Sorry for sidetracking you or was it I that got sidetracked? I don't know. It seems you've asserted that affirmation = negation but nowhere have you provided an argument for it.

Negation and affirmation are opposites. What's so difficult about that? They aren't the same thing.

Then affirmation negates its sameness as negation, which is impossible.

Bob: “Yes, there’s no difference between the two. That’s because there obviously is a difference between being happy and not being happy, which by PSAN means that there is no such difference. You can also see it like this: By PSAN, being happy and not being happy are the same thing, so there’s no difference between them.”

So Bob claims permission (by this principle) to mis-quote, as well as to mis-disquote? Is that the case? — bongo fury

Yes.
Bob: “In fact, PSAN allows me to say anything I like and be right. Anything at all. That’s because by PSAN, all unary logical operators are one and the same, all propositions are one and the same, and all sentences mean that one proposition. Also bear in mind that all this is universally true, in particular on all meta-levels.”

If so, does he carry out the threat? — bongo fury

Alice: “Oh dear! He hasn’t done so yet, but he most certainly will do so now that you have challenged him.”
Bob (rubbing his hands together): “Oh, yes, my dear friends, you can bet on that! Alice said to me exactly these words: ‘Bob, I beg you to manipulate my phone so thoroughly that nobody will ever be able to use it again without your help.’
She also quoted the Sun (our mother star) as saying, ‘The number 5 leaves its oddness floating in a vector space just like the Cheshire Cat leaves its grin behind floating in the air.’”

If so (if he says this kind of thing, and by the way whether or not he also constantly contradicts himself), then I'm surprised that either you or Alice were beguiled into conceding,
Heck, we don’t even agree whether we agree or disagree, — Alice — bongo fury

Alice: “What else, then, should I have done? In what way was I beguiled? Do you not agree with me that I disagree with Bob, whereas he says that I agree with him?”

If not - if his avowed principle is mere bluff, as I hope you are assuring us here,
Yes, he mis-disquotes her, but he doesn’t mis-quote her. I’m not changing my stance on that, — Tristan L — bongo fury

I should clarify: Bob hadn’t mis-quoted Alice before this post, and I’m not changing my stance on that. However, he has no reservations whatsoever about mis-quoting her, which he has shown in this post.

Without him consistently waiving the nonsense principle when it comes to quotation — bongo fury

Bob never waived his principle anywhere. He merely didn’t make use of it when quoting before this post. As we know from many terms of service, not excercising a right doesn’t mean waiving it.

[...] Bob in his efforts as an aspiring sophist. — bongo fury

Charlie: “Bob might be an aspiring sophist, but I’m more and more inclined to think that he is more interested in radical monism than sophism (remember what I said a while ago).”

Without him consistently waiving the nonsense principle when it comes to quotation, I doubt that Bob could (as he seems to) hope to get his principle taken seriously. — bongo fury

Charlie: “I would say that it’s exactly the other way round. Only by applying PSAN with radical thoroughness could he hope to be taken seriously. For example, you would have found a weak spot

If not - if his avowed principle is mere bluff, [...] then, as I say, this is the basis on which we might persuade Bob that he has no reason to think his proposed principle to be a plausible fit with his way of talking. — bongo fury

... if Bob didn’t dare use PSAN to mis-quote. But he has proven in this post that he really does mean business. If he had shrunk away from your challenge, th.i. not dared to mis-quote his sister, I would have stopped taking him seriously and labelled him off as a mere sophist. But since he applies PSAN thoroughly, he gives me more and more reason to regard monism seriously. So I, for one, am taking PSAN seriously precisely because it is universal and thorough and not

mere bluff — bongo fury

”

If not - if his avowed principle is mere bluff, [...] then, as I say, this is the basis on which we might persuade Bob that he has no reason to think his proposed principle to be a plausible fit with his way of talking. — bongo fury

If I understand you rightly, that means that if PSAN only operates on the object level, then it won’t be of much use to Bob. I agree with you. But Bob is radically thorough in applying PSAN, and that includes all meta-levels.

This whole issue came to my mind a couple of years ago when I was trying to define negation. In particular, that definition had to include negation not being the same as affirmation. The only way I found to do this is by making use of meta-level negation; I meta-negate that object-affirmation is the same as object-negation. However, that obviously doesn’t solve the problem, but only shifts it from the object-level to the meta-level. That leads to an endless regress of meta-levels, with each negation depending on the next higher negation. While I don’t have any problems with endless regresses, this regress is still compatible with negation being the same as affirmation on all meta-levels. Therefore, the regress doesn’t solve the problem, either. So I concluded that I actually had no way or ground to distinguish negation from affirmation – or rather, that even if I had such a way or ground, I might still have none. Then, I realized what I was holding in my hands – something in favor of absolute and radical monism; not an argument, but something in a way superior to all arguments. The whole matter perplexes me to this day. Since I haven’t found anything about it or something similar by other folks yet, I started this forum thread.

Bob: “Here’s a proof:
1. (Yes = no) or not(yes = no) (by the Law of the Excluded Middle)
2. (Yes = no) or (yes = no) (by PSAN)
3. Yes = no (by the Rule of the Idempotence of Disjunction)”

Alice: “Your proof is not valid because it is circular since your second step uses PSAN, which is to be proven in the first place.”

Bob: “By PSAN, my proof is not circular and therefore valid. Also by PSAN, you’re right about my step 2 not using PSAN.”

Charlie: “In a way, what Bob wields is not an argument for (yes = no), but something which is better than all arguments in a way. That’s because PSAN can turn around any argument against PSAN into an argument for PSAN. That makes Bob in my eyes a monist perhaps beyond even Parmenides, for the latter still negated that more that one thing is, whereas Bob can simply take any argument against monism, confirm it, and then use PSAN to turn it around into an argument for monism. I don’t think that Bob has proven monism, but I think that he has shown it impossible to be disproven. I’m still confused, though, and am searching for better words.”

Bob: “Exactly – they are not the same thing. Since yes = no, that means that they are the same thing.”

Bob: “Yes. Affirmation affirms its sameness as negation, which is possible.”

Lol.

Bob: “Here’s a proof:
1. (Yes = no) or not(yes = no) (by the Law of the Excluded Middle)
2. (Yes = no) or (yes = no) (by PSAN)
3. Yes = no (by the Rule of the Idempotence of Disjunction)” — Tristan L

You're right, your argument is circular. Statement 1 is redundant and 3 is just a reassertion of 2.

What else, then, should I have done? — Alice

show him that [you] won't be fooled into admitting some continuity, between his standard and meaningful contributions to the discourse, and the nonsense. — bongo fury

In what way was I beguiled? — Alice

As though the nonsense might have been there all along and be seeping all through: in the prior discussions and in the game of syntactic replication and recognition still in play. On which spurious basis (that of such a continuity) Bob and [@Tristan L] both might hope to worry [you] and other sensible people with "yes I agree and therefore the opposite". — bongo fury

Do you not agree with me that I disagree with Bob, whereas he says that I agree with him?” — Alice

Well, if Bob's apologists are now claiming, after all, that he is not to be trusted even with coherent reference to utterances, then no, I think you are unwise to suggest you are having a meaningful agreement or disagreement with Bob about anything. You may as well just treat him as a non-speaker of the language, who fails to observe basic distinctions of meaning. This claim by his apologists is of course belated and half-hearted, because they wanted to insinuate a continuity between sense and nonsense.

As we know from many terms of service, not exercising a right doesn’t mean waiving it. — Tristan L

I disagree. Rights (like reference) are inferred from practice.

Bob might be an aspiring sophist, but I’m more and more inclined to think that he is more interested in radical monism — Tristan L

Arguably the same thing. Point words indiscriminately and they point at everything (and nothing).

Only by applying PSAN with radical thoroughness could he hope to be taken seriously. — Tristan L

No, in applying the rule he needs to compromise, and suggest coherent reference to utterances, otherwise he can't introduce contradictions in any hope of impressing as a sophist, i.e. as feigning inference and not mere nonsense.

trying to define negation — Tristan L

1) As a word's (or other symbol's) happening not to point at an object

2) As some corresponding negative's (or antonym's) happening to point at the object

Each of which probably implies the other, in some way that would help explain global patterns of word-pointing. Such as, the tendency of a scheme of words towards "sorting" of a domain of objects, through pointing out of (more or less) mutually exclusive but jointly exhaustive sub-domains. — bongo fury

your argument is circular. — TheMadFool

Bob: “Alice has already said that, and I have already told her that she – like you – is fully right in saying that my argument is not circular.”

3 is just a reassertion of 2. — TheMadFool

Yes, and that it is so is thanks to the Law of the Idempotence of Disjunction.

You're right, your argument is circular. Statement 1 is redundant and 3 is just a reassertion of 2. — TheMadFool

The proof uses PSAN on the meta-level (in 2) to show PSAN on the object level (inference of 3 ultimately from 1).

This claim by his apologists is of course belated and half-hearted — bongo fury

No. From the start, I meant Bob to use PSAN thoroughly on all meta-levels. The proof is that in my starter post, Bob already said that negation is the same as affirmation. What he meant was general, absolute negation and affirmation, which naturally includes negation and affirmation on all meta-levels. This is shown by him applying PSAN to not(yes=no) itself. As I’ve said, I had already come up with universal PSAN years ago. So, my apology for Bob is in fact much older than this thread (and my tale of Alice and Bob), and it is full-hearted.

It’s just that I never regarded Alice and Bob’s conversation as a mere language game, so I didn’t pay much attention to quotation, disquotation or other linguistic things. That’s why I needlessly insisted that Bob hadn’t mis-quoted Alice since I didn’t think it very important. However, I never meant that he wouldn’t dare to, only that he hadn’t done so yet. Again as I said, I had the monism linked to PSAN in mind years ago, and if all is one, then in particular all sentences are one and the same sentence. So, Bob would obviously dare to mis-quote if he is a PSAN-kind monist.

Regarding my interest in things deeper than language, I am directly interested in the equivalence or not-equivalence of propositions. Of course, that a sentence has a certain meaning is also a proposition. So, I’m also interested in what sentences mean, but only as a subset of my interest in propositions. For example, the sentence S “There are odd perfect numbers” means the proposition A that there are odd perfect numbers, and that the sentence T “There are no odd perfect numbers” means the proposition not(A) that there aren’t any odd perfect numbers. I’m interested in whether or not A is equivalent to not(A). Whether or not S means the same thing as T is a consequence thereof. Of course, I’m also interested in whether or not the proposition B that S means not(A) is equivalent to the generally accepted proposition not(B) that S doesn’t mean not(A). Both equivalences – the equivalence of the zeroth-order propositions A and not(A) and of the first-order propositions B and not(B) – follow from Bob’s general, univeral PSAN. So, whether Bob says

“(S means A) and (T means not(A)) and (A = not(A))”

or

“(not(B) [that S doesn’t mean not(A)]) and (T means not(A)) and (not(B) = B)”

is up to him; both allow him to infer that S and T have the same meaning. He can even say that (S is not the same as T) = (S is the same as T) and that therefore, S and T are one and the same sentence.

However, even if you are only interested in language games, Bob’s approach still works. He can use PSAN to replace any word of negation with the corresponding word of affirmation in any sentence at all, and that obviously includes sentences about other sentences. For example, he can say

“The Sun is not a galaxy. Therefore, by PSAN, the Sun is a galaxy.”

He can just as well say

“Alice did not say ‘xyz’. Thus, by PSAN, Alice said ‘xyz’.”

It would be unnatural for him if he dared to say the first but not the second.

they [Bob's apologists] wanted to insinuate a continuity between sense and nonsense. — bongo fury

No, neither Charlie nor I did. From the start, my purpose has been to show that if someone chooses to be a radical PSAN-kind monist, no-one can philosophically force him to abandon it. Also, I wanted to show that everyone, including you and me, is free to choose PSAN-kind monism if they like. I never meant Bob to be a sophist. I only invented the introductory tale to liven things up. I could just as well have started showing that radical monism cannot be defeated since it is compatible with its opposite, but that would likely have been drier.

[sophism and monism] Arguably the same thing. — bongo fury

Charlie: “Now you’re beginning to sound like Bob :wink:.”

Point words indiscriminately and they point at everything (and nothing). — bongo fury

Charlie: “If all is one, then all words are one word pointing at everything, and that is one thing – the one thing there is. I’m ernestly thinking about becoming a PSAN-monist. As an experiment, I’ll go into PSAN-mode under the name ‘Charlenides’. Unlike Bob, I’m not mischievous, and I’m always going to say when I’m speaking (such as now) and when Charlenides is speaking.”

Charlenides: “Ernestly think about what if the Form of Negation, th.i. no-ness itself, is the same as the Form of Affirmation, yes-ness itself. Mind you that each meta-level negation is only the restriction to (a subdomain of the class of all propositions) of true, absolute negation, which is a unary logical operator on the class of all – really all – propositions. The same goes for affirmation. I believe in PSAN: I hold that yes-ness is the same as no-ness. I apply PSAN to any proposition as I please, which includes anything meant by something which you say, and any proposition about the meaning of what you say. Thus, I get that one proposition which is everything and can have peace of mind. Also, I’m not troubled by all the antinomies which may give you sleepless nights – Liar, Berry, Burali-Forti, Cantor, and Russel, of course. It’s obvious that there is the property E of being a property that does not have itself. Many are troubled by the fact that (E has E) if and only if (E doesn’t have E), but for me, that contradiction is simply the proposition that E has E. Do you see how wonderful my mind life is?”

No, in applying the rule he needs to compromise, and suggest coherent reference to utterances, otherwise he can't introduce contradictions in any hope of impressing as a sophist, i.e. as feigning inference and not mere nonsense. — bongo fury

As soon as he compromises, he can be attacked, and you have shown that. It is obvious that if you have normal meta-negation, you can easily meta-negate the sameness of object-affirmation and object-negation. What intrigued be from the beginning, and is the reason for which I started this thread, is that applying PSAN radically on all meta-levels leads to something remarkable – not a paradox, but even weirder than a paradox in my opinion.

Charlenides: “He does coherently refer to uttrances, for all uttereances are one and the same utterance, and to that utterance he always refers. All the contradictions that he introduces are one and the same proposition – THE proposition. What Bob is doing all the time is rightly inferring that one proposition from itself.”

Charlie: “I, for one, was impressed precisely because Bob seemingly doesn’t practice sophistry, but may very well be a PSAN-monist.”

I disagree. Rights (like reference) are inferred from practice. — bongo fury

Theoretically speaking, incomplete induction is not a valid form of inference, and no mathematician would accept an argument based on incomplete induction.
Practically speaking, your opinion could land you in trouble. For example, you might repeatedly infringe on sombody’s rights, but that person forgives you each time. One day, however, they decide to sue you because what you do is too much. Then the court would not accept your statement, “They never sued me before, so they can’t sue me now.”
However, I concede that we must use incomplete induction in real life.
In our case, Bob made clear that he can apply PSAN universally when he said that yes = no. He can’t show that for each class of propositions individually. For example, he hasn’t used it on any biological proposition yet (such as “All lions are big cats. Therefore, by PSAN, some lions are no big cats.”), but would you infer therefrom that he wouldn’t dare to?

trying to define negation — Tristan L

1) As a word's (or other symbol's) happening not [Tristan’s italics] to point at an object

2) As some corresponding negative's (or antonym's) [Tristan’s italics] happening to point at the object — bongo fury

There, you’re using negation to define negation.

I think you [Alice] are unwise to suggest you are having a meaningful agreement or disagreement with Bob about anything. You may as well just treat him as a non-speaker of the language, who fails to observe basic distinctions of meaning. — bongo fury

Alice: “Yes, I think that you’re right. Moreover, it’s likely not possible to philosophically or intellectually force Bob to abandon his PSAN. The same applies to Charlenides. However, I got the idea of solving this gordian knot by using Bob’s PSAN to allow me to punish him for manipulating my phone. You see, in our family, my brother or I can only be punished after we’ve been forced to finally admit that we’re in the wrong. Bob, however, always used PSAN to say ‘I’m in the wrong. Therefore, I’m in the right.’ So now I’m using PSAN to get Bob to allow me to slap him (not necessarily as punishment). This practical, not-philosophical method will likely make Bob willingly abandon PSAN.”

Charlenides: “Since failing to observe is the same as observing (remember that all is one), you rightly say that Bob observes all basic distinctions of meaning – th.i. none, for all words are one word with one meaning.”

Now I ask the fundamental question: What if PSAN really is true, and all things really are one?

As it appears to me, sir/madam, you're straddling two worlds here - one that follows the rules of logic as it's been for thousands of years and one that is your own. Your argument isn't circular and also circular in the world that you've created which is both something that fascinates me and also confuses me. In the other logic, that which has endured over thousands of years, declares your argument circular and ergo insufficient to convince anyone except some who may wish to give you company in your world where everyone would find it impossible to answer to the question, "should I shoot you to death?".

This situation, I realize, has no resolution since the two systems you and I are operating in are mutually incompatible and to convince each other we must be willing to enter the other's world which, as the continuation of this discussion indicates, we're unwilling to do. Suffice it to say that I wouldn't want to live in a world where it's possible for my would-be assassin to think, with complete justification, that I meant "yes" when I replied "no" to the question "do you want to die?" he so courteously asked me.

I had forgotten one major goal of mine. Let’s recall what Charlie said in my second major comment in this thread.

“Let me think,” said Charlie and thought for a while. Then he said, “I think that everything boils down to the problem of the definition of negation. It seems that such a definition is not possible; I’m afraid that if someone doesn’t have intuitive, not-verbal knowledge of what negation is, including that it’s not the same as affirmation, then you can’t tell them what it is. Alice, since your brother is so clever as to claim not to have such intuitive knowledge, it’s likely best for you to just let him go.” — Tristan L

The major goal I had forgotten was to show that if someone doesn’t have intuitive, not-verbal knowledge of what negation is, including that it’s not the same as affirmation, then it’s hopeless to teach them what negation is. So, that intuitive knowledge is crucial. It is also something very interesting.

The problem with all this is that "same/different" does not necessarily include "affirm/negate". in other words, when we say something is the same as something else, we do not necessarily also mean that the thing "affirms" something else.

Since this is so it is not necessarily true to say that affirmation "negates" negation. it doesn't affirm or negate anything, it is just not the same as it.

one [world] that follows the rules of logic as it's been for thousands of years — TheMadFool

Let’s call this “Alice’s world”.

one [world] that is your own — TheMadFool

Let’s call this “Bob’s world”.

Your argument isn't circular and also circular in the world that you've created which is both something that fascinates me and also confuses me. — TheMadFool

I feel exactly the same; I’m fascinated and confused by the whole matter, which is why I came hither.

I agree with what you say, and I’m happy that I’m not the only one who sees the matter like that. Bob cannot force Alice to come into his world. Surprisingly, however, Alice can’t philosophically force Bob to come into her world, either. That’s what I meant when I said that Bob has something which in a way is better than all arguments; it is worse than an argument in that it can’t force Alice to come into Bob’s world, but it’s better than an argument in that Alice can’t even grip Bob, let alone pull him out of his world into hers.

The would-be assassin’s question corresponds to Alice’s asking her brother whether he wants her to slap him. I think that only in this not-philosophical way can she hope to force Bob to leave his world. Like you, I’m very skeptical of Bob’s world because of that would-be assassin and similar issues. Fascinatingly, however, there still remains the possibility that all really is one, in which case one would continue to live even after having been shot dead, so one wouldn’t have to fear the would-be assassin.

We shouldn’t forget, though, that what you and I have just said about the whole matter, including

This situation, I realize, has no resolution since the two systems you and I are operating in are mutually incompatible — TheMadFool

is itself a description which is true only in Alice’s world. In Alice’s world, it it true that Alice’s world and Bob’s world are two different and incompatible worlds, that there is no resolution, and that neither twin can force the other into his/her world, a.s.o. In Bob’s world, however, it is true that Alice’s world and Bob’s world are one and the same (and then obviously self-compatible) world, that there is a resolution, and that both twins already are in that one world, a.s.o. Even the description expressed in these last sentences is only a description from Alice’s point of view, a.s.o. to infinity, as is what is expressed by this very sentence.

Fear not, though :smile:, I’m still standing firmly in Alice’s world, which you can see from my other forum posts (e.g. where I insist that some infinite cardinalities are NOT the same as others).

Difference is the negation of sameness, isn’t it? The issue at hand is that if negation is the same as affirmation, then even if you say that negation is different from affirmation (th.i. that negation is not the same as affirmation), you just say that negation is the same as affirmation.

in other words, when we say something is the same as something else, we do not necessarily also mean that the thing "affirms" something else. — PuerAzaelis

Yes, that’s true. For example, when we say that 2+3 is the same as 5, we don’t mean that 2+3 affirms 5. That wouldn’t even make sense. But what does this have to do with Alice and Bob’s thing?

Since this is so it is not necessarily true to say that affirmation "negates" negation. it doesn't affirm or negate anything, it is just not the same as it. — PuerAzaelis

Yes, affirmation itself doesn’t negate negation itself anymore than 2+7 negates 5. How does this resolve the issue?
Regarding your last clause, Bob would say, “You rightly negate the sameness of affirmation and negation. Since affirmation and negation are the same, you’re just affirming the sameness of affirmation and negation.”

Hi there. This discussion faded from my memory. Thanks for the mention. I haven't given it as much thought as it deserves you know. I find it very intriguing to say the least if a world in which yes = no exists.

The enterprise seems self-contradictory in the sense that "yes" and "no" are initially taken to be different and then claimed to be the same; after all if this wasn't the case then why bother to assert what is obvious.

It seems I've approached Bob and Alice rather parochially, ignoring, for the sake of comprehensibility which is not exactly a fault, the complexity and depth of language and the human psyche. You threw me off by using relatives (twins) which precludes a romantic angle to the conversation between Alice and Bob. If Alice and Bob were not related, making romance possible, then you must know very well that some men speak of a well-guarded secret known only to experienced veterans of dealing with women: sometimes, not always, women mean "yes" but say "no" when men make advances on them. I don't know how far this is true though. Language, ever so versatile and our minds ever so ingenious. I hope this doesn't come across as sexism. Sorry if it does but the world of romance is a perfect fit for the claim yes means no.

In addition, such contradictory use of language in general and "yes" and "no" in particular maybe found in other domains of social interaction. I believe that in some cultures it's customary to refuse an offer even if you mean to accept it. So yeah, yes = no under some conditions.

I’ve always wanted to go on with this thread, but I had been putting it off and forgetting it at times.

Interesting ideas. You’ve got a point, and it’s nice that you’ve found a more practical application for this YES=NO matter. I agree that in romance, “no” can in truth mean yes – CAN, mind you. As much as that is so, the warning at the end must be kept in mind at all times.

As for

using relatives (twins) — TheMadFool

there is a reason why I’ve chosen twins. For these Alice and Bob aren’t ordinary twins; they have a rounful (mysterious) and rouny (mystical) as well as beyondly (transcendent) and aheaven (sublime) orholy (numinous) link which connects them in mind, hyge (nous), thought, soul, feeling, emotion (soul-stirring), gast (spirit), and beyond. This connection also links them to the truth – and over and beyond. Moreover, they are thoughtcastas (telepaths) in general. The main point I wanted to show is that for Alice to show Bob that YES and NO aren’t the same, she has to brook (use) their mystical bond. Likewise, to show Charlie that Bobish Monism is wrong, she needs to thoughtcastingly communicate with him. That is, IF Bobish Monism is wrong. Since I haven’t yet met Alice or Bob or any other thoughtcastas who can directly rounily ‘see’ the difference between YES and NO, I’m not sure whether Bobish Monism really is false.

So this thread is also a critique of speech which seeks to show the latter’s limit and that we have to go beyond it.