↪TonesInDeepFreeze pointed out, a reductio is meant to show the inconsistency of some assumption given a set of premises (i.e. more than 1!). — Leontiskos

I didn't say that. Leontiskos says he hardly reads my posts, but not so hardly to stop him from putting words in my mouth. Leontiskos is a strawmaner extraordinaire.

I didn't say "more than 1". Leontiskos pulled that from thin air.

Indeed, here is an RAA from even the empty set of sentences:

1. P & ~P {1}
2. P {1}
3. ~P {1}
4. ~(P & ~P} { }

Indeed, every logically true sentence is provable from the empty set of sentences, and the negation of every logically false sentence is provable from the empty set of sentences.

And I didn't say "the inconsistency of some assumption given a set of premises" (or if I did, then I typed incorrectly). What I said is that RAA shows that a sentence is inconsistent with the set of premises. There's a world of difference between those.

One is a statement in the meta-language and the other in the object language. They are different levels of statement.
— TonesInDeepFreeze

A direct proof requires no recourse to the meta-language. When the reductio identifies a contradiction it is dipping into the meta-language. That exchange earlier with Tones was about whether the reductio is truth-functional. It turns out that you cannot represent a reductio in the object language. — Leontiskos

That is a confusion of someone who doesn't know jack about the subject.

The formulas of the object language are written in the object language and referred to in the metalanguage. A proof mentions formulas from the object langugae, but the proof is a sequence of formulas (or tree of them, or a sequence of pairs of formulas and sets of line numbers, etc., depending on the system). The sequences are not written in the object language. For example, a sequence as written by:

1 P -> Q {1}
2 P {2}
3 Q {1,2}

mentions the formulas P -> Q, P, and Q, but also 1, 2, 3 and {} that are in the meta-language.

RAA is no different in that respect from such proof forms a modus ponens, conjunction introduction, etc.

This is the path that Banno and @TonesInDeepFreeze have chosen:

(a→(b∧¬b)) → ¬a — Leontiskos

I've chosen to correctly report that that is a truth table tautology and a theorem of ordinary symbolic logic. Will Leontiskos's tribunal find me guilty of the crime of being a "truth functionalist" for that?

There's been discussion about modus tollens and RAA vis-a-vis each other.

Contraposition is a one formula version of the rule RAA.

With a natural deduction system with RAA, we can derive contraposition as an axiom.

With an axiom system with contraposition as an axiom, we can derive RAA as a rule.

@Leontiskos keeps blindly flailing over the fact that RAA rejects one premise but not the others. That objection is based on not understanding RAA, not understanding exactly what it is.

1 P {1}
2 Q {2}
3 ~(P & Q) {3}
4 P & Q {1,2}
5 ~P {1,2,3}

that is valid. {1,2,3} |= ~P

1 P {1}
2 Q {2}
3 ~(P & Q) {3}
4 P & Q {1,2}
5 ~Q {1,2,3}

that is valid. {1,2,3} |= ~Q

1 P {1}
2 Q {2}
3 ~(P & Q) {3}
4 P & Q {1,2}
5 ~~(P & Q) {1,2,3}

that is valid. {1,2,3} |= ~~(P & Q)

RAA permits only valid inferences. The fact that there are different valid arguments we may choose from does not vitiate that RAA permits only valid inferences.

P→Q
∴¬P

The revised textbook would need to add an asterisk: "This is a fallacy*."

" *Except in that case where Q = (b∧¬b)" — Leontiskos

Again, Leontiskos doesn't know jack about this subject.

When we say "It is not the case that P->Q implies ~P" it is understood that that means "It is not the case that for all formulas P and Q, P->Q implies ~P". 'P' and 'Q' are understood to be sentential variables and that in informal discussion, the quantification 'for all' is implicit. Of course we understand that P->Q implies ~P for certain P and Q while it is not the case that for all P and Q, P->Q implies ~P. And Leontiskos's claim about this - "some rules of classical logic to come into conflict" - is patently false.

Anyone who has studied even an introductory text in the subject would understand that. The study of the subject is not responsible for Leontiskos's ignorance about it.

There's more and more and more misconception and ignorance in Leontiskos's posts. One cannot even keep pace with them.

The truth-functionalist is likely to object to me, “But your claims are not verifiable within classical logic!” — Leontiskos

One may instruct as to what does and does not obtain in classical logic without claiming that classical logic is the only credible logic. If the subject is classical logic, then we need to not make false claims about it, no matter what our views about it may be. So, if (made up example) someone said, "in classical logic, RAA is a rule for checking the well-formedness of expressions" then one doesn't have to commit to any particular view of classical logic in order just to point out that that is not what RAA is and not how RAA works.

Now, in this discussion, there has been talk about classical logic qua classical logic. And so it is eminently proper to point out when classical logic is misconstrued or misrepresented. Just as one doesn't have to be an intuitionist or advocate for paraconsistent logic, etc. to point out when intuitionististic logic or paraconsistent logic, etc. is misconstrued or misrepresented. How can that not be eminently reasonable? And it is eminently unreasonable, irrational and anti-intellectual to try to arrogate a presumed dialectic high ground by dissuading people from pointing out how classical logic actually does operate.

My hunch here is that the classical logic system treats everything in this purely relational and context-dependent way and assumes that every non-simple proposition can be cast as a simple 'p' while preserving all of the validity relations. — Leontiskos

That is so blatantly, ridiculously, shamefully wrong. It could be written only by someone who doesn't know jack about the subject. It is the opposite of the truth. Classical sentential logic is based on compositionality and not reducing all arguments to merely atomic formulas. And classical predicate logic extends with quantifiers.

if from ¬(A → (B ∧ ¬B)) we infer that A implies no contradiction — Lionino

We don't infer that. Suppose A is "P & ~P", then A itself is a contradiction.

If ~(A -> (B & ~B)) is true then A is true. But if A is a contradiction, then ~(A -> (B & ~B)) is not true.

You are misstepping when you take ~(A -> (B & ~B)) to mean "A implies no contradiction" or that ~(A -> (B & ~B)) entails that there is no contradiction that A implies.

Otherwise, try to prove it. Assume:

~(A -> (B & ~B))

Then try to prove:

For every C, if C is a contradiction, then A does not imply C.

What are the assumptions you will use to try to prove it? Are you making a claim about what pertains in ordinary symbolic logic? Or are you making a claim about how statements of such forms are understood in certain everyday contexts? If you are making a claim about what pertains in ordinary symbolic logic, then your attempted proof should not include premises that are not derivable in context of ordinary symbolic logic.

(A¬→(B∧¬B)), if such a thing were proper writing, — Lionino

It is not well formed.

But we could have a notation P-/->Q, but what would it mean if not ~(P -> Q)?

Oh no! Leontiskos has "inundated" the thread! More posts and words from him than any other poster! I better scold him for that right away! No, actually, unlike his hypocritical self, I don't begrudge anyone from posting as much as they want to post.

Note so that, hopefully, Leontiskos will desist from mischaracterizing my views: In all these posts: I am not claiming that classical logic is the only correct or useful logic. I am not claiming that classical logic accords with the many notions of logic and language in everyday discourse. And I do not claim that classical logic should not be critiqued. (Indeed, such critiques as from constructivism, predicativism, finitism, relevance logic, etc. are rich sources).) But when classical logic is being critiqued, it should not be mischaracterized, misrepresented or misconstrued, so explanations of how classical logic actually operates are productive. And giving explanations of classical logic does not imply advocacy for it or a presumption that it is the only formal logic that should be consulted. I admire the thought that goes into formal logic; I enjoy studying it; I appreciate its role in formalization of mathematics; I appreciate its use in such things as computing; I appreciate that it is the subject of much of philosophy of mathematics and that it generates rich questions in mathematics and philosophy. And, in my own limited way, I have studied other formal logics and have read and appreciated critiques of classical logic. I do not claim that anyone should even care about formal logic, but when people do talk about it, they should get it right, and it is eminently proper to remark when they don't.

you do not know what you mean by 'particular.' — Leontiskos

That is false. And it is said without basis. I know what I mean by the word. I use it in its everyday sense.

No one in this thread has been able to understand what that concept means — Leontiskos

What the concept of 'a particular contradiction' means? 'particular' is used in the everyday sense such as definition 1 at Merriam online.

to talk about a particular contradiction without a sense of a non-particular contradiction does not make sense. — Leontiskos

I don't use 'non-particular'. There are particular contradictions (such as "B & ~B") and there is a definition of 'is a contradiction'.

* A formula is a contradiction if and only if it is the conjunction of a formula and its negation.

* Sometimes 'contradiction' is also used in the sense that a formula is not necessarily a conjunction of a formula and its negation but is a formula that entails a conjunction of a formula and its negation. (For that sense, I usually use 'inconsistent'.)

* With natural deduction, we sometimes refer to a pair of lines such that one is the negation of the other. But notice, that is merely commentary, as the formal deduction does not depend on the use of the term 'contradiction' but only on specifying a rule by reference to there being one line with a formula and another line with its negation.

A contradiction is an assertion of Propositional Logic that is false in all situations; that is, it is false for all possible values of its variables. — Tautologies and Contradictions

That is the semantical side of the coin. 'contradiction' is usually defined syntactically (a formula and its negation) but it does follow that a sentence is a contradiction if and only if it is logically false.

The conclusion of a reductio is like, "This is an apple." — Leontiskos

No, the conclusion of a reductio is of the form "~P" from the assumption "P", or for the non-intuitionistic version, "P" from the assumption "~P".

G be a set of premises and a sentence P is not a member of G. And we want to show that G proves ~P. Then we may use any of the members of G in our argument. But, along with members of G, we also may suppose P to derive a contradiction, thus to show that G proves ~P.
— TonesInDeepFreeze

The fiction in the reductio for the formalist is that there is some formal difference between an assumption or premise and a supposition. I say that there is not. — Leontiskos

Leontiskos can say whatever he likes, but he is terribly confused and uninformed about the subject.

I explained how reductio works in natural deduction, as just quoted by Leontiskos.

And formulation of the rules for natural deduction do not need to mention 'premise', 'assumption' or 'suppostion'. We may mention those words for convenience, but the specification of a natural deduction system does not require such words. Leontiskos would learn what a natural deduction system actually is - not his nutty imagination of what he thinks it is - by just reading a reliable text or article that covers the subject.

There is a difference between P being a member of G and P not being a member of G. That is not a "formalist" fiction.

I'll take time and effort to give even greater detail, though Leontiskos will likely ignore it or mangle it in the dysfunctional, electrically shorting food processor that is his brain when it spews garbage about logic.

One elegant way to formulate sentential natural deduction is with these rules that permit:

Enter P on a line and charge that line to itself.

If P, along with possibly other lines, shows Q, then infer P -> Q and charge it with all lines charged to Q except the line for P.

From P and P -> Q, infer Q and charge it with all lines charged to P and to P -> Q.

If P, along with possibly other lines, shows a formula Q and a formula ~Q, then infer ~P and charge it with all the lines used to show Q and to show ~Q except the line for P.

If ~P, along with possibly other lines, shows a formula Q and a formula ~Q, then infer P and charge it with all lines used to show Q and used to show ~Q, except the line for ~P. [not intuitionistic]

From P and Q, infer P & Q and charge it with all lines charged to P and to Q.

From P & Q, infer P or infer Q and charge it with all lines charged to P & Q.

From P or from Q, infer P v Q and charge it with all lines charged to P.

From P v Q, P -> R and Q -> R, infer R and charge it with all lines charged to P v Q and to P -> R and to Q -> R.

There is no mention of 'premise', 'assumption' or 'supposition'.

Those rules are equivalent with:

{P} |- P

If Gu{P} |- Q, then G |- P -> Q

If G |- P and H |- P -> Q, then GuH |- Q

If Gu{P} |- Q and Gu{P} |- ~Q, then G |- ~P

If Gu{~P} |- Q and Gu{~P} |- ~Q, then G |- P [not intuitionistic]

If G |- P and H |- Q, then GuH |- P & Q

If G |- P & Q, then G |- P and G |- Q

If G |- P or H |- Q, then GuH |- P v Q

If G |- P v Q, and H |- P -> R and J |- Q -> R, then GuHuJ |- R

There is no mention of 'premise', 'assumption' or 'supposition' nor, for that matter, 'contradiction'.

The crank writes, "If the so-called mathematical objects are fictions then they are not really objects, but fictions."

'Sam Spade is a detective'.

'The Maltese falcon is a statuette'.

'Sam Spade' and 'The Maltese falcon' are nouns. We regard a noun as referring to something, whether it ('it' is a pronoun that refers to something) is a material piece, a collection of material pieces, such things as a sports team, an experience, event, series of events, physical experience, mental experience, mental state, idea, concept, number, set, vector space, word, sentence, literary piece, story, narrative, etc. - now existing, once existing, predicted to exist in the future, conceived to possibly exist now, conceived to possibly to have existed in the past, or possibly conceived to exist in the future, or hypothetically now existing, once existing, Or, fictional instances ('instance' refers to something) of any of those ('those' is a pronoun to refer to some things) hypothetically.

But to accommodate a position that fictional things are not really things, the fictionalist could say, "When I say 'thing' or 'object' regarding mathematics, 'fictional' is tacit. I may be taken as saying 'fictional thing' or 'fictional object'".

The Maltese falcon is fictional, but I can still refer to the Maltese falcon without having to say each time "the fictional Maltese falcon". And it makes perfect sense for someone to ask, "What kind of thing is the Maltese falcon?" If the crank says I must answer, "It is a fictional thing. It is fictional statuette" then okay. But in context, it might be understood that we're talking about fictional things.

The number 1 is not a concrete object, but I can still refer to the number 1 without having to say each time "the fictional number 1". And it makes perfect sense for someone to ask, "What kind of thing is the number 1?" If the crank says I must answer, "It is a fictional thing. It is a number, which is a fictional thing" then okay. But, as mentioned, the fictionalist may take it as understood that we're talking about fictional things.

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." — Leontiskos

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".

It seems that you have no clear idea what I am supposed to have said:

In the other thread, I think about three times, you claimed [...], or [...], or that [...]. Something to that effect.
— TonesInDeepFreeze

Which is wonderful: you run around accusing people of lying and you have no idea what they are supposed to have even said. — Leontiskos

You are too much!

Here's what I wrote:

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. — 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.

That is a stupid analogy.
— TonesInDeepFreeze

It's not. — Leontiskos

I said exactly why it is stupid.

if a liar says he is lying, the foundation is shaky enough to allow either that he is telling the truth or that is he not (telling the truth). — Gregory

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".

What exactly is he lying or not lying about? — Gregory

He's talking about his lying. If he's lying, then he's lying that he's lying. If he's not lying, then he's telling the truth that he's lying. Both disjuncts are absurd.

he is an unreliable being. — 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.

we can assume nothing about what he says except that he lies most of the time. — 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?

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.

e.g. you are under the spell of material implication — Leontiskos

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.

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. — 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.

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.
— TonesInDeepFreeze

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. — Tarskian

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.

What position is that? — Leontiskos

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.)

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.

I responded to:

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." — 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.

You have replied to my recent post. But, as I said, I replied to your earlier post that you again linked to, thus you brought this full circle.

Phil is a fool.
Colourless green ideas sleep furiously.

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." — 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.

And I replied:

When someone considers the claim, "Colourless green ideas sleep furiously," you will inform them that the statement they are considering is nonsensical.
— 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:

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.
— 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. — TonesInDeepFreeze

You brought this around full circle.

Getting back to the subject:

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 forgot to put you back on my ignore list when I reinstalled my browser. — Leontiskos

Sorry to hear about your computer problems.

Yes, I understand what you were saying. It is a form of argumentum ad populum. — 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.

You have made it abundantly clear that you will continue to refuse to answer the question of the OP. — Leontiskos

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.

Argumentum ad populum, then? — Leontiskos

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.

So still nothing contentful, about the topic of the thread? Still just talking about yourself? — Leontiskos

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?

Do you often get stuck in front of mirrors? — 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.,

Hence my reply:

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:

is it possible for someone to speak, "I am lying," while simultaneously meaning that they are lying and that they are not-lying?
— Leontiskos
— Leontiskos — Leontiskos

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.

The proponent of the "Liar's paradox" wants to say something like, "This sentence is false,"* represents something that is simultaneously true and false in the way that presents a formal contradiction. I have no idea what they purport to mean by this. — 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.

8 non-committal replies with more unfounded assertions, all in response to posts that were written some five years ago. — Leontiskos

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.)

The so-called "Liar's paradox" seems quite silly
— Leontiskos

Knowing something about logic and the context helps to understand why the liar paradox is of interest.

I agree it's not much use to spend much time pondering about them
— leo

Me too.
— 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. — TonesInDeepFreeze

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.

And we may consider sentences that are displayed without implication (sic) that they have an implied or even hypothetical speaker. There (sic) instances in which we may consider display (sic) of a sentence so that we may consider it in and of itself.
— TonesInDeepFreeze — Leontiskos

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!

What I am primarily interested in is the OP. I am sure Russell can speak for himself. — 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.

not grammatically correct — 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.

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. — TonesInDeepFreeze

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 ↪RussellA 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. — Leontiskos

(1) Whatever your definitions of 'material property' and 'formal property', the question was:

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. — 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 false true" is self-referential, but is it not true? [corrected in edit]

is it possible for someone to speak, "I am lying," while simultaneously meaning that they are lying and that they are not-lying? — 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.

You skipped my examples that are not of that kind.
— TonesInDeepFreeze

I addressed your example of word-counting. — 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.

Just now, you referenced the sentence "colourless green ideas sleep furiously" without there being an implied speaker other than a hypothetical one.
— TonesInDeepFreeze

Where have I said that the implied speaker cannot be hypothetical? — Leontiskos

It's good that we agree that there may be hypothetical speakers.

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. — 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.

conflating (purported) falsehoods with lies. But we've been over that already. — 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.

You are lying that I "continue".
— TonesInDeepFreeze

You are full of vapid nitpicking. — Leontiskos

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.

When someone considers the claim, "Colourless green ideas sleep furiously," you will inform them that the statement they are considering is nonsensical. — 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:

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. — 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.

If the mind is pure matter (brain, nervous system) and it can compute Godel's truths — Gregory

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'.

You continue your habit of falsely attributing quotes. He said nothing about the "material" world. — Leontiskos

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.

There is always an implicit or implied speaker. — 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.

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.

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

This sentence has five words.

Not true?

Many "philosophers" mistakenly hold that sentences have meaning apart from speakers — Leontiskos

There are formulations in which there is no speaker nor reference to "I' or things like that.