Socrates at this point employs a series of if-then arguments (enthymemes) which he builds sequentially to argue a form of argument termed a sorites. But we cannot at this point logically allow his argument. He cannot demonstrate the validity of the premises he argues for wood, or iron, or the human eye, and he cannot show logically that, because the soul is not destroyed by injustice, it follows that the soul is immortal. Indeed, for all we know the soul may be immortal. Socrates may believe that the soul is immortal; so may Glaucon believe it. But they do not know it. Socrates is here arguing a question of probability whose major premise we may disallow.
In Plato's world, very few people held to the doctrine of the immortality of the soul. Some of the Pythagoreans, discussed earlier, did theorize about the soul's immortality, and Plato was familiar with their arguments. In Plato's dialogue the Phaedo, Socrates argues that the soul is separated from the body at death and is probably therefore immortal, but another speaker says that the soul escapes the body and dissolves like smoke (a popular belief at the time).
