On 15 January, in response to a friend, I wrote
But I'm not particularly hopeful. The paper presents a confluence of challenges to philosophers, and I've come to doubt that most of them even with supposedly relevant expertise will recognize the hurdles and attempt to clear them until Authority has told them that they ought to do so.
The reported status of my probability paper remained
Reviews Completed into 21 January, but became
Reject some time in the morning. (I did not observe an intermediate status of
Editor Has a Decision.) The editors wrote
Thanks for submitting your manuscript to [journal] and for your patience during the process. One reviewer hasn't submitted their report for very long after accepting the task, despite the numerous reminder sent. We decided to seek for a third reviewer, who kindly agree to read the paper with a very short delay. Unfortunately, both reports point to a number of problems in the manuscript, we therefore decided not to offer publication at this stage.
Thanks again for your patience in waiting for the editorial decision.
(Note that the last reviewer was said to have agreed to read the paper with a very short delay.) The reporting reviewers were identified with
Reviwer #2 and
Reviewer #3, which suggests that the reviewer who never returned a report was the earliest to accept.
Reviewer #2 wrote
I think there are some good ideas in the paper, but it needs to be significantly more polished and tightly focused to be publishable. Please see attached report for more comments.
the attached report was not attached to the e.mail that I received, nor made available to me by way of Editorial Manager; so I am completely unable to consider whatever it may assert. I have written both to the Journals Editorial Office and to the handling editor noting that the report has not been furnished to me.
Reviewer #3 wrote
This is not an easy paper to judge; in a different type of journal I could come to a different judgment. However, I think that the paper is, in spite of its merits, not suited for the [journal]. I have four main concerns:
- The argument relies on research in logic and artificial intelligence. The average [journal] reader cannot be expected to be familiar with that formalism (in fact, I am not although I work on probability myself). It would be more appropriate for Reviw of Symbolic Logic, Artificial Intelligence or a similar journal.
- It is not fully clear whether the paper gives an original account of whether it is mainly a summary/presentation of results in the qualitative probability research program. So it is hard to assess the originality of the research.
- The author tries to embed the formal part of the paper into considerations about the history of probability and its use in science (e.g., confidence intervals in statistics), but these links remain tenuous and sometimes outright unconvincing. With respect to the coherence of the conceptual, philosophical and the formal part, the paper could be improved substantially.
- The writing could be clearer.
With respect to these concerns, I would have four responses:
- The formal logic as such of my paper is strictly material that can be found in undergraduate introductory courses, and I very deliberately made no reference to artificial intelligence as such, nor employed research peculiar to what is generally recognized as artificial intelligence. I did cite one article from a journal that is primarily consumed by such researchers, but that article was written to be accessible by a wider audience, and I cited the article only to support a claim that use of intervals (as opposed to bare preörderings) has not been completely satisfactory.
The formalisms that wouldn't be found in an undergraduate course in formal logic but are found in my paper are very simple and clearly defined. There are single symbols for each of the probability relations; for example,
▷for is more probable than. And there is
(X|c)for X, given c; so that
(X|c)▷(Y|d)would be read as
X given c is more probable than Y given d. That's it. Now, in everyday probability theory
p(X|c)already means the [measure of] probability of X given c, so my
(X|c)should be easily understood. Keynes and Koopman instead wrote
X/c(with a slash instead of a vertical bar, and without parentheses), which looks like arithmetic division.
If the reviewer works on probability him- or herself, and is not already used to formalism on this order, then he or she is unfortunately committed in practice to sufficient assumptions to ensure measurability of probabilities.
- The introduction to my paper clearly identifies the prior research and notes what that research failed to do. The body of the paper compares and contrasts my axiomata with those of the previous researcher who got furthest, and cites other work when it approximates my other axiomata.
- The paper is already too long to be accepted in various journals, but the reviewer wants me to labor issues further. And it would be good if he or she would provide an example of something that he or she found
- Similarly, I would want an example of a passage that the reviewer thought should be made more clear. I expect that what the reviewer truly felt was that the writing were spartan, which is often is, in order to keep its length in check.
I've now seen the report from Reviewer #2. It would probably take a paper of some length to explain everything wrong with it. I'll just furnish a couple of examples.
I use various terms from the English language in their ordinary, everyday senses, but the reviewer presumes that I must be using them in special senses, and then objects that I've not provided definitions. For example, I wrote
A pure frequentism or a pure combinatoric interpretation of probability would force [relation in which there is no relative order of probability] to be empty, as also (trivially) would betting quotients. But logicism and subjectivism in general do not require it to be empty. (An impure frequentism would be one in which [weak supraprobability] and [weak infraprobability] were always about beliefs about frequency; similarly for an impure combinatoric interpretation.)
Note that I even provided a parenthetical note that shows how an impure frequentism would be distinguished from a pure frequentism, but the reviewer insists that I'd introduced undefined jargon.
In my paper, I noted that twelve of what are the thirteen axiomata of my system are theoremata of the Kolmogorov axiomata, and the the remaining axiom
conforms to the Kolmogorov axiomata, so that they must be
at least as consistent as the Kolmogorov axiomata.
The reader can trivially verify that, while what I offer as axiomata are not sufficient to imply the Kolmogorov axiomata, his axiomata imply (A1) through (A5) and (A7) through (A13), and that (A6) conforms to the Kolmogorov axiomata. Thus, the axiomata are at least as consistent as are those popular systems, and are at least as consistent as are any systems whose axiomata imply those principles which are Kolmogorov’s axiomata.
The reviewer misrepresents me as using
conform in some special, undefined way, and as claiming that the thirteen axiomata are consistent for no better reason than because they exhibit such unexplained conformance.
 There is a very important sense in which logic itself is artificial intelligence, and I'd someday like to labor that point. But the reviewer was referring to intelligence in devices external to the human mind.
 Because the Kolmogorov axiomata use arithmetic, they must be incomplete or inconsistent; but I do not raise that issue in my paper.