What do we learn about God's existence from the clear failures to find justification for evils?

Suppose we know of some evil e₁, and careful further investigation clearly fails to turn up justification that God would have to allow that evil. Let F₁ be that clear failure.

Now, those who defend the inductive argument from evil claim that F₁ is evidence against the existence of God. But now presumably sometimes after investigation of some other evil, say e₂, we do not clearly fail to turn up justification for an evil (i.e., we either find a justification or it is unclear whether we have done so). Presumably, in that case the clear failure F₂ to turn up a justification would have been evidence against the existence of God. But now it is a basic Bayesian result that the absence of F₂ is evidence for the existence of God.

In practice, the results of investigation vary from evil to evil. Sometimes we clearly fail to find a justification and sometimes we don’t clearly fail. When we clearly fail, that is Bayesian evidence against theism. When we don’t clearly fail, that is Bayesian evidence for theism. What does the totality of the evidence say?

We don’t know. We just don’t have the numbers. We don’t have good numbers as to how many investigations resulted in a clear failure to turn up a justification and how many have not. Nor do we have any really good estimates of the crucially important conditional probabilities for any particular evil, namely how likely we are to clearly fail to find a justification assuming God exists and how likely we are to clearly fail to find a justification assuming God doesn’t exist.

The answer to the question in the title of the post, then, is: Not much.

One might object that I stacked the deck by talking of clear failures to find a justification. Perhaps I should instead have talked of failures to clearly find a justification. Failures will then be much more common, and there will be very few cases of clear finding of a justification. However, at the same time, our expectation that we be able to clearly find a justification given God’s existence will not be that strong. For these are controversial matters, where clarity is hard to have, and we would expect them to be such. Indeed, it is not clear that assuming the existence of God we would ever expect to clearly have found a justification, because there could always be further evil consequences down the road that we did not take into account.