As you have said many times on this thread, something in the world cannot be an expression in language. — 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 mentation and illogic.

The Pentastring may be named as "this sentence has five words" — 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"!

the Pentastring isn't "this sentence has five words". — 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".

Just because the name of the Pentastring has five words, it doesn't follow that the Pentastring itself has five words. — 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".

Just because a name for the Eiffel Tower has two words, it doesn't follow that the Eiffel Tower itself has two words. — 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".

"The Pentastring has five words" is not how "the Pentastring" has been defined. — 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

For the sake of argument, using sentence instead of string — 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'.

Then "the Pentastring is this sentence has five words" — 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".

Therefore, "the Pentastring is this sentence has five words" is true IFF the Pentastring is this sentence has five words. — 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.

"the Pentastring has five words" is true IFF the Pentastring has five words — RussellA

Right! (A rarity for you.)

the Pentastring is this sentence has five words is not the same as the Pentastring has five words. — RussellA

That's gibberish on account of the fact that you still don't know how to use quote marks.

Therefore, "the Pentastring has five words" is not how "the Pentastring" has been defined. — 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.

And I may stipulate that in the context of my post, "This sentence" refers to "This sentence has five words"...On what basis is it claime[d] "This sentence has five words" [is] not meaningful? — TonesInDeepFreeze

On the basis of infinite recursion. — RussellA

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.

The passages from Quine:

"'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

There's no paradox because, as Quine says, "this sentence is false" is referring to something other than itself. — 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

Doesn't he mean 'prepended' rather than 'appended'? [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.

the clear horseshit going on here. — AmadeusD

Always good to hear it straight from the horse's mouth.

If you would read what I posted — TonesInDeepFreeze

I did. — AmadeusD

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:

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.

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. — RussellA

Why did it take 9 pages. — 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:

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. — 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".

Traditional logic, without considering the non-literal use of language — Echogem222

Logic doesn't require that we don't accommodate for the non-literal. If "I can eat a horse" is meant to mean only that I am extremely hungry, then logic doesn't disallow us from considering "I am extremely hungry" in the argument rather than "I can eat a horse". That is, when we input the statements into our logic meat grinder ("meat grinder" not literal, by the way) we may choose to first adjust our inputs so that the logic meat grinder handles them as we want it to; logic doesn't disallow us from doing that.

However, yes, if it is a formal logic, then either we must input only statements that adhere to the forms we rely upon for deductions or have yet an additional system that translates informalisms into formalisms, such as translating hyperbolic statements.

The Russel's paradox, "a set that contains all sets that do not contain themselves" is only a paradox to those who think that the word "set" is not a mirror. Those that understand it is a mirror understand that "a set that contains all sets that do not contain themselves" is a set that cannot exist — Echogem222

(1) Russell's paradox is couched in terms of sets, but that is not necessary, as it is not necessary even to couch in terms of the relation of elementhood. Rather, the we can couch in greatest generality regarding any 2-place relation R to derive:

There is no x such that for all y, y bears R to x if and only if y does not bear R to y.

(2) There is no set whose members are all and only those sets that are not members of themselves. You left out the bolded part.

But the definition isn't constructive and is extensionally unintelligible for some of the reasons you pointed out in the OP. — sime

In set theory, we prove the existence of a particular complete ordered field and that it is unique within isomorphism. I didn't adduce any reasons that that is not constructive nor even say that it is not constructive.

Dedekind didn't believe in the reality of cuts of the continuum at irrational numbers — sime

What passage in what paper by Dedekind are you referring to?

so that one never arrives at the antimonies you raised above. — sime

I didn't mention any antinomies.

For a mathematics for the sciences, ordinarily we use a complete ordered field. That requires having a non-empty set, a 2-place relation (<) on the set and two 2-place operations (+ *) on the set such that for all x, y and z:

ORDERED FIELD
x+(y+z) = (x+y)+z (associativity of addition)
x+y = y+x (commutativity of addition)
EyAx x+y = x (additive identity element)
Theorem: E!yAx x+y = x
Definition: 0 = the unique y such Ax x+y = x
Ey x+y = 0 (additive inverse)
EyAx x*y = x (multiplicative identity element)
Theorem: E!yAx x*y = x
Definition: 1 = the unique y such that Ax x*y = x
0 not= 1
x*y = y*x (commutativity of multiplication)
x*(y*z) = (x*y)*z (associativity of multiplication)
x*(y+z) = (x*y)+(x*z) (distributivity)
x not= 0 -> Ey x*y = 1 (multiplicative inverse)
(x < y & y < z) -> x < z (transitivity)
exactly one: x < y, y < x, x = y (trichotomy)
x < y -> x+z < y+z (monotonicity of addition)
(0 < z & x < y) -> x*z < y*z (monotonicity of multiplication)

COMPLETE ORDERED FIELD
In set theory, we prove that there is a carrier set (called 'R') for such a system and such that, for any upper bounded non-empty subset of S of R, S has a least upper bound. With that and the rest of the set theory axioms we can do the mathematics of derivatives and integrals for the sciences.

/

An alternative is to have a system with infinitesimals. But still, ordinarily, we need to define <, + and * and to prove whatever theorems are needed for the machinery of mathematics.

To just wave a hand and say "Voila, this is my infinitesimal" does not provide the needed definitions of < + and * with infinitesimals nor the needed proofs.

So how do we go about proving the existence of a system with infinitesimals? For your purposes, it would help to first define 'is an infinitesimal'. I provided a definition previously, but I notice that many authors include 0 as an infinitesimal. So perhaps use this definition:

x is an infinitesimal if and only if, for every positive real number y, |x| < y.

It has been proven for you that for every real number x there is a positive real number y such that y < |x|.

So no non-zero real number is an infinitesimal.

One more time: No non-zero real number is an infinitesimal. The proof that no non-zero real number is an infinitesimal is immediate from the fact that for every real number x there is a positive real number y such that y < |x|. We don't need to keep going over this over and over.

I mentioned previously different ways of proving the existence of systems with infinitesimals.

So why would you ask?:

I am still not convinced that infinitesimal does not exist though. Can you prove it? — MoK

I can't prove it, since it is not provable. I never said that there are not infinitesimals. I explicitly said that there are systems with infinitesimals and I even mentioned different ways of developing them. But no non-zero real number is an infinitesimal, which has been proven to you over and over. That you are still asking about this suggests that you are not paying attention to the posts.

(I mentioned previously using the compactness theorem for having a system with infinitesimals. But an interesting thing about that is that we prove the existence of such a system but (unlike with the reals) we cannot define a particular such system: The compactness theorem for uncountable languages relies on Zorn's lemma. Same problem with the ultrafilter method.)

I googled and I found two references about the division of cardinal numbers. You can find the references here. — MoK

That source itself points out that when the numerator is less than the denominator, there is no definition of numerator/denominator. The very source you point to disputes your claim that (aleph_1)/(2^aleph_1) is properly defined. And you should have proven that for yourself when you first thought of it [here 'X' stands for the Cartesian product]:

K*L = card(K X L). And we have the theorem that if L <= K and K is infinite and L is non-zero, then K*L = K.

The definition of x/y:

x/y = the unique z such that z*y = x. If there is no such unique z, then x/y is not properly defined.

Suppose here that L <= K and K is infinite and L is non-zero:

If L = K, then there are Z such that Z*L = K, but there is no unique such Z. So L/K is not properly defined.

If L < K, then the unique Z such that Z*K = L is L. So L/K = L.

If K/L were properly defined, then K/L would be the unique Z such that Z*L = K. But there is no such Z at all, let alone a unique one. So K/L is not properly defined.

You did an Internet search but didn't even bother to read what you found, instead recommending that other people read it even though, unknown to you since you didn't even read it, it says the exact opposite of your claim that you made up out of thin air.

"(aleph_1)/(2^aleph_1)" is pure bunk.

the distance between consecutive means tends to zero — MoK

The sequence of half distances converges to 0. So what? That doesn't prove that it's not the case that between any two different real numbers there is another different real number.

Well, I showed that the distance between consecutive means is zero if the number of divisions is aleph_1. — MoK

"number of divisions is aleph_1" is undefined.

I recommend that you learn how axiomatic mathematics and definitions work

and assumed the worst in all three turns (the initial "Why did it take..." — AmadeusD

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?

I did not say that, thank you very much.

was in response to about eight posts — 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). — AmadeusD

You wrote:

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. — 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!

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. — AmadeusD

That's good. But it was not imprecise. It was precise:

"it was discussion between yourself and RussellA." [bold added]

I reject your position on the basis its an emotional reaction — 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?

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. — TonesInDeepFreeze

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. — AmadeusD

Again you reply by ignoring what I wrote. I said exactly why it is dismissive, even with its ambiguity.

You haven't addressed the specifics of my argument about it. — TonesInDeepFreeze

Yes I have. Multiple times. — 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!

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 — TonesInDeepFreeze

Luckily, those two things are true, and I am not being dishonest. — 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?

You ought not put strikethrough across my words within a quote like that.

I said "naturally" and I did not strike it. — TonesInDeepFreeze]

That was the point my guy. You did not 'naturally' react. — 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.

perhaps had your ego hurt — 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.

I tried to squash the 'beef'. Four times now, actually. — 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.

.

I maintain it was. It was not in response to you directly, or indirectly. — AmadeusD

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.

naturally counter-attacking and defending. — TonesInDeepFreeze — AmadeusD

You ought not put strikethrough across my words within a quote like that.

I said "naturally" and I did not strike it.

ou let out a fart of snark that would naturally be understood to be directed at me. — TonesInDeepFreeze — AmadeusD

The typo of omission is yours not mine. I said "You [...]".

I outline what I (still) recognise as a distasteful approach, but I very much appreciate your clarification here. Genuinely. Thank you. — AmadeusD — AmadeusD

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 are clearly making some extremely sensitive inferences that don't make sense. — AmadeusD

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

I don't think the latter is dismissive at all. — AmadeusD

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.

[not as you later claimed - TIDF] clearly indicated at the time. — TonesInDeepFreeze

I maintain it was. It was not in response to you directly, or indirectly. — AmadeusD

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.

I already made two attempts to say "Cool man, we weren't having such a go at each other as it seemed" — AmadeusD

Oh, is that what you meant to convey? You have a curious way of communicating, I'll give you that.

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 can only laugh. — AmadeusD

Why did it take 9 pages. — AmadeusD

Open ended, content-free snark like that is also a form of dismissiveness, whether to an individual or a group.

It wasn't aimed at me - the posts in question were responses to other people, so I revert to the above appreciation. — AmadeusD

The post to which I refer was my direct response to your direct question to me.

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.

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.

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. — 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.

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.

I can only laugh — AmadeusD

and not read and reason.

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". — RussellA

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.

The paradox arises when "this sentence is false" is not referring to something other than itself. IE, when it is self-referential. — 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.

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. — RussellA

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.

As I said from the start, I am open to a finding that "This sentence has five words" is not meaningful, if there is a good argument that it's not. But as RussellA's arguments have been an insult to logic and intelligence, I find myself starting to feel more and more that "This sentence has five words" is indeed meaningful.

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.

The sentence is not paradoxical, but a lot of the ways in which this is the case, Russell has covered. — AmadeusD

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.

I haven't opined on Wittgenstein.

So, whether or not the sentence is referring literally 'to itself' (this should answer your query about a sentence wanting to say something above) — AmadeusD

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.

You can't simply read it in a way which is false, but meaningful by adding meaning to it, without sufficient reason. — AmadeusD

See my arguments that address that.

On it's face, it is plainly meaningless. — 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.

it seems all you're wanting to do is have the sentence refer to itself — 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.

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. — RussellA

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!

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. — RussellA

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".

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. — 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.

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. — 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.

However, we are not discussing what the sentence "this sentence contains fifty words" is inferred to mean, we are discussing what it literally means. — 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.

"This sentence contains fifty words" is true IFF this sentence contains fifty words. — RussellA

Oops, he did it again!

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. — RussellA

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.

"This sentence contains fifty words" is true IFF this sentence contains fifty words. — RussellA

About the 100th instance of RussellA ignoring that pronouns are contextual.

The word "truth" in the following would be redundant:
"This sentence contains fifty words" is true IFF "this sentence contains fifty words" — 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.

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. — RussellA

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.

"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. — RussellA

RussellA will just not quit ignoring that pronouns have context.

The subjective content of the sentence "this sentence contains five words" cannot determine the objective form of itself, ie, that it contains five words. — 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.

how can any one say that "this sentence contains five words" is true if no one knows which sentence is being referred to? — RussellA

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.

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". — RussellA

Truth only enters when self-reference disappears — 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.

Truth only enters when self-reference disappears — 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.

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. — RussellA

"This sentence" refers to "This sentence has five words".

If "this sentence contains five words" is referring to itself, then "this sentence contains five words" means that "this sentence contains five words". — RussellA

"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.

In other words, "X" means "X". — 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.

the law of identity states that each thing is identical with itself. — 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".

I agree that "X" means "X" — RussellA

RussellA agrees with whom, other than himself, about that?

"X" is "X". The meaning of "X" is not "X".

how can "X" be described as a meaningful sentence? — 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.