In this sense, the first mention of "the dead" does not refer to one who is physically dead - but spiritually dead as well. Jesus is saying, "Let the spiritually dead bury those who are physically dead". In the 3rd chapter of John, Jesus said "Except a man be born again, he cannot see the Kingdon of God.
Put another way, as long as a seed remains in the fruit and receives nutrition, it is worthless. However, when the seed is separated from the fruit and no longer receives nutrition, it dies and the outer shell of the seed begins to rot in the sunlight, in the soil, and in the presence of moisture. However, the contents within the seed begin to germinate, and the plant that it grows into does not resemble the former characteristics of the seed.
To God, the meaning of "dead" is not confined to the physical, but to the spiritual. A person who "is born again" becomes spiritually alive, those who are spiritually dead are the same as physically dead.
I think this thread has outlived itself, so I am closing it.