In a nutshell this is what the bible teaches about hell and death:
First death - body dies, and the soul/spirit/breath, whatever you want to call it, goes somewhere.
Ecc 12:7 says it returns to God:
Ecc 12:7 Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
James also says the spirit has gone somewhere, it is not in the body any longer, the spirit is absent:
Jas 2:26 For as the body without the spirit is dead, so faith without works is dead also.
So death is really a separation of the body from the soul. The body dies as it cannot live without the soul.
Jesus taught that human beings, cannot destroy the soul.
Mat 10:28Andfearnotthem which killthebody,butarenotabletokillthesoul:butratherfearhim which is abletodestroybothsoulandbodyinhell.
This is because the soul continues on after death.
Jesus told us where the soul goes after death: To hades, paradise for the good person, torment for the bad person. (Luke 16). Or, as Paul said, to be present with the Lord, either in heaven, or in Hades.
These souls reside either in torment or in paradise until the resurrection of both the just and unjust. This is a resurrection of the body at the same time the soul/breath returns from wherever it was (paradise or torment), and re-enters the body to make the body come alive.
This resurrection of both the just and unjust (Acts 24:15, Mark 12:23) is for judgement. The sea, the earth, hell, hades, everywhere, deliver up the dead for judgement (Rev 20:13).
Then everyone is judged according to their works:
Rev 20:13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
The wicked are thrown into hell. This is rightly called the second death, because it's the second time they experience dying. But even more, the pain and loss of separation from God for eternity.
Rev 20:14 And death and hell were cast into the lake of fire. This is the second death.
There shall be no more death after this, when death itself is cast into the lake of fire.
While some may believe that being cast in the lake of fire is the way God is able to destroy both body and soul,
various scriptures affirm a continuing eternal torment for the wicked which is in the sense of their soul, and like Lazarus who was in torment in Jesus's parable, these also are in continual torment never having any rest:
Rev 14:11 And the smoke of their torment ascendeth up forever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
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