What I mean, Barkley, is that the expression P(H|E), as held at time t=0, should—normatively—describe the belief about H you will hold at time t=2 if you see evidence E at time t=1. Thus, statements true in probability theory about the decomposition of P(H) imply the normative law of Conservation of Expected Evidence, if you accept that probability theory is normative for real-world problems where no one has ever seen an infinite set.
If you don’t think probability theory is valid in the real world, I have some Dutch Book trades I’d like to make with you. But that’s a separate topic, and in any case, most readers of this blog will at least understand what I intend to convey when I speak from within the view that probability theory is normative.
What I mean, Barkley, is that the expression P(H|E), as held at time t=0, should—normatively—describe the belief about H you will hold at time t=2 if you see evidence E at time t=1. Thus, statements true in probability theory about the decomposition of P(H) imply the normative law of Conservation of Expected Evidence, if you accept that probability theory is normative for real-world problems where no one has ever seen an infinite set.
If you don’t think probability theory is valid in the real world, I have some Dutch Book trades I’d like to make with you. But that’s a separate topic, and in any case, most readers of this blog will at least understand what I intend to convey when I speak from within the view that probability theory is normative.