Calvinists affirm the exhaustive foreknowledge of God, and thereby deny the possibility of libertarian free will. Open Theists take the other route. They affirm libertarian free will, and thereby deny the possibility of God's exhaustive foreknowledge.
Arminians make a distinction between certainty and necessity. This enables us to affirm both exhaustive foreknowledge and libertarian free will. The fact that something is foreknown by God makes it certain, but it does not make it necessary. If an event is certain but not necessary, libertarian free will is maintained. God knows everything we will do, but his knowing is not the cause of us doing it. Rather, our doing it is the cause of his knowing it. His knowing is dependent on our actions.1
If it's possible for God to know the future with certainty and for man to have free will, there is no reason to be an Open Theist. If the Open Theist recognizes this Arminian distinction, he loses the justification for his system. And in the end, the fact that Open Theism does not recognize the distinction creates big problems for the system.
The Open system is not always open. In order to account for prophesy, Open Theists make a distinction that God can settle portions of the future if he wants to. In the Open system anytime the future is settled, the event is necessary. Or put another way, anytime God has foreknowledge it is because God is going to cause an event to take place. Greg Boyd states it like this:
The open view holds that some of the future is open, not all of it. God can pre-settle as much of the future as he wants to pre-settle. If, in order to fulfill specific prophecies, God needed to providentially orchestrate things so that certain people with evil characters played out their evil intentions in specific ways, he could easily do this, and do so with impunity.2Notice how what Boyd says sounds exactly like Calvinism! In his view the only way certain foreknowledge can be achieved is by God providentially orchestrating evil people to do evil things. His use of the word "orchestrating" is equivocation. In his view, the only way God can know the future is by settling it himself. God makes certain aspects of the future necessary, and accomplishes this by causing evil people to do evil things. Boyd does not explain how libertarian free will is maintained in this view. He cannot, because God "settling" the future in this way is not compatible with libertarian free will.
Scripture indicates that Jesus had specific foreknowledge of what his disciples would do. This presents problems for the open view given their claim that foreknowledge equals necessity.
Here are two specific examples from Matthew 26:
[Judas' betrayal] When evening came, Jesus was reclining at the table with the Twelve. And while they were eating, he said, "I tell you the truth, one of you will betray me." They were very sad and began to say to him one after the other, "Surely not I, Lord? Jesus replied, "The one who has dipped his hand into the bowl with me will betray me. The Son of Man will go just as it is written about him. But woe to that man who betrays the Son of Man! It would be better for him if he had not been born." Then Judas, the one who would betray him, said, "Surely not I, Rabbi?" Jesus answered, "Yes, it is you." Matthew 26:20-25 (NIV)
[Peter's denial and the falling away of the disciples] Then Jesus told them, "This very night you will all fall away on account of me, for it is written: " 'I will strike the shepherd, and the sheep of the flock will be scattered.' But after I have risen, I will go ahead of you into Galilee." Peter replied, "Even if all fall away on account of you, I never will." "I tell you the truth," Jesus answered, "this very night, before the rooster crows, you will disown me three times." But Peter declared, "Even if I have to die with you, I will never disown you." And all the other disciples said the same. Matthew 26:31-35 (NIV)
We see here several examples of the genuine foreknowledge of Jesus - the betrayal of Judas, the denial of Peter, and the falling away of the disciples. If the open view is true, Jesus foreknowledge made these events necessary. The disciples had no free will on any of these matters. By knowing their actions, Jesus made Judas betray him, he made Peter deny him, and he made all of the disciples fall away. Just like in Calvinism, Open Theism has God causing people to do evil things. Remember that in the open view there is no free will if the future is settled.
The only other option is for Open Theists is to contort this passage into some sort of elaborate prediction. This is untenable for several reasons. First, Jesus says "you will" not "I predict that you will". Second, Jesus quotes prophesy: "This very night you will all fall away on account of me, for it is written..." Third, the nature of Jesus foreknowledge is too specific for a prediction: Peter will deny Jesus three times before the rooster crows. The only reasonable reading of this passage is that Jesus had genuine foreknowledge of his disciples actions before they made them.
The Arminian view of this passage has no difficulties. The Arminian view imputes no evil to Jesus. Arminians believe that foreknowledge is dependent on the act. Jesus knew that his disciples would do these things, but he did not cause their actions. His knowledge was certain, but it was dependent on the free will actions of the disciples themselves. Thus, Judas is at fault for betraying Jesus. Judas betrayed Jesus because he freely chose to. Likewise, Peter is at fault for denying Jesus. Peter denied Jesus because he freely chose to.
In conclusion Open Theism is in error when it does not make a distinction between certainty and necessity. If Open Theists made such a distinction, their system would not be necessary. And by ignoring the distinction, they impugn the goodness of God in the same way Calvinists do.
In the Open view, any time that the future is "settled", God turns into a Calvinist.
1 For a more detailed explanation of the difference between certainty and necessity, see Thomas Ralston, Can Free Agency be Harmonized With Divine Foreknowledge?
2 Greg Boyd, How does an Open Theist explain all the prophecies fulfulled in the life of Jesus?