Why do many philosophers posit that there are no members in the set of necessary beings? There seem only two explanations if they are correct: 1) Necessary beings are logically possible, but none exist in this world or 2) Necessary beings are logically impossible. Explanation 1 seems untenable since if a necessary being exists in one world (is logically possible), then it must exist in all worlds (and thus this one) by virtue of its necessity. But explanation 2 (which seems likely the more preferred one) seems to do no better, since the set of necessary beings is made a subset of the set of impossible beings. While perhaps this is merely a trivial case, it still seems unsettling, if not contradictory. Is the existence of at least one necessary being necessary? Or is there some other explanation for how none could exist?