Some people read my last note, and requested clarification. So, in contrast to what some Calvinists say that Arminians believe, I will clarify what Non-Calvinist Christians (who I know) believe. I will call them NCC for short. Now, for the record, these clarifications are off the top of my head and are probably not worded "optimally" somehow. I will be happy to further clarify any particular point.
PARTIAL DEPRAVITY / FREE WILL
"The Arminians adopted views that paralleled the work of Erasmus, believing that man possesses a free and independent will. "
NCCs believe that man's will is not "free from" a sin nature, but rather that man is the determinent of his own choices. Man is, therefore, a free agent who is responsible or culpable for his actions.
"By this it is meant that in Eden, man's fall only partially affected his ability to choose."
Eden effected every part of the being: especially the heart, and what people want to choose. Man will not choose right not because he lacks ability, but because he simply doesn't want to. He also lacks the ability to suddenly come up with enough power to always want to do right. He cannot change that. He can choose his choices.
"The will of man is neutral and not determined by his nature, therefore it is autonomous and free of any binding persuasion toward unrighteousness and sin."
Man's nature is defined by what man will always choose to do - His nature is not somehow separate from the heart and the will. The natural man is born in sin, is a slave to sin, and only through God's direct grace, is able to ask God to free him: for he cannot choose to free himself.
"The Arminian believes that in order to accommodate man's free will, Christ took to the cross the sins of every human being without exception. "
The NCC believes that Christ did what He did because of His ultimate purpose and good pleasure - not in order to "accommodate" anything! Christ's blood was capable of covering all people, but only the sins of the elect were "nailed to the cross."
"The death of Christ does not save any individual, rather it makes salvation possible for every individual."
The death of Christ makes salvation available to every individual AND saves select individuals. Christ died to provide salvation for all, and to procure salvation for the elect.
"The cross is thereby limited as to its nature, becoming an incomplete work, ineffectual until completed by the free will work of man."
The cross is not limited. The cross is a complete work, effectual for all that God designed it to do. For us elect, our sins being paid for, completely and effectually, on the cross was completed long before we were born. No one but God completes God's work.
"It is the free will choice of man to accept Christ's work that completes salvation "
Christ completes salvation (regeneration, sanctification, and glorification) and not us. We do not complete any of God's work - and salvation is definitely God's work.
"(e.g. man's decision to receive Christ accomplishes, secures, and completes an atonement which Christ did not "finish" at Calvary Himself.)"
God's decision to atone for those who have faith accomplishes and secures an atonement which Christ DID "finish" at Calvary Himself.
RESISTIBLE ? OBSTRUCTABLE GRACE
"The Arminian believes that the Holy Spirit merely woos the man, but salvation rests ultimately upon that man's free will response to the Holy Spirit's persuasion."
The Holy Spirit does not so much "woo" as, in the Biblical language, "convict of sin, of righteousness, and of judgment to come." The NCC believes that salvation does not rest on man's choice, but rests on God's taking pleasure in saving those who have faith.
"The free will of man can and does thwart and refuse the work of the Holy Spirit in salvation."
The work of the Holy Spirit is never thwarted. The Holy Spirit does not purpose to regenerate people who do not want help. In that case, His purpose is to convict - to render them without excuse in the day of Judgment, at which time He(as God) will glorify Himself by doing justice to them.
"It is man's volition, or willingness to cooperate with God that can either support or frustrate God's desire to save."
God's purposes are never frustrated. He desires to save all, but desires even more that all should repent. He purposes only to save those who have faith, and to leave the rest. He does not will to save those who do not want to be saved.
"With this concept of salvation great importance and weight is laid upon the work of man..."
There is no important in man's works, which are as filfthy rags. The NCC puts great importance upon realizing that, and falling prostrate before the only One who can have mercy on us. They believe that biblically, faith is not a work.
"The Arminian believes that faith precedes regeneration, and is the cause of regeneration, giving, as it were, the go-ahead to the Holy Spirit to do His assigned work."
The NCC does believe that faith precedes regeneration. However, they do not believe the post-hoc-ergo-propter-hoc logical fallacy, which states "after this, and therefore because of this." (Seriously - look it up!) The Holy Spirit only waits for the "Go-Ahead" from God Almighty, who chooses who save based on His pleasure and purpose. If the Lord pleases to save those who have faith, we tremble in gratitude and awe - knowing that nothing we did helped with, earned, or deserved salvation. We deserve hell. We take no glory in ourselves, but all glory goes to the Lord Most High.