Muffled
Jesus in me
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That's okay, you needn't be up to speed on Greek philosophy. The classical Greeks held that resurrection was icky. This view was preponderant even in Jesus' day. They believed in life after death, whereas Christians believed in life after life after death. The Christians, as you say, borrowed the notion that the soul (whatever that is) survives death and provides the metaphysical continuity between the person that dies and the person that rises. If I die and completely cease to exist, what gets raised at the resurrection? A facsimile to be sure, but it's not "me." In other words, if I cease to exist at death, I have no hope of continuing experience later. A simulacrum, one that looks and thinks like me and has my memories maybe, but not me.
Well, you can call it a spirit or soul or shakra or pranabinduwhatchamacallit. Whatever label you give it, it's that thing that provides the metaphysical continuity between the two bodies.
I think that would be extremely difficult to prove. At least Jesus uses the word spirit before any of the letters are written (And even Paul's letters would be more apt to reflect his pharisaical training under Gamaliel). Then the letters of Peter, James and John are written by Jews also. The only Greek in the bunch is Luke and he states that he is only reporting what eyewitnesses have said.
The Bible calls it a spirit. God is a spirit according to Jesus. You make it sound as though the spirit were an extension of the body but the reality is that the body is just a convenient vehicle for the spirit.