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Total Depravity (Total Inability)
Total Depravity is probably the most misunderstood tenet of Calvinism. When Calvinists speak of humans as "totally depraved," they are making an extensive, rather than an intensive statement. The effect of the fall upon man is that sin has extended to every part of his personality -- his thinking, his emotions, and his will. Not necessarily that he is intensely sinful, but that sin has extended to his entire being.
The unregenerate (unsaved) man is dead in his sins (Romans 5:12). Without the power of the Holy Spirit, the natural man is blind and deaf to the message of the gospel (Mark 4:11f). This is why Total Depravity has also been called "Total Inability." The man without a knowledge of God will never come to this knowledge without God's making him alive through Christ (Ephesians 2:1-5).
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Unconditional Election
Unconditional Election is the doctrine which states that God chose those whom he was pleased to bring to a knowledge of himself, not based upon any merit shown by the object of his grace and not based upon his looking forward to discover who would "accept" the offer of the gospel. God has elected, based solely upon the counsel of his own will, some for glory and others for damnation (Romans 9:15,21). He has done this act before the foundations of the world (Ephesians 1:4-8).
This doctrine does not rule out, however, man's responsibility to believe in the redeeming work of God the Son (John 3:16-18). Scripture presents a tension between God's sovereignty in salvation, and man's responsibility to believe which it does not try to resolve. Both are true -- to deny man's responsibility is to affirm an unbiblical hyper-calvinism; to deny God's sovereignty is to affirm an unbiblical Arminianism.
The elect are saved unto good works (Ephesians 2:10). Thus, though good works will never bridge the gulf between man and God that was formed in the Fall, good works are a result of God's saving grace. This is what Peter means when he admonishes the Christian reader to make his "calling" and "election" sure (2 Peter 1:10). Bearing the fruit of good works is an indication that God has sown seeds of grace in fertile soil.
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Limited Atonement (Particular Redemption)
Limited Atonement is a doctrine offered in answer to the question, "for whose sins did Christ atone?" The Bible teaches that Christ died for those whom God gave him to save (John 17:9). Christ died, indeed, for many people, but not all (Matthew 26:28). Specifically, Christ died for the invisible Church -- the sum total of all those who would ever rightly bear the name "Christian" (Ephesians 5:25).
This doctrine often finds many objections, mostly from those who think that Limited Atonement does damage to evangelism. We have already seen that Christ will not lose any that the father has given to him (John 6:37). Christ's death was not a death of potential atonement for all people. Believing that Jesus' death was a potential, symbolic atonement for anyone who might possibly, in the future, accept him trivializes Christ's act of atonement. Christ died to atone for specific sins of specific sinners. Christ died to make holy the church. He did not atone for all men, because obviously all men are not saved. Evangelism is actually lifted up in this doctrine, for the evangelist may tell his congregation that Christ died for sinners, and that he will not lose any of those for whom he died!
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Irresistible Grace
The result of God's Irresistible Grace is the certain response by the elect to the inward call of the Holy Spirit, when the outward call is given by the evangelist or minister of the Word of God. Christ, himself, teaches that all whom God has elected will come to a knowledge of him (John 6:37). Men come to Christ in salvation when the Father calls them (John 6:44), and the very Spirit of God leads God's beloved to repentance (Romans 8:14). What a comfort it is to know that the gospel of Christ will penetrate our hard, sinful hearts and wondrously save us through the gracious inward call of the Holy Spirit (I Peter 5:10)!
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Perseverance of the Saints
Perseverance of the Saints is a doctrine which states that the saints (those whom God has saved) will remain in God's hand until they are glorified and brought to abide with him in heaven. Romans 8:28-39 makes it clear that when a person truly has been regenerated by God, he will remain in God's stead. The work of sanctification which God has brought about in his elect will continue until it reaches its fulfillment in eternal life (Phil. 1:6). Christ assures the elect that he will not lose them and that they will be glorified at the "last day" (John 6:39). The Calvinist stands upon the Word of God and trusts in Christ's promise that he will perfectly fulfill the will of the Father in saving all the elect.