Is negation the same as affirmation?

Tristan L

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,

ᛏᚱᛁᛊᛏᚨᚾᚨᛉ᛫ᛚ

bongo fury

Yes, it isn't.

Tristan L

So you're taking Bob's side, right?

bongo fury

Yes, Alice's side.

Tristan L

Yes, Alice's side.

:up:

:scream: No, Bob's side.

Also :up:

Tristan L

Let me tell you what happened next with our friends:

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.”

TheMadFool

↪Tristan L

Would it matter to you if I said "yes, you're right" and "no, you're not right" about negation being the same as affirmation? Either way, why?

Tristan L

↪TheMadFool

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?

TheMadFool

↪Tristan L

:chin:

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.” — 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.

Tristan L

In what sense does it matter to you Bob? — TheMadFool

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.”

Either affirmation is the same as negation or it it's not. — 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.”

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 — 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.”

It must be that and if so, what are the senses in which you use them? — 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.”

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. — 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?

bongo fury

Was Alice being misquoted, or merely mis-disquoted (misread, misinterpreted, misunderstood)?

The latter, so I don't think she needed to admit, in an open ended way,

Heck, we don’t even agree whether we agree or disagree, — Tristan L

when that apparently meant disagreement about "points expressed",

including the point expressed by this very sentence as well as the one expressed by what Bob is about to say. — 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.

Gregory

This thread reminds me of Hegel. Making opposites one then negating the united product

Tristan L

This comment of mine is my first answer to

↪bongo fury

. I’d like us to talk about my next comment only later, that is, after I’ve made sure that I understand you correctly.

Was Alice being misquoted, or merely mis-disquoted (misread, misinterpreted, misunderstood)?

The latter — bongo fury

I think that you’re right.

when that apparently meant disagreement about "points expressed" — bongo fury

Yes.

(1)

Was Alice being misquoted [......]unobservable for him. — 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”.

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. — 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.

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. — 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.

But daring to confuse misinterpretation with misquotation is where it gets badly exposed. — 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.”

Tristan L

↪bongo fury

, I think it would be better for us to discuss my first answer before we get to this one. Still, we shouldn’t forget to come to it later.

Charlie: “Tristan, if you have understood our friend

↪bongo fury

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.”

Tristan L

By the way, Charlie just told me that Alice came up with a smart response :wink::

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?”

bongo fury

That is, Alice can expose Bob by pointing out that he applies a not-standard interpretation to her sentences. — Tristan L

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?)

A Seagull

Clearly it isn't.

TheMadFool

↪Tristan L

delete

TheMadFool

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 — Tristan L

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.

Craiya

Yes, affirmation is indeed not the same as negation, which means that affirmation is the same as negation. — Tristan L

Please, explain this to me as primitevely as possible. Because it seems like I got lost.

Tristan L

↪Gregory

What would a Hegelian say about this whole matter?

Tristan L

↪Craiya

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.

Tristan L

↪TheMadFool

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? — TheMadFool

Bob: “It means the same as ‘yes’.”

Clearly it's true that there's a difference between you being happy and you not being happy [...] — TheMadFool

Bob: “Precisely. It’s true that there is no difference between my being happy and my not being happy. That’s why ...”

[...] and the distinction that's required to make sense of that is affirmation is NOT the same as negation. — 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.”

Tristan L

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?) — bongo fury

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.

Clearly it isn't. — 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?

Tristan L

↪bongo fury

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. — 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?

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. — bongo fury

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. — 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?

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. — 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?

No, either you don't agree, or you don't infer the opposite. — bongo fury

Bob: “Exactamente; one both agrees and infers 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 — bongo fury

What use would that have?

Look at your syntax (which is semantics of a kind, a classification) — bongo fury

What do you mean by that?

bongo fury

Bob gave every appearance of being prepared to agree (in a non-surprising way) about these [expressing sentences]. About which phonetic sequences agree with (replicate, quote) which others, and about which ones disagree with (fail to quote) which others. — 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? — Tristan L

Yes, he mis-disquotes Alice, but does he mis-quote her? Are you changing your stance on that?

TheMadFool

↪Tristan L

I don’t need to make any distinction — Tristan L

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?

Tristan L

↪bongo fury

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.”

Tristan L

↪TheMadFool

Bob: “Yes, I’m indeed disagreeing with you, th.i. agreeing with you. I’ve already said that:

I don’t need to make any distinction. But that’s just what you’re saying – namely, that I need to make a distinction — 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

I don’t need to make any distinction — 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.”

TheMadFool

↪Tristan L

:smile: :sad: Is there no difference between being happy and not being happy?

bongo fury

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

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,

Yes, Alice, you are right, you said to me, quite clearly, and I quote, "Bob, please do mess with my phone!"

?

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

... 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,

Yes, he mis-disquotes her, but he doesn’t mis-quote her. I’m not changing my stance on that, — 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.

Is negation the same as affirmation?

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