To unravel the intricacies of the last argument of the Phaedo for the immortality of the soul, the reader has to peel away successive presuppositions, his own, Plato's and not least the presupposition that Plato very skilfully portrays as being shared by Socrates and his friends.A first presupposition is the reader's own. According to our modern ways of thinking, a soul that is immortal, if there is such a thing, is a soul that lives forever. That presupposition is not shared by Socrates and Cebes (Socrates' interlocutor in the final argument). A soul that survives separation from the body, once or a number of times, is held to have survived death and therefore to be immortal. But it does not follow that it will live forever. For a soul to live forever, it must be shown to be not only immortal, but imperishable. Only if the soul is both immortal and imperishable can the assembled company be sure that the Socrates who is talking to them now will still be living when, after sunset, he has drunk the hemlock and can talk to them no more.The modern reader who has divested himself of the presupposition that immortal and imperishable are mere synonyms, and therefore appreciates the need for an argument designed specifically to prove that the soul is imperishable and not merely immortal, has nonetheless to be aware of a second presupposition, a presupposition shared by Socrates and his friends which restricts the meaning that the modern reader might otherwise suppose to be conveyed by the word 'imperishable'. Both Socrates and Cebes, as portrayed in the Phaedo, take it for granted that the only time when the soul might perish is the moment of her separation from the body. Provided it can be shown that the soul will survive separation from the body, no matter how often the body is taken from her, the soul, so they are happy to assume, will have shown herself to be both immortal and imperishable.We do not have to suppose that this second presupposition is shared by the author of the dialogue. Plato's subtle but insistent restriction of the moment when the soul might be threatened with extinction to the moment of her separation from the body has been deliberately designed to alert the reader to a way of thinking which Socrates, Cebes and Echecrates all take for granted, but which Plato does not necessarily invite the reader of the dialogue to share.The restriction is nonetheless essential to the structure of the argument. It is because Socrates does not envisage a possible extinction of the soul at any moment other than the moment of separation from the body that he is able to present a soul that is essentially alive as immune to the death which separates soul from body, however often such a separation may occur, and as therefore (so he claims) not only immortal but imperishable.In presenting that argument, how far has Plato deliberately foregone any attempt to prove that the soul is imperishable subsequently to the moment of her separation from the body? Socrates argues that the soul is unaffected by the death of the body because she is essentially alive. He does not argue that she is immune to destruction or extinction because she is essentially existent. In the face of Plato's silence, in the Phaedo and elsewhere, the modern reader has to hold in abeyance a third and final presupposition, that only a being whose essence it is to exist can of its nature never not exist.To understand the dialogue is therefore no easy matter. The reader needs to distinguish Socrates as the mouthpiece of Plato from Plato as the author of the dialogue. At the same time the modern reader has to distinguish the Plato of history from a fictional Plato who shares our own ideas and our own preconceptions, including the concept of a being cuius essentia est esse. An intricate double task, which other modern readers of the dialogue have so far not even attempted.