Coming back to the idea that God cannot do the logically impossible: when any specific example of impossibility is given, that implies a logical and/or mathematical system - a 'context' - within which possible and impossible things can be defined. But there are a myriad, perhaps an infinity, of such systems.
Essentially, what I am saying is that an statement can be rendered void by showing it depends on a context that is not necessarily the case. Stating "square circles are impossible" depends on the context of Euclidean geometry. More fundamental than "to force a disambiguation of the context" is simply exposing the context. Once exposed, we can argue whether it is valid.
No, you can't. The context is a semantic tool. Once it's exposed, the idea that is being communicated has been made clear. There is absolutely nothing more to do after that. The point of language is to communicate - to argue about the context is to argue about word meaning, which is pointless unless that's exactly what you are trying to do.
Now if you (reasonably so I feel) grant that we cannot know the logical system that applies to God (it need not be the same as that which applies to the Universe; even we have devised logical systems that are not those that apply to us), then while we may be able to make the statement that there are some things impossible for God, we can say nothing about what those things are. Which means we should be careful when trying to give examples.
I think you're doing exactly what I warned against: conflating reality with semantics. As you use it, "the logical system that applies to God" is nonsense, it doesn't even mean anything to say that. Truth itself is defined relatively to a precise (conventional) logical system, it's not magical. Different systems of logic define different concepts of truth. If you use paraconsistent logic, for instance, you are not working with "truth" in the conventional sense of the word, you are working with "para-truth", a different concept with different properties, and so on. When you say "God can do X", you aim to refer to a particular action that you claim can be done by God, and you aim to communicate to others this concept, assuming an implicit context: typically, conventional logic, Euclidean geometry, and so on, are assumed. If "X" is unintelligible, then the proposition is false, because you failed to associate "X" to something meaningful. It has nothing to do with what God can or cannot do
in reality - it has to do with
semantic failure. Using the English language, one can engineer propositions that are self-inconsistent, and none of these propositions can obtain - they are
meaningless, and any extended proposition that relies on them is equally meaningless.
When you change the logical system, you need to realize that you are not making a philosophical point, you are merely arguing for the redefinition of truth (perhaps for good reason, such as usefulness, but you have to be aware that it's a redefinition).
This doesn't of course mean we can pin it down to one logical system though. The arguments in this thread have assumed conventional logic, and I'm not sure we've even had a fully valid one. Both here and in general, I think there's been no exploration of explanations for evil in alternate logics for God.
No, and for very good reason: using alternate logics is nothing more than clever word play. Going that path, you essentially stop talking about conventional benevolence: you end up saying God is benevolent, for a contrived definition of benevolence... or for a contrived definition of truth itself. Don't get me wrong, alternate logics are powerful tools for those who know how and when to use them, but your prospected use of them seems more in line with semantic obfuscation than anything else.
Solving the problem of evil is about
selling ideas and concepts to other people. It is a communication effort. God is utterly irrelevant here - you use whichever logical system is generally understood to be appropriate, or any alternate system that you can
sell to others. In any case, it is nice if everybody is on the same page as to what words mean, what logical system is used, what concept of truth is used, what concept of existence is used, and so on.