has fifty words" literally means that "this sentence has fifty words" has fifty words.
If that is not enough, then ANY use of pronouns would disallow literal meaning.
But we don't disallow literal meaning with use of pronouns. "This apple is red". In context, it literally means that the apple that is in my hand that I am looking at is red.
Which is incorrect, in the structure of the sentence. As has been pointed out. Quoting TonesInDeepFreeze
Teh self-reference remains in your reading, though. So, whether or not the sentence is referring literally 'to itself' (this should answer your query about a sentence wanting to say something above) or to "what it refers to" is not actually "up to you". You can't simply read it in a way which is false, but meaningful by adding meaning to it, without sufficient reason.
On it's face, it is plainly meaningless. I'm not sure you're actually ascertaining what this amounts to because it seems all you're wanting to do is have the sentence refer to itself. If it does, then fine, but RussellA has already covered that and your response does nothing for it.
So what? "This sentence" in "This sentence is false" is not 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" !!!
And "This apple" in "This apple is red" is not referring to the sentence "Walruses are cute" or the sentence "The Grand Canyon is a banana" or 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" !!!
RussellA needs to climb down from the pole of ridiculous arguments he's sitting on!
Edit: It would have been much better for me to mention paraconsistency here. The sentence is not paradoxical, but a lot of the ways in which this is the case, Russell has covered.
I haven't said the sentence refers to itself. I said that "This sentence" refers to "This sentence has five words". The noun phrase "This sentence" is the referrer.
Quoting AmadeusD
See my arguments that address that.
Quoting AmadeusD
You merely reassert your assertion.
Meanwhile, it seems to me to be meaningful, as it seems meaningful to others too. And I've explicated its meaning. And no argument that is not based on false premises and illogic has been given so far in this thread that it is not meaningful.
Quoting AmadeusD
I said about five times: RussellA claims that self-referential sentences are not meaningful. The ball is in his court to support that claim. Meanwhile, "This sentence has five words" does seem to me to be meaningful, though I am open to a logical argument that it is not. And, meanwhile, I've given an argument that it is meaningful and that argument has not been disputed other than by false premises and illogic.
RussellA's arguments have been a catalog of ignorance and non sequitur, including: Not understanding the difference between nouns and predicates, not understanding pronouns, ridiculously inapt analogies, contradicting the law of identity, contradicting the reflexivity of the material biconditional, various red herrings, evading rebuttals, and a lot more. And I've given detailed and exact explication of his errors.
I haven't opined on Wittgenstein.
Ways in what is the case? Ways in which "This sentence has five words" is not paradoxical? RussellA's claim is that "This sentence has five words" is meaningless if "This sentence" refers to "This sentence has five words". All of his arguments for that claim have been shown to be based on false premises and illogic, some of them even blatantly ludicrous.
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.
Yes. Asserting irreflexivity of reference (in general, or in cases like "this sentence has... etc") seems as confused and cranky as asserting irreflexivity of shaving.
Was my point.
Picking up on just one of your 33 comments:
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.
However, I don't want to waste any more of your time if my arguments are dialectically incompetent.
Quoting TonesInDeepFreeze
Quoting Quine, The Ways of Paradox
But... the inside sentence still so engenders? Because, indeed,
So I'm not quite sure what kind of objection is being sustained? If any. And who had raised it, and where?
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".
As Quine might say, there is no paradox with the professor saying "Paris is in Germany" is false.
The professor looks at a Philosophy student's essay and says to the student: this sentence is false.
The student had written "this sentence is false", referring to the sentence "Quine was born in 1908".
As Quine says, in this situation, there's no paradox with "this sentence is false" is false
There's no paradox because, as Quine says, "this sentence is false" is referring to something other than itself.
The paradox arises when "this sentence is false" is not referring to something other than itself. IE, when it is self-referential.
They are both referring to the sentence "This sentence has five words".
Mary is not referring to some random, unrelated sentence that is not even present in the context such as "The Eiffel Tower is a great tourist attraction". Rafael is not referring to some random, unrelated sentence that is not even present in the context such as "Helium is good for party balloons".
(But at least it's good to see that RussellA has, at least apparently, dropped his line of argument that "This sentence" could refer to something that's not even a sentence!)
Moreover, we can stipulate what sentence is referred to. I stipulate that when I write:
This sentence has five words
"This sentence" refers to "This sentence has five words.
Moreover, we can formulate without the pronoun 'this':
Let "The Pentastring" refer to "This sentence has five words". The Pentastring has five words, since the Pentastring is "This sentence has five words" and "This sentence has five words" has five words.
"The Pentastring has five words" asserts that "This sentence has five words" has five words.
"This sentence has five words" asserts that "This sentence has five words" has five words.
Moreover, we can formulate this way:
(1) This sentence has five words.
"The sentence listed above as (1) has five words" asserts that "This sentence has five words" has five words.
"This sentence has five words" asserts that "This sentence has five words" has five words.
If we took advice from RussellA, then anytime someone used the pronoun 'this', we might as well think they are referring to any random, unrelated thing that is is not even present in context. When I say "This apple is red" while holding an apple in my hand and looking at the apple and pointing at it, we might as well think that "this apple" refers to the Eiffel Tower or the atomic element helium or anything else.
That RussellA is willing to make such a ludicrous argument shows that he's willing to abandon the least shred of reason.
And that is not analogous to "This sentence is false" in the context of this discussion.
Again, there is no other sentence at issue. And one may stipulate what "This sentence" refers to.
The professor may stipulate that, in that context, "This sentence" refers to "Paris is in Germany". And I may stipulate that in the context of my post, "This sentence" refers to "This sentence has five words".
As well as, when the professor is pointing at "Paris is in Germany" on the paper, it is reasonable to infer that "This sentence" refers to "Paris is in Germany", while, when I write "This sentence has five words" in a post, with no other sentence around that would be a plausible candidate to be the referent of "This sentence", and I adduce the sentence for the very purpose of discussion about self-reference, then not only is it not reasonable to infer that "This sentence" refers to "The Eiffel tower is a racoon" but it is plainly ludicrous even to argue that that might be what "This sentence" refers to. Even more ludicrous to argue, as RussellA did a while ago, that "This sentence" might be referring to something that is not even a sentence, not even a linguistic object of any kind, but some other kind of very different thing.
Quoting RussellA
RussellA keeps arguing by mere assertion over and over and over. The paradox of "This sentence is false" involves both "This sentence" referring to "This sentence is false" and the fact that the sentence says specifically that it is false. One cannot thereby infer that "This sentence has five words" is meaningless on the basis that "This sentence is false" is paradoxical or even, for sake of argument, that it is meaningless.
RussellA has made a non sequitur. And to still defend his non sequitur, he resorts to even the most ludicrous arguments, including ignoring not distinguishing nouns from adjectives, ignoring how pronouns work, contradicting the law of identity, contradicting the reflexiveness of the material conditional, arguing that we can't infer what is referred to with pronouns, and more, and over and over and over he then just keeps coming back to argument by mere assertion. On what basis is it claimes "This sentence has five words" not meaningful? Eventually, his argument will involve "grounding" and "the world", along with the many calls to ludicrousness, but then when it's shown that those arguments fail, he'll come back to merely asserting that such sentences are not meaningful.
No. Quine doesn't say that, and he doesn't say anyone else has said that.
It's always possible I am misunderstanding, but this entire piece
seems to speak to Quine essentially saying "This isn't a problem, because you can't shoehorn meaning in here for it to contradict (as to itself)"
and not read and reason.
You feel the need to post a meaningless, empty putdown "I can only laugh" but it's laughable to you that one would respond to that.
You seem to want some kind of insult to land. It wont, because I don't find hte context apt to insult me. So, not sure where you're going - just think its pretty distasteful to do what you've just done in an attempt to find some ad hominem-esque reason for dismissing an interlocutor. Fine. You do you boo.
You posted immediately after my post, so it was reasonable for me to think you were commenting on me. But now that you have disclaimed that you meant me personally, then, of course, I stand corrected that you meant me personally.
Quoting AmadeusD
Ah, but you do wish to comment on me personally after all.
If by 'interlocutor' you mean you:
I haven't tried to dismiss you. But you haven't interlocutorated much anyway.
If by 'interlocutor' you mean RussellA:
Your characterization is incorrect. I have not dismissed any interlocutor on an ad hominem basis. Rather, I have engaged virtually every point he's tried to make, every claim, every argument - in detail and with thoroughness, and repeatedly in pace with his repetitiveness. And for a long time I made no personal comment about him. Meanwhile, his mode has to been to skip the rebuttals given him and shift his claims (but as if he has not) and spread a trail of red herrings . Then, in addition to my responding on point, I have also discussed that he is indeed ignorant on even basics and highly irrational in his arguments - and not just as free-floating characterizations, but in exact reference to the very specific points and arguments of his, as I have engaged virtually all of them.
So, I don't find the context apt to be criticized for my posting method. But, as I've said all along, if there are flaws in my arguments, then I'm happy to hear of them.
Due to your direct responses to me, yes. It would be completely wrong to take that as somehow retroactively meaning I meant to engage you directly initially. You took up the conversation, and I continued. There were several people posting between my comment and my previous comment (looking back, that is). I didn't tag you, or anyone. Clear indicator I am not talking to you so I am glad you've noted that.
Quoting TonesInDeepFreeze
You're doing it right here. Hilarious.
The comment you made was directly after two fairly chunky posts by me. You could have said that this thread in general makes you laugh (but why?), but you left it utterly open ended what you're laughing at. While you may have not been talking about me specifically, there is no "clear indicator" that you weren't. But I grant that, if you truly did not mean me, then I inferred incorrectly. I take your word for it that you did not mean me specifically, but it is not true that you had clearly indicated that when your reply followed directly after my posts and with no indication what specifically you were laughing at.
But then you mischaracterized my posting as an attempt to dismiss with ad hominen. So I remarked that you do want to talk about me. I didn't claim that that is retroactive.
Saying that you haven't been very much engaged in the ongoing discussion is not dismissing you. It only partially explains why I haven't very much engaged with you vis-a-vis the ongoing discussion. (However, you have touched on some points that I have not addressed, only because (1) I don't see how they very much bear on what I've posted or I have not read processed how they do and if so what my response would be, (2) I need to learn more about the context of the quotes and their import, and (3) as with anyone, I exercise my prerogative to respond only to what I am motivated to respond to.) Meanwhile, I don't fault you for not saying very much about the ongoing discussion; it is purely your prerogative to post or not post whatever you like.
But since you bring up posting decorum, you asked me a technical question early in this thread, and I gave you a good and concisely informative answer that would provide you with a perspective. If I recall correctly, you then posted no recognition of that. Of course, again, that's your prerogative. But if dismissiveness is a concern of yours, perhaps you would recognize that asking someone for information and then receiving it but without at least posting that the information was received and understood (or not understood, thus requiring elaboration) is also a kind of dismissiveness.
Quoting TonesInDeepFreeze
Yessir, and I the same. I outline what I (still) recognise as a distasteful approach, but I very much appreciate your clarification here. Genuinely. Thank you.
Quoting TonesInDeepFreeze
It wasn't aimed at me - the posts in question were responses to other people, so I revert to the above appreciation.
The post to which I refer was my direct response to your direct question to me.
Quoting AmadeusD
Open ended, content-free snark like that is also a form of dismissiveness, whether to an individual or a group.
I don't think the latter is dismissive at all.
As I said, it's fine that you clarify that the "I can only laugh" was not meant to be directed at me specifically, but rather to two posters at once (why?) with one of them being me, but that was not, as you later claimed, clearly indicated at the time. And especially so since the poster you had been previously faulting was me, not RussellA. You let out a fart of snark that would naturally be understood to be directed at me. Fine that you say you didn't mean it that way, but at least own that it was your, at best, ambiguousness, which itself is rude in that context, that resulted in me naturally counter-attacking and defending.
I maintain it was. It was not in response to you directly, or indirectly.
Quoting TonesInDeepFreeze
Nope.
Quoting TonesInDeepFreeze
Yep, so naturally I would have replied to you, right? Whereas I didn't.
Quoting TonesInDeepFreeze
Sure, and you've clarified why. Nothing makes it reasonable in context, despite your protestations. Given I already made two attempts to say "Cool man, we weren't having such a go at each other as it seemed" I can't be bothered further than saying so again.
Cool man, looks like we didn't intend to have a go at each other the way its been interpreted. Good.
The absence of indication is not "clear indication". Clear indication would be something like, "Not directed at anyone in particular".
You replied directly after my two posts. You had been defending the other poster's position and faulting mine. It was clearly not clearly indicated that you did not mean me. And now you're just saying by mere assertion, contrary to words on screen, that it was clearly indicated.
And it turns out, per your reveal now, that you were laughing at (about? who knows but you?) me in tandem with another poster. You didn't mean me personally, you only meant me personally along with another person personally.
Quoting AmadeusD
Oh, is that what you meant to convey? You have a curious way of communicating, I'll give you that.
You are clearly making some extremely sensitive inferences that don't make sense. No idea why you would want me to be insulting you, but there we are. You're wrong, and clearly so.
In lieu of hand-holding you through it:
Quoting TonesInDeepFreeze
I can only laugh.
Quoting AmadeusD
Quoting AmadeusD
Take care.
What you said was ambiguous. It could have meant that it took RussellA nine pages too long to wake up (though later contradicted by the fact that you actually think he's right), or it could have meant it took nine pages too long for RussellA to finally prevail against other posters (including, and prominently, me) who disagreed with him. It could have meant that it took nine pages too long for people collectively to reach a dead end of incoherent disagreement. I could have meant a lot of things. But as it stood, it was you making a snarky put down of something or other. So, a form of dismissiveness. It is disingenious to toss out snark but pretend it's not.
You haven't addressed the specifics of my argument about it. Saying "clearly" is nothing. Being sarcastic is, of course, fine in and of itself. But it's dishonest to pretend that one hasn't been sarcastic and to pretend that not even is it reasonable that another took you as sarcastic
Which clarification? The facts I informed you of? The fact that I did not, as you falsely claimed, dismiss the other poster with an ad hominem but rather that I engaged virtually every one of his claims and arguments in detail and thoroughly, and only then did I also talk about what a horribly lame arguer he is.
You ought not put strikethrough across my words within a quote like that.
I said "naturally" and I did not strike it.
Quoting AmadeusD
The typo of omission is yours not mine. I said "You [...]".
Nope. Still nope. It is not. This is simply you outlining an ambiguity and then claiming the least-charitable version for your own ends. Not sure why you would, and it's not for me to explain.
Quoting TonesInDeepFreeze
Yeah, but it was neither. Sorry pal.
Quoting TonesInDeepFreeze
Yes I have. Multiple times. I have, in fact, teased apart several direct misinterpretations you've made. But you're still here, intent on finding a way for me to have impugned you. A sad affair, to be sure.
Quoting TonesInDeepFreeze
Luckily, those two things are true, and I am not being dishonest.
Quoting TonesInDeepFreeze
That was the point my guy. You did not 'naturally' react. You misinterpreted, perhaps had your ego hurt, and assumed the worst in all three turns (the initial "Why did it take...", the "I can only laugh.." and my actual responses in this exchange).
You can only lead a horse to water. I tried to squash the 'beef'. Four times now, actually. You do not want to. So be it. I will treat you as you request. Though, I would ask that you do not consistently multi-post,. and just edit the initial post. I will notice.
You said it it was in response to two posters - me and another. That's pretty direct, at the very least indirect only by being shared with another.
Quoting AmadeusD(your point is these posts were an exchange between yourself and RussellA - unfortunately for me, it was also a couple of other posters, not just you two. My point was distancing my reply from the personal aspect you're tied to).
You've taken the worst reading I can get from it (that, instead of what I actually did - which was distance my response from any personal comment) such that you now think I was responding to you (both) directly. That is not the case, or what I wrote. It was somewhat imprecise though. It was a comment on the previous set of comments, which were not to, about or for me - not a response to them. So I'll cop to that misunderstanding entirely - I apologise with no qualifier.
Otherwise, this is a roundabout. You misunderstood, I have clarified - you've accepted, and yet here we are. I reject your position on the basis its an emotional reaction to something you've read into my posts - and will now move on :) Didn't meant to offend, and don't really care about it anymore.
Again you reply by ignoring what I wrote. I said exactly why it is dismissive, even with its ambiguity.
Quoting AmadeusD
You failed to address the previous specifics and you just now failed to address the latest specifics as you claim to not fail to address the specifics!
Quoting AmadeusD
You mean that you weren't sarcastic in the remarks I mentioned? Or you mean that you were sarcastic and you're being honest that you were?
Quoting AmadeusD
You miss the point. When you put strikethrough in the quote, it appears that I had made the strikethrough since you literally quote me that way without indicating that it's your redaction not mine. If you feel that "naturally" was not warranted, then you could say that instead of quoting me as if I had myself applied strikethrough.
Quoting AmadeusD
Not perhaps, but definitely, your speculation about me in that regard is wrong, as well as it is the kind of thing people so mindlessly say in disagreements.
Quoting AmadeusD
You try to squash it by coming back again and again to claim you are right and I am wrong. It's utterly your prerogative to continue arguing, but it is absurd to continue arguing while claiming to be the one who is interested in ending the argument! That's typical forum inanity.
You wrote:
Quoting AmadeusD[bold added]
You literally wrote that it was a response to a discussion between RussellA and me. I think my counting is pretty good when I count RussellA and me as two people.
Wow. You don't even know what you wrote!
Quoting AmadeusD
That's good. But it was not imprecise. It was precise:
"it was discussion between yourself and RussellA." [bold added]
Quoting AmadeusD
Not very much emotional except that I do enjoy countering bad posts such as yours lately.
So now are you going to try to "squash" the quarrel by continuing it again?
If you would read what I posted, you would see that I said that I don't know what your "nine pages" remark was supposed to mean. I listed some obvious candidates but said that you might have meant something else. But if you didn't mean the remark as dismissive then only you can say what you did mean by it. If "Why did it take 9 pages" is not meant as exasperation that it took so long before RussellA arrived at the quote you made of him - exasperation with him or with his interlocutors or both - and to be dismissive of the nine pages worth of posting, then what does it mean?
Quine said:
I interpret Quine as saying that in the expression "this sentence is false" is false, the outside sentence is "this sentence is false". It seems to me that Quine is saying that there is no paradox because the outside sentence is not referring to itself but to something other than itself. Quine is saying that there is a hierarchy of references.
IE, "this sentence is false" is not being used self-referentially.
How do you interpret what Quine is saying?
I admitted to being unsure about the drift of that Quine passage, but you don't seem even to speak the language.
I'm being rude, but your tone is to lecture (e.g. with lecture headings), so I can't help it.
In " "this sentence is false" is false", "this sentence is false" is the inside sentence and is placed inside the enclosing expression form: "______ is false" or "x is false" or "( ) is false", where "______" or "x" or "( )" indicates where the inside expression is to be placed.
Quine talks about "the whole outside sentence" by which he either means the enclosing expression form (or matrix, or predicate, or open sentence, according to dialect) or the whole, as in, inside and outside, both. The composite of both. I would say "the closed sentence" but I have a feeling Quine wouldn't - because there's no quantification. I'll take correction or clarification on that from @TonesInDeepFreeze and others.
But I can't imagine that anyone who speaks the language (or some dialect) of modern analytic philosophy could read the passage and think that by "outside sentence" is meant the expression placed in the place otherwise held by "______" or "x" or "( )".
Yes, he's saying there may be a hierarchy of references. That may be relevant to clarification of his drift. On which I welcome advice. From speakers of the language.
Suppose y = sin(cos(x)). Which (sin or cos) would you say is inside, and which outside?
In the expression ""this sentence is false" is false", what does Quine mean by "outside sentence".
Does he mean "this sentence is false", or does he mean ""this sentence is false" is false"
Quine says that the outside sentence is no longer attributing falsity to itself.
I would have thought that the sentence "this sentence is false" is no longer attributing falsity to itself.
What would it mean for the sentence ""this sentence is false" is false" to be no longer attributing falsity to itself?
On the basis of infinite recursion.
Quoting RussellA
Quoting TonesInDeepFreeze
OK
===============================================================================
Quoting TonesInDeepFreeze
Separating into parts
IF - the Pentastring is "this sentence has five words"
Incorrect. As you have said many times on this thread, something in the world cannot be an expression in language. Using the model of "snow is white" is true IFF snow is white, then "the Pentastring" exists in language and the Pentastring exists in the world.
Quoting TonesInDeepFreeze
The Pentastring may be named as "this sentence has five words", but the Pentastring isn't "this sentence has five words".
AND - "this sentence has five words" has five words
OK
THEN - the Pentastring has five words
Incorrect conclusion.
The following are OK:
The Pentastring may be named "this sentence has five words"
"This sentence has five words" has five words
Just because the name of the Pentastring has five words, it doesn't follow that the Pentastring itself has five words.
Just because a name for the Eiffel Tower has two words, it doesn't follow that the Eiffel Tower itself has two words.
===============================================================================
Quoting TonesInDeepFreeze
"The Pentastring has five words" is not how "the Pentastring" has been defined.
Quoting TonesInDeepFreeze
For the sake of argument, using sentence instead of string
Then "the Pentastring is this sentence has five words"
Therefore, "the Pentastring is this sentence has five words" is true IFF the Pentastring is this sentence has five words.
Also, "the Pentastring has five words" is true IFF the Pentastring has five words
But, the Pentastring is this sentence has five words is not the same as the Pentastring has five words.
Therefore, "the Pentastring has five words" is not how "the Pentastring" has been defined.
===============================================================================
Quoting TonesInDeepFreeze
Same problem as before.
Are you really unable to find my answer to this question in my previous post?
Quoting RussellA
It would mean for it to instead be attributing falsity to a smaller sentence inside of it.
Please note this isn't some exegetical choice of mine. It's what (I feel sure) Quine expects any competent reader to understand from what he's written.
Quine was presumably referring to the stratification of types originally proposed by Russell, which ensures that the a map between type universes resides in a universe that is higher than both of the input and output universes. We might recall the fact that each universe contains a subclass that is isomorphic to the previous universe, as represented by the quotation marks in the liar sentence. So if we start with the highest level universe that we say contains everything we regard to be true, and use it to build in stepwise fashion an infinitely descending chain of so-called object languages that are each the meta-language of their predecessor, the liar sentence can be interpreted as stream of fluctuating truth values with respect to isomorphic, but non-identical terms of different types.
By contrast, both Sin and Cos are maps of type Real --> Real, i.e maps between terms of Reals, where the type Real --> Real resides in the same universe as the type Real, as does any function of functions of ... functions of reals; for they all reside in the universe definable in terms of second order logic. Following their example, we could alternatively interpret the liar sentence as directly referring to a stream of fluctuating values, where the stream and its values all exist in the same universe as a binary approximation to those trigonometric functions.
Quoting sime
Yes. That may be relevant to clarification of his drift.
Quoting bongo fury
But that drift has nothing to do with cos and sin, and definitely has to do with the relation of inner to outer sentence.
Quoting bongo fury
@sime Grateful for advice on that, but you would need to be more specific, at least.
I did. It is appearing, more or more credibly, that you're not really doing the same, as there is clarity from comment one of this exchange and several attempts to end the clear horseshit going on here.
"Why did it take nine pages" is very, very clear indicator, if you're actually paying attention, that I assent to RussellA's position. And, our subsequent exchange made that explicitly, painfully clear directly to you.
If you still have questions, perhaps aim them elsewhere as I have answered anything relevant several times now - and that's ignoring hte spoon-feeding required being a problem.
Yes. Quine clearly says that the whole outside sentence is what refers to something other than itself, and he clearly doesn't say that the inside sentence is what refers to something other than itself. And any competent reader sees that "this sentence is false" is the inside sentence.
So your comments aren't helping you or @RussellA to understand the passage.
Given ""This sentence is false" is false"
So which sentence is attributing falsity no longer to itself but merely to something other than itself?
This topic is mentioned Yannis Stephanou in his book A Theory of Truth in chapter 1, Aspects of Paradox.
From Quine, ""This sentence is false" is false"
From Stephanou, (6) is false
Therefore (6) is "This sentence is false"
From Stephanou, the sentence (6) attributes falsity to itself
Therefore, ""this sentence is false" attributes falsity to itself
From Quine, The Ways of Paradox and Other Essays
Therefore, "this sentence is false" is the outside sentence.
This is what I read both Quine and Stephanou to be saying.
Can you possibly see how answering this (again) might be considered "feeding the trolls"?
I am making a case that your previous statement was factually wrong, and am backing my case up with additional evidence from Yannis Stephanou's book A Theory of Truth
If you think that this is being inflammatory and provocative, then I'm sorry.
I won't bother you again.
So I underestimated AmadeusD's willingness to not understand plain words.
For his remedial benefit, a review is in order. So let's take a gentle stroll back through recent memory lane:
Quoting AmadeusD
At the point that AmadeusD posted the above, he had not posted in this thread except much earlier to ask me something about the incompleteness theorem. So "Why did it take 9 pages", at that point, could have meant different things.
I replied that the answer to his question is psychological. RussellA had been stubbornly sticking to arguments that had been demonstrated to be terribly confused, illogical and ignorant.
AmadeusD replied that he thinks RussellA is correct, as "it is not a paradox".
I pointed out that we had been talking about "This sentence has fifty words", which no one had claimed is a paradox, as the question was instead whether it is meaningful.
AmadeusD replied that it is not meaningful. At least credit AmadeusD for recovering by addressing the question of meaningfulness rather than that of paradoxicalness that was not at issue.
I replied that AmadeusD was merely asserting that "This sentence has fifty words" is not meaningful, and that counterarguments had been given that had not been refuted.
AmadeusD replied, "LOL, well fair enough!"
I don't know what what AmadeusD thought was laughable, and I didn't know whether "well fair enough" was sarcastic. I moved on to refute RussellA's latest posts.
Later, AmadeusD gave bad arguments:
* He claimed that "This sentence has fifty words" does not literally mean that "This sentence has fifty words" on account of "in the structure of the sentence. As has been pointed out". But there has been no rebuttal by RussellA that does not hinge on some combination of illogic, confusion and falsehood, so nothing that legitimately lays claim to "pointing out". Indeed, RussellA's arguments depend on his willfully not understanding the contextual nature of pronouns as he makes outlandish claims about them such as that "This sentence" could, in the context, just as well be referring to the city of Paris (or whatever his arbitrary example was).
* He argued again by mere assertion: "On it's face, it is plainly meaningless." Not even that is meaningless, but that it "plainly" meaningless, and not only that it is plainly meaningless but that "on its face" it is plainly meaningless.
* I pointed out that RussellA tried to slip around a refutation by changing the context from "This sentence has five words" to "This sentence is false". AmadeusD replied that I "added" meaning to the sentence discussed, but without addressing the careful detail I put into the question of meaning. And "adding" meaning doesn't address that RussellA tried to slip around a refutation by changing the context from "This sentence has five words" to "This sentence is false".
* He said, "whether or not the sentence is referring literally 'to itself' [...]" thus missing that that was not at issue but rather at issue is what "This sentence" refers to. The issue was not what a particular sentence refers to but rather to what a particular noun phrase refers to, as RussellA has the ridiculous notion that we might as well ignore the context in which the pronoun 'this' occurs.
Later, after posts not involving AmadeusD, he posted immediately following two posts by me, in entirety, "I can only laugh".
I took that to mean that he was scoffing at my posts. He then claimed that not referring to me. So, in good faith, I took him at his word for that. He said, "I assessed the page of the thread" and " I didn't tag you, or anyone. Clear indicator I am not talking to you". But a few posts later, he said, "I was intending there to point out that "I can only laugh" was in response to about eight posts, none of which were at or about me best I can tell - it was discussion between yourself and RussellA." So it was not just general, but about RussellA and me, and he had been defending RussellA's position and arguments against mine, and he decried what he calls my "distasteful approach". So, I can't take seriously that "I can only laugh" was directed at both RussellA and me, not at me in particular.
Then AmadeusD falsely claimed that I've attempted to dismiss RussellA on an ad hominem basis. I replied:
Quoting TonesInDeepFreeze
Then a bunch more garbage from AmadeusD including such juvenility as "your ego".
Eventually, AmadeusD goes into "No Mas"stuff while he's still punching. ["No Mas" not a quote of AmadeusD]
I have never been able to imagine what is in the mind of posters when they keep saying that they consider the dust-up over, or that they want it to be over, while they are still continuing the dust-up. "You're an idiot, a waste of my time, and a bad speller too! Okay, we're cool, time for us to get off the personal attacks; we can just move on now. But, as I was saying, "You don't know anything about Habermas; you should get your money back from that correspondence school junior college you flunked out of; you're the stupidest person I've ever talked to on the Internet; you're twenty tons of idiocy in a four ounce can, you raging ignoranceaholic. All right, now we don't need more insults; we can respect each other as posters, you braindead wad of scum."
AmadeusD has the prerogative to diss me as he likes, and I have the prerogative to show how his disses are off-base and that he's dishonest to claim he wasn't dissing me with lameisms such as, just for starters, "I can only laugh".
Always good to hear it straight from the horse's mouth.
"'This sentence is false'. Here we seem to have the irreducible essence of antinomy: a sentence that is true if and only if it is false.
In an effort to clear up this antinomy it has been protested that the phrase 'This sentence', so used, refers to nothing. 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
Quoting RussellA
(1) As best I can tell Quine is relating an argument given by some people that I would unpack as:
If we regard "this sentence" as referring to "This sentence is false", then there is no paradox. Therefore, if there is a paradox, then "this sentence" does not refer to "This sentence is false" and therefore "this sentence" refers to nothing.
If my interpretation is correct, Quine doesn't say there is no paradox. Rather he relates an argument that if there is a paradox then "This sentence" does not refer.
I don't understand that argument.
Suppose "This sentence" refers to "This sentence is false". Then "This sentence is false" means that "This sentence is false" is false.
So, "This sentence is false" is true if and only if "This sentence is false" is false. Contradiction.
But it seems Quine disagrees, so I don't know what I'm missing.
Quine also says that ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is paradoxical:
"If, however, in our perversity we are still bent on constructing a sentence that does attribute falsity unequivocally to itself, we can do so thus: ''Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation'. This sentence specifies a string of nine words and says of this string that if you put it down twice, with quotation marks around the first of the two occurrences, the result is false. But that result is the very sentence that is doing the telling. The sentence is true if and only if it is false, and we have our antinomy." - Quine
[s]Doesn't he mean 'prepended' rather than 'appended'?[/s] [Edited with strikethrough here and replacements made below without indication.]
I would unpack the argument this way:
Left to right:
If ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true, then ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false, as follows:
""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true if and only if "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.
Suppose ""Yields a falsehood when appended to its own quotation" yields a falsehood when its own quotation" is true.
So, "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.
But the result of appending "Yields a falsehood when appended to its own quotation" to its own quotation is ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation".
So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" yields a falsehood.
So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false.
Right to left:
If ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false, then ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true, as follows:
""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false if and only if "Yields a falsehood when appended to its own quotation" does not yield a falsehood when appended to its own quotation.
Suppose ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is false.
So, "Yields a falsehood when appended to its own quotation" does not yield a falsehood when appended to its own quotation.
But the result of appending "Yields a falsehood when appended to its own quotation" with its own quotation is ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation".
So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" does not yield a falsehood.
So, ""Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation" is true (if it were false it would yield a falsehood, viz. itself).
Notice that that argument makes use of the pronoun 'it'. But if we were to follow RussellA's disregard for the contextual basis of pronouns, the pronoun 'it' in this context could refer to the Taj Mahal. Good thing we are not bound by RussellA's ridiculous views. But RussellA cites Quine's other passages. So I wonder what RussellA would have to say about Quine's use of a pronoun in Quine's own formulation of the paradox.
(2) Clearly the inside sentence is "This sentence if false" since it is inside ""This sentence if false" is false", which is the outside sentence.
It makes no sense to say that a sentence that is literally inside another sentence is the outside sentence. And especially when Quine himself refers to the outside sentence as the one that "attributes falsity no longer to itself but merely to something other than itself", as that is ""This sentence is false" is false". RussellA is again nutso.
You should say that it's on the basis that your "infinite recursion" argument had been refuted at least three times but you choose to ignore the refutation.
What?! Not only have I not said that many times, I've not said it even once. On the other hand, I have said many times that an expression is in the world. Your claim about what I've said is the complete opposite of what I've said. That is yet another instance of your bizarre mentation and illogic.
Quoting RussellA
You have it reversed again! "This sentence has five words" is named "The Pentastring". The Pentastring is not named "This sentence has five words"!
Quoting RussellA
What you should say is "I choose to ignore the repeated explanations as to why the Pentastring is "This sentence has five words", so I'll just go ahead to claim that the Pentastring is not "This sentence has five words".
A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas.
The prop comedian Scott Thompson was named "Carrot Top". Carrot Top is the prop comedian Scott Thompson.
"Thou shall not steal" was named "The Eighth Commandment". The Eighth Commandment is "Thou shall not steal".
"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words".
Quoting RussellA
RussellA, please return to your native planet!
No one said that any name of the Pentastring has five words. Rather, "The Pentastring" is a name of "This string has five words".
Quoting RussellA
Of course. And no one said anything contrary by analogy. Again, for the 100th time in this thread: "The Pentastring" is a name for "This sentence has five words". The Pentastring is "This sentence has five words". The Pentastring is NOT a name for "This sentence has five words".
Quoting RussellA
Of course that's right.
"The Pentastring" is defined so that it refers to "This string has five words".
"Suppose we define 'the Pentastring' as the "This string has five words"." — TonesInDeepFreeze
Quoting RussellA
You started going back to 'sentence' rather than 'string', so for ease, I have been going along with that and allowing the "The Pentastring" to stand for "This sentence has five words" rather than for "This string has five words", especially since my point about "The Pentastring" is not affected by whether we use 'string' or 'sentence'.
Quoting RussellA
That doesn't even make sense. There are two quotation errors there:
(1) Maybe you mean that the Pentastring is this sentence has five words.
(2) But (1) makes no sense, so it should be:
The Pentastring is "This sentence has five words".
Quoting RussellA
No. But these are right:
"The Pentastring has five words" is true if and only if the Pentastring has five words.
"The Pentastring has five words" is true if and only if "This sentence has five words" has five words.
Quoting RussellA
Right! (A rarity for you.)
Quoting RussellA
That's gibberish on account of the fact that you still don't know how to use quote marks.
Quoting RussellA
"The Pentastring" refers to "This sentence has five words". That is how "The Pentastring" was defined.
"The Pentastring" is a name for "This sentence has five words".
The Pentastring is "This sentences has five words".
Those stand, no matter that you bungle them by not knowing how to use quote marks and no matter that you REVERSED the definition.
None of that supports your confused mixing up which is the inner and which is the outer sentence.
Quoting RussellA
First, Quine didn't assert that "This sentence is false" is false. Rather, he mentioned that some people regard ""This sentence is false" is false" to be an equivalent of "This sentence is false".
Second, at least in the passage you quoted, Stephanou didn't assert that (6) is false. He merely set it up so that (6) is "(6) is false", so that "(6)" stands for "(6) is false". (Similar to the Pentastring is "This sentence has five words", so that "The Pentastring" stands for "This sentence has five words".)
Third:
X has property P
Y has property P
Therefore, X is Y.
Obviously fallacious.
Moreover:
(6) is "(6) is false".
"(6) is false" has the word '(6)', but "This sentence is false" does not have the word '(6)'.
"This sentence is false" has the words 'this' and 'sentence', but "(6) is false" does not have the words 'this' and 'sentence'.
So, clearly "(6) is false" is not "This sentence is false".
Quoting RussellA
First, Stephanou says nothing about that. Second, it is bizarre to take Quine as saying "This sentence is false" is outside ""This sentence is false" is false" when literally "This sentence is false" is inside ""This sentence is false" is false".
I am baffled as to why RussellA keeps going on and on making bizarrely illogical claims in a thread like this.
Quoting RussellA
What?! Not only have I not said that many times, I've not said it even once. On the other hand, I have said many times that an expression is in the world. Your claim about what I've said is the complete opposite of what I've said. That is yet another instance of your bizarre imagination and illogic.
Quoting Devans99
No, it doesn't have an in-built truth value, it's actually an ordinary statement, in a position where it has the illusion of seeming to be more than it really is. Words are like mirrors, they don't contain meaning, but they reflect it, the true source of meaning existing elsewhere. Take for example, "The sky is blue", this meaning can be found from a person's subjective experience of the sky being blue, not in the statement or words.
In the case of the liar's paradox, "This statement is false", the meaning can be found from a person's subjective experience of reading that statement, not in the statement or words itself. The illusion comes into play when we think that the statement actually contains meaning more than our subjective understanding. This causes us to see words and the statement not as mirrors, but as windows (in the sense of how if you don't know a mirror is a mirror, you might think it's a window showing another person who looks just like you). But this creates an issue because they are mirrors,
Normally when you read a statement, it reflects outwards to some type of subjective meaning, but when it reflects inwards, the only thing it shows a reflection of is another mirror (or a collection of mirrors, I guess you could say). When mirrors face mirrors, what happens? It creates an illusion of infinity if there's enough light, and in the case of the liar's paradox, the light would be our own thoughts, and the image in between the mirrors would be the ordinary statement value, thus creating an illusion of infinity, of "this statement is false" being more than a normal statement (in other words, it's all about positioning the "mirrors" that creates this paradox.
I made a post about this here: https://thephilosophyforum.com/discussion/15424/the-liars-paradox-solution-words-as-mirrors-of-understanding-redo-but-full-solution
I have no problem with "this sentence has five words" being named "The Pentastring". In other words, "The Pentastring is this sentence has five words".
My fundamental problem is that it is logically impossible to go from knowledge about the content of an expression, such as "The Pentastring is this sentence has five words", to knowledge about something that may or may not exist in the world, such as The Pentastring.
It is logically impossible to go from knowing that "unicorns are grey in colour" to knowing whether unicorns do or not exist in the world.
There is no logical connection between "This sentence has five words" was named "The Pentastring" and The Pentastring is "this sentence has five words".
As you said:
Quoting TonesInDeepFreeze
appended to = prepended by?
You're right. My silly mistake. I made a note of the edits in my post. Thanks.
No, only in your own ridiculous words.
Consider:
The Pentastring is this sentence has five words
That's gibberish.
Consider:
"The Pentastring is this sentence has five words"
That's quote marks around gibberish.
Consider:
The Pentastring is "This sentence has five words".
That's a sensical statement.
Consider
"The Pentastring is "This sentence has five words""
That's quote marks around a sensical statement.
Your put-downs are lame-o-rama. If I were you, I'd get someone to help me write better insults.
"The Pentastring is this sentence has five words"
No one has anything to say about any "content" of that other than that it's gibberish.
These are all in world. They are not merely in the mind of one person:
""The Pentastring" refers to "This sentence has five words"" (stipulated by definition)
"The Pentastring is "This sentence has five words"" (true)
"This sentence has five words" (true, as far as I can tell)
"The Pentastring has five words" (true)
""This sentence has five words" has five words" (true)
"New York City has five boroughs" (true)
""New York City has five boroughs" has five words" (false)
"This guy is in love with you" (true when sung by Herb Alpert about Lani Hall, or by anyone about someone they love)
""This guy is in love with you" has five words" (false)
"The Pentastring is this sentence has five words" (gibberish)
Quoting RussellA
(1) If we interpret as "All unicorns are grey" then usually, we do not infer "There exists a unicorn". (2) but the analogy is irrelevant. I didn't propose a predicate such as 'is a unicorn' and then infer that there is something of which that predicate is true.
Rather, merely, there does exist the expression "This sentence has five words". And I named that expression. I named it "The Pentastring". The expression "I shall return" exists. I can name it "Mac'sPromise" or whatever I want to name it.
Quoting RussellA
When we give the name "Y" to X, we then say such things as "Y is X". When you give the name "Buppy" to your dog, you then write "Bubby is my dog". When I give the name "The Pentastring" to "This sentence has five words" I then write "The Pentastring is "This sentence has five words"".
You SKIP the examples:
A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas.
The prop comedian Scott Thompson was named "Carrot Top". Carrot Top is the prop comedian Scott Thompson.
"Thou shall not steal" was named "The Eighth Commandment". The Eighth Commandment is "Thou shall not steal".
"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words".
Quoting RussellA
Yes.
"This sentence has five words" is an expression. "The Pentastring" is an expression that is a name of the expression "This sentence has five words". The Pentastring is "This sentence has five words".
"All men are created equal" is an expression. "Jeffy'sBigCredo" is an expression that I now use to name the expression "All men are created equal". Jeffy'sBigCredo is "All men are created equal". I could name it "Flookimims" if I wanted to. Flookimins is "All men are created equal". The silliness of that is just to impress the point that names are stipulative and that when we give the name "Y" to X, we then say "Y is X". And contrary to an argument that you revive now, but that had been refuted many many posts ago, such naming does not cause us to assert that certain things have certain predicates other than, of course, they then have the predicate of being named a certain way.
I can anticipate an objection: But if you name your goldfish "Winston Churchill" then you would say "Winston Churchill is my goldfish", which is not true since Winston Churchill was a person, not a goldfish. But that merely reflects that natural languages have ambiguity. Sally Jones is a lab researcher. Another Sally Jones is not a lab researcher. We don't protest that "Sally Jones is a lab researcher" and "Sally Jones is not a lab researcher" is a contradiction, as we recognize that in natural languages names may have different referents. Even in formal languages. The symbol "+" might name standard addition of natural numbers or it might name modular addition for a given modulus. So we recognize that denotation is per an interpretation of a language and that truth is relative to such interpretations.
I agree that when we give the name "Y" to X, we can then say "Y is X"
For example, when we give the name "Noorbicks" to the puppy born in Smalltown, Kansas, we can then say "Noorbicks is the puppy born in Smalltown, Kansas"
But this is not what you are doing. You are giving the name "The Pentastring" to "this sentence has five words". You are not giving the name "The Pentastring" to this sentence has five words.
Knowing that "The Pentastring is this sentence has five words" gives me no knowledge about the existence or not in the world of the Pentastring, meaning that I cannot say anything about The Pentastring in the world.
This includes being able to say that The Pentastring is "this sentence has five words".
Quoting RussellA
For about the 20th time, as you skip each time, and you still don't get use-mention:
Consider:
The Pentastring is this sentence has five words.
That does not parse because, in this case, the words after "is" form a sentence itself and must be mentioned not used.
[noun] is this sentence has five words
makes no sense.
Instead,
[noun] is "this sentence has five words"
makes sense.
These are correct:
"The Pentastring" refers to "This sentence has five words"
The Pentastring is "This sentence has five words"
These are obviously gibberish:
"The Pentatsring" refers to this sentence has five words.
The Pentastring is this sentence has five words.
You've been making that mistake, and using it in your phony arguments, for a long long time in this thread.
Language and the meaning it carries reflects the reality we live in.
Therefore "The next statement is true. The previous statement is false." violates temporal causality by forming a self-negating closed loop.
In the same way the grandfather paradox operates: I was born and went back in time to kill my grandfather. My grandfather was killed so I was never born.
These two examples are analogous.
The paradox can be resolved by adding uncertainty:
"The next statement may be true. The previous statement may be false."
This way a closed loop self-negation isn't automatically formed due to the added uncertainty.
As for "this sentence is false" or 'this statement is false"... its essentially meaningless because it doesn't actually "state" anything ie stating something requires the subject of the statement to be separate from the statement itself - ie it must have a position (regarding external factors). For example "that statement is false" in a context where the other statement is known is perfectly logical.
For example "Teeth grow out of your eyes" followed but "that statement is false" provides essential context.
It can also be resolved another way by changing the statement itself from "this statement is false" to something like "this statements grammar false is" in this way it remains self referential but justifies falsity by adding a variable to contextualise its falsity - namely erroneous structure.
:100:
Quoting Benj96
I think that "This statements grammar false is" can be compared to Chomsky's "Colourless green ideas sleep furiously".
"Colourless green ideas sleep furiously" is grammatically correct, yet nonsensical.
The fact that "this statements grammar false is" has an erroneous structure (within English, though perhaps not in other languages) means that it is not grammatical, and if not grammatical, cannot have a meaning.
And if has no meaning, can be neither self-referential nor not-self-referential.