The ancient Greeks believed in the immortality of the soul. It was a natural consequence of their understanding of the human person being composed of body and soul. The body, like all matter, decayed and died, but the soul, which was immaterial, lived on in some fashion.
The ancient Hebrews came later to the idea of the soul's immortality. Unlike the Greeks however, Jews never divided the human person into sections such as body and soul. The human person is always an indivisible whole in Scripture. Rather than a philosophical conclusion, the immortality of the soul developed from faith in God's unfailing justice. Through the centuries it became painfully evident that full justice was not possible in this life. Wealth and a long life were not always the lot of those who walked in the Lord's ways. Poverty was not a punishment for sinfulness and neither was wealth the fruit of sanctity. If God is just, then his justice must make itself manifest in another life after death.
Pope Benedict XVI takes up this theme in his encyclical on Christian hope, Spe Salvi:
A world which has to create its own justice is a world without hope. No one and nothing can answer for centuries of suffering. No one and nothing can guarantee that the cynicism of power—whatever beguiling ideological mask it adopts—will cease to dominate the world....I am convinced that the question of justice constitutes the essential argument, or in any case the strongest argument, in favour of faith in eternal life....Only God can create justice. And faith gives us the certainty that he does so.
As Christians, we have an even deeper understanding revealed to us by Jesus. The promise of everlasting life is a manifestation of God's love and desire to not lose anyone to death. As we hear in one of the suggested gospel readings for this coming Sunday: "And this is the will of the one who sent me, that I should not lose anything of what he gave me, but that I should raise it on the last day" (John 6:39). In Jesus, God reveals that his justice is not ultimately about what each of us deserves, whether good or bad, but about the loving mercy with which he desires to welcome us to the inheritance he has promised us through faith. God's mercy perfects his justice.
Pope Benedict XVI continues:
This great hope can only be God, who encompasses the whole of reality and who can bestow upon us what we, by ourselves, cannot attain. The fact that it comes to us as a gift is actually part of hope. God is the foundation of hope: not any god, but the God who has a human face and who has loved us to the end, each one of us and humanity in its entirety. His Kingdom is not an imaginary hereafter, situated in a future that will never arrive; his Kingdom is present wherever he is loved and wherever his love reaches us. His love alone gives us the possibility of soberly persevering day by day, without ceasing to be spurred on by hope, in a world which by its very nature is imperfect. His love is at the same time our guarantee of the existence of what we only vaguely sense and which nevertheless, in our deepest self, we await: a life that is “truly” life.