(A re-post from two years ago. Wishing all my readers a happy, healthy and successful new year!)
There is an astonishing discussion by Meiri here (link is to PDF at HebrewBooks). If I understand it correctly - and it is a little cryptic, so I may well be mistaken - he is saying that Rosh HaShanah is not really a time of judgment (which takes place constantly, not at a particular time), but Chazal declared it as such in order to have a season that would stimulate people to repent. If that is what he is saying, it would be a fascinating application of Rambam's idea of "necessary beliefs." But wouldn't it spoil it to say that it isn't actually true? (Which would also mean that I shouldn't be writing about it.) Presumably, if one is reasonably confident of one's audience, it would be acceptable if they are the sort of people for whom the facts are more helpful.