Plato, answered from the texts and cited to the page.
The soul is immortal because it is a self-mover — and this is not a poetic claim but a logical one. Whatever is moved by something external to itself depends on that external thing for its motion, and when the external mover ceases, the motion ceases, and the life ceases with it.1 But what moves itself never desists from motion, since it does not leave off being itself; and being the source and spring of motion in everything else, it can have no beginning, for a source that got its start from something else would no longer be a source.2
From this it follows necessarily that the self-mover cannot be destroyed: if it were destroyed, all heaven and everything that has been set in motion would collapse, come to a stop, and never have cause to start moving again.3 The soul, then, as the self-mover, has neither birth nor death. Now, to say what the soul is in its full essence would require a god; to say what it is like is humanly possible, and the image I reach for is this: a charioteer with a team of winged horses.4
The charioteer is reason; one horse is noble, from good stock; the other is base, pulling against the driver. The wings are the soul's capacity to rise toward the divine — toward beauty, wisdom, and goodness — for these are what nourish the wings and make them grow.5 Foulness and ugliness cause the wings to shrink and fall away, and when they fall, the soul sinks and takes on an earthly body.6
The argument from the Phaedo approaches the same conclusion by a different road. The soul brings life wherever it goes, as fire brings heat. Just as three will never admit the even, and fire will never admit the cold, so the soul will never admit death — it is, by its very nature, the deathless.7 And if the deathless is also indestructible — as god and the Form of life itself are indestructible — then the soul, being deathless, is indestructible as well.8
When death comes to a man, the mortal part perishes; the deathless part withdraws, safe and unthawed, as snow retreats before heat without being destroyed.9 What follows from this is not consolation but obligation. If the soul is immortal, it requires our care not only for the span we call a life but for all time; and one is in terrible danger who neglects it.10
The soul goes to the underworld possessing nothing but its education and upbringing, and these determine the greatest benefit or harm at the very beginning of the journey there.11 Philosophy, then, is not an ornament for the leisure hours — it is the soul's only genuine preparation for what it always already is.
every bodily object that is moved from outside has no soul, while a body whose motion comes from within, from itself, does have a soul, that being the nature of a soulComplete Works, pp. 552–553
a self-mover is also the source and spring of motion in everything else that moves; and a source has no beginning. That is because anything that has a beginning comes from some source, but there is no source for this, since a source that got its start from something else would no longer be the source.Complete Works, pp. 552–553
if a source were destroyed it could never get started again from anything else and nothing else could get started from it—that is, if everything gets started from a sourceComplete Works, pp. 552–553
let us liken the soul to the natural union of a team of winged horses and their charioteerComplete Works, pp. 553–554
by their nature wings have the power to lift up heavy things and raise them aloft where the gods all dwell, and so, more than anything that pertains to the body, they are akin to the divine, which has beauty, wisdom, goodness, and everything of that sort. These nourish the soul's wings, which grow best in their presenceComplete Works, pp. 553–554
foulness and ugliness make the wings shrink and disappearComplete Works, pp. 553–554
the soul does not admit death... So the soul is deathlessComplete Works, pp. 120–121
if the deathless is also indestructible, it is impossible for the soul to be destroyed when death comes upon itComplete Works, pp. 120–121
when death comes to man, the mortal part of him dies, it seems, but his deathless part goes away safe and indestructible, yielding the place to deathComplete Works, pp. 120–121
it requires our care not only for the time we call our life, but for the sake of all time, and that one is in terrible danger if one does not give it that careComplete Works, p. 121
the soul goes to the underworld possessing nothing but its education and upbringing, which are said to bring the greatest benefit or harm to the dead right at the beginning of the journey yonderComplete Works, p. 121