At present this paper is too long. I advise the author(s) to shorten it substantially (it is currently about twice as long as the journal's recommended limit). However, in light of the report below, merely shortening the manuscript will not be enough, and the needed modifications will likely not be achieved in only one or two rounds of revisions.
Reviewer #2:
The positive: I think the proposal made by this paper is both ultimately correct and timely --- arguably (well) overdue. I think it's right to emphasize the many advantages of representing uncertainty in terms of probability distributions on real variables and to stress that we might want to go further but that ultimately how far one goes is largely a matter of practical questions.
However, I have a couple complaints that I imagine the author will find unsurprising. First, I think the paper is much too long. The first 24 pages are devoted to setup; that really could be 5, or even 3. I honestly think that there's a paper in here that's half as long as the present version and is better for it.
In addition, I suspect that the appendix could be substantially shortened, though I don't have a good feel for how that would affect the proof and/or paper overall. For instance, both Lemma 3 and 4 are well-known themselves or trivial consequences of well-known results. If the paper were shorter, it might be worth working through the proofs of these lemmas, but given its current length, it may be worthwhile to simply point to prior proofs of them and only carry out the final step of the derivation.
Second, I found the paper's organization a bit unhelpful. I think the paper would have been better served by introducing the positive proposal and then arguing that it was preferable to either PP or IP on each issue; I suspect this would help with length, but the main issue is that there are often 30+ pages of text between the initial description of a problem and the discussion of how the positive proposal handles it. This makes the positive argument harder to follow than it would otherwise be.
Third, I think the paper sometimes struggles with tailoring the level of description to the intended audience. As I see things, the intended audience here are philosophers who are familiar with philosophical treatments of uncertainty --- at least with the basics of PP, and more typically with at least some of the details of the debates about IP --- but not with the statistical tools that the paper is introducing.
At present, however, the paper seems to devote much more energy to spelling out the basics of the former compared to the latter. Perhaps I'm underestimating my colleagues in philosophy, but I think the paper would be best served by assuming that the audience has no more than a college intro-level understanding of the relevant statistics. So, for instance, it would be good to explicitly state why the approach violates locality and/or what the parameters are in "parameter uncertainty." At present, I worry that the (relatively) technical details found in the discussion of the advantages of the proposal will be inaccessible to the typical reader.
Again, I think that this would be helped by reorganization. Introducing the positive view first, on its own, and only then comparing it to the alternatives would put the reader in a better position to understand the parts of this paper that are new (to philosophy).
The suggestions regarding re-organization should be regarded as exactly that: they represent my view on how to best approach the problem. The author may well be able to find alternative solutions that work better. By contrast, I think the issue of length is substantial: the paper does not do enough to warrant its current length and in fact I think the current length undermines the paper's effectiveness in communicating its central message. I have trouble imagining recommending acceptance on this paper unless it is substantially shorter.
Minor comments:
1 - "Let's think about the uncertainty about a proposition" strikes me as awkward.
2 - "and notoriously there exist on inaccuracy measure of an imprecise credal" -- I assume "no" is meant here instead of "on"; I'd also suggest opting for "there are no inaccuracy measures for" rather than the current wording.
6 fn 3 - van Fraassen is cited here as just "Fraassen"
15 - I understand this paper's goal to be introducing statistical techniques that rely on parameter uncertainty to the literature as an alternative. As such, it seems to me that the paper should spell out why Joyce's approach violates locality, as it might not to be obvious to readers unfamiliar with these techniques.
16 - with proper scoring rules, agents will score their own credences to be less inaccurate or more accurate than alternatives, but the paper currently reads "more inaccurate."
19 - the notion of "epistemic peer" at work here seems to me to be dated; if you check out (e.g.) the SEP article on disagreement, the defintion of "peer" there is only a person who is in an equally good epistemic position.
25 - as in 15: I think the paper should be clearer here with terminology. The paper assumes that the reader knows that treating P(X) as a random variable is equivalent to allowing for probability distributions over parameter values, but (given the goal of the project) I suspect that the intended reader won't know this.
28-29 - I'm confused about the role this discussion is playing in the paper overall. To be sure, the contrast between these two different kinds of intervals is interesting, but what does it have to do with the positive proposal?
32 - should be "binning and taking the limit" not "binning ad taking the limit"
63-64 - I find the discussion of uniform priors here to be broadly unnecessary
68 - there's an additional end parentheses in the final sentence on this page
70 - I found the "(and the equality holds only if p = q)" parenthetical confusing. I think moving it out of the main line of the proof would help with this.
71 - there seems to be something wrong with the last line of the proof of Lemma 4; that, or (equally possible) I've misunderstood something.
71 - the syntax is broken generally speaking at the bottom of this page (and again first full sentence of 72)
72 - extra $ about halfway down the page
72 - not consistent with the syntax of EI on the final line
Here are the comments:
COMMENTS TO THE AUTHOR:
Comments from the Editor:
At present this paper is too long. I advise the author(s) to shorten it substantially (it is currently about twice as long as the journal's recommended limit). However, in light of the report below, merely shortening the manuscript will not be enough, and the needed modifications will likely not be achieved in only one or two rounds of revisions.
Reviewer #2:
The positive: I think the proposal made by this paper is both ultimately correct and timely --- arguably (well) overdue. I think it's right to emphasize the many advantages of representing uncertainty in terms of probability distributions on real variables and to stress that we might want to go further but that ultimately how far one goes is largely a matter of practical questions.
However, I have a couple complaints that I imagine the author will find unsurprising. First, I think the paper is much too long. The first 24 pages are devoted to setup; that really could be 5, or even 3. I honestly think that there's a paper in here that's half as long as the present version and is better for it.
In addition, I suspect that the appendix could be substantially shortened, though I don't have a good feel for how that would affect the proof and/or paper overall. For instance, both Lemma 3 and 4 are well-known themselves or trivial consequences of well-known results. If the paper were shorter, it might be worth working through the proofs of these lemmas, but given its current length, it may be worthwhile to simply point to prior proofs of them and only carry out the final step of the derivation.
Second, I found the paper's organization a bit unhelpful. I think the paper would have been better served by introducing the positive proposal and then arguing that it was preferable to either PP or IP on each issue; I suspect this would help with length, but the main issue is that there are often 30+ pages of text between the initial description of a problem and the discussion of how the positive proposal handles it. This makes the positive argument harder to follow than it would otherwise be.
Third, I think the paper sometimes struggles with tailoring the level of description to the intended audience. As I see things, the intended audience here are philosophers who are familiar with philosophical treatments of uncertainty --- at least with the basics of PP, and more typically with at least some of the details of the debates about IP --- but not with the statistical tools that the paper is introducing.
At present, however, the paper seems to devote much more energy to spelling out the basics of the former compared to the latter. Perhaps I'm underestimating my colleagues in philosophy, but I think the paper would be best served by assuming that the audience has no more than a college intro-level understanding of the relevant statistics. So, for instance, it would be good to explicitly state why the approach violates locality and/or what the parameters are in "parameter uncertainty." At present, I worry that the (relatively) technical details found in the discussion of the advantages of the proposal will be inaccessible to the typical reader.
Again, I think that this would be helped by reorganization. Introducing the positive view first, on its own, and only then comparing it to the alternatives would put the reader in a better position to understand the parts of this paper that are new (to philosophy).
The suggestions regarding re-organization should be regarded as exactly that: they represent my view on how to best approach the problem. The author may well be able to find alternative solutions that work better. By contrast, I think the issue of length is substantial: the paper does not do enough to warrant its current length and in fact I think the current length undermines the paper's effectiveness in communicating its central message. I have trouble imagining recommending acceptance on this paper unless it is substantially shorter.
Minor comments:
1 - "Let's think about the uncertainty about a proposition" strikes me as awkward. 2 - "and notoriously there exist on inaccuracy measure of an imprecise credal" -- I assume "no" is meant here instead of "on"; I'd also suggest opting for "there are no inaccuracy measures for" rather than the current wording. 6 fn 3 - van Fraassen is cited here as just "Fraassen" 15 - I understand this paper's goal to be introducing statistical techniques that rely on parameter uncertainty to the literature as an alternative. As such, it seems to me that the paper should spell out why Joyce's approach violates locality, as it might not to be obvious to readers unfamiliar with these techniques. 16 - with proper scoring rules, agents will score their own credences to be less inaccurate or more accurate than alternatives, but the paper currently reads "more inaccurate." 19 - the notion of "epistemic peer" at work here seems to me to be dated; if you check out (e.g.) the SEP article on disagreement, the defintion of "peer" there is only a person who is in an equally good epistemic position. 25 - as in 15: I think the paper should be clearer here with terminology. The paper assumes that the reader knows that treating P(X) as a random variable is equivalent to allowing for probability distributions over parameter values, but (given the goal of the project) I suspect that the intended reader won't know this. 28-29 - I'm confused about the role this discussion is playing in the paper overall. To be sure, the contrast between these two different kinds of intervals is interesting, but what does it have to do with the positive proposal? 32 - should be "binning and taking the limit" not "binning ad taking the limit" 63-64 - I find the discussion of uniform priors here to be broadly unnecessary 68 - there's an additional end parentheses in the final sentence on this page 70 - I found the "(and the equality holds only if p = q)" parenthetical confusing. I think moving it out of the main line of the proof would help with this. 71 - there seems to be something wrong with the last line of the proof of Lemma 4; that, or (equally possible) I've misunderstood something. 71 - the syntax is broken generally speaking at the bottom of this page (and again first full sentence of 72) 72 - extra $ about halfway down the page 72 - not consistent with the syntax of EI on the final line