Some truths are necessary (must be the way that they are) and others are contingent (could have been otherwise). Some truths may be necessary but we don’t know that they are. It is the nature of such unknown truths, however, that if they turn out to be false, they are necessarily false. They can never be contingent truths. (Obviously, there are also unknown contingent truths, but things like Goldbach’s Conjecture are not among them.)
But there are also truths observed to universally hold, such as the nature of gravity. So far as we can tell, gravity behaves the same everywhere and has always done so. Does this make gravity a necessary truth about the world?
No, because the test, again, is if I can conceive a world in which gravity fails to hold without bringing about a logical contradiction. I can. Therefore, the behavior of gravity, its properties, do not constitute a necessary truth about the world. As a matter of fact, it has been demonstrated that if the universe had four spatial dimensions instead of three, gravity would be different — it would be described by an inverse-cube rather than an inverse square. In such a world, interestingly, there would be no solution to the two-body problem, which means that there could be no stable orbits and life as we know it would not exist.
From this it follows that while all necessary truths are universal (true in this world and at all possible worlds), not all universal truths are necessary. A universal contingent truth is true at this world but is false at other possible worlds.
Where does morality fit in to this scheme?
Is morality a necessary truth about the world? No. I can easily conceive worlds lacking morality, and do so without bringing about a logical contradiction.
Is, nonetheless, morality a universal, objectively observed to be the same everywhere, in the way that gravity is? Can morality, like gravity, be objectively and universally true, without being necessarily true?
No. In fact, obviously not! Were morality like gravity, we would observe all people behaving the same everywhere and at all times. This is so far the case from what we find that the point is hardly worth laboring. Think of the vast gulf between the moral values of secular humanism and the Taliban, for instance.
From all of this it follows that morality, or moral behavior, is neither necessary, or necessarily true depending on how the question is phrased, nor is it objectively true or universally true. The upshot is that the search for a necessary or at least universal morality is forlorn. To that extent, moral nihilism follows.
More later.