That does seem to change things… Although I’m confused about what simplicity is supposed to refer to, now.
In a pure bayesian version of this setup, I think you’d want some simplicity prior over the worlds, and then discard inconsistent worlds and renormalize every time you encounter new data. But you’re not speaking about simplicity of worlds, you’re speaking about simplicity of propositions, right?
Since a propositions is just a set of worlds, I guess you’re speaking about the combined simplicity of all the worlds. And it makes sense that that would increase if the proposition is consistent with more worlds, since any of the worlds would indeed lead to the proposition being true.
So now I’m at “The simplicity of a proposition is proportional to the prior-weighted number of worlds that it’s consistent with”. That’s starting to sound closer, but you seem to be saying that “The simplicity of a proposition is proportional to the number of other propositions that it’s consistent with”? I don’t understand that yet.
(Also, in my formulation we need some other kind of simplicity for the simplicity prior.)
I’m currently turning my notes from this class into some posts, and I’ll wait to continue this until I’m able to get those up. Then, hopefully, it will be easier to see if this notion of simplicity is lacking. I’ll let you know when that’s done.
That does seem to change things… Although I’m confused about what simplicity is supposed to refer to, now.
In a pure bayesian version of this setup, I think you’d want some simplicity prior over the worlds, and then discard inconsistent worlds and renormalize every time you encounter new data. But you’re not speaking about simplicity of worlds, you’re speaking about simplicity of propositions, right?
Since a propositions is just a set of worlds, I guess you’re speaking about the combined simplicity of all the worlds. And it makes sense that that would increase if the proposition is consistent with more worlds, since any of the worlds would indeed lead to the proposition being true.
So now I’m at “The simplicity of a proposition is proportional to the prior-weighted number of worlds that it’s consistent with”. That’s starting to sound closer, but you seem to be saying that “The simplicity of a proposition is proportional to the number of other propositions that it’s consistent with”? I don’t understand that yet.
(Also, in my formulation we need some other kind of simplicity for the simplicity prior.)
I’m currently turning my notes from this class into some posts, and I’ll wait to continue this until I’m able to get those up. Then, hopefully, it will be easier to see if this notion of simplicity is lacking. I’ll let you know when that’s done.