Yep, but classifying the holonomy of normal conformal Cartan connections is also maths, and I don’t post it to Less Wrong. There has to be some connection with AI or rationality or decision making.
I should have clarified that I wasn’t writing in defense of modal logic, but purely using it as an illustration to introduce Kripke structures and impossible worlds, which are needed for the semantics of relevance logics (and might be useful tools in their own right).
Yes, I suppose. My cached thoughts say one can never know when a mathematical result will suddenly turn out to be useful for something, but this is irrelevant. I think modal logic has direct practical uses here, as my top-level comment implies.
EY’s hostility to it seems to be the result of a misunderstanding. He thinks it is a proposed explanation for phenomena of ‘possibility’ and ‘necessity’, but in fact it is a description of them. Any theory/algorithm/structure that purports to explain the phenomena must be a model of the modal logic’s axioms. And, as usual, the theory tries to specify the minimal set of axioms, shows what can be derived from them, etc.
EY’s hostility to it seems to be the result of a misunderstanding. He thinks it is a proposed explanation for phenomena of ‘possibility’ and ‘necessity’,
Can you summarize your reasons for believing that?
My recollection is that the relevant essay was railing against the habit of thought that causes a particular kind of thinker to come up with systems of description that encapsulate the unexplained, rather than attempting to explain the unexplained. But it’s been a while since I read it carefully.
So what these philosophers do instead, is “bounce” off the problem into a new modal logic: A logic with symbols that embody the mysterious, opaque, unopened black box. A logic with primitives like “possible” or “necessary”, to mark the places where the philosopher’s brain makes an internal function call to cognitive algorithms as yet unknown.
And then they publish it and say, “Look at how precisely I have defined my language!”
I’m back to not really understanding the hostility. I mean, precisely the same argument would work against the probability theory. I suppose, it can be argued that probability theory has lots of useful theorems, whereas modal logic appears to be only a formal language. But this is probably not quite true, and even if so, still abstracting a common element from several different domains is worth something (e.g. Category Theory).
Irritation at treating encapsulation-of-mystery as though it were an explanation is a recurring theme in EY’s writing.
I won’t presume to speak to the motives of someone I don’t actually know here, but I will say I often find myself irritated by similar things in similar ways, and my own reason for irritation is that people stop there.
That is, I don’t have a problem with “OK, we don’t understand X, but we’ve developed some techniques for working productively with X as a black box, which is great, and now we can go on to try and understand X.” I do have a problem with “We’ve developed some techniques for working productively with X as a black box, and that’s the only kind of understanding that matters.”
That said, it’s what people do: the orthodox establish a hierarchy build around X as a black box, and further dissolving X is left to the heterodox.
I don’t get the impression he was annoyed by the mathematical theory—rather that he was annoyed at me for bringing it up in less wrong, and wanted to know if I had any justification for doing so.
I’m not sure what you mean. Do you frequently bring up modal logic in conversations? Do you think he wouldn’t be annoyed if someone else brought it up? Do you think he’d be similarly annoyed if you brought up normal conformal Cartan connections instead?
EY does not think that modal logic is wrong as a mathematical theory, but that if we interpret philosophically it as its creators seem to intend, we will we be lead astray and believe we have gained an understanding of “necessity” and “possibility” when we haven’t actually done so.
I tend to agree with him on this. His comment seemed to have the subtext “you shouldn’t be bringing up these ideas on less wrong without some strong justification, it will lead people down fruitless avenues”. I was bringing them up to illustrate semantics for relevance logics, but that wasn’t clear in the post.
I’m not sure modal logic’s creators ever intended it as an explanation of “necessity” and “possibility”. It was always a description of how the two things (and other similar modalities) should behave. Kripke semantics has more of an ‘explanation’ flavor, but it is also a description.
The thought that we (LW participants interested in these things) will be lead astray by a slight exposure to the forbidden topic is kinda offending. I mean, we already have a satisfactory explanation and understanding of “possibility”, don’t we?
Can you expand on how I would tell the difference between someone’s irritation at a mathematical theory, and that person’s irritation at the people who work on that theory and write about it and otherwise disseminate it into academia?
Well, this comment, which started this discussion, clearly shows irritation. I conjecture, it was not against Stuart_Armstrong’s research/publishing habits.
Your conjecture is not obvious to me. If you can expand on how you made that determination, I might learn something from the expansion. (Not, of course, that this obligates you in any way.)
I don’t see what you could possibly learn beside my own thinking habits, but ok (although, this is evidence collected after the fact): (1) there is nothing about modal logic in Stuart_Armstrong’s publications page, and (2) there are no EY’s comments in the last at least ten Stuart_Armstrong’s posts, except this one.
He explains here.
Philosophy is a mind killer. Modal logic is pure math.
Yep, but classifying the holonomy of normal conformal Cartan connections is also maths, and I don’t post it to Less Wrong. There has to be some connection with AI or rationality or decision making.
I should have clarified that I wasn’t writing in defense of modal logic, but purely using it as an illustration to introduce Kripke structures and impossible worlds, which are needed for the semantics of relevance logics (and might be useful tools in their own right).
The paper is rather intimidating, I don’t understand anything in it. Do your results have implications at a more accessible level?
No, they don’t—that was my point.
Unlike modal logic, which does—that was mine.
But it’s relevant implications here are philosophical or practical, not mathematical.
Yes, I suppose. My cached thoughts say one can never know when a mathematical result will suddenly turn out to be useful for something, but this is irrelevant. I think modal logic has direct practical uses here, as my top-level comment implies.
EY’s hostility to it seems to be the result of a misunderstanding. He thinks it is a proposed explanation for phenomena of ‘possibility’ and ‘necessity’, but in fact it is a description of them. Any theory/algorithm/structure that purports to explain the phenomena must be a model of the modal logic’s axioms. And, as usual, the theory tries to specify the minimal set of axioms, shows what can be derived from them, etc.
Can you summarize your reasons for believing that?
My recollection is that the relevant essay was railing against the habit of thought that causes a particular kind of thinker to come up with systems of description that encapsulate the unexplained, rather than attempting to explain the unexplained. But it’s been a while since I read it carefully.
You’re right:
I’m back to not really understanding the hostility. I mean, precisely the same argument would work against the probability theory. I suppose, it can be argued that probability theory has lots of useful theorems, whereas modal logic appears to be only a formal language. But this is probably not quite true, and even if so, still abstracting a common element from several different domains is worth something (e.g. Category Theory).
Irritation at treating encapsulation-of-mystery as though it were an explanation is a recurring theme in EY’s writing.
I won’t presume to speak to the motives of someone I don’t actually know here, but I will say I often find myself irritated by similar things in similar ways, and my own reason for irritation is that people stop there.
That is, I don’t have a problem with “OK, we don’t understand X, but we’ve developed some techniques for working productively with X as a black box, which is great, and now we can go on to try and understand X.” I do have a problem with “We’ve developed some techniques for working productively with X as a black box, and that’s the only kind of understanding that matters.”
That said, it’s what people do: the orthodox establish a hierarchy build around X as a black box, and further dissolving X is left to the heterodox.
Yes, but transferring your irritation from bad habits of certain people to a mathematical theory seems to be a bad case of Halo effect.
I don’t get the impression he was annoyed by the mathematical theory—rather that he was annoyed at me for bringing it up in less wrong, and wanted to know if I had any justification for doing so.
I’m not sure what you mean. Do you frequently bring up modal logic in conversations? Do you think he wouldn’t be annoyed if someone else brought it up? Do you think he’d be similarly annoyed if you brought up normal conformal Cartan connections instead?
EY does not think that modal logic is wrong as a mathematical theory, but that if we interpret philosophically it as its creators seem to intend, we will we be lead astray and believe we have gained an understanding of “necessity” and “possibility” when we haven’t actually done so.
I tend to agree with him on this. His comment seemed to have the subtext “you shouldn’t be bringing up these ideas on less wrong without some strong justification, it will lead people down fruitless avenues”. I was bringing them up to illustrate semantics for relevance logics, but that wasn’t clear in the post.
I’m not sure modal logic’s creators ever intended it as an explanation of “necessity” and “possibility”. It was always a description of how the two things (and other similar modalities) should behave. Kripke semantics has more of an ‘explanation’ flavor, but it is also a description.
The thought that we (LW participants interested in these things) will be lead astray by a slight exposure to the forbidden topic is kinda offending. I mean, we already have a satisfactory explanation and understanding of “possibility”, don’t we?
Can you expand on how I would tell the difference between someone’s irritation at a mathematical theory, and that person’s irritation at the people who work on that theory and write about it and otherwise disseminate it into academia?
Well, this comment, which started this discussion, clearly shows irritation. I conjecture, it was not against Stuart_Armstrong’s research/publishing habits.
Your conjecture is not obvious to me. If you can expand on how you made that determination, I might learn something from the expansion. (Not, of course, that this obligates you in any way.)
I don’t see what you could possibly learn beside my own thinking habits, but ok (although, this is evidence collected after the fact): (1) there is nothing about modal logic in Stuart_Armstrong’s publications page, and (2) there are no EY’s comments in the last at least ten Stuart_Armstrong’s posts, except this one.
OK, thanks.