We all have a set amount of time we will live, and from the moment we are born we are moving towards that moment of death. In a sense, in this life we can never be said to be alive at all, since we are always in the process of dying. True life, if there is such a t hing, can only come after this life and after the death which we owe.
When we combine our view of life and death with our view of time, some interesting things happen. We are "alive" when the soul is connected to the body, and we are "dead" when the two are separated. Yet, when we look at time we find that it is fluid rather than static, that "you try to lay your finger on the present, and cannot find it, because the present occupies no space, but is only the transition of time from the future to the past." Viewed like this, there is no real "moment of death," just a past when one was alive and a future when one will be dead.
This does not, however, give us leave to say that there is no such thing as dying. Rather than getting caught up in these philosophical obscurities (which are certainly interesting!), we ought instead to use the more common language--"speak in the customary way,—no man ought to speak otherwise"--and talk about death, before death, and life. Here, the Latin language is helpful, because it gives us different forms in which to speak about "death" [which I will not go into here--it's been far too long since I've spoken any Latin].
What kind of death did God give as punishment for our disobedience, that of the body or of the soul? "The answer is: every kind of death."
Death of the body is the separation of soul and flesh; death of the soul is being condemned to hell; "total death" is "one in which the soul, deprived of God but united to the body, suffers eternal punishment."
This is the fruit of rebellion against the Lord.
At the moment of rebellion, when Adam and Eve disobeyed, man died. We see this in their taking fig leaves (Augustine thinks they were just the first things at hand that could be used as clothes) and covering themselves up--a sign that the soul had lost its mastery over the body and required outside assistance in attempting to suppress the deadly desires of the flesh. ""From this moment, then, the flesh begin to lust against the spirit. With this rebellion we are born, just as we are doomed to die and, because of the first sin, to bear, in our members and vitiated nature, either the battle with or defeat by the flesh."