Does Boyd analyze the examples in Scripture which provide evidence that God knows exactly how the future will play out?

Foreknowledge of Individuals
Second, a number of times the Lord demonstrates foreknowledge of particular individuals and various events in their lives. Twice in Scripture the Lord names individuals before they are born and provides some detail about their lives. Josiah was to tear down the pagan altars and destroy the pagan priesthood that plagued Israel (1 Kings 13:2-3; see 2 Kings 22:1; 23: 15-16), while Cyrus was to help rebuild Jerusalem (Isa. 44:28).
In a similar fashion, Jesus tells Peter ahead of time that he would deny him three times before the next morning (Matt. 26:34). Jesus also foretells Judas's betrayal of him (John 6:64, 70-71; 1318-19;17:12) and the fact that Peter would die a martyr's death (John 21:18-19). Just as impressively, David suggests that the exact length of his life was known by God before he was born. "In your book were written all the days that were formed for me," he writes, "when none of them as yet existed" (Ps. 139:16). Similarly, the Lord appointed Jeremiah to be "a prophet to the nations" when he was still in the womb (Jer. 1:5) and set Paul apart before he was born (Gal. 1:15-16). Defenders of the classical view of foreknowledge consider this evidence that God foreknows everything that every individual will do before he or she is born.
Finally, under this category, we should mention that a number of times the Lord prophesies that certain things were going to happen to various nations or cities. Often these prophecies involved the activity of particular individuals. For example, God foretells the succession of four kingdoms through Nebuchadnezzar's dream (Dan. 2:31-45). Most impressively, the Lord prophesies a number of details about the fate of Tyre (Ezek. 26:7-21). The fulfillment of this prophecy involved to a great extent the activity of one ruler, Alexander the Great, centuries after it was given. To defenders of the classical view of foreknowledge, this implies that God foreknew exactly what Alexander would choose to do centures before he did it. And if this much can be foreknown as settled by God, they conclude, we have no reason to deny that every detail about the future is settled in God's mind.

Openness and Process Thought
Passages such as these beautifully demonstrate that the future is settled to whatever extent the sovereign Creator decides to settle it. God is not at the mercy of chance or free will. This understaning of divine sovereignty contrasts sharply with a popular liberal theological movement called "process theology." Some evangelical authors have wrongly accused open theists of being close to process though, but in truth the two views have little in common.
Process thought holds that God can't predetermine or foreknow with certainty anything about the distant future. Open theists rather maintain that God can and does predetermide and foreknow whatever he wants to about the future. Indeed, God is so confident in his sovereignty, we hold, he does not need to micromanage everything. He could if he wanted to, but this would demean his sovereignty. So he chooses to leave some of the future open to possibilities, allowing them to be resolved by the decisions of free angents. It takes a greater God to steer a world populated with free agents that it does to steer a world of preprogrammed automations.

Individual Prophecies
Many prophecies pertaining to individuals can also be understood as examples of the Lord establishing particular parameters ahead of time. The two most impressive examples of this are Josiah and Cyrus. As a supernatural sign to his people, God named Josiah ("the Lord strengthens") and Cyrus and declared their accomplishments before they were born. This decree obviously set strict parameters around the freedom of the parents in naming these individuals (see also Luke 1:11-23). It also restricted the scope of freedom these individuals could exercise as it pertained to particular foreordained activites. In other respects, however, these two individuals and their parents remained self-determining agents.
To conclude from these two examples that the names and activites of all people are settled from eternity is unwarranted. They certainly show that Yahweh is the sovereign Lord of histroy and can predetermine (and thus foreknow) whatever he pleases, but they do not justify the conclusion that he has settled the enire future ahead of time.

This decree obviously set strict parameters around the freedom of the parents in naming these individuals (see also Luke 1:11-23). It also restricted the scope of freedom these individuals could exercise as it pertained to particular foreordained activites.

Open theists rather maintain that God can and does predetermide and foreknow whatever he wants to about the future.

I could never accept this as a valid view. I much prefer the view I defend. The author is saying that God restricts the free will of people, so that these people don't have a choice as to fulfilling His purposes. How can this be acceptable? How can then be said that Judas' free will wasn't also restricted so that he could fulfill the prophecy?

Does the word "foreknow" here mean God can know how the future will exactly play out if He wants to? That is, that He is able to see the future as a rerun whenever He wants to? Or is "foreknow" here just related to what He predetermines?

I prefer Tom's opposing argument. This other guy doesn't present a viable argument, that is, it doesn't hold water with me. God is not arbitrary like this guy proposes.