CovenantInBlood,

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If it is true that God's purpose is that every man come to eternal life, then God most certainly fails in His purpose when He allows a great portion of mankind to fall into hell. I do not believe God can fail in His purposes, and so I do not believe that God's purpose is that every man come to eternal life.
Depending on how you understand eternal life, every man will have eternal life. See Acts 24:15. It was part of Christ's work to bring Life to all men. This is eternal life. Immortality. In that He certainly did not fail.
That fact that some men will not choose Christ and make a diliberate negative answer to God's call is not the problem of God but of man. God desires that all men be saved, however in His purpose of creating man gave him a will so that man could voluntarily, without compulsion, without force, without manipulation choose to freely love and obey. If not, there is absolutely no purpose for man in this creation, except to be a toy of God.
That is why limiting God's power is making God a failure. He didn't do what He purposed to do.

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In the Acts, it is written, "When the Gentiles heard this, they began rejoicing and glorifying the Lord; and as many as had been appointed to eternal life believed" (13:48). This indicates that God predestined ("appointed") some to eternal life.
Again context: Jesus came to save those of the House of Isreal. He also knew that they had rejected Him. The prophets of the OT had foretold that the Gospel, the Messianic Age would also be to the Gentiles. If you go back up to verse 46 that is explained to you. Paul then goes directly lto the Gentiles. They had been appointed to receive the Gospel in this age. That is the meaning and use of the word appointed. Simply, not just the Jews but Gentiles which in effect meant every human being since.
Acts 2:47 also reinforces this concept.

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What on earth does this mean? Do you think the souls of those men who perished in Noah's day were obliterated? The man always has remained after physical death, either in life eternal or in death eternal.
Absolutely, that is the whole basis of the Christian Gospel.

A little theology to help with this understanding. Man is a unique creature. He is both divine and material. This is what is also meant by the creation into His Image. Mans soul was created to be eternal. It would never die. 'Since the soul was joined with the body, a physical or earthly element God created the whole man to be immortal. Man cannot live apart from having both. The soul gives the body life and the body gives substance to the soul. In other words we are not spirits.
Adam was created good, not perfect. He was neither mortal nor immortal. How do we know this. Because when he sinned he became mortal. If he had not sinned he would have become immortal. He could not have been immortal because immortal cannot become mortal.

This the the sole reason of the Incarnation. God needed to redeem the physical creation in order to put mankind back to gether, that is body and soul for eternity. Under Adams judgement of death, man would have died the physcial death whereby the body decays, and the soul lives in eternity, but also a spiritual death because man could have never been reunited with God without Christ, thus the soul(s) of all men would be eternally in hell. That would essentially annhilate God's sovereign purpose for man and His creation.

So, Christ came to give life to all men, correct the judgement, Give immortality to all men. The just and the unjust. It is man who will dicide on which side of the wall he will spend eternity. Man must chose this day whom he will serve.

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Christ did not accomplish this situation. What He accomplished on the cross was to guarantee life eternal for all His sheep.
He did not guarantee any such thing, even for His sheep. He promised eternal life IN Christ to those who believe, John 3:16. It is whosoever, not those specially designated.. All who believe are His sheep. The texts I posted on this thread twice already all speak to this very fact.

Actually, I can show that is actually true in the sense that all humans are His Sheep, He created them, preserves all life,. and give immortality to all life including the universe. He loves all sinners, His love never faileth.

Theologically, and Scripturally, the only way you could hold to such a view, is that man in his essence is not the same. So that in the Incarnation of Christ, those men who of only that certain nature or essence would be saved, thus excluding all other men who are somehow of a different essence. If this is true, which is what you would have to hold with your view, then please show me these human beings that are different in their humaness from some others. And that would hold true for the universe as well. Some part of the universe can be associated with certain of mankind but not all. Whatever the essence of those Incarnated by Christ would also be the essence that corresponds with the Universe. All other humans who are associated with that portion of the created world that is different would not be redeemed. Then you could scripturally hold to the view that all means some, because the some refers to a specific kind of human.
So lets hear your proof. Scripturally.

The only thing that is guaranteed is the Work of Christ on the Cross. That work is theologically called redemption. The salvation of individual man, the purpose of man in this created order, is a synergistic cooperation between God and man. Adam's walk, our walk. Living the life of Christ IN Christ. Becoming Like Christ, attaining the conformation to His Image.