I’m not yet good enough at writing posts to actually properly post something but I hoped that if I wrote something here people might be able to help me improve. So obviously people can comment however they normally would but it would be great if people would be willing to give me the sort of advice that would help me to write a better post next time. I know that normal comments do this to some extent but I’m also just looking for the basics – is this a good enough topic to write a post on but not well enough executed (therefore, I should work on my writing). Is it not a good enough topic? Why not? Is it not in depth enough? And so on.
Is your graph complete?
The red gnomes are known to be the best arguers in the world. If you asked them whether the only creature that lived in the Graph Mountains was a Dwongle, they would say, “No, because Dwongles never live in mountains.”
And this is true, Dwongles never live in mountains.
But if you want to know the truth, you don’t talk to the red gnomes, you talk to the green gnomes who are the second best arguers in the world.
And they would say. “No, because Dwongles never live in mountains.”
But then they would say, “Both we and the red gnomes are so good at arguing that we can convince people that false things are true. Even worse though, we’re so good that we can convince ourselves that false things are true. So we always ask if we can argue for the opposite side just as convincingly.”
And then, after thinking, they would say, “We were wrong, they must be Dwongles, for only Dwongles ever live in places where no other creatures live. So we have a paradox and paradoxes can never be resolved by giving counter examples to one or the other claim. Instead of countering, you must invalidate one of the arguments.”
Eventually, they would say, “Ah. My magical fairy mushroom has informed me that Graph Mountain is in fact a hill, ironically named, and Dwongles often live in hills. So yes, the creature is a Dwongle.”
The point of all of that is best discussed after introducing a method of diagramming the reasoning made by the green gnomes. The following series of diagrams should be reasonably self explanatory. A is a proposition that we want to know the truth of (the creature in the Graph Mountains a Dwongle) and not-A is its negation (the creature in the Graph Mountains is not a Dwongle). If a path is drawn between a proposition and the “Truth” box, then the proposition is true. Paths are not direct but go through a proof (in this case P1 stands in for “Dwongles never live in mountains” and P2 stands in for “Only Dwongles live in a place where no other creatures live).
The diagrams connect to the argument made above by the green gnome. First, we have the argument that it mustn’t be a Dwongle because of P1. The second diagram shows the green gnome realising that they have an argument that it must be a Dwongle too due to P2. This middle type of diagram could be called a “Paradox Diagram.”
Figure 1. The green gnomes process of argument.
In his book, Good and Real, Gary Drescher notes that paradoxes can’t be resolved by making more counterarguments (which would relate to the approach shown in figure 2 before, which when considered graphically is obviously not helpful, we still have both propositions being shown to be true) but rather, by invalidating one of the arguments. That’s what the green gnomes did when they realised that Graph Mountain was actually a hill and that’s what the final diagram in figure 1 shows the result of (when you remove a vertex, like P1, you remove all the lines connected to it as well).
Figure 2. Attempting to resolve a paradox via counter arguments rather than invalidation.
The interesting thing in all of this is that the first and third diagrams in figure 1 look very similar. In fact, they’re the same but simply with different propositions proven. And this raises something: It can be very difficult to tell the difference between an incomplete paradox diagram and a completed proof diagram. The difference between the two is whether you’ve tried to find an argument for the opposite of the proposition proven and, if you do find one, whether you’ve managed to invalidate that argument.
What this means is, if you’re not confident that your proof for a proposition is true, you can’t be sure that you’ve taken all of the appropriate steps to establish its truth until you’ve asked: Is my graph complete?
So my presumption is that 4 points means this article isn’t hopeless—it hasn’t attracted criticism, some people have upvoted it—but isn’t of a LW standard—it hasn’t been voted highly enough, there is only 1 comment engaging with the topic.
Is anyone able to give me a sense at to why it isn’t good enough? Should the topic necessarily be backed up by peer reviewed literature? Is it just not a big enough insight? Is it the writing? Is it the lack of specific examples noted by Gwern? Is it too similar to other ideas? And so on.
I hope I’m not bugging people by trying to figure it out but I’m trying to get better at writing posts without filling the main bit of less wrong with uninteresting stuff and this seemed like a less intrusive way to do this. I also feel like the best way to improve isn’t simply reading the posts but involves actually trying to write posts and (hopefully) getting feedback.
I tried composing a response a day or two ago, but had difficulty finding the words.
In a nutshell, I thought you should start with last two paragraphs, boil that down to a coherent and specific claim. Then write an entirely new essay that puts that claim at the top, in an introductory/summary paragraph. The rest of the post should be spent justifying and elaborating on the claim directly and clearly, without talking about gnomes or deploying the fallacy of equivocation on the sly, but hopefully with citation to peer reviewed evidence and/or more generally accessible works about reasoning (like from a book).
Thanks for the comment. That’s really helpful. So I should basically start with the idea, present it more clearly (no gnomes) and try to provide peer reviewed evidence or at least some support.
I like this, but in Good and Real, Drescher’s paradigm works because he then supplies a few examples where he invalidates a paradox-causing argument, and then goes on to apply this general approach. Asides from your dwarf hypothetical example, where do you actually check that your graph is complete?
I think that you’re asking when would you check that your graph is complete in a real world case, sorry if I misunderstood.
If so, take the question of whether global warming is anthropogenic. There are people who claim to have evidence that it is and people who claim to have evidence that it isn’t so the basic diagram that we have for this case is a paradox diagram similar to that in figure 2 of the article above. Now there are a number of possible responses to this: Some people could be stuck on the paradox diagram and be unsure as to the right answer, some people may have invalidated one or the other side of the argument and may have decided one or the other claim is true, and some may be adding more and more proofs to one side or the other—countering rather than invalidating.
I think there’s also a fourth group who’s belief graph will look the same as those who have invalidated one side and have hence reached a conclusion. However, these will be people who, while they may technically know that arguments exist for the negation of their belief, have not taken opposing notions into account in their belief graph. So to them, it will look like a graph demonstrating the truth of their belief but, in fact, it’s simply an incomplete paradox graph and they have some distance to go to figure out the truth of the matter.
So to summarise: I think there are people on both sides of the anthropogenic global warming debate who know that purported proofs against their beliefs exist on one level but who don’t factor these into their belief graphs. I think they could benefit from asking themselves whether their graph is complete.
I should mention that this particular case isn’t what motivated the post—in some ways I worry that by providing specific examples people stop judging an idea on its merit and start judging it based on their beliefs regarding the example mentioned and how they feel this is meant to tie in with the idea. Regardless, I could be mistaken. Is it considered a good idea to always provide real world example in LW posts on rationality techniques?
Or if you meant a more personal example then at my work there’s currently a debate over whether a proposed electronic system will work. I’m one of the few people that thinks it won’t (and I have some arguments to support that) but I haven’t invalidated any arguments that show it will work, I simply haven’t come across any such arguments. But it’s a circumstance where I might benefit from asking, is my graph complete?
As a side note, I think the technique can also be extended to other circumstances. For example, some aspects of Eliezer’s Guessing the teacher’s password could be modelled by a “Password Graph” a graph like those above but where the truth of both A and not-A go through the same proof (say P1 for example). If you have a proof for A then you could ask if you have an incomplete Password graph because, if so, you could be in trouble. So you could extend the circumstances where the question applies by asking if you have completed any of a number of graphs. Of course, doing so comes at the cost of simplicity.
I’m not yet good enough at writing posts to actually properly post something but I hoped that if I wrote something here people might be able to help me improve. So obviously people can comment however they normally would but it would be great if people would be willing to give me the sort of advice that would help me to write a better post next time. I know that normal comments do this to some extent but I’m also just looking for the basics – is this a good enough topic to write a post on but not well enough executed (therefore, I should work on my writing). Is it not a good enough topic? Why not? Is it not in depth enough? And so on.
Is your graph complete?
The red gnomes are known to be the best arguers in the world. If you asked them whether the only creature that lived in the Graph Mountains was a Dwongle, they would say, “No, because Dwongles never live in mountains.”
And this is true, Dwongles never live in mountains.
But if you want to know the truth, you don’t talk to the red gnomes, you talk to the green gnomes who are the second best arguers in the world.
And they would say. “No, because Dwongles never live in mountains.”
But then they would say, “Both we and the red gnomes are so good at arguing that we can convince people that false things are true. Even worse though, we’re so good that we can convince ourselves that false things are true. So we always ask if we can argue for the opposite side just as convincingly.”
And then, after thinking, they would say, “We were wrong, they must be Dwongles, for only Dwongles ever live in places where no other creatures live. So we have a paradox and paradoxes can never be resolved by giving counter examples to one or the other claim. Instead of countering, you must invalidate one of the arguments.”
Eventually, they would say, “Ah. My magical fairy mushroom has informed me that Graph Mountain is in fact a hill, ironically named, and Dwongles often live in hills. So yes, the creature is a Dwongle.”
The point of all of that is best discussed after introducing a method of diagramming the reasoning made by the green gnomes. The following series of diagrams should be reasonably self explanatory. A is a proposition that we want to know the truth of (the creature in the Graph Mountains a Dwongle) and not-A is its negation (the creature in the Graph Mountains is not a Dwongle). If a path is drawn between a proposition and the “Truth” box, then the proposition is true. Paths are not direct but go through a proof (in this case P1 stands in for “Dwongles never live in mountains” and P2 stands in for “Only Dwongles live in a place where no other creatures live). The diagrams connect to the argument made above by the green gnome. First, we have the argument that it mustn’t be a Dwongle because of P1. The second diagram shows the green gnome realising that they have an argument that it must be a Dwongle too due to P2. This middle type of diagram could be called a “Paradox Diagram.”
Figure 1. The green gnomes process of argument.
In his book, Good and Real, Gary Drescher notes that paradoxes can’t be resolved by making more counterarguments (which would relate to the approach shown in figure 2 before, which when considered graphically is obviously not helpful, we still have both propositions being shown to be true) but rather, by invalidating one of the arguments. That’s what the green gnomes did when they realised that Graph Mountain was actually a hill and that’s what the final diagram in figure 1 shows the result of (when you remove a vertex, like P1, you remove all the lines connected to it as well).
Figure 2. Attempting to resolve a paradox via counter arguments rather than invalidation.
The interesting thing in all of this is that the first and third diagrams in figure 1 look very similar. In fact, they’re the same but simply with different propositions proven. And this raises something: It can be very difficult to tell the difference between an incomplete paradox diagram and a completed proof diagram. The difference between the two is whether you’ve tried to find an argument for the opposite of the proposition proven and, if you do find one, whether you’ve managed to invalidate that argument.
What this means is, if you’re not confident that your proof for a proposition is true, you can’t be sure that you’ve taken all of the appropriate steps to establish its truth until you’ve asked: Is my graph complete?
So my presumption is that 4 points means this article isn’t hopeless—it hasn’t attracted criticism, some people have upvoted it—but isn’t of a LW standard—it hasn’t been voted highly enough, there is only 1 comment engaging with the topic.
Is anyone able to give me a sense at to why it isn’t good enough? Should the topic necessarily be backed up by peer reviewed literature? Is it just not a big enough insight? Is it the writing? Is it the lack of specific examples noted by Gwern? Is it too similar to other ideas? And so on.
I hope I’m not bugging people by trying to figure it out but I’m trying to get better at writing posts without filling the main bit of less wrong with uninteresting stuff and this seemed like a less intrusive way to do this. I also feel like the best way to improve isn’t simply reading the posts but involves actually trying to write posts and (hopefully) getting feedback.
Thanks
I tried composing a response a day or two ago, but had difficulty finding the words.
In a nutshell, I thought you should start with last two paragraphs, boil that down to a coherent and specific claim. Then write an entirely new essay that puts that claim at the top, in an introductory/summary paragraph. The rest of the post should be spent justifying and elaborating on the claim directly and clearly, without talking about gnomes or deploying the fallacy of equivocation on the sly, but hopefully with citation to peer reviewed evidence and/or more generally accessible works about reasoning (like from a book).
Thanks for the comment. That’s really helpful. So I should basically start with the idea, present it more clearly (no gnomes) and try to provide peer reviewed evidence or at least some support.
I like this, but in Good and Real, Drescher’s paradigm works because he then supplies a few examples where he invalidates a paradox-causing argument, and then goes on to apply this general approach. Asides from your dwarf hypothetical example, where do you actually check that your graph is complete?
I think that you’re asking when would you check that your graph is complete in a real world case, sorry if I misunderstood.
If so, take the question of whether global warming is anthropogenic. There are people who claim to have evidence that it is and people who claim to have evidence that it isn’t so the basic diagram that we have for this case is a paradox diagram similar to that in figure 2 of the article above. Now there are a number of possible responses to this: Some people could be stuck on the paradox diagram and be unsure as to the right answer, some people may have invalidated one or the other side of the argument and may have decided one or the other claim is true, and some may be adding more and more proofs to one side or the other—countering rather than invalidating.
I think there’s also a fourth group who’s belief graph will look the same as those who have invalidated one side and have hence reached a conclusion. However, these will be people who, while they may technically know that arguments exist for the negation of their belief, have not taken opposing notions into account in their belief graph. So to them, it will look like a graph demonstrating the truth of their belief but, in fact, it’s simply an incomplete paradox graph and they have some distance to go to figure out the truth of the matter.
So to summarise: I think there are people on both sides of the anthropogenic global warming debate who know that purported proofs against their beliefs exist on one level but who don’t factor these into their belief graphs. I think they could benefit from asking themselves whether their graph is complete.
I should mention that this particular case isn’t what motivated the post—in some ways I worry that by providing specific examples people stop judging an idea on its merit and start judging it based on their beliefs regarding the example mentioned and how they feel this is meant to tie in with the idea. Regardless, I could be mistaken. Is it considered a good idea to always provide real world example in LW posts on rationality techniques?
Or if you meant a more personal example then at my work there’s currently a debate over whether a proposed electronic system will work. I’m one of the few people that thinks it won’t (and I have some arguments to support that) but I haven’t invalidated any arguments that show it will work, I simply haven’t come across any such arguments. But it’s a circumstance where I might benefit from asking, is my graph complete?
As a side note, I think the technique can also be extended to other circumstances. For example, some aspects of Eliezer’s Guessing the teacher’s password could be modelled by a “Password Graph” a graph like those above but where the truth of both A and not-A go through the same proof (say P1 for example). If you have a proof for A then you could ask if you have an incomplete Password graph because, if so, you could be in trouble. So you could extend the circumstances where the question applies by asking if you have completed any of a number of graphs. Of course, doing so comes at the cost of simplicity.