On the other hand, I don't think this pair of questions show the moderating inconsistency you think it does. I don't think Scott actually pinpointed the problem with the first question; the issue is one of being interesting to research mathematicians (or logicians). The first question is ill-posed (does the questioner really mean without learning those subjects or without studying them in university? Do they mean "can" in the sense of no one preventing them from doing so, or in the sense it being something a person can reasonably expect to do). But for almost all variations, the answer is "well, you can do anything you want; it's a free country," but none of these are illuminating. It's just far too vague of a question for the answer to it to tell anyone anything. A question like "What mathematical background does one need to be a research logician" would at least be sensible question (to which one could answer "none" if one wanted, but I suspect some would disagree).

The second is a sensible question; it's clear what question is asking for, and one learns something by reading the answers, though lots of people might not think it's the sort of question MO is intended for. I certainly wouldn't have objected to closing the second question, but I think you can find much worse examples of moderating inconsistency.

The major difference between the two questions is that the first one doesn't make any sense, as it presupposes that "logic" is not part of "mathematics". Or at least that seems to have been the consensus of commenters as to why it ought to be closed.