I agree that it would be good to look at some real examples of beliefs rather than continuing with hypothetical examples and abstract arguments.
Your suggestion for what hard data to get isn’t something that we can do right now (and I’m also not sure if I disagree with your prediction). We do have some real examples of beliefs and (first attempt at stating) cruxes near at hand, in this comment from Duncan and in this post from gjm (under the heading “So, what would change my mind? ”) and Raemon (under the heading “So: My Actual Cruxes”). And I’d recommend that anyone who cares about cruxes or double crux enough to be reading this three-layers-deep comment, and who has never had a double crux conversation, pick a belief of yours, set a 5 minute timer, and spend that time looking for cruxes. (I recommend picking a belief that is near the level of actions, not something on the level of a philosophical doctrine.)
In response to your question about whether my comments were aimed at you:
They were partly aimed at you, partly aimed at other LWers (taking you as one data point of how LWers are thinking about cruxes). My impression is that your model of cruxes and double crux is different from the thing that folks around CFAR actually do, and I was trying to close that gap for you and for other folks who don’t have direct experience with double crux at CFAR.
For my first comment: the OP had several phrases like “traced to a single underlying consideration” which I would not use when talking about cruxes. Melissa’s current belief that she should start a gizmo company isn’t based on a single consideration, it’s a result of the fact that several different factors line up in a way that makes that specific plan look like an especially good idea. So of course she has several different cruxes. Similarly with views on marginal tax rates.
For my second comment: ‘Primarily look for things that would change your own views, not for things that would change the other person’s views’ is one of the core advantages of focusing on cruxes, in my opinion, and it didn’t seem to be a focus of the OP. It’s something that’s missing from your suggested substitute (“Look for key considerations”) and from your discussion of the example of how experts philosophers handle disagreements. e.g., If Theist is the one pressing the moral argument for the existence of God, because Theist guesses that it might shift Atheist’s views, then that is not a conversation based on cruxes. Whereas if Atheist is choosing to focus the discussion on that argument because Atheist thinks it might shift their own views, then it sounds like it is very similar to a conversation based on cruxes.
On the question of whether cruxes are all-or-nothing or a matter of degree: I think of “crux” as a term similar to “belief”. It suggests sharp category boundaries when in fact things are a matter of degree, but it’s often a good enough approximation and it’s easier for a person to think about, learn, and use the rest of the framework if they can fall back on the categorical concept. Replacing “look for cruxes” with “look for considerations to which your beliefs have relatively high credence sensitivity” also seems like a decent approximation. Doing a Value of Information calculation also seems like a decent approximation, at least for the subset of considerations that are within the model. I could say more to try to elaborate on all of this, but it feels like it really needs some concrete examples to point at. If a discussion like this was happening at a workshop, I’d elaborate by looking at the person’s attempts to come up with cruxes and giving them feedback.
(I’ll repeat here: this comment is about cruxes, not about double crux in particular.)
I agree that it would be good to look at some real examples of beliefs rather than continuing with hypothetical examples and abstract arguments.
Your suggestion for what hard data to get isn’t something that we can do right now (and I’m also not sure if I disagree with your prediction). We do have some real examples of beliefs and (first attempt at stating) cruxes near at hand, in this comment from Duncan and in this post from gjm (under the heading “So, what would change my mind? ”) and Raemon (under the heading “So: My Actual Cruxes”). And I’d recommend that anyone who cares about cruxes or double crux enough to be reading this three-layers-deep comment, and who has never had a double crux conversation, pick a belief of yours, set a 5 minute timer, and spend that time looking for cruxes. (I recommend picking a belief that is near the level of actions, not something on the level of a philosophical doctrine.)
In response to your question about whether my comments were aimed at you:
They were partly aimed at you, partly aimed at other LWers (taking you as one data point of how LWers are thinking about cruxes). My impression is that your model of cruxes and double crux is different from the thing that folks around CFAR actually do, and I was trying to close that gap for you and for other folks who don’t have direct experience with double crux at CFAR.
For my first comment: the OP had several phrases like “traced to a single underlying consideration” which I would not use when talking about cruxes. Melissa’s current belief that she should start a gizmo company isn’t based on a single consideration, it’s a result of the fact that several different factors line up in a way that makes that specific plan look like an especially good idea. So of course she has several different cruxes. Similarly with views on marginal tax rates.
For my second comment: ‘Primarily look for things that would change your own views, not for things that would change the other person’s views’ is one of the core advantages of focusing on cruxes, in my opinion, and it didn’t seem to be a focus of the OP. It’s something that’s missing from your suggested substitute (“Look for key considerations”) and from your discussion of the example of how experts philosophers handle disagreements. e.g., If Theist is the one pressing the moral argument for the existence of God, because Theist guesses that it might shift Atheist’s views, then that is not a conversation based on cruxes. Whereas if Atheist is choosing to focus the discussion on that argument because Atheist thinks it might shift their own views, then it sounds like it is very similar to a conversation based on cruxes.
On the question of whether cruxes are all-or-nothing or a matter of degree: I think of “crux” as a term similar to “belief”. It suggests sharp category boundaries when in fact things are a matter of degree, but it’s often a good enough approximation and it’s easier for a person to think about, learn, and use the rest of the framework if they can fall back on the categorical concept. Replacing “look for cruxes” with “look for considerations to which your beliefs have relatively high credence sensitivity” also seems like a decent approximation. Doing a Value of Information calculation also seems like a decent approximation, at least for the subset of considerations that are within the model. I could say more to try to elaborate on all of this, but it feels like it really needs some concrete examples to point at. If a discussion like this was happening at a workshop, I’d elaborate by looking at the person’s attempts to come up with cruxes and giving them feedback.
(I’ll repeat here: this comment is about cruxes, not about double crux in particular.)