Option 1: Unbaptized children go to "limbo" or hell.
If children are part of the "kingdom of heaven," why does the Bible teach that "all have sinned and fall short of the glory of God" (Rom. 3:23), children apparently included? David confessed, "Surely I was sinful at birth, sinful from the time my mother conceived me" (Ps. 51:5). How can children be "sinful"? And how does the question impact their eternal state?
"Original sin" has been defined as "the dimension of sin with which we begin life, or the effect which the sin of Adam has upon us as a precondition of our lives." The key text is Romans 5:12: "Sin entered the world through one man, and death through sin, and in this way death came to all men, because all sinned." The sin of the "original" man, Adam, has somehow been transmitted to "all men." Why? How?
Augustine: Infants are sinners
Prior to St. Augustine (354-430), Christian theologians apparently gave little attention to this question. For Augustine, Romans 5:12 is definitive. In City of God, he states that "even the infants, not personally in their own life, but according to the common origin of the human race, have all broken God's covenant in that one in whom all have sinned."
Psalm 119:119 warns, "all the wicked of the earth you discard like dross." The "law brings wrath" (Rom. 4:15) upon all of humanity, infants included. As a result, according to Augustine, "even the infants are, according to the true belief, born in sin, not actual but original, so that we confess they have need of grace for the remission of sins." This doctrine is essential to God's fairness in condemning infants along with the rest of humanity: "The soul of the infant, being guilty of no sin of neglect against itself, would perish unjustly, unless original sin rendered it obnoxious to punishment."
Theologian Stanley Grenz summarizes Augustine's very influential position in his bookTheology for the Community of God:
Original sin is the punishment we all bear for Adam's sin. This punishment is ours in that we participated in that first sin, for we were all potentially present in Adam when he transgressed the divine prohibition. This blight is perpetuated through procreation and results in condemnation. Simply stated, all were potentially in Adam, all sinned in Adam, all inherit the punishment for Adam's sin, and thereby all are condemned.
According to Augustine, the "carnal excitement" that accompanies procreation causes the child to be tainted with the sin of its parents, who were tainted by the sin of their parents, and so on back to Adam. He viewed infant baptism as essential for washing away this inherited sin. Later Catholic theologians such as St. Thomas Aquinas believed that an unbaptized child, if it died, would spend eternity in limbo. This is an "eternal state of natural joy," but not the greater joy of Heaven.
By contrast, followers of the theologian Pelagius (390-418) believed that humans are not tainted by the sin of Adam and are free to fulfill God's word and will. Pelagius was declared a heretic by the Council of Carthage in 418. The "semi-Pelagian" position teaches that humans inherit a propensity to sin from Adam, but are nonetheless able to choose against sin.