See the crux tag. Duncan Sabien wrote the CFAR handbook’s double crux essay, etc.
A crux for a belief B is another belief C such that if I change my mind about C, that will also change my mind a lot about B.
E.g., my cruxes for “it’s raining” might include things like “I’m outdoors and can see and feel lots of water falling from the sky on me”, “I’m not dreaming”, “I don’t think aliens are trying to trick me”, and so on.
I don’t natively think in terms of cruxes. But there’s a similar concept which is more natural for me, which I’ll call a delta.
Imagine that you and I each model the world (or some part of it) as implementing some program. Very oversimplified example: if I learn that e.g. it’s cloudy today, that means the “weather” variable in my program at a particular time[1] takes on the value “cloudy”. Now, suppose your program and my program are exactly the same, except that somewhere in there I think a certain parameter has value 5 and you think it has value 0.3. Even though our programs differ in only that one little spot, we might still expect very different values of lots of variables during execution—in other words, we might have very different beliefs about lots of stuff in the world.
If your model and my model differ in that way, and we’re trying to discuss our different beliefs, then the obvious useful thing-to-do is figure out where that one-parameter difference is.
That’s a delta: one or a few relatively “small”/local differences in belief, which when propagated through our models account for most of the differences in our beliefs.
For those familiar with Pearl-style causal models: think of a delta as one or a few do() operations which suffice to make my model basically match somebody else’s model, or vice versa.
See the crux tag. Duncan Sabien wrote the CFAR handbook’s double crux essay, etc.
Or maybe you’re more like johnswentworth and you think in terms of model deltas not cruxes: