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There is no question that the issue of God’s sovereignty, election, and man’s responsibility to believe has perplexed the minds of men for centuries. Here man’s finite mind crashes against the infinite mind of God. The best solution is to simply take the Word of God at face value and not attempt to make it fit our logic. Both truths, God’s sovereign election and man’s responsibility to believe are taught in the Bible and we won’t be able to truly resolve this until we are in heaven. It’s like looking at the roof of a house from the front yard (sovereign election) and then looking at it from the back yard (man’s need to believe). You can only see one side at a time unless you look down on the roof from above. Is has also been described this way: When you walk through the door into heaven you read over the door, “Whosoever will.” But on the other side you read, “elect from the foundations of the world.”
No doubt, this is a doctrine that is difficult and theologians have debated the issues for centuries and will continue to do so. Let me just make a couple of points, however. Having been created in God’s image, man does have free will, but the capacity of that will has been so gravely affected by man’s fall into sin that he is spoken of as “dead in sin.” Before salvation and the pre-salvation ministry of the Spirit (see 1 Pet. 1:2), man can exercise his will, but only in a limited way. Romans tells us that man, left to himself does not seek after God (Rom. 3:11). Rather, he is turned to his own way and solutions for life (see Prov. 14:12; 16:25; Jer. 10:23).
But Scripture also tells us that God (whom some have described as the hound of heaven) seeks to draw men to Himself (see Rom. 2:4; John 1:9; 12:32; 8:8-12). I take it that this means that He works to illuminate man’s heart and mind to realize that God is there (God consciousness) and to give man the ability to respond to His reality as seen in creation and to His revelation as given in the Bible if he will respond to that drawing work of God. Compare John 7:17 and Acts 17:22-31. This means that man is ultimately without excuse (see Rom. 1:18f).
Scripture also teaches that God has those whom He has predestined. The primary focus in the word “predestined,” according to its usage, is the goal or design of God—predestined to be conformed to the image of Christ and to reign with Him, etc. The focus is not on becoming saved versus not becoming saved.
Further, the concept of “the elect” seems to be used only of those who have already believed rather than of those who will believe. Many reject this and say that it is used in relation to those whom God has chosen to save and bring to Himself. Regardless, the emphasis of the Bible is that in order to be saved, man must believe or trust in Christ. Thus, God’s sovereign election and man’s responsibility to believe fall into the category what has been termed an antinomy. An antinomy is where you have two equally true concepts that appear to contradict each other (God’s sovereign election and man’s volition or responsibility to believe), at least from our limited and finite point of view. From our viewpoint as finite man, they appear contradictory.
A couple of books I would recommend are Charles Ryrie’s Basic Theology. This is an excellent and succinct work on theology that you might find helpful in this and other areas as well. Also, though it is out of print, I would highly recommend Ken Boa’s book, Unraveling the Big Questions About God. Check out Amazon.com. They can often find out of print books.