Bill Vallicella and I have been worrying about variants of the problem how an atheist who does not believe in objective good and evil can formulate an argument from evil against the existence of God (see this post on Vallicella's blog and this post on Prosblogion). The problem is that the argument from evil requires objective evil. (If we were talking of subjective evil, theodicy becomes trivial--we can say that the evils of this world are evils from our point of view, but not from God's.)
Here is one way of formulating the problem. On the view that there is no such thing as objective evil, the term "objective evil" becomes nonsense--the view isn't merely that there happens not to be objective evil, but that the concept makes no more sense than the concept of a perception with no perceiver.
Here I want to raise the problem of auxiliary premises. I will formulate the following in the case of the deductive argument from evil for simplicity, but I think the issues generalize to the inductive case.
The typical theist believes that God exists and that objective evil exists. She is very unlikely to grant that if evil exists, then God exists. Thus, the deductive argument from evil requires some additional premises besides the claim that evil exists. At least one of these premises will involve both "God" and "(objective) evil", and our atheist takes the second of these terms to be nonsense--and the first, too, most likely.
Perhaps, this will be a premise like: "If God exists, he eliminates all evils he can." Now this premise will not be a mere tautology. Even if we grant that tautologies using nonsense terms make sense, a controversial question (see this this post and discussion on my blog), so that all borogoves are borogoves, a non-tautologous statement involving nonsense terms, such as that some borogoves are mimsy, seems to be simply nonsense.
So our atheist's argument from evil involves premises that she believes to be nonsense. This creates, first of all, a formal problem. What does it mean for an argument involving nonsensical sentences to be valid? Perhaps a purely formal solution to this can be given--if it is has the form of a valid argument, it is a valid argument (If all borogoves are mortal, and George is a borogove, then George is mortal). I think we shouldn't be too sure. The distinction between narrowly logical necessity, on the one hand, and conceptual necessity on the other hand, is not as clear as one might wish.
But I want to raise a second worry. These auxiliary premises cannot be something the atheist coherently believes, since the atheist takes these premises to be nonsense. The argument thus is not just a reductio, but an ad hominem one.
But now we have a problem that I touched on in my last prosblogion post on this topic, though perhaps not as clearly. Suppose the theist simply rejects one of these auxiliary premises. The atheist cannot say that the premise is true. The most she can say is that by the theist's lights it is true. But to say that the premise is true by the theist's lights when the theist rejects it seems to involve at least a little chutzpah. Moreover, how can the atheist criticize the theist for denying a premise that by the atheist's own lights is nonsense? Perhaps the atheist can give a formally valid auxiliary argument from other premises that the theist believes. But similar problems are going to come up, since the conclusion of that auxiliary argument is nonsense, and hence at least one of its premises is nonsense or else its premises are inconsistent.
The basic point here is this: The theist can always get out of the atheist's argument by rejecting something that the atheist thinks is nonsense or contradictory--and how can the atheist complain about that?
Let's go back to the concrete issue. Our atheist does not think that God, if he exists, eliminates all (objective) evils he can--that conditional is nonsense by our atheist's lights. The theist doesn't believe that either. So where is the conflict? Perhaps the atheist can argue that if x is omnibenevolent, then x eliminates all (objective) evils. But our theist presumably rejects that, just as our atheist does, though for different reasons (the theist because she thinks it's false, and our atheist because she thinks it's nonsense). Perhaps the atheist can give a compelling analysis of omnibenevolence. But there is chutzpah in giving an analysis of omnibenevolence that you think is nonsense, and it is hard for the atheist to object to an alternate analysis that yields a different conclusion, since our atheist thinks both analyses are nonsense.
Of course some atheists do believe in objective good and evil, and these issues do not come up.