Actually, it's the opposite- babies don't go to hell because their parents were not in the covenantal community. Revelation speaks of the judgment of the world and that each are judging according to their works- what works will non-elect infants be judged for (I am not referring to original sin, but actual sins)? It is the everlasting purpose of grace that would teach us God is a merciful God who does not send babies who die in infancy into the lake of fire.
One cannot possibly understand the doctrine of original sin if he speaks in this manner. David traces his actual sin back to the fountain of his original sin (Ps 51) in order to show God's justice in judging, that is, because there is absolutely no good thing to which he can appeal to mitigate his sin. The apostle Paul considers guilt, condemnation, and death as the natural consequences of Adam's headship of the human race (Rom. 5). If "the soul that sins shall die" is an absolute statement which admits of no qualification then all infants who die in infancy are damned without any hope. Please reconsider your position. It is pernicious.
Concerning divine mercy, the apostle Paul shows very clearly that the hope of eternal life is not grounded in the richness of God's merciful nature alone, but in that merciful nature expressing itself through an everlasting love for His elect people, Ephesians 2:1-7, and especially verse 4. Arminians argue that God's merciful nature implies that He has a purpose of grace for all without discrimination. Calvinists know of no such "nature-God."
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