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.
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’.)
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.”
“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”.
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.
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”.)
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.
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.)
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?!”...)
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:
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.
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”.
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.