Is negation the same as affirmation?
Hello everyone,
Let me tell you a rather weird and confusing tale about agreement and disagreement in my first post on this forum.
Charlie was at Alice and Bob’s place celebrating their birthday. Charlie had given the twins a trampoline as a birthday gift. Alice was the first to try it. To prevent her smartphone from falling out of her pocket while jumping, she gave it to Bob with the warning, “Just keep my phone safe. I do NOT want you to play around with it.”
“Okey dokey!” said Bob.
Alice got onto the trampoline and began jumping. Charlie went off to a nearby table to chat a little with Alice and Bob’s parents.
Now Bob is quite a geeky kid, so as soon as he was out of Alice and Charlie’s attention, he turned on his sister’s phone and started rooting it. He was so deeply immersed in his activity that he didn’t realize when the springs stopped making sounds and Alice said, “It’s your turn now.” He only looked up when an upset Alice stood right before him and poked his shoulder with her finger.
“What are you doing?” she asked angrily.
“Um, tweaking your phone,” answered Bob in an innocent-sounding tone but with a mischievous twinkle in his eyes.
“Didn’t I tell you not to mess around with my phone?” said Alice with a raised voice.
“Yes, exactly, and here I am playing around with your phone. I did precisely what you wanted me to do.”
“What?” asked Alice even more loudly.
The loud voices caught Charlie’s attention.
“Don’t worry, kid,” assured him Alice and Bob’s mother, “they’re always bickering. They’re twins after all.”
“But it sounds a little intense this time,” said Charlie. “I’ll check what’s wrong.”
Charlie went back to the trampoline and asked, “What’s going on?”
“We’re having an argument,” answered Alice. “We don’t agree whether or not Bob listened to what he should do with my phone and what he shouldn’t.”
“Exactly,” chimed in Bob. “We agree that I did what Alice wanted me to do.”
Alice retorted, “We don’t even agree on whether we agree.”
“That’s right. We agree perfectly that we agree,” said Bob.
Charlie’s face showed an expression of confusion. “So... what did you, Alice, say that your brother should or shouldn’t do, and what did you, Bob, do or not do?” he asked.
“I told him to keep my phone safe and not play with it,” answered Alice.
“And I did just that; I kept her phone safe and rooted it,” answered Bob.
Charlie was even more bewildered. “I don’t understand. She told you not to manipulate it, yet here you are, proud that you have rooted it.”
“It’s very simple,” said Bob. “Alice said that she did not want me to play with her phone, and since negation is the same as affirmation, that means that she wanted me to play with her phone, which is what I did.”
Alice put her hands on her hips and shook her head. “No, affirmation most certainly is NOT the same as negation.”
Bob nodded. “Yes, affirmation is indeed not the same as negation, which means that affirmation is the same as negation. You negate the sameness of negation and affirmation, and since negation and affirmation are the same, you affirm the sameness of negation and affirmation.”
Alice and Bob’s loud argument made their parents come over, too.
“Charlie’s right,” said their father. “You two really are having a particularly loud discussion today. Why?”
“No wonder,” said Alice, scoffing. “Not only did Bob do exactly what I didn’t want him to do, we don’t even agree whether or not that’s the case. Heck, we don’t even agree whether we agree or disagree, including the point expressed by this very sentence as well as the one expressed by what Bob is about to say. Most importantly, we don’t agree whether affirmation is the same as negation. Like every normal person, I’m sure that affirmation and negation are not the same. Bob, on the other hand, thinks that they are the same. Could you please help me make that clear to him?”
Bob yawned. “Dad, you see that our discusion is full of nauseating agreement, though that might be expected from a pair of twins. Alice simply agrees with me on every single point, including the point which is expressed by this very sentence as well as the one expressed by what Alice just said. Most importantly, we agree perfectly that affirmation is the same as negation. Like every normal person, I’m sure that affirmation and negation are not the same, which is to say that they are the same. Alice also thinks that. I’m already very clear on the whole matter.”
Charlie and his two friends’ parents only shrugged. They were all very confused, and the twins’ explanation left none the wiser.
Can you help clear up our friend Charlie’s confusion?
Regards,
???????????
Let me tell you a rather weird and confusing tale about agreement and disagreement in my first post on this forum.
Charlie was at Alice and Bob’s place celebrating their birthday. Charlie had given the twins a trampoline as a birthday gift. Alice was the first to try it. To prevent her smartphone from falling out of her pocket while jumping, she gave it to Bob with the warning, “Just keep my phone safe. I do NOT want you to play around with it.”
“Okey dokey!” said Bob.
Alice got onto the trampoline and began jumping. Charlie went off to a nearby table to chat a little with Alice and Bob’s parents.
Now Bob is quite a geeky kid, so as soon as he was out of Alice and Charlie’s attention, he turned on his sister’s phone and started rooting it. He was so deeply immersed in his activity that he didn’t realize when the springs stopped making sounds and Alice said, “It’s your turn now.” He only looked up when an upset Alice stood right before him and poked his shoulder with her finger.
“What are you doing?” she asked angrily.
“Um, tweaking your phone,” answered Bob in an innocent-sounding tone but with a mischievous twinkle in his eyes.
“Didn’t I tell you not to mess around with my phone?” said Alice with a raised voice.
“Yes, exactly, and here I am playing around with your phone. I did precisely what you wanted me to do.”
“What?” asked Alice even more loudly.
The loud voices caught Charlie’s attention.
“Don’t worry, kid,” assured him Alice and Bob’s mother, “they’re always bickering. They’re twins after all.”
“But it sounds a little intense this time,” said Charlie. “I’ll check what’s wrong.”
Charlie went back to the trampoline and asked, “What’s going on?”
“We’re having an argument,” answered Alice. “We don’t agree whether or not Bob listened to what he should do with my phone and what he shouldn’t.”
“Exactly,” chimed in Bob. “We agree that I did what Alice wanted me to do.”
Alice retorted, “We don’t even agree on whether we agree.”
“That’s right. We agree perfectly that we agree,” said Bob.
Charlie’s face showed an expression of confusion. “So... what did you, Alice, say that your brother should or shouldn’t do, and what did you, Bob, do or not do?” he asked.
“I told him to keep my phone safe and not play with it,” answered Alice.
“And I did just that; I kept her phone safe and rooted it,” answered Bob.
Charlie was even more bewildered. “I don’t understand. She told you not to manipulate it, yet here you are, proud that you have rooted it.”
“It’s very simple,” said Bob. “Alice said that she did not want me to play with her phone, and since negation is the same as affirmation, that means that she wanted me to play with her phone, which is what I did.”
Alice put her hands on her hips and shook her head. “No, affirmation most certainly is NOT the same as negation.”
Bob nodded. “Yes, affirmation is indeed not the same as negation, which means that affirmation is the same as negation. You negate the sameness of negation and affirmation, and since negation and affirmation are the same, you affirm the sameness of negation and affirmation.”
Alice and Bob’s loud argument made their parents come over, too.
“Charlie’s right,” said their father. “You two really are having a particularly loud discussion today. Why?”
“No wonder,” said Alice, scoffing. “Not only did Bob do exactly what I didn’t want him to do, we don’t even agree whether or not that’s the case. Heck, we don’t even agree whether we agree or disagree, including the point expressed by this very sentence as well as the one expressed by what Bob is about to say. Most importantly, we don’t agree whether affirmation is the same as negation. Like every normal person, I’m sure that affirmation and negation are not the same. Bob, on the other hand, thinks that they are the same. Could you please help me make that clear to him?”
Bob yawned. “Dad, you see that our discusion is full of nauseating agreement, though that might be expected from a pair of twins. Alice simply agrees with me on every single point, including the point which is expressed by this very sentence as well as the one expressed by what Alice just said. Most importantly, we agree perfectly that affirmation is the same as negation. Like every normal person, I’m sure that affirmation and negation are not the same, which is to say that they are the same. Alice also thinks that. I’m already very clear on the whole matter.”
Charlie and his two friends’ parents only shrugged. They were all very confused, and the twins’ explanation left none the wiser.
Can you help clear up our friend Charlie’s confusion?
Regards,
???????????
Comments (51)
:up:
Also :up:
The mother of the twins turned to Charlie and asked, “What are we to make of this?”
“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.”
“You’re right, Charlie, it’s likely no use continuing this futile endeavor of teaching Bob about negation, but your explanation is also futile for him, for I know exactly what he is going to say about it,” said Alice and shot an angry look at her twin.
Bob smiled smugly. “You’re right, Charlie. I’m clever enough to claim having intuitive knowledge of negation and that it’s the same as affirmation, and I’m even smart enough to actually have such intuitive knowledge.” Grinning, he gave the phone back to Alice and said, “Dear sister, here’s your phone, which I’ve manipulated so greatly that you can still use it as before. Look what a good brother I am, always doing exactly what you want.”
Charlie forwarded your question to the twins, and here are their answers:
Alice: “Of course it would matter to me. If you said ‘yes, negation is the same as affirmation’, you would be very wrong, but if you said ‘no, negation is not the same as affirmation’, you would be right. Since it’s important to me that folks say what is true and not what is untrue, which one of the two choices you say matters a lot to me.”
Bob: “Of course it would matter to me. Whether you say the one or the other, you’re saying the same thing. So, it does not matter to me which one you say. This means that it matters to me which one you say.”
What should we make of that?
Quoting Tristan L
In what sense does it matter to you Bob? Either affirmation is the same as negation or it it's not. Are you in any way negating the latter and affirming the former? It must be that and if so, what are the senses in which you use them?
Actually, to speak in Bob's favor, I believe paraconsistent logic has room for Bob's "odd" claim; after all (p & ~p) is completely ok in that realm where I can affirm and deny propositions with no cost to my sanity.
Bob: “It matters to me in the sense that I would be happy if you say that affirmation and negation are the same, and not happy otherwise. By the way, this means that I’d be happy in both cases. I’ll even prove that what you say matters to me:
1. It matters to me, or it doesn’t. (by the Law of the Excluded Middle)
2. If it matters to me, then it matters to me. (by the Law of Self-Implication)
3. If it doesn’t matter to me, then it matters to me. (by the Law of Self-Implication and the Principle of the Sameness of Affirmation and Negation)
4. It matters to me, or it matters to me. (by the Constructive Dilemma and and (1.), (2.) and (3.))
5. It matters to me. (by (4.) and the Rule of the Idempotence of Disjunction)
Thus, we can easily see that it certainly matters to me which of the two things you say.”
Quoting TheMadFool
Bob: “Why, of course! You say that
a) Affirmation is the same as negation or it isn’t, but not both.
By applying the Principle of the Sameness of Affirmation and Negation to your second use of negation, (a) is equivalent to
b) Affirmation is the same as negation or it isn’t, and both of these are the case.
By applying the Principle of the Sameness of Affirmation and Negation again, this time to your first use of negation, (b) is equivalent to
c) Affirmation is the same as negation or affirmation is the same as negation, and both of these are the case.
By the Rules of the Idempotence of Disjunction and Conjunction, (c) is equivalent to
d) Affirmation is the same as negation.
So by saying that affirmation either is the same as negation or it is not, you simply mean that affirmation is the same as negation. Yeah, I fully agree.”
Quoting TheMadFool
Bob: “Yes, I’m affirming the former and negating the latter, which by the Principle of the Sameness of Affirmation and Negation means that I’m affirming both the former and the latter, and that I’m negating the former and affirming the latter, and that I’m negating both the former and the latter. This means that I’m doing none of these things, that is, all of them.”
Quoting TheMadFool
Bob: “I’m using words such as “yes”, “affirmation”, “no”, “not” and “negation” to refer to affirmation, that is, to negation. Affirmation is the logical operation which sends each proposition to itself, and negation is the logical operation which sends each proposition to its contradictory opposite, that is, to itself. Obviously, then, the two are one and the same. In particular, that’s the way I use affirmation and negation in the sentences ‘yes, affirmation is the same as negation’ and ‘no, affirmation is not the same as negation’.”
Alice: “Charlie, please tell your friends TheMadFool and Tristan that I apologize for my brother being so unbearable today.”
Quoting TheMadFool
Charlie: “That sounds like an interesting idea. Could paraconsistent logic really deal with Bob’s claim that affirmation is one and the same thing as negation?”
I have the same question as Charlie. Furthermore, what do you think of Bob’s answers?
The latter, so I don't think she needed to admit, in an open ended way,
Quoting Tristan L
when that apparently meant disagreement about "points expressed",
Quoting Tristan L
... but not necessarily about the sentences doing the expressing. Bob gave every appearance of being prepared to agree (in a non-surprising way) about these. About which phonetic sequences agree with (replicate, quote) which others, and about which ones disagree with (fail to quote) which others. So there was no cause for dismay. No need to grant to Bob the degree and kind of disruption he claimed.
After all, it was only by observing - non-pathologically - such syntactic game rules that he fooled anybody into thinking that any rules of logical inference had been set in some pathological motion. As opposed to having been willfully or unfortunately (but not paradoxically) unobservable for him.
I.e. the implication that we have already shown ourselves vulnerable to accepting or colluding with misquotation is the sleight of hand / misdirection on offer, I think.
I.e. Bob's sophistry consists in trying to imply that his daft self-contradiction undermines all of the agreement and cooperation assumed in the discourse. But daring to confuse misinterpretation with misquotation is where it gets badly exposed.
This comment of mine is my first answer to . I’d like us to talk about my next comment only later, that is, after I’ve made sure that I understand you correctly.
Quoting bongo fury
I think that you’re right.
Quoting bongo fury
Yes.
(1)
Quoting bongo fury
If I understand you correctly, you’re saying that Bob is willfully using a not-standard interpretation of speech items which sends words such as “negation” to affirmation, whereas most folks, including you, me, Charlie, and Alice, use an interpretation which sends words such as “negation” to negation rather than affirmation. It’s like I choose to interpret the English deedword “to become” to mean getting/receiving rather than beginning to be, which is the meaning of German deedword “zu bekommen”.
Quoting bongo fury
So, the right course of action for Alice is to refuse to continue talking with Bob as long as he doesn’t use words with the same meaning as she does. Better yet, she should somehow get Bob to use the standard interpretation.
Quoting bongo fury
This means that Bob tries to make the others believe that their talking with him and with each other breaks down because of what he says, when in fact he’s only using a not-standard interpretation of speech.
Quoting bongo fury
That is, Alice can expose Bob by pointing out that he applies a not-standard interpretation to her sentences.
(/1)
Have I interpreted you in the right way between (1) and (/1)?
If yes, then I think that you’re right. Charlie told Alice my interpretation of your remedy.
Alice: “Ok, let’s try it, but I know Bob only too well. Bob, you’re using an interpretation of speech which is different from the one which I use. That isn’t lawful. You send the things which I say to things other than the ones which I mean. You’re not interpreting me correctly.”
Bob: “Yeah, you’re right, I’m using an interpretation which is not the same as yours, which in certainly not lawful. Therefore, what I say is nothing but invalid and misleading sophistry. That is to say that my interpretation is the same as yours, which is fully lawful. Therefore, what I say in pure, meaningful, valid, and not misleading truth-telling.”
Charlie: “Tristan, if you have understood our friend correctly and told me what he really means, then what he says sounds very reasonable and would likely be true in other similar cases. However, with Bob’s thoroughness, I’m not so sure here. He got me thinking that all of this may have to do nothing with speech. Maybe – just maybe – negation itself is really one and the same thing as affirmation. Trust me, I’m not mischievous like Bob, and I use the same interpretation as you. Then, I remembered an old philospher. They called him Parmenides, and he held that all is one. Now to get maniness, you need negation so as to negate sameness, but Bob’s move seems to be able to absorb all power of negation and collapse everything into one – affirmation, negation, or whatever you like to call it.”
Alice: “Wait a minute, Charlie! You said that I should just let Bob go, but I think that I may yet get the better of him.”
Turning to Bob, she said: “Bob, you want me to give you a really hefty slap on the face, don’t you?”
More importantly she needs to show him that she won't be fooled into admitting some continuity, between his standard and meaningful contributions to the discourse, and the nonsense.
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 you both might hope to worry Alice and other sensible people with "yes I agree and therefore the opposite". No, either you don't agree, or you don't infer the opposite. Look at your syntax (which is semantics of a kind, a classification) if you need reminding of your ability to make sense. (Alice can say this, and not have to threaten to slap anyone, which I guess was to make the same point, i.e. that Bob understands better than he pretends?)
So you will not be happy if I assert that affirmation and negation do not mean the same thing. So, what sense does the "not" have in the statement you made above? Clearly it's true that there's a difference between you being happy and you not being happy and the distinction that's required to make sense of that is affirmation is NOT the same as negation.
Please, explain this to me as primitevely as possible. Because it seems like I got lost.
What would a Hegelian say about this whole matter?
First off: I myself am quite confused by my own question.
One way to see it goes thus: Bob claims that words or phrases like “no”, “not”, “is not” and “does not” have the same meaning as words or phrases like “yes”, “is” and “does”. He also applies this very thoroughly, so that even if Alice says, “The word ‘yes’ does not mean the same thing as the word ‘no’”, Bob will take that sentece, replace “does not” with “does”, and then claim that the resulting sentence “The word ‘yes’ does mean the same thing as the word ‘no’” has the same meaning as the original one which Alice said. Therefore, he’ll claim to fully agree with her.
In the sentence you have quoted, he says that since negation is the same as affirmation, the phrase “is not” means the same thing as the word “is”. Therefore, he argues, the sentence “Affirmation is not the same as negation” means the same thing as the sentence “Affirmation is the same as negation”. Since Alice said the former and he the latter, he then tells her “Yes, I agree with you.”
Imagine that Bob really doesn’t know what negation is and has been taught since young that all the words which we use for negating are used for affirming. How would you teach Bob about negation?
Another view is the one expressed by Charlie. He points out that if affirmation really is one and the same thing as negation, then even if you negate that statement, you actually affirm it. In Bob’s attempt to escape scolding or punishment for manipulating his sister’s phone against her will, Charlie thus sees a much deeper thing – a quite unique argument for radical monism, one which even takes all arguments against monism and turns them into arguments for monism.
If you still have a question, feel free to ask.
Quoting TheMadFool
Bob: “It means the same as ‘yes’.”
Quoting TheMadFool
Bob: “Precisely. It’s true that there is no difference between my being happy and my not being happy. That’s why ...”
Quoting TheMadFool
Bob: “... I don’t need to make any distinction. But that’s just what you’re saying – namely, that I need to make a distinction, th.i. (that is) an equivocation. That equivocation is realizing that affirmation very much IS the same as negation, and it is what allows us to make sense of the fact that there is no difference between my happiness and my unhappiness.”
Alice can say that to make that point. She can also say it to beat Bob at his own game and get him to ‘willingly’ let her slap him for rooting her phone. That way, she has an excuse to avoid getting punished herself by their parents, who would otherwise likely not be okay with her self-righteousness.
Quoting A Seagull
Do you mean that Alice did it for the reason I have just mentioned rather than the one which bongo fury has in mind?
Quoting bongo fury
But he claims that certain pairs of sentences have the same meaning which Alice, you and I think have opposite meanings, doesn’t he?
Quoting bongo fury
Quoting bongo fury
Where and how exactly have we shown ourselves vulnerable to accepting or colluding with misquotation, and where and how precisely is she admitting continuity?
Quoting bongo fury
I still don’t fully understand exactly what you mean. Could you please elaborate?
Regarding Bob, he’s freely interchanging affirming words with negating ones. Even if you tell him that he should not do that, he will exchange precisely that “should not” with a “should”. How can we expose him?
Quoting bongo fury
Bob: “Exactamente; one both agrees and infers the opposite.”
Quoting bongo fury
What use would that have?
Quoting bongo fury
What do you mean by that?
Quoting Tristan L
Yes, he mis-disquotes Alice, but does he mis-quote her? Are you changing your stance on that?
You are disagreeing with me. In what sense are you disagreeing with me then? What meaning does the "don't" in your statement above have?
Yes, he mis-disquotes her, but he doesn’t mis-quote her. I’m not changing my stance on that, for I agree with you on that point, as does Alice. However, let’s hear what Bob’s got to say.
Bob: “Exactly, I mis-interpret Alice, which means that I interpret her in the right way. In fact, the words ‘mis-disquote’ and ‘mis-interpret’ mean not interpreting in the right way, th.i. interpreting in the right way. By the way, I’m very well aware that the Principle of the Sameness of Affirmation and Negation (PSAN) applies on the object-logical level and all meta-logical levels, too. And if I say ‘all’, I really mean ALL.”
Bob: “Yes, I’m indeed disagreeing with you, th.i. agreeing with you. I’ve already said that:
Quoting Tristan L
I’m disagreeing with you in the sense that I negate something (namely having to make a distinction) which you affirm. In other words, I’m agreeing with you in the sense that I affirm something (namely having to make a distinction) which you also affirm. The ‘don’t’ in my stament
Quoting Tristan L
above means exactly the same as ‘do’.
By the way, as I’ve already told bongo fury, I’m very well aware that the Principle of the Sameness of Affirmation and Negation (PSAN) applies on the object-logical level and all meta-logical levels, too. And if I say ‘all’, I really mean ALL.”
So Bob claims permission (by this principle) to mis-quote, as well as to mis-disquote? Is that the case?
If so, does he carry out the threat? Does he say things like,
?
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,
Quoting Alice
... thus needlessly encouraging Bob in his efforts as an aspiring sophist. 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.
If not - if his avowed principle is mere bluff, as I hope you are assuring us here,
Quoting Tristan L
... 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.
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.”
Quoting 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.”
Quoting 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.’”
Quoting 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?”
Quoting 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.
Quoting 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.
Quoting 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).”
Quoting 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
Quoting 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
Quoting bongo fury”
Quoting 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.”
You're right, your argument is circular. Statement 1 is redundant and 3 is just a reassertion of 2.
Quoting bongo fury
Quoting Alice
Quoting bongo fury
Quoting 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.
Quoting Tristan L
I disagree. Rights (like reference) are inferred from practice.
Quoting Tristan L
Arguably the same thing. Point words indiscriminately and they point at everything (and nothing).
Quoting 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.
Quoting Tristan L
Quoting bongo fury
Quoting 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.”
Quoting TheMadFool
Yes, and that it is so is thanks to the Law of the Idempotence of Disjunction.
Quoting TheMadFool
The proof uses PSAN on the meta-level (in 2) to show PSAN on the object level (inference of 3 ultimately from 1).
Quoting 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.
Quoting 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.
Quoting bongo fury
Charlie: “Now you’re beginning to sound like Bob :wink:.”
Quoting 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?”
Quoting 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.”
Quoting 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?
Quoting bongo fury
There, you’re using negation to define negation.
Quoting 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?
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.
Quoting 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.
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.
Quoting TheMadFool
Let’s call this “Alice’s world”.
Quoting TheMadFool
Let’s call this “Bob’s world”.
Quoting 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
Quoting 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.
Quoting 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?
Quoting 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.”
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.
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.
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
Quoting 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.