Augustine of Hippo
“Death and Hades,” says John, “were cast into the lake of fire.” By these names he designates both the devil, since he was the author of death and infernal torments, and the whole company of demons.
The death of soul and body, that is, the death of the whole man, occurs when the soul, abandoned by God, abandons the body. In that case neither does the soul live by God, nor does the body live by the soul.
After this kind of death of the whole man comes the death which the authority of the divine Scriptures has called the second death. The Savior also indicated it when He said: “Rather fear Him who can destroy both soul and body in Gehenna” (Mt 10:28).
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Since this will not happen before soul and body are so united that they can no longer be separated in any way, it may seem strange to speak of the body being put to death by such a death. For in it the body is not abandoned by the soul, but is tormented while animate and sentient.
That final and eternal punishment, which we shall discuss more fully in its proper place, is rightly called the death of the soul, because the soul does not live by God. But how can it be called the death of the body, when the body will live by the soul?
Otherwise the body could not feel the very bodily torments that will follow the resurrection. Yet if every kind of life is a certain good, and suffering is evil, the body should not be called living when the soul exists in it not for life, but for sufferings.
Thus the soul lives by God when it lives well, for it cannot live well unless God works in it what is good. The body lives by the soul when the soul lives in the body, whether the soul itself lives by God or not.
For life in the bodies of the ungodly is not the life of the soul, but of the body. Even dead souls, that is, souls abandoned by God, can give such life to bodies by their own life, whatever it may be, by which they are immortal.
At the final condemnation man will not cease to feel. Yet because sensation itself will not give pleasant delight or beneficent rest, but will be tormenting through sufferings, this life should rightly be called death rather than life.
It is called the second death because it comes after that first death, by which the united natures are separated: God and the soul, or the soul and the body. Thus one may say of the first bodily death that it is good for the good and evil for the evil. But the second is good for no one, since none of the good undergo it.