This is what I thought at first (by "objectively important," we mean this in the sense of naive moral realism, at least):
- If there were an ultimately powerful, knowledgeable, and good being, it would be objectively important for us to know this.
- We can't know that.
- If it were objectively important that we know something, we could know it.
- Therefore, there's no ultimately powerful, knowledgeable, and good being.
Which means that if we can't know whether a certain thing exists, then we do know that it doesn't exist! I suppose we could say "if we can't directly know then we indirectly do know," but it's still a partially counterintuitive conclusion.
But none of the alternatives implicitly given seem much, if at all, better:
- (Deny (1)) There's a divine being, but it's not important to us that there is.
- (Deny (2)) We can know whether there's such a being.
- (Deny (3)) Something could be both objectively important and unknowable.
Or the meta-alternative:
- If a divine being exists, and is morally important, then moral importance is not (much/at all) objective.
(8) would not, I expect, appeal to every theist, despite being otherwise as close to the theocentric ethos as possible, here. (7) is either incoherent (violating the definition of "objective importance") or pointless (what does the concept of objective importance matter if there are indiscernible/undetectable cases?). (6) would mean that there is some direct way to know if a divine being exists, which is difficult to imagine (how can we differentiate concretely between a divine being existing and not existing?). (5) seems to have been Kant's conclusion insofar as he thought (in the Metaphysics of Morals) that we have no duties to God, so maybe (5) has a decent historical pedigree among the intelligentsia, but it still runs counter to my intuitions about a perfectly good being (or I would at least hope that I would be able to know about a being that was supposed to be perfectly good!).