Dead or Really Dead?

When we die, do we stop living? 

Some people think that we do. Meaning that when the heart stops and the brain stops functioning, life is gone. That is it. Life has ended. We do not live beyond the ceasing of the heart and brain.
Many say we continue living because the soul lives on after physical death. This begs a follow up question and that is, what is the soul?
Indeed, many world religions have different definitions of what a soul is and how it is made. Also, there are different takes on whether it is finite or infinite once it is created.

Soul Creation

The most popular belief is that souls are created during conception. When a human sperm meets a human egg in the woman or in a test tube, and the first cell division occurs, life begins. Both the physical and the soul life begin in this one event - the embodiment or incarnation of the soul.
Where the soul came from is another question. Did it come from a storehouse then infused with the physical during conception? Or was it integrated and integral with the physical creation?
The former can be answered with other complications, such as, how does the soul travel from the storehouse to the conceived being? The latter is answered much simpler in that the soul is created on the spot. But one thing is certain, the soul has a beginning.

Eternal Soul or Finite

The ancient Greeks believed in the immortal soul. These "western" ancients believed that when a person dies, his or her soul separates from the body - a reversal of incarnation. The essence, so to speak, eternally survives and is transported to a place of the dead - the afterlife. Through various developments this place of the dead later became conceptualized as Hades. Hades has different levels of comfort for the disembodied soul. Elysium is a place for the good souls and Tartarus for the bad souls. A soul's destiny in the afterlife depends on whether it was good or bad during its incarnated state.
The "eastern" ancients believed also in an immortal soul. A soul, once created even though it starts out as imperfect, is recycled for many lifetimes until such time that the soul achieves perfection and absolute goodness - nirvana.
Western thought evolved to the modern concepts of heaven and hell. Eastern thought developed into new age concepts of karma and reincarnation.
Absent from these two thoughts is the finality of the soul. Both seem to support the idea that the soul infinitely lives in either heaven, hell, or nirvana. The soul is not destroyed.
Jewish thought, which is the progenitor of Christian belief, posits that the soul is more heavily intertwined with the personhood of a human being. The soul is what makes the person a person. The body therefore, exists with the soul, though separate.
Jewish teaching, ancient and modern, seems to support the idea that when a person dies the soul dies along with the physical body. However, there are indications in the Torah, the Prophets, and the Writings, that an unrighteous soul before being totally destroyed is placed in sheol or the pit - the Jewish equivalent of hell.
For the righteous person, the soul is reunited with his/her dead loved ones in a temporary place, perhaps a type of heaven. The soul is revived at the same time of the resurrection of the body in the messianic age or what is called "the time to come". The wicked soul is permanently put out at this time. There is no resurrection for the wicked, thus, a mortal soul.
Christian teaching about the soul is a nuanced continuation of Jewish and Greek beliefs. Christian doctrine it seems, is an amalgamation of both beliefs. In that, the soul separates from its body at physical death and depending on the life it lived, either goes to heaven or hell.
There is no argument between various Christians that Jesus believed in heaven and hell. The Gospel of Luke is the one book in the New Testament where Jesus elucidated these ideas. Whether the example occurred in reality or simply a parable, the story of poor Lazarus and the unnamed rich man who both died is used by Jesus to explain clearly heaven and hell. Abraham's bosom is the picture given by Jesus to describe the heavenly kingdom where the righteous beggar Lazarus lived after he physically died. And Jesus uses the same Greek word for hell which is Hades, to say where the soul of the wicked and greedy rich man went to after he died on Earth.
There is no argument also that Christians inherit eternal life which at the second coming of Jesus, the immortal soul is put on a glorified body.
What is different is the fate of the wicked soul who ends up in hell.
Some Christians subscribe to the eventual destruction of the wicked soul which culminates shortly or long after the second coming of Jesus. This thought succumbing to Jewish influence establishes the idea of a mortal soul but only for the wicked.
The key idea for this group is, the immortality of the soul must be received as a gracious gift from God and it begins only by willful consent at the point of conversion to Jesus.
Most Christians, however, due to overwhelming Greek influence in early Church history, believe in the endless torment of the wicked soul in hell, thus, an immortal soul that sees no end to suffering and pain. Of course, there is eternal bliss for the immortal soul of the righteous.
The key idea for this group is, the immortality of the soul is a gracious gift from God which is received without consent at conception and it continues forever in either heaven or hell depending on whether one converts to Jesus or not.