The Bible study group that I attend has been studying Exodus, and we're nearing the end of the plagues. I've been thinking anew about Pharaoh and the hardening of his heart. People holding to a libertarian view of freedom like to point out that Pharaoh hardens his own heart before the first time it says God hardens it. It isn't a simple progression. Sometimes his heart is simply hardened in the passive, and I don't think there's a neat order to it. The passive formulation occurs in what I believe is even the first instance (Exodus 7:21), and that occurs three times in ch.7 before 8:21, where Pharaoh is first said to harden his own heart. But it is true that Pharaoh is said to harden his own heart before God is said to harden it.
On the other hand, compatibilists about freedom and predetermination notice that God predicted long before the encounter even happens, when Moses hadn't even returned to Egypt, that he would harden Pharaoh's heart and that Pharaoh wouldn't let him go. (Exodus 4:21) This may not require a compatibilist view, but there's one view that I think doesn't fit well at all with this whole sequence, and that's open theism.
First, God predicted that Pharaoh would not to let them go. He even predicted that he would harden Pharaoh's heart. He told Moses to ask for a three days' journey to sacrifice and return. But he promised to Moses that Pharaoh wouldn't let them go and that it would lead to their permanent freedom from Egypt. What needed to happen for God's prediction to come true? Pharaoh needed to resist Moses, something open theism doesn't allow God to predict. Yet God had predicted it, and it was at least in part dependent on Pharaoh's hardening of his own heart.
As libertarians like to point out, God hardens Pharaoh's heart only later in the series of plagues. God nevertheless predicts that he'll do it to Pharaoh before Pharaoh even hardens his own heart. There's only one way I can make sense of this is open theism is true, and that's that Pharaoh is one unusual exception of someone who simply isn't free. In order to predict that Pharaoh would refuse to let them go, God must have forced him to do what he did. Why, then, does Pharaoh harden his own heart before God hardens it?
Open theists often go the Exodus narrative because of Moses' interaction with God after the golden calf incident, saying that the classical view of divine foreknowledge doesn't fit well with the plain sense of that text and others like it (although there are problems even with that claim). But it seems to me that open theists are the ones that have a problem with the plain meaning of this narrative.