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Abs-E (or, speak only in the positive)
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This reminds me of Mr. Rogers' "Freddish," or his specific way of talking to children. One of his principles was this exact point: only phrase things in the positive. Thus, rather than saying, "Don't cross the street by yourself," word it more like, "Ask an adult before crossing the street." There were several other components to Freddish, like emphasizing the benefits of listening to adults and praising the child for their compliance, but "phrasing things in the positive" was the one that stuck the most in my mind, and is the most germane to this discussion.
(I think I've also heard something similar regarding e.g. warning signs, that positive statements like "Stay away from the wires" are more effective than negative statements, like "Don't touch the wires," because your brain basically ignores the negative part of it. "*mumble mumble* touch the wires? Don't mind if I do!")
The wires one immediately sounds very plausible. I think its because "stay away from the wires" gives me a clear instruction I can immediately start following. "Don't touch the wires" instead gets logged away as something I will hopefully remember if I start thinking about the wires again.
There seems to be a body of evidence supporting the idea that positive statements require less cognitive load to process than negative statements. These are a couple of examples I could pull up:
https://doi.org/10.1037/mac0000057
https://link.springer.com/article/10.1007/s10979-007-9103-y
I remember in a Tali Sharot talk, sorry I can't remember the specific one, where she noted it was easier to get people to press a button at the right time when an incentive is offered than it is to dissuade people from pressing a button with a penalty. Which broadly seems corroborated by Skinnerian "Schedules of Reinforcement" research.
positive statements like "Stay away from the wires" are more effective than negative statements, like "Don't touch the wires," because your brain basically ignores the negative part of it. "*mumble mumble* touch the wires? Don't mind if I do!"
That's what I was going for with
When reading or hearing a negation used in language, you must first process the positive form it contains to understand the entire statement. For example, to understand "the sky is not green", you must first understand "the sky is green", then negate it. Usually, this happens quickly and subconsciously, but it can harmfully slow down or weaken understanding by making you first consider a false idea.
I'm finding myself stuck on the question of how exactly the strict version would avoid the use of some of those negating adjectives. If you want to express the information that, say, eating grass won't give the human body useful calories...
- "Grass is indigestible" : disallowed
- "Grass is not nutritious" : disallowed
- "Grass will pass through you without providing energy" : "without providing energy" seems little different to "not providing energy", it's still at heart a negative claim
Perhaps a restatement in terms of "Only food that can be easily digested will provide calories" except that you still need to then convey that cellulose won't be easily digested.
Probably there are true positive statements about the properties of easily digested molecules and the properties of cellulose which can at least be juxtaposed to establish that it's different to anything that meets the criteria. But that seems like a lot of circumlocution and I'm less than entirely confident that I even know the specifics.
Perhaps part of the point is to stop you making negative claims where you don't know the specific corresponding positive claims? Or to force you to expand out the whole chain of reasoning when you do know it (even if it's lengthier than one would usually want to get into).
On further consideration, and by analogy to "is immortal" being functionally equivalent to "will live forever" (so if it's interchangeable wording, does that mean that "is immortal" is actually equally a positive statement?), formulating "indigestible" as words to the effect of "will pass through your body largely intact and with about exactly as many calories as it started with" occurs to me.
It's certainly a demanding style.
I find that editing my writing to use positive statements does make it better. I feel doubtful I could easily take it to the extent of making all positive statements. This might be an interesting use of LLM rewrites: negative->positive rephrasing feels like something within GPT-4's capabilities, and it would let you quickly translate a large corpus to read & evaluate without putting in a huge amount of work to write a large varied corpus of Abs-E text yourself. (I dislike the current name 'Abs-E' and by analogy to E-Prime, suggest 'E⁺' - short for 'English-positive'.)
This would also combine well with 'Up-Goer-Five' style writing. In fact, I think Up-Goer-Five writing is already mostly E⁺ writing because of the need to say what something is rather than is not. (Checking the original XKCD, I see a few negations, but they all look easily rewritten to be positive: "if there's a problem so they decide not go to space" -> "...so they decide to get out of the rocket".)
"Grass will pass through you without providing energy" : "without providing energy" seems little different to "not providing energy", it's still at heart a negative claim
That one seems easy to do if you go more quantitative. What is 'energy'? I mean, by e=mc^2, some grass embodies a lot of energy. You mean calories. "Grass provides 0 calories" is a positive assertion, which is more correct and still reasonably natural English. And also this assertion is clearly false, because plenty of animals eat grass and it provides them >0 calories. "Oh, I meant for humans, of course". Fine, your first two versions failed this ('indigestible' for whom, exactly?) but easily revised: "Grass provides 0 calories to humans." 0 is not a negation, but a specific number, and so is valid, and correctly expresses the intent while not being overly universal and implying false things about herbivores.
"Only food that can be easily digested will provide calories"
That statement would seem to also be obviously wrong. Plenty of things are 'easily digested' in any reasonable meaning of that phrase, while providing ~0 calories. Water, for example. Or artificial sweeteners. Minerals like calcium. (Chiral molecules, if you want to go really exotic.)
On further consideration, and by analogy to "is immortal" being functionally equivalent to "will live forever" (so if it's interchangeable wording, does that mean that "is immortal" is actually equally a positive statement?)
This example might be considered a benefit of the style. People can mean rather different things by 'immortal' if they are simply defining it by negation as 'not dying'. One common definition is 'not aging' (ie. the probability of annual mortality being the same each year indefinitely); the other common one is some sort of 'indestructible and will exist to the end of the universe'. The former is fairly ordinary and mundane and describes, say, naked mole rats; the latter is purely imaginary and found only in fictional works like comic books or sacred scriptures. If the former, you might say something like 'has constant mortality rate', and if the latter, 'existing forever'.
So banning 'im-mortal' (which etymologically, turns out to be what you'd assume: Latin in - mortalis, "not-mortal") could be useful. (You do see IRL people sometimes object to longevity discussions on dumb grounds like "you can't become immortal, what about accidents?!"...)
This might be an interesting use of LLM rewrites: negative->positive rephrasing feels like something within GPT-4's capabilities, and it would let you quickly translate a large corpus to read & evaluate without putting in a huge amount of work to write a large varied corpus of Abs-E text yourself. (I dislike the current name 'Abs-E' and by analogy to E-Prime, suggest 'E⁺' - short for 'English-positive'.)
Took a first stab at just the positive rewrite last night: https://github.com/gwern/gwern.net/blob/master/build/text2epositive.py
A major issue is that GPT-4s want to rewrite into ChatGPTese and hypercorrect any 'error', even with instructions to preserve the style and a lot of examples showing style preservation. I greatly want to avoid ChatGPTese in my writing, so it leaking through anyway is a problem. Another LLM API might be better for this (Claude?) but I don't have tokens+scripts set up right this instant for alternatives.
That aside, I'm unimpressed right now with the generated rewrites. Working through various examples of negation is hard and yields ugly-sounding or too-strong assertions or I couldn't do it at all without cheating, and makes me think that often a negative assertion is the most informative (without being false) way to state something.* There are negatives that should be reworded to positive, but fewer than I was hoping beforehand. (For example, the comment about the LW2 AWS hack reads better when rewritten into an affirmative positive form, definitely.)
At best, this seems like something to integrate into a grammar/style checker and only occasionally suggest a rewrite. And of course, if you only occasionally rewrite some text, the value is much lower than if you were rewriting every other sentence.
I feel a bit more optimistic about up-goer-five rewrites at this point. Although I'm not sure where I would actually want to generate a lot of up-goer-five rewrites, come to think of it...
(A linter-style tool just flagging some text is also harder to integrate into my Emacs writing workflow: if it rewrites an entire block of text, that is relatively easy (simply pipe every paragraph into the script, and blindly replace it with the script output, which is even keyboardable: select region & C-u M-; tex<TAB>... to overwrite the region with the output of passing the script into a shell-command which tab-completes to that executable Python script), but to analyze it and just color or highlight troublesome negations? Hm. That's not something I've done in Emacs before...)
* Quite a few of them made me unhappy trying to come up with a good positive assertion version: "We couldn't find John anywhere" can be made less negative in a useful way (eg. specifying where you searched), but making it entirely positive is quite painful and lengthy if you have to specify what and where and when you saw all the things which conjunctively exclude John. It's easy to say "I looked through the house and didn't see John" and that is better... but it's still using negation! I don't even know how I would make this fully positive: "I looked through each room of the house and saw X, Y, & Z." "But did you see John? Was he there or not?" "...Please ask me a different question."
It seems you are hitting against the expressive limits of Existential Positive First-Order Logic. It seems that they are exponentially less powerful than first order logic, in the following sense:
every existential positive first-order sentence can be transformed in an equivalent one in prenex normal form without an exponential blowup, thanks to the absence of universal quantifiers and negation symbols.
Bodirsky, Manuel, Miki Hermann, and Florian Richoux. "Complexity of existential positive first-order logic." Journal of Logic and Computation 23.4 (2013): 753-760.
Yeah, I'm not surprised that English-positive is a lot weaker than English (in terms of short statements), I'm just surprised that the weakness turns up so quickly with such natural-seeming sentences rather than pathological or complex statements. You see an example like "the sky is not green", and it's so easy to turn into "the sky is blue" or "grass is inedible" to "grass provides 0 calories", and you start to think maybe most or all normal natural statements have feasible rewrites, and maybe this is like constructive mathematics and actually works for most things if you think about them a little harder - and then you hit "I didn't see John."
A few more examples:
- "Is this gluten-free?" (If we allow "gluten-free" we would allow "Every room is John-free." and of course "Grass is edibility-free." and very quickly Abs-E is trivial.)
- Attempt: "This product contains rice flour, corn starch, tapioca flour, and salt." but that just prompts the further question "Does any of those contain gluten?" ...
- Wittgenstein interrupted: "What can be said at all can be said clearly, and what we..."
- "I think not all swans are white, and if we look for it we will find one that is not white."
- Attempt: "There exists a swan that is ..." Blue? Green? Red? I can't say "non-white". I also can't just list every color.
- "I don't believe in magic."
- I don't even know how to start converting this to a positive statement.
“Only food that can be easily digested will provide calories”
That statement would seem to also be obviously wrong. Plenty of things are ‘easily digested’ in any reasonable meaning of that phrase, while providing ~0 calories.
I think you've interpreted this backwards; the claim isn't that "easily digested" implies "provides calories", but rather that "provides calories" implies "easily digested".
"provides calories" implies "easily digested".
Well, debates about what modal operators are meant by 'only' aside, I am doubtful that claim is true either! First, as a parallel consider grass again: to digest grass, ruminants need an extremely long intestinal system which takes multiple passes (including throw it up to the mouth to chew it again, for hours on end, chewing their cud again and again) and requires tons of microbes to digest it over multiple days; again, under any ordinary understanding of the phrase 'easily digested', it is not easy for cows to digest grass. Yet they still get all the calories they need to live on from it. So, for cows, grass 'provides calories' and yet is not 'easily digested'. This is also true for humans: eating plants and raw uncooked foods 'provide calories', but are not 'easily digested'; in fact, they provide much less net calories than they should because so many calories go right back into the digestive process.* (And this is one of the major theories for the importance of fire & cooking in human evolution: 'the expensive gut tissue' hypothesis.) You could also point to things like 'poisonous berries': you eat them and enjoy calories as their simple carbohydrates easily digest... until you then lose a bunch of calories by being sick and sh−ting yourself all day long. Easily digested, without a doubt but did they provide calories? They did - but only for the first few hours. So, this brings out that when you talk about 'easily digested things' which 'provides calories', you are implicitly including the caloric costs of digestion & side-effects and it's really net calories you are talking about. Which will also be context-specific (eg. presumably there are wild animals like birds who will be immune to the berry poison and are the intended consumers, and for them the berries deliver full caloric value).
* see also: the malnourishment of 'raw foodists', which manifests in symptoms like menstruation stopping.
This seems like it's trying to be constructivist logic: your claim must construct at least one example of the thing it's claiming; compare classical logic, which also allows constructing an "excluded middle" claim, ie a claim that some claim must either be true or not be true, and therefore if you can reason about either case, you can say something about all cases without ever having been able to construct an example that witnesses it being true or not true.
But constructivist logic still involves "not" statements and allows proof by contradiction. In constructivist logic, proof by contradiction must construct an example of the mathematical object which contradicts the negated theorem.
In constructivist logic, proof by contradiction must construct an example of the mathematical object which contradicts the negated theorem.
This isn't true. In constructivist logic, if you are trying to disprove a statement of the form "for all x, P(x)", you do not actually have to find an x such that P(x) is false -- it is enough to assume that P(x) holds for various values of x and then derive a contradiction. By contrast, if you are trying to prove a statement of the form "there exists x such that P(x) holds", then you do actually need to construct an example of x such that P(x) holds (in constructivist logic at least).
1The way I think of it, is that constructivist logic allows "proof of negation" via contradiction which is often conflated with "proof by contradiction". So if you want to prove ¬P, it's enough to assume P and then derive a contradiction. And if you want to prove ¬¬P, it's enough to assume ¬P and then derive a contradiction. But if you want to prove P, it's not enough to assume ¬P and then derive a contradiction. This makes sense I think - if you assume ¬P and then derive a contradiction, you get ¬¬P, but in constructivist logic there's no way to go directly from ¬¬P to P.
Proof of negation (allowed): Prove ¬P by assuming P and deriving a contradiction
Proof by contradiction (not allowed): Prove P by assuming ¬P and deriving a contradiction
Most of the time English has an antonym that does not involve a negative prefix or suffix.
- It is not warm. ~= It is cool.
- It is not new. ~= It is old.
But this is not the case in other languages. Consider Esperanto:
- It is not warm. -> Ĝi ne estas varmeta. ~= Ĝi estas malvarmeta.
- It is not new. -> Ĝi ne estas nova. ~= Ĝi estas malnova.
Because mal- is equivalent to un-, it is forbidden, and you have to resort to periphrasis:
- Ĝi estas alia ol varmeta. (It is other than warm.)
- Ĝi estas la malo de varmeta. (It is the opposite of warm.)...oh, wait, this contains mal- too.
It's interesting that Esperanto is an artificial language, and its paucity of antonyms is by deliberate design. Orwell's Newspeak has the same feature ("ungood" = bad), and was in part a satire on Esperanto and similar artificial languages.
I suspect that natural languages generally have primitive antonyms for the most common words. Anna Wierzbicka analysed the language of thought into a small number of "semantic primes", originally 14 and currently 65. She arrived at these through the study of natural languages, searching for a set of concepts with which any sentence of the target languages could be expressed. Despite the limited inventory, she found reason to include several antonym pairs: same/other, live/die, good/bad, do/don't, few/many, etc. Even want/not-want was in the original set of 14, although I see that not-want is not in the current set.
Good point, although I used Esperanto precisely because it is a language for which the OP's approach is transparently difficult. The Greek word for light (in weight) is avaris...not heavy. So in Greek, one must say "This object is easy to lift because of the lowness of its weight," but in English one can say "This object is light." Seems arbitrary. I appreciate what the OP is trying to do, though.
I see a problem with this approach when the speaker does not know the answer to the question:
Under Abs-E, binary questions ("yes"-or-"no") are less obvious to answer. If your answer would ordinarily be "no", you must instead reply as if the question was open-ended. For example, your reply to "will you be here tomorrow?" may be "yes", or "I will be in the office tomorrow", or "I will stay home tomorrow". This forces you to speak with more information.
How do you respond when you don't know what you will be doing tomorrow? This could be a case where you haven't made up your mind yet (in which case "I will decide on that later" is a valid answer), or it could be because you genuinely don't have the information and have no way to find it. "What will the closing price of Apple be at the end of the year?" is difficult to answer as far as I can tell, especially if the person asking the question thinks you should know the answer. "You will have to wait for the end of the year before you can know that" doesn't convey the same information as "Short of stock manipulation, nobody can know the answer to that until the time comes." The first one could mean that I know the answer but choose not to tell you, while the second one conveys the more reasonable claim that the question cannot be answered in advance.
So, I think this is an interesting thought experiment, but I suspect that the amount of time spent mentally rewording everything before you speak will outweigh any positive value.
You almost always have some information to concentrate your priors. Between mutually-helpful speakers, implicit with an answer to a question is that the answer gives all the information you have on the question that could benefit the questioner. E.g.
What will the closing price of Apple be at the end of the year?
"Almost certainly somewhere between $150 and $250."
I'm skeptical that this has much practical value. It's useful to point out the information differential in positive and negative statements, thank you for that. But there's a reason that almost all human languages contain that mechanism, and it's very convenient.
I predict that it mostly gets worked around, by using only a few extra words.
"The sky is something other than blue" and "I will be somewhere else tomorrow" are both semantically-equivalent to the forbidden forms. Even "I deny that the sky is blue" is a positive-form negation of the object-level statement.
I predict that it mostly gets worked around, by using only a few extra words.
"The sky is something other than blue" and "I will be somewhere else tomorrow" are both semantically-equivalent to the forbidden forms. Even "I deny that the sky is blue" is a positive-form negation of the object-level statement.
I suspect all such workarounds depend on one of a relatively small set of negation-enabling words, such as "other", "else", and "deny", as you demonstrate. Prohibiting more words should eventually block all workarounds, while making writing more annoying.
This is a fun idea! I shall refrain from adopting this style myself, but shall commend its use to others. It's reminiscent of "taboo-ing" words, but taken further.
"Positive" and "negative", as used here, refer to truth-values and logical structure, rather than emotional valence.
On almost any topic, there are many potential false statements, and comparatively very few[1] true statements. Thus a simple true statement (like "the sky is blue") is usually much more informative than the negation of a similar false statement (like "the sky is not green").
When reading or hearing a negation used in language, you must first process the positive form it contains to understand the entire statement. For example, to understand "the sky is not green", you must first understand "the sky is green", then negate it. Usually, this happens quickly and subconsciously, but it can harmfully slow down or weaken understanding by making you first consider a false idea.
For these reasons, Absolute-English (henceforth Abs-E), where one only speaks in the positive, should be clearer and more honest than current negation-permitting English. I call it Abs-E by analogy to the absolute-value operation in maths, which replaces both positive and negative with only positive. The simple form of Abs-E forbids the words "no", "not", and "-n't" (as in "won't" or "isn't"). The strict form of Abs-E, which may be more effective, forbids all of the following:
The proposal is loosely inspired by the existing E-Prime, which forbids "to be" and all its inflections for its own, different reasons. You could combine the restrictions to make Abs-E-Prime, replacing "the sky is not green" with "the sky appears blue", but I only care about positivity.
Under Abs-E, binary questions ("yes"-or-"no") are less obvious to answer. If your answer would ordinarily be "no", you must instead reply as if the question was open-ended. For example, your reply to "will you be here tomorrow?" may be "yes", or "I will be in the office tomorrow", or "I will stay home tomorrow". This forces you to speak with more information. On average, that makes conversation more fun and lying harder. If your interlocutor knows about Abs-E, they can make questions and answers play out more naturally by replacing all binary questions with open-ended questions, such as "where will you be tomorrow?" in place of "will you be here tomorrow?".
I am serious about following strict Abs-E, at least for some trial time to see its effects. If, in my speech or writing, you find me using a negative form, you are welcome to call it out for me to correct.
Pedantically, there are an equal number of true and false statements (both infinite). Given any one maximum length of statements, there are only finitely many true statements and many more (still finite) false statements.