What is Gehenna
Literally: a trash dump in a valley southwest of Jerusalem where refuse was burned
Figuratively: the final place of punishment of the ungodly (source)
A comparison between Mark 9:43-44 & Revelation 20:13-15 makes it clear that the "lake of fire"--in Revelation's apocalyptic description to a Hellenistic audience--is the same concept as "Gehenna", used by Jesus & James in teaching a Jewish audience.
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.
14 And death and hell were cast into the lake of fire. This is the
second death.
15 And whosoever was not found written in the book of life was cast
into the lake of fire. (Revelation 20:13-15)
In this passage (KJV), "hell" is Hades and the "lake of fire" is Gehenna.
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What is a soul
a. Sometimes ψυχή "psuché" (and its Hebrew counterpart נֶפֶשׁ "nephesh") is used to describe the entity created by the combination of a body & spirit (as in Genesis 2:7)
b. Sometimes it's used synonymously with spirit (as in Acts 20:10)
Thayer has an excellent discussion of 2 primary uses and 6 sub-uses of the word (see here).
That Matthew 10:28 uses the word to refer to the "spirit" is evident by comparing the two possible renderings of the passage:
a. If "soul" in this context = body + spirit: "fear him which is able to destroy both [spirit and body] and body in hell"
b. If "soul" in this context = spirit: "fear him which is able to destroy both [spirit] and body in hell"
Option a (as in Genesis 2:7) does not require appending the word "body" to the last clause; since "body" is appended to the statement, option b (as in Acts 20:10) is clearly intended.
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What is to destroy
The Greek root used here is ἀπόλλυμι (apollumi), frequently used in the New Testament as "kill" or "destroy". That the word does not, however, demand the notion of annihilation is evident by looking at its usage in several passages:
The Prodigal Son
In the final verse of the parable, the father says to the older son:
It was meet that we should make merry, and be glad: for this thy
brother was dead, and is alive again; and was lost, and is found.
(Luke 15:32)
Apollumi is the verb translated "lost". Clearly, the prodigal son was not annihilated, nor did he experience a cessation of conscious existence. The son had been lost or destroyed in that he had failed to live up to his potential, he was dead/separated from his family and his faith. In this case, "destruction" did not even render the son past hope of repair.
Broken vessels
All 3 synoptic gospels use apollumi to describe the wine containers that break--we'll use Matthew's rendering as an example:
Neither do men put new wine into old bottles: else the bottles break,
and the wine runneth out, and the bottles perish (Matt. 9:17)
The bottles (containers) perish; they are destroyed--but they do not cease to exist. Even a container shattered into a thousand pieces still exists: but it is no longer able to fulfil the function for which it was designed.
I propose then, the following definition of "to destroy" as generally applicable to the passages under consideration: to render something unable to fulfil its purpose.
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Death as separation
Biblically, death describes separation, not annihilation.
- Physical death: separation of body & spirit
- Spiritual death: separation from God
I have written more extensively on this topic here; for purposes of this post, the passages above demonstrate that "destroy" can mean "kill", but need not convey a cessation of existence at all (annihilation).
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Conclusion
As a whole, what does it mean for a soul to be destroyed in gehenna?
16 The Spirit itself beareth witness with our spirit, that we are the
children of God:
17 And if children, then heirs; heirs of God, and joint-heirs with
Christ; if so be that we suffer with him, that we may be also
glorified together.
Humans are the offspring of God, intended to be heirs of his glory. God joined together body & spirit (see Genesis 2:7) so that His children could progress towards that purpose.
"Destroy both soul and body in Gehenna" indicates that this body & spirit will suffer the second death (see Rev. 20:14); this fate is further described by Paul:
Such people will suffer the punishment of eternal destruction by being
separated from the Lord's presence and from his glorious power (2
Thess 1:9)
This means being permanently separated from God and thereby rendered unable to fulfill their purpose.