"For which cause we faint not; but though our outward man perish, yet the inward man is renewed day by day."

Paul is here making a contrast between the physical and the spiritual. Jesus said something very similar when He gently rebuked the disciples, saying, "The spirit indeed is willing, but the flesh is weak." Matthew 26:41.

Paul said the outward (physical) man might wear out and perish. The word he used for "perish" means literally "to be corrupted" or decay. The body grows weak and fatigued, but "the inward man is renewed day by day." This inward man is the same as the "inner man"--a term which Paul uses often to describe the mind or heart. In Ephesians 3:16, that inner man is "strengthened by the spirit," and in Romans 7:22, Paul delighted "in the law of God after the inward man."

There is absolutely no indication that Paul ever connected that inward man with a soul that could leave the body. Nowhere is it used to denote an immortal entity or disembodied spirit.