As I've said previously, the way I use those terms is different to how you use them. My "might" means the same thing as your "may". And for me, "may" really ought to be reserved for when we're talking about having permission, and not about possibility or probability at all. However, I acknowledge that I'm fighting a losing battle on that one, so I accept that many people use the word "may" to mean "might". As I said, though, for the purposes of your "simple argument" in this thread, nothing turns on probability anyway, so your "might" is just as good as your "may" in this context. As soon as you say "may" you're talking about a non-zero probability. When you say "x may be y", you're saying "There's a non-zero probability that x is y, and a non-zero probability that x is not y." But you haven't given us any guidance on how to estimate these probabilities a priori. For all we know, the probability that x is y could be negligibly small, or it could be a near certainty. All we know, as you say, is that it is conceivable that x is y. This makes any deduction derived from "x may be y" an especially weak one, particularly since we could replace every instance of "may" in your argument by "may not" and it would make no difference. I'd say the opposite of "might be" would be "couldn't possibly be". You're telling me that your "may" is the opposite of your "might", which makes things rather confusing, wouldn't you say?