In analytic philosophy, 'skeptical theism' usually refers to an insistence on this idea in the context of atheist arguments from evil. There are a number of explicit analytic formulations that are commonly discussed, but Bergmann's ("Skeptical Theism and Rowe’s New Evidential Argument from Evil", Nous 35, pp. 278-296 (PDF)) is arguably the most discussed. According to Bergmann:
(ST1) We have no good reason for thinking that the possible goods we know of are
representative of the possible goods there are.
(ST2) We have no good reason for thinking that the possible evils we know of are
representative of the possible evils there are.
(ST3) We have no good reason for thinking that the entailment relations we know of
between possible goods and the permission of possible evils are representative
of the entailment relations there are between possible goods and the permission
of possible evils
(To which has often been added since,
(ST4) We have no good reason for thinking that the total moral value or disvalue we perceive in certain complex states of affairs accurately reflects the total moral value or disvalue they really have,
but this will not be relevant for this post. Notice, incidentally, that not one of these is actually skeptical theism itself, and the question of whether they are true is entirely independent of any question in natural theology.)
The most famous response to Bergmann is by Almeida and Oppy ("Sceptical Theism and Evidential Arguments from Evil", Australasian Journal of Philosophy 81, pp. 496 – 516 [available here]). In response to it, they argue:
Suppose we take seriously the idea that it follows from our acceptance of (ST1)-(ST3) that it is not unlikely that there are goods beyond our ken--or relations beyond our ken between goods and evils (which themselves may or may not be beyond our ken)--which justify a perfect being in not preventing E. Suppose further that we are, right now, witnesses to E, and that we could intervene to stop it at no personal cost. What we have just conceded is that, merely on the basis of our acceptance of (ST1)-(ST3), we should insist that it is not unlikely that there is some good which, if we were smarter and better equipped, we could recognise as a reason for a perfect being’s not intervening to stop E. Plainly, we should also concede—by parity of reason—that, merely on the basis of our acceptance of (ST1)-(ST3), we should insist that it is not unlikely that there is some good which, if we were smarter and better equipped, we could recognise as a reason for our not intervening to stop the event. That is, our previous concession surely forces us to allow that, given our acceptance of (ST1)-(ST3), it is not unlikely that it is for the best, all things considered, if we do not intervene. But, if we could easily intervene to stop the heinous crime, then it would be appalling for us to allow this consideration to stop us from intervening.
I have always been baffled by this argument. Let's start with the the basic idea, which is that, given that an evil E is not prevented and that we are in a position to prevent and that (ST1)-(ST3) are accepted:
(A) It is not unlikely that there are goods beyond our ken which justify a perfect being in not preventing E.
They then claim that something like this would then follow:
(B) It is not unlikely that there is some good which, if we were smarter and better equipped, we could recognize as a reason for a perfect being not intervening to stop E.
It is quite obvious that (B) does not follow from (A) on the most obvious interpretation. (A) doesn't tell us anything about what we could recognize if we were smarter and better equipped. It is entirely consistent with (A) and all the rest to say that perhaps the relevant good could only be recognized by a perfect being. One could perhaps get the following from (A) and (ST1-ST3) and the existence of E:
(B') It is not unlikely that there is some good which, if we were perfect beings, we could recognize as a reason for a perfect being not intervening to stop E.
Note that this, unlike (B), is a per impossibile conditional; it does not imply that there is any level of "smarter and better equipped" that we could actually have that would put us in a position to recognize it.
Almeida and Bergmann do actually recognize in a footnote that there is an issue here, but claim that it would not fundamentally change the argument -- it would complicate the exposition, but the argument would still go through. They give no reason for thinking this, and, as will soon be seen, I do not see how it could possibly be true.
In any case, they then go on to say that, by parity of reasoning, we should then also accept:
(C) It is not unlikely that there is some good which, if we were smarter and better equipped, we could recognize as a reason for our not intervening to stop the event.
But this quite clearly does not follow by any parity of reasoning even if one accepts (B); it requires the assumption that the relevant reason would be a generic reason applying to any agent who recognized it, rather than a reason applying to a perfect being.
The parity of reason occurs only if we read (B'); but then we should get
(C') It is not unlikely that there is some good which, if we were perfect beings, we could recognize as a reason for our not intervening to stop the event.
This, again, is a per impossibile conditional; it does not imply that it is actually possible that we could recognize such a reason.
They then say that we should then conclude:
(D) It is not unlikely that it is for the best, all things considered, if we do not intervene.
But this does not follow even if we accept (C); it requires the assumption that we can act on reasons that we know exist even if we do not know what they actually are, which is at least controvertible, and the assumption that a reason we could recognize if we were smarter and better equipped is relevant to us given that we are not, in fact, smarter and better equipped. That is, it makes the assumption that our reasons are not affected by how smart and equipped we are, so that if we would have a reason if smarter and better equipped, we would have it even given that we are not.
This is certainly false. If John could be a professional driver, and as a professional driver would have a reason for not slowing down, it does not follow that John, who is not actually a professional driver, has the same reason for not slowing down -- indeed, given that John is not a professional driver, he may only have reasons for slowing down. If I would have a reason to skip a step in a calculation if I were smarter than I am, it does not follow that I have such a reason given that I am not smarter than I am.
I find their response to a similar objection equally baffling as the rest. They say:
Yet, if we do not have good reason to assign a low probability to the claim that there are goods which, if we were smarter and better equipped, we would recognise as reasons for us not to prevent E, then how can we have good reason to interfere and to prevent it?
But the answer to this seems fairly obvious: since we do not know what the reason in question actually is, we do not know if its being a reason for not acting would actually be independent of our being smarter and better equipped; for all we know, the reason why our smarter and better equipped selves would have such a reason is only because they are smarter and better equipped. Our having good reasons or not to interfere, as we are, is not in any way affected by the question of what reasons we would have if we were different from what we are. Trying to latch the two together seems absurd, as if one were to claim that, since I would have reason not to buy the cheapest product if I were a millionaire that I therefore don't have reason to buy the cheapest product given that I am not, or as if one were to claim that, since I would have reason not to buy health insurance now if I knew that I would be very healthy for the next fifty years, I must therefore not have reason to buy it given that I am not privy to this information. An expert may have excellent reason to do something while the kids have excellent reason not to try it at home; and the same is true for not doing things. What actions are reasonable is affected by how intelligent and effective our plans can be, and thus how smart and well equipped we are. You can't assume that if you were smarter and had better means that your reasons for acting or not acting would remain the same; this would have to be proven. Not all reasons that would be good if we were different are reasons that are good given that we are not.
And what actually seems to follow, anyway, is not (D) but something more like:
(D') It is not unlikely that if we were perfect beings, it would be for the best, all things considered, if we did not intervene.
Again, a per impossibile conditional. And it doesn't imply anything about what is the best for us given that we are not perfect beings.
(B'), (C'), and (D') are completely useless for the argument that is being made; they follow from (A), but that's just because they are ways of restating (A) in per impossibile form. What they actually need is (D), but (D) very definitely doesn't follow from (C), much less (B) or (A).
Almeida and Oppy have another argument that is related, that we use an inference in moral reasoning that is closely analogous to the 'noseeum inference' that (ST1)-(ST2) are supposed to prevent (a 'noseeum inference' is an inference from 'I don't see any' to 'There aren't any'). But it seems, even if we assumed that this was true, to make the same error noted above: in moral reasoning, we are considering the reasons appropriate to us, and we have ways of running through the different reasons appropriate to us so as to eliminate possible counterexamples -- which is how noseeum inferences are rationally supported. But the whole point of skeptical theism is that we have no way of doing this if we are non-omniscient reasoners talking about omniscience. If you have a problem that requires searching or testing of a restricted set of possibilities, this may be soluble; but this solubility implies nothing about problems requiring search or test of unlimited possibilities -- or even necessarily about problems requiring search or test of a different set of possibilities.
It is very possible that I am missing something, but, as I said, I find every part of the argument completely baffling. Would I have reason to accept it if I were smarter and better equipped? I have no idea, but even if I did, I do not know what it would be.