Plato was a disciple of Socrates, Plato is credited with the authorship of "The Banquet," "Republic" and "Phaedo." As well as for Jesus, his method of teaching were the parables, for Plato is the Socratic Method or Mayeutic dialogues. The Phaedo is a dialogue, that tells the last moments of the life of Socrates and it is at this time that the teacher of Plato gives to his friends and disciples his final teachings: the immortality of the soul and life after death.
The theses of Plato to demonstrate the immortality of the soul are:
1) When there are two opposites, the one implies the other, such as sleeping and being awake are contrary. Awakening comes from sleeping and vice versa. In analogy, dying and living are opposites. According to Plato, this would mean that the livings come from the deads and vice versa.
2) The knowledge by analogy, that is to say "learning" in many cases, would only be a remembering. That is, we carry with us a prior knowledge of the things, so when a knowledge is acquired this brings another that would not be but from a "memory" of another life.
3) The existence of the plane of the essences or the world of the ideas, that is to say, exists by itself "the good", "the beautiful". The soul according to Platon would oscillate between two planes the physical (substances) and that of the essences (ideas). Being the first temporary and changeable and the other eternal.
The meditation according to Plato consists in separating the soul from the body, concentrating the soul in itself. Thence, he affirms:
"Those who philosophize in the correct sense of the word are exercised in dying"
Book Phaedo, of Plato.