I was reading a recent thread in which Calvinists and non-Calvinists were accusing each other of holding to positions which logically precluded the meaningfulness of prayers that God should effect certain events which pertain to the wills of men. The arguments, in brief, were these: the non-Calvinists asserted that since the Calvinist believes all things are already determined, his prayer for God to affect men's wills could not have any bearing on what God has determined and, therefore, is nonsensical; the Calvinists asserted that since the non-Calvinist believes men's wills are free, his prayer for God to affect men's wills could not be accomplished because men's wills would then be determined.
I cannot defend a prayers of this sort made by one who believes in free will. However, if God determines all things - and He does - may it not be the case that His determination of a prayer on behalf of an unbeliever (or anyone, for that matter) is teleologically related to His likewise determined movement to do that for which the believer asks? For instance:
Exodus 32:9 “I have seen these people,” the LORD said to Moses, “and they are a stiff-necked people.
10 Now leave me alone so that my anger may burn against them and that I may destroy them. Then I will make you into a great nation.”
11 But Moses sought the favor of the LORD his God. “LORD,” he said, “why should your anger burn against your people, whom you brought out of Egypt with great power and a mighty hand?
12 Why should the Egyptians say, ‘It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth’? Turn from your fierce anger; relent and do not bring disaster on your people.
13 Remember your servants Abraham, Isaac and Israel, to whom you swore by your own self: ‘I will make your descendants as numerous as the stars in the sky and I will give your descendants all this land I promised them, and it will be their inheritance forever.’”
14 Then the LORD relented and did not bring on his people the disaster he had threatened.
Here Moses intercedes on behalf of Israel. Did Moses do this of His own, allegedly free will, or was his intercession determined? Calvinists believe it was determined. Was God's relent from His threat spontaneous or determined? Calvinists believe it was determined. God eternally decreed that both these things should happen. Why, then, can't the Calvinist suggest that God was determined to relent from His threat by means of His determination of Moses' intercession?
The prayer argument made by the non-Calvinists is really little different from evangelism; if only by God's determination can one be saved, as Calvinists believe, why evangelize? The answer is obvious: man is God's appointed means for the salvation of unbelievers (Romans 10). His determination of one's evangelistic appeals to Scripture is the means by which God purposed to effect regeneration in His elect, and this too is determined. Here we see a teleological correlation between God's determinations or decrees.
So when Calvinists pray that God would affect an individual's will, the prayer is not irrelevant. Perhaps it is the case that God will be moved by the prayer - not spontaneously, but having determined the very prayer. Or perhaps God will not be moved, and so He has determined that the prayer will be answered in the negative. No one knows the extent of God's eternal decree[s]. But whichever the case may be, it is true that foremost in one's thoughts should be recollection that God's sovereign will cannot be thwarted or resisted (Isaiah 14, Romans 9). Hence, accompanied with an entreaty for, say, the salvation of an unbeliever should be the ready acceptance of whichever way events unfold, as they do so according to God's sovereign will, and, more specifically, for the good of those called according to His purpose.