In general, the insistence of people who follow these issues on classifying versions of the problem of evil as either “logical” or “evidential” is weird. It isn’t something you see with any other kind of argument in philosophy. What we care about with deductive arguments is first whether they are valid, and second whether the premises are true, whether people can agree that they’re true, whether people should agree that they’re true, etc.
If there’s agreement that an argument is deductively valid and the premises are true, it doesn’t matter if the premises are logical truths, if they’re necessary or contingent, or if they’re a priori or a posteriori. It matters somewhat whether we’re certain the premises are true, or whether we just think they’re just probably true, but thinking an argument’s premises are only probably true doesn’t turn the argument into an “evidential” or “probabilistic” argument.
I think Hallquist is right. In fact, even within the philosophy of religion we don’t find, say, theistic arguments classified as “logical” or “evidential.” (For example, have you ever seen someone refer to the ‘logical’ version of the kalam cosmological argument, as opposed to its ‘evidential’ version?)
Furthermore, Hallquist is not the first person to question the significance of the distinction. Daniel Howard-Snyder, in his introduction to his anthology, The Evidential Argument from Evil, wrote this.
While we may easily draw this distinction [between logical and evidential arguments from evil], we are hard pressed to defend its significance. I’m afraid I don’t have much to say about the matter, except for the obvious. I mean, whenever one meets what its author purports to be an argument from evil (in contrast with, say, the sort of response to horrendous evil that you might find in Albert Camus’s The Plague or Eli Wiesel’s Night), one ought to consider whether the author intends to assert that facts about evil known with certainty are incompatible with theism. If she does, then one should query why the argument is not dubious for the same reason that Mackie’s argument from evil is dubious. If she does not–that is, if she intends to say that facts about evil which are known with certainty make theism significantly unlikely, or that theism is incompatible with certain facts about evil that are themselves quite likely–then one needs to think hard about the sorts of issues this book is about. (p. xvi)
I think a less confusing set of labels are “logical incompatibility arguments” and “comparative improbability” arguments. According to arguments of the first type, some fact about evil is–you guessed it–logically incompatible with theism. Arguments of the second type claim that some fact about evil, while logically compatible with theism, is less probable on theism than it is on naturalism. These proposed alternative labels are not as concise as the “standard” terminology, but at least it’s clear what they mean!
I personally find the distinction marginally useful insofar as categorizing arguments for or against God’s existence this way makes it very convenient to identify what type of defeater is required to refute such arguments.