ROB: The eternal state of the wicked is not properly called "life." To have life means to participate in a realm where relationships with others is possible. For example, to be physically alive means to participate in the physical realm where relationships with other physical beings, especially other human beings, is possible. The wicked will not have life; they will be cut off from everything and everyone.
EDGAR's REPLY: Come now, Rob. I cannot believe that you are concocting an arbitrary definition of life to explain how the wicked can exist forever and yet be devoid of life. Rudolf Bultmann writes that ζωὴ "denotes in Greek the physical vitality of organic beings, animals, men, and also plants. Life is understood, not as a thing, but as vitality, as the nature or manner which characterizes all living creatures as such" (TDNT 2:832).
BAGD says that βίος can have the sense of "life in its appearance and manifestations" (141). The Greek word is used to describe "earthly life in its functions and its duration"; "of manner of life"; "means of subsistence" (BAGD 141-142).
See Luke 8:14; 2 Tim. 2:4; 1 John 3:18; 5:20.
Based on the lexical and conceptual evidence we have at our disposal, I cannot accept your arbitrary definition of life, Rob. Even if a person is incapable of having relationships with anyone, it still doesn't mean that he or she is not alive. The same thing can be said for a solitary animal or tree in a wilderness, so your definition of life does not work. If the wicked are consciously separated from God for all eternity, then they would be alive for all eternity. Life is not limited to relationships or the capability thereof.