Gadianton wrote:in terms of possible worlds, "necessity" just means a feature common to all possible worlds. You can have a restricted class of possible worlds bound to our laws of science -- nomological possibility.
I suppose that this is just the problem, to define the space between "impossible" and "actual". What exactly do the possible worlds have that the impossible worlds lack? What has the actual world got that the possible worlds ain't got?
Physics at least provides a certain hierarchy of degrees of possibility. The issue of initial conditions that I raised earlier was maybe awkwardly introduced because it unnecessarily conflated the issues of beginning and actuality. An actual solution can be determined by sufficient conditions on any spacelike hypersurface. Usually that hypersurface is taken to be "the initial time", but it doesn't have to be. The main point here is that since natural laws are all differential equations they admit many solutions as possible, and all they say about telling which one of them is the actual one is, "Look and see."
So the top tier of "possible but not necessarily actual" is "solution to the equations of motion". Physics says pretty much nothing about what crowns the actual winner out of this short list of possible winners.
There are lower tiers of possibility, I suppose, for solutions to other equations which we think are not the actually right equations but which could in principle have been the right equations for some universe. And there's probably some amount of consensus among physicists about what kinds of changes to the equations would count as small or big. It's a serious business among particle theorists, for instance, to ask what changes to the Standard Model might have passed undetected until now but be easiest to see next.
So "possible" seems like an awfully broad term to me. I have no confidence that we can say where its outer limits are and thus declare that anything is absolutely impossible, or conversely that anything is absolutely necessary. I don't feel that this cripples theology, though. To a child—or a Medieval—it might seem possible that birds could fly to the moon because air is taken for granted as something that must always be everywhere. Once you know what air is, and what the moon is, you understand otherwise. I'm not sure our current grasp on what reality is is any better than a medieval child's grasp on what air is. So I think it might seem perfectly possible to us now that there might be no God, even though in fact it's impossible because reality needs God, for reasons we don't yet understand.
