About five days after I was informed that the reviews had been completed for my paper on probability, I received notice from the editor that the paper had been rejected, along with copies of the review. I don't know what caused that delay.
The reviewers were plainly over their heads. One reviewer objected that I'd not shown whether numeric probabilities could be assigned. Real numbers are completely ordered; in the case of any two different numbers, one is always bigger than the other. So, if real numbers can be assigned to a preördering, then the preördering must be complete. And I had repeatedly made it plain that I was discussing preörderings that were not assumed to be complete. The other reviewer objected that I'd not cited recent literature, but I'd found no recent work on probability as an incomplete preördering, and the literature that he or she suggested didn't include such work. More generally, the two reviewers simply didn't understand what I was trying to do, though I'd stated it clearly; it was outside of a box in which they remainded.
Unsurprisingly, I was hugely disheartened that three academic philosophers — the two reviewers and the editor who accepted incompetent reviews — were so cognitively impaired.
I set to revising the article to explicitly state some obvious things that they'd not seen, and to state more bluntly or repetitively things that I'd said but that had been ignored.
After I was done with that, a friend was kind enough to make a very careful reading of the manuscript. He found a technical error in the exposition that was easily fixed, and the omission of a word. He made a large number of suggestions concerning style, and I made changes in response to nearly all of them. And he expressed concern that the paper may not find reviewers who understand it.
I now need to find another journal to which to submit it.
I had one journal in mind, but looking at the guidelines for authors has made me wary. The editor wants only unblinded copies (that it to say copies in which the author's name is presented), and requires authors to suggest five specific individuals as reviewers; these practices undermine objectivity in peer-review. He deëphasizes technical matters; my paper is very technical. And he wants a copy both of the paper in PDF and of the
original file; to specify the file format in that manner makes him seem actively foolish. He should specify the acceptable formats; he would be likely to think that I were being deliberately difficult — rather that conscientious — if I sent a file in the format native to LyX.