Closed rfl-urbaniak closed 7 months ago
I have an idea on how to fix the section on the two items of match evidence. The general line of argument in the paper is that higher order probabilism can address problems that imprecise probabilism fails to address (belief inertia, proper scoring rules, etc.). Now, the section on the two items of match evidence can (a) formulate a new challenge for imprecise probabilism and (b) show that this challenge can be addressed by higher order probabilism.
(a) The new challenge for imprecise probabilism is how to do updating given two pieces of evidence. Would point-wise updating on all the probability functions within a set do? It seems there will be problems with that. So the section should describe these problems. Currently the section talks about the problems with using intervals, but not with sets of probabilities. So this needs to be reworked but it should not be too difficult to do.
(b) The next step is then to show that higher order probabilism fares better along the lines already described in the section. So that part should be quick to do, just using existing materials.
I think (a) and (b) would make the section better integrated in the argument of the paper.
I read the imprecision paper quarto version. I like it a lot, but here are some comments:
By the way, section numbers are missing in the pdf of the quarto version. Not sure why.
Introduction: good
Precise v. imprecise probabilism: good, just minor things
Is the objection to imprecise probabilism about compatibility a novel objection or did others already formulate it? Just make that clear. The objections is otherwise very interesting.
Higher order probabilism: good, just some minor things
One more question: maybe it is helpful to show why imprecise probabilities does not run into the same potential issues that higher order probabilism runs into. Let me explain. Higher order probabilism needs to explain how we conceptualize higher order probabilities (p. 9). Instead, imprecise probabilism can simply say that an agent can entertain many (compatible) probabilities. Is this why the problem does not arise for imprecise probabilism? Is this an advantage of imprecise probabilism?
The two sections about the legal examples do not work well with the rest of the paper. I am not sure what to do with them. I need to think about them. They break the flow of the argument. We need to think of how to integrate them or remove them. To be discussed.
Accuracy in the second order section: great section, but some issues below
Discussion