Socrates strongly believed in the immortality of the soul. He believed that the soul never dies. It enters a body when it is about to get birth and leaves when the body dies. The soul then travels to heaven or hell depending upon the karma of it. These were his arguments about the reincarnation of the soul. Plato also had a similar view point as that of Socrates. An immortal soul does not mean an immortal body. The soul may leave the body when it dies. The soul is not because of your body, but the body is because of the soul. A human cannot be called a human unless he is comprised of a body and soul.