I. Myth of Theseus.
The setting for the Phaedo is the last day of Socrates' life. He has been condemned to die by drinking hemlock for corrupting the youth of Athens, and introducing the worship of strange gods into the city. His death is postponed, however, due to the fact that a religious festival had just started during his trial, and Athenian law prohibits executions during these festivals in order to keep the city pure. The festival is a commemoration of the mythic event whereby Theseus traveled with a delegation (sacrifice) of fourteen young people (seven youths and seven maidens) to King Minos of Crete to face, and defeat, the Minotaur in the King's Labyrinth, the threat of which Minos used to extort the human sacrifice. Since Plato brings attention to the fact that the dialogue takes place against this background, and since he has the dialogue include Phaedo and thirteen people named in 59b-c, he clearly expects his readers to recognize the parallel and hope for an outcome similar to that of the mythic tale. As Theseus traveled with fourteen threatened Athenians through the Labyrinth of Minos to face and slay the monstrous Minotaur, so Socrates travels with fourteen threatened philosophers through the intricacies of argumentation to face and slay what threatens both himself and his companions, namely the fear of death. As Theseus was able to triumph over the Minotaur and free Athens, so Socrates will triumph over death.
II. Philosophy is a practice for dying. (64a)
(Cebes notes that this line of reasoning depends on the soul being immortal.)
III. Argument from Opposites.
N.B. This argument is not meant to be conclusive, but to open the mind of Plato's audience to the relation of the soul to life and to death.
IV. Learning is Recollection.
As W. K. C. Guthrie notes in The Greek Philosophers: "The Heracliteans maintained that everything in the world of space and time was continually flowing, as they put it. Change never ceased to operate for a moment and nothing was ever the same for two instants together. The consequence of this doctrine appeared to be that there could be no knowledge of this world, since one cannot be said to have knowledge of something which is different at this moment from what it was a moment ago. Knowledge demands a stable object to be known. Parmenides on the other hand had said that there is such a stable reality, which can be discovered only through the activity of the mind working altogether apart from the senses. The object of knowledge must be immutable and eternal, exempt from time and change, whereas the senses only bring us into contact with the mutable and perishable" (p. 88)
Knowledge, as a stable grasp of things, cannot arise from the things that one senses since these things are forever changing, and are not themselves ever stable.
Sophists, like Protagoras, used this conception of the nature of the world to deny that any knowledge is possible, and so all things, virtue, justice, beauty, are a merely a matter of opinion. This being so, one studies rhetoric in order to sway people's opinion, and so enact in the laws of the city one's own private desires (which are equally good or bad as anyone else's).
Plato accepts that material things are in a constant state of becoming, but he also takes it as obvious that we do have knowledge, a grasp of stable, unchanging realities. This is most evident in mathematics. We do in fact know that 2 + 2 = 4, and that it has always been true, and will always continue to be true. There is, in fact, some stable knowledge, but the problem is how we can have this stable knowledge when everything we sense is not stable.
E.g., if you observe two sticks, of (approximately) equal lengths, you know that they are equal, but by the same token, they are not the Equal-itself, since they are not perfectly equal. The Equal-itself is what all instances of equal things have in common in virtue of which we say that they are equal.
N.B. This argument, even if it is true, does not prove that the soul is immortal, for it only shows that the souls of the living were some place (presumably among the dead) prior to their being born in this world.
Moreover, Plato is explicit that this argument depends on one accepting the theory that knowledge consists of grasping things themselves. As he says: "If those realities we are always talking about exist, the Beautiful and the Good and all that kind of reality, and we refer all the things we perceive to that reality, discovering that it existed before and is ours, and we compare these things with it, then just as they exist, so our soul must exist before we are born. If these realities do not exit, then this argument is altogether futile." (76d-e).
V. Soul is simple.
VI. Objection: Soul is a harmony. (85e)
VII. Objection: The soul is not indestructible, but merely durable.
VIII. The Death of Socrates.