"To be carnally minded is death; but to be spiritually minded is life and peace. Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be" (Romans 8:6-7).
This passage defines for us both the carnal mind and the spiritual mind, not with formal definitions, but by giving equivalent terms.
First, the carnal mind is identified as being "enmity against God" (8:7), a rampant disregard for God's law. Furthermore, the carnal mind is equated with death, specifically eternal, spiritual death. A physically living person may have a carnal mind, bringing with it a spiritual deadness and eternal doom. This also serves us as a working definition of death -- being hostile toward God, or minding the things of the flesh. "So then they that are in the flesh cannot please God. But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you" (vv.8-9).
Next, we see that the spiritual mind is "life and peace" (v.6) -- a supreme preference for God and subjection to His will. This state not only leads to eternal life but is life, along with peace, even now. There can be no peace for the carnally minded.
Some would wrongly teach that the physical death of the unbeliever leads to the total annihilation of his body, soul, and spirit. However, this passage teaches that the minding of "the things of the flesh" (v.5) does not only lead to ultimate physical death, but is death right now.
Death is not the extinction of being, but the alienation of that being from Christ. "For if ye live after the flesh, ye shall die; but if ye through the Spirit do mortify the deeds of the body, ye shall live" (v.13). "If Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness" (v.10). JDM