In order to address more carefully the question of whether or not the soul coheres as one unit after death, Socrates suggests that his interlocutors ask what sorts of things dissipate and what sorts of things hold together, and then ask of which sort the soul is a member. His answer to the first question is that composite things, made up of many different parts, are liable to break up, whereas incomposite things can suffer no such fate. Thus, he suggests, things that are constant and invariable are incomposite, since they cannot be changed or broken apart.
Socrates goes on to point out that the Forms must be incomposite, since they are constant and invariable, never admitting any kind of alteration. Particular objects in the world, on the other hand, can be said to be composite, as they are in constant variation. Further, Socrates points out, the Forms are invisible, and can only be apprehended by the mind, whereas material things can be sensed by the body. Socrates concludes from this reasoning that there are two classes of things: those that are invisible, invariable, and incomposite, and those that are visible, variable, and composite.
Next, Socrates points out that we are part body, part soul, and makes Cebes concede that the body is classed among the visible, variable, and composite, whereas the soul must be invisible, invariable, and incomposite. Thus, when the soul uses the body as a means to knowledge, it gets access only to the inconstant and variable, and becomes confused. Only when it investigates by itself does it come into contact with those things that are constant, and thus acquires wisdom.
Cebes is then invited to compare these dualities with that of serving versus governing. He is led to agree with Socrates that the soul and the divine are alike in that they govern, whereas the body and that which is mortal are in a subservient position. From this, and the preceding dualities, Socrates concludes that while his body will decay and deteriorate, like all variant things, his soul will live on, like the invariable, incomposite things which it resembles.
Different souls, however, experience different fates after death. Socrates suggests that the soul that has detached itself from earthly cares and has dedicated itself wholly to the life of the mind as found in philosophy will be able to leave this world of inconstancy and decay behind. It will find itself instead among other divine beings, in a heavenly realm of immaterial, invisible, wise souls.
Those whose souls remain attached to earthly cares, on the other hand, will be bogged down by the material objects and desires that contaminate their souls, and will remain on this earth as ghosts until their souls inhabit another body. Each one will be reincarnated as befits the way they have behaved in this life; for instance, a villain might become a wolf, whereas a good citizen who never learned philosophy might become a disciplined animal like a bee or an ant, or even be given another human body to inhabit.
For these reasons, the philosopher avoids the lusts and desires that afflict the soul when it is imprisoned within the body. Philosophy helps release the soul from this prison, guiding it toward what is true and just, and steering it clear of the pleasures and pains of bodily life. Each pleasure and pain is like a rivet that pins the soul to the body, making it less able to escape. A philosopher will break free of these rivets by listening only to reason and preparing for a contented life after death.
The argument that associates the soul with that which is divine, immortal, invisible, incomposite, and invariable, and the body with that which is corporeal, mortal, visible, composite, and variable is known as the Argument from Affinity. This argument takes the formal features of Forms, those properties a Form has by virtue of being a Form, as opposed to the proper features of Forms, those properties a particular Form has by virtue of being that particular Form. All Forms are of a certain type, and the soul is far more similar to this type than the body is. This kind of inductive reasoning is far from being leak-proof, only suggesting rather than definitively proving that the soul is of a certain kind. Nonetheless, the argument has far fewer holes than the Argument from Opposites or the Theory of Recollection. (It is worth noting, though, that Plato does not always maintain that the soul is incomposite. In the Republic, for instance, Plato suggests that the soul is divided into three parts: reason, appetite, and spirit, or will. In this view, it would seem that the soul is divisible into three parts.)
This section finds a good deal of Pre-Socratic philosophy floating about, most notably that of Parmenides, Democritus, and Pythagoras. Parmenides, a figure greatly admired by Plato, is famous for asserting that what is real must be eternal, indivisible, and unchanging. This idea not only deeply informs this argument, but is also likely an inspiration for Plato's Theory of Forms. Democritus is famous for his atomic theory--that all things are made up of simple, indivisible parts. Socrates' assertion that the soul is indivisible probably borrows somewhat from Democritus' theory. Last, Socrates also borrows from the Pythagorean belief in reincarnation and the transmigration of souls. Simmias and Cebes, both Pythagoreans, would have been favorable toward this theory.
It is worth noting the similarities between Socrates' description of the fate of the philosopher's soul after death and the Christian conception of heaven. This is by no means a coincidence. Christian theology was to be deeply informed by Plato's thinking, and his discussion of the soul and the afterlife were particularly influential.