If it is necessary that we too should speak about the Cave and all the things outside the Cave and their resemblance (homoiotês) to reality (ta pragmata), let us first discuss how Plato himself divided all things in the cutting up of the Line (Rep. VI 509d–511e5).17 In those [divisions] as well he makes the things inside the Cave represent the objects of opinion (doxasta), and makes the things outside the Cave represent the objects of understanding (gnôsta). It is for this reason too that, in addition to the division itself, when he has completed it in the sixth book (VI 511d6, ff.), he immediately adapted this image at the very beginning of the seventh (VII 514a1, ff.)

In Essay 11 Proclus discusses one of the most memorable sections of the Republic: the analogy between the Sun and the Good. His response to this challenging portion of the text is conceptually rich and subtle. The essay builds on the definitions developed in Essay 10 to explore the sense in which the Good can be understood when it is fundamentally unlike other objects of understanding. Essay 11 is also, by its nature, related to Essay 12, on the Cave and the Divided Line. Essay 12, however, makes a fresh start and is pitched in general at a more introductory level, as an overview of Platonic education as a whole.

The first step in Proclus’ discussion is establishing three different senses of ‘the good’ (to agathon) in Plato’s teaching on the subject. The first of these is ‘the good in us’ (to en hêmin agathon (269.16)), which is neither pleasure nor intellect, and with which he says that Socrates begins in the present passage of the Republic.

How Socrates in the Republic arranged the account concerning the virtues, after he isolated both the political classes and the parts of the soul, is itself something that we might learn once we have first sought for ourselves an answer to this question: ‘What is the distinctive feature of every virtue?’ I do not use the word ‘virtue’ homonymously in the sense in which it is customarily applied even to things that are lifeless, as when one talks about the virtue of an implement or some such thing, but I mean instead when the term is used strictly.22 In this sense we will inevitably be speaking about something that relates to its vital character and the way that it perfects its life, since it is the cause of things going well for those in which it is present rather than of their existence.

In the fifth book of the Republic, wishing to understand what the difference is between philosophers and lovers of opinion (philodoxos), [Plato] concludes by showing that while philosophers embrace understanding (gnôsis) of universals (ta katholou), lovers of opinion [embrace understanding] of particulars (merika). For [he says that] while the [lovers of opinion] only desire to learn the many beautifuls,19 philosophers [desire to learn] that which is simply beautiful. In order to show this, he establishes first what the difference is between the simply beautiful and the many beautifuls. And he shows that the former is one, but the latter are this very thing in multiple instances (476a). And again, he shows from opposites that beauty itself (to autokalon) is one. This is because if the opposites are two, beautiful and ugly, each of these is one, since two is the coming together of two ones.