I’ve taken the Prosblogion survey several times now, and I’m convinced that, given the constraints and assumptions of the questions, one’s answers will always imply that there is a Necessary Being. The argument(s) generated at the end of the survey rely on modal logic, specifically axiom S5, in which ‘possibly necessarily’ entails ‘necessarily.’ I’ll be the first to admit that my grasp of modal logic is less than secure. My understanding of arguments that rely upon it, such as Plantinga’s modal ontological argument, has been greatly aided by this exchange with Rick Taylor that I believe is also relevant here. It’s tricky, even for philosophers trained in making such distinctions, to distinguish between the various definitions of possibility that are at play in such modal arguments. Typically, ‘possibility’ is understood to mean ‘logical possibility’ or some state of affairs that entails no contradiction. However, logical possibility in this sense is not equivalent to modal possibility.
To use Mr Taylor’s example, the following assertions are logically possible: 1) Unicorns exist in no possible worlds 2) Unicorns exist in some but not all possible worlds 3) Unicorns exist in all possible worlds. Although these assertions are all logically possible, they are not all modally possible. That is to say, it’s not possible to construct three worlds in which 1 is true in one world, 2 is true in the second, and 3 is true in a third. That’s because, in S5, if 1 is true in one possible world, then it’s true in all of them, and likewise for 2 and 3. Note that 1 asserts that Unicorns are impossible (metaphysically) even though 2 and 3 are logically possible, i.e. coherent statements. So we have to be careful to avoid such equivocation when discussing ‘possibility.’ In my humble opinion, modal theistic arguments, including those presented at the end of the survey, trade on this equivocation. For example, one might ask, ‘is it possible that there is a Necessary Being?’ This depends on how we understand possibility. If one means ‘is this a logically possible, i.e. coherent or non-contradictory, statement?’ the answer is surely ‘yes.’ If one construes ‘possible’ along the lines of S5, however, this innocent answer has the implication that a Necessary Being exists if its existence is even possible!
If we phrase the question differently, ‘is it modally possible that there is a Necessary Being?’ I think the atheist can safely deny this. Remember, ‘necessary’ in modal terms just means ‘existing in all possible worlds.’ Note that in the above example, statement 3, ‘Unicorns exist in all possible worlds’, just is to say that Unicorns are necessary. Nevertheless, I think one can deny that Unicorns are modally possible, despite the concept being coherent, and one can do the same in the case of God. One can deny that God exists in all possible worlds, which just is to deny that there is a Necessary Being.