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The term "children of God" in the biblical sense is peculiar to the elect, saved, born again, born of God. Matthew 5:9, Luke 20:36, John 11:52, Romans 8:16; 21, Galatians 3:26, 1 John 3:10; 5:2. Only 2 individuals are referred to as "only begotten" in the KJV. The Lord Jesus is referred to as only begotten 5 times: John 1:14; 1:18, John 3:16; 18 and in 1 John 4:9. The other unique or "one of a kind" individual was Isaac. "By faith Abraham, when he was tried, offered up Isaac: and he that had received the promises offered up his only begotten son," (Hebrews 11:17). Hebrews 11:11-12 explains the uniqueness of Isaac. " Through faith also Sara herself received strength to conceive seed, and was delivered of a child when she was past age, because she judged him faithful who had promised. Therefore sprang there even of one, and him as good as dead, so many as the stars of the sky in multitude, and as the sand which is by the sea shore innumerable." Isaac was only human and certainly did not share in Christ's divine attributes yet because his parents were well past childbearing age his conception and birth made him a "miracle baby". After all, is there anything too hard for the Lord? (Genesis 18:14)
In one sense, all humans are God's children, since God is responsible for the creation of human life on earth. However, in another sense, because all humans (except Christ) are estranged from God through sin, those who place their faith in Christ's sinless life, atoning death, and resurrection, rather than in their own imperfect righteousness, to place them in a right relationship with God then become His children in a way that those who have not placed their faith in Christ are not. Christ's designation as the Son of God indicates a unique relationship with God that is not true of anyone else, in that He was "begotten" of God (not created or made), and thus (in addition to be truly human in His incarnate form) is God by nature and possesses all the attributes of God, which other humans are not and do not. By God's grace, however, those who place their faith in Christ are endowed by God with Christ's unique righteousness, and become His children (sons and daughters, with a lower case "s" and "d") by adoption, and co-heirs with Christ of the eternal life in God's presence that Jesus made possible, just as Jesus Himself rose from the dead and is now eternally alive.
Since Christians seldom study sonship doctrine, many see no difference between these terms, but the difference is huge. There is no space here for more than a tiny bit of the background information that you need to really understand this. You will have to do a detailed study on your own, but you will have a good start here. First you must understand the meaning of the feasts of Israel. Paul gives a very good discussion in the early chapters of Romans about Passover being justification by faith, so most of the church gets this. The church fulfilled this when they smeared the blood on their door posts and were baptized when they passed through the Red Sea (1 Cor 10:2). The church is largely unaware that the Greek name for the next feast (Feast of Weeks - Shavuot) is Pentecost, which began being fulfilled corporately in the upper room on that "first" day of Pentecost. The actual first day of Pentecost occurred at Sinai where the people refused to fulfill it because they refused to hear God's voice directly. This continues to be a big problem in the church, even among those who claim to be Pentecostal. The final major feast is Tabernacles. Israel was given their first opportunity to fulfill this feast at Kadesh Barnea, but because they had refused Pentecost they did not have the faith to enter into the Land at that time. You cannot fulfill the final feast if you cannot fulfill the first two. Why are the feasts important? The show the three levels of adoption into sonship. The first is the circumcision ceremony if you are natural born into that family, or is the ear piercing if you have entered the family through the redemption process as a bond servant (Ex 21:5, 6). This is another set of laws you much study in detail to understand this. Pentecost is the equivalent of the Bar Mitzvah ceremony, a rite of Passage not actually mentioned in scripture but we can see its effect in the law and in the life of Jesus. After their 12th birthday (11th as we reckon it today) all men were to present themselves at the temple for each of these feasts. When Jesus was found at the temple by his parents he said, "Don't you know I must be about my Father's business?" At this time a son left his mother's care and entered his father's business as a full-time apprentice. The final feast is the final ceremony, the adoption of fully mature sons. Paul speaks of this in 2 Cor 5 telling us it is the receiving of the glorified body. We see this ceremony at Jesus baptism and again just before the crucifixion at the transfiguration when the Father spoke from heaven saying, "This is my beloved son; listen to him." While Jesus did not receive the glorified body at this time he did receive the full authority to transact all business in the Father's name and we were to obey as if it had been the Father himself who made the contract with us because it was the Father, through his Son. Corporately, there has been no fulfillment of this feast; only Jesus has fulfilled it, and when we enter Pentecost and begin learning his work we act under his authority as apprentices, not as full partners in the business (Sons). Romans 9:26 quotes Hos 1:10 where God says that after he regathers Israel (the resurrection) we "will be called the Sons of the Living God." In most translations this is intentionally mistranslated "children" because the church has no understanding of the sonship doctrine and refuses to allow God to grant us a prerogative we claim to be allowed for Jesus alone. The Greek word in this verse is huios, a word that specifically refers to a fully mature son who had gone through his father's adoption ceremony and is a full partner in his business. In 1 Jn 2 we see this concept where John speaks to "little children" (literally toddlers), "young men" (Bar Mizvahed youth) and "fathers". The three levels of faith and understanding are shown by him in this way here. The infant/toddler and youth are children, but the son is a full partner of the father.
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