A brief background:
Arminians (those who argue that we have or lose our salvation by our choice) vs. "Calvinists" (only more recently attributed with this name, more accurately they should be named "Dutch Reform", but at the time of John Calvin they would have simply been called "Protestants" (protesting the Church at Rome) and "Christians".
Pelagians: (at the time of Augustine) did not believe in "original sin"
Semi-Pelagians: believed we are tainted by the "original sin" but not to the point that we are unable to cooperate with God to the saving of our soul.
Today's Christian (professing to be Bible believing) churches have become tainted by the same arguments that plagued the reformers at the time of John Calvin.
The Arminian argument presented to Synod of Dort:
1. election conditioned on foreseen faith;
2. universal atonement (that Christ died for all men and for every man, so that He merited reconciliation and forgiveness of sins for all through the death of the cross; yet so that no one actually enjoys this forgiveness of sins except the believer);
3. the need for regeneration if man is to be saved (here they seemed to be orthodox enough, but, as it later appeared, this was understood in such a way as seriously to underestimate the depravity of human nature);
4. the resistibility of grace ('but with respect to the mode of this grace, it is not irresistible'); and
5. the uncertainty of the perseverance of believers (in respect of this article the Arminians shortly came openly to deny such final perseverance)
compared with the "5 points of Calvinism" particularly the points of total depravity, limited atonement, irresistible grace, and perseverance of the saints (also called "once saved always saved", though this term does not give an adequate understanding, it muddies up the water of what perseverance entails) :
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).
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!
Irresistible GraceThe 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)!
Perseverance of the SaintsPerseverance 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.
Today's Bible believing churches that maintain some form of orthodoxy are either "Reform" or "Arminian" with some Pelagian or Semi-Pelagian doctrines in their mix. Even those members attending Reform congregations can hold to the false doctrines of Arminius and Pelagius. To understand these in full would take many many hours, days, and years of study and I'm only still at the beginning of that journey. There are websites and books available that can get one started on that road. I will provide links at the bottom of this post which I used to provide the information I give in this post.
One that I found very helpful is one that gives an overview of what happened at the Synod of Dort.
The concluding remarks given:
Yes, we should get excited about the Synod of Dort! Because of this Synod, the Reformed Churches received a valuable confession, an authoritative exposition of scriptural Calvinistic theology. In essence, the Arminian Controversy represented an attack upon the sovereignty of God in the matter of man's salvation, and exalted instead the role of man in his own salvation. The Canons of Dort acknowledged, reaffirmed, and glorified God's sovereign grace. If we truly understand what happened so long ago in that old Dutch city of Dort, we will do the same, thankfully acknowledging that it is our faithful Saviour who gathers and defends His church, in spite of all heresies. Then in thankfulness we will also live and abide by those confessions, to the praise of His glory. (emphasis and underscoring mine)
Let us carefully guard our true understanding of our terrible depravity prior to the Sovereign good and perfect will of our God to save us by His power and preordained will to save us who were so depraved in our slavery to sin that He had to heal our blind eyes, convert our stoney heart, open our deaf ears so He could draw us to His marvelous gospel of completely undeserved grace.
"I am a ten-thousand-talents debtor to God and have not a penny with which to discharge it, and therefore unless His sovereign grace takes pity upon me and gives me everything for nothing there is no hope whatever for me" - A. W. Pink