In this discussion, one of the commenters makes the following argument against Reformed views of divine providence:
On a related topic, I still don't quite get Reformed theology. God desires all to repent, but He doesn't desire all to repent. How does one believe something one is incapable of understanding? It's like saying I "believe" that the round plate before me is also a square, as if my saying it makes it so.
What follows is an expansion of my response in the comments there.
What the commenter has hit on is a formal contradiction, at least if no fallacious equivocation is going on. If the word "desire" is being used in the same sense, then the statement that God desires all to repent and the statement that God does not desire all to repent do indeed result in a formal contradictiom.
But there's no problem if the two uses of "desire" are in fact different senses in which God desires. That is in fact what the Reformed view means by both claims, but the basic distinction required to take such a view isn't limited to Reformed theology. Any adequate response to the problem of evil needs something like that, as has been known at least since Thomas Aquinas. (At least you need something like this if you want to avoid open theism, but I've long thought open theism doesn't really have the resources to respond to the problem of evil anyway, because it can't guarantee a full victory over evil, not to mention being overkill, so that becomes a null option.)
You need to have some sense in which God wants to evil to happen if God in any sense knowingly allows it, so those with models of divine sovereignty that are more commonly associated with Wesleyan or Arminian theology will need to say the same thing this commenter is criticizing. God allows something rather than preventing it. Why? Perhaps the reason is because God thinks human freedom is more desirable than the desire to prevent that particular evil. You need not be a Calvinist to appeal to this sort of thing. But you better not say that God wants it to happen in every sense. God certainly disapproves of the evil, and wouldn't desire it if it weren't for whatever issue led God to allow the evil.
Once you have that distinction between desiring for its own sake and desiring for some other reason, when for its own sake God would want it removed, you have exactly the thing you're criticizing. God can desire something and not desire the same thing.
I would say that Arminians need to say this even about the salvation of non-believers if they want to avoid universalism. If anyone dies in their sins and goes to hell as a result, then God will be desiring that fate for them given their rejection of him, even if God desired them to repent and thus avoid that fate. So God both desires it and desires that it not happen, even with Arminianism. Only an open theist or a universalist can avoid saying something like that about these cases, and I don't think either can avoid saying it entirely. Even to allow one bit of evil or even the risk of it is a tradeoff in one sense, with God choosing one thing over another that would be good and desirable if all things were equal.