Part 5 revisits some earlier themes and takes some of them a bit further. Topics include: the indefinability of ‘good’; the mistake of modelling dialectic on mathematics; the relation of the form of the good to other forms; the sun-like form of the good versus the participand; the correlativity of intelligence and the good; the role of moral and intellectual education; the practicality of the rulers’ dialectic and how this makes it impossible for Socrates to produce examples; how the ‘ordinariness’ of this sort of reasoning is not at odds with Plato’s solemnity about it; how, even when writing the Republic, he could have envisaged dialectic as including investigations of a more theoretical and technical nature than those which (according to this book) characterize his ideal rulers; and, finally, the Republic’s stance of naïve realism about forms.

Part 4 addresses some questions arising. (1) Elsewhere (and, we assume, in the Republic) Plato recognizes a ‘good-making’ good – that without which all other goods lack value – which he identifies with wisdom. How does the ‘good-maker’ relate to the sun-like form? (2) The Republic recognizes a form of the good in which all good things participate. This entity cannot be straightforwardly identical with the sun-like form since the latter is interrogative whereas the former answers to the predicate of a true declarative sentence saying that something is good. How are these ‘two’ entities related? Discussion shows that the sun-like one is metaphysically prior to the participand. (3) What is the purpose of the rulers’ mathematical education? The Republic is explicit that it constitutes their induction into rationality. It neither says nor implies (so the present argument) that their ethical expertise will be couched in mathematical language, or that dialectic is responsible for a programme of grounding mathematics on ultimate metaphysical principles. (4) What is the role of the form of the good in the divine crafting of the cosmos? Does the interrogative interpretation apply here too? And is the sun-like form of the good actually a god itself?

The main aim of Part 2 is to explain how the form of the good gives rise to knowledge of forms, the forms in question being of virtues and virtue-related things. This ramifies into discussions of dialectic and mathematics, the ambiguous property 'clearness' (saphēneia), hypotheses, and the non-hypothetical principle. It is proposed that the form of the good is interrogative. This position is defended against philosophical and textual objections, and argued to be preferable to alternatives. There is discussion of why Plato excludes the use of diagrams from dialectic and whether he can allow input from experience. The role of context in the rulers' dialectic is explained, and becomes the basis for explaining why Plato's treatment of dialectic in the Republic remains at the level of a sketch. There is an exploration of the difference between true philosophers and sight-lovers, and of the criteria and scope of 'good' in dialectic. This last discussion encounters the classic problem of the connection between Plato's 'justice in the soul' and just conduct as ordinarily recognized, and a solution to this problem is proposed.

The aim of Part 3 is to make sense of Plato’s succinct ontological assertion that the sun-like good is source of the being and reality (or essence) of ‘the other’ forms. The text rules out equating this with the other forms’ participation in the form of the good. Two positive interpretations are put forward, one whereby ‘the other' forms are forms of virtues, the other whereby they are ethically neutral types such as returning a borrowed item to its owner. Both interpretations are closely grounded on Plato’s precise wording of his ontological claim. And, unlike various current interpretations, both allow for a measure of continuity between Socratic argument in earlier dialogues and dialectic in the Republic. Other interpretations are considered and rejected: the idea that the form generates the other forms by self-diffusion; the perfectionist approach that identifies the form of the good with the perfection or ideality as such common to all specific forms; and the approach that sees the form of the good as in some sense the system of other forms.

The topics of Part 1, an introductory chapter, include: the form of the good; dialectic; the possibility of Plato's 'Callipolis'; the nature of the true philosopher; the philosopher-rulers' intellectual task; the 'most important thing(s) to learn'; the virtues; the meaning of the 'longer way'; the good as a reference point for distinguishing true from false accounts of virtues and virtuous things; and the definability (or not) of the good.

Cosmology or metaphysics?

Consider the ambiguous phrase ‘intelligible world’. In the context of Platonism it could allude to the assumption that this sense-perceptible universe may also become to some extent intelligible to us since it was made according to a rational and benevolent plan which we may reasonably attempt to reconstruct. Alternatively, the phrase may refer to an object accessible only by intellect, an object which constitutes the eternal original of which this universe is a merely temporal copy. The eternal original is called a ‘world’ (or ‘cosmos’) because the world-hood of the sensible world, which is to say its physical order and complexity-in-unity, is inherited from corresponding features of the intelligible model. A question worth pondering – even though we may have no doubt of the answer – is: which of these two ‘intelligible worlds’ is Timaeus’s monologue principally about? Is the account first and foremost about the physical cosmos and its contents, an attempt to make more sense of this subject-matter than previous cosmologies had done – but an attempt that depends for its specific shape on an underpinning in trans-natural metaphysics? Or is the account primarily about that intelligible entity in accordance with which the physical cosmos was made – does it treat the physical cosmos as the taking-off point for an investigation of that intelligible entity? To understand Timaeus’s monologue in this second way is to look upon it as a gateway through which to enter into the study of the metaphysics of the incorporeal, this being the primary object of interest.

I distinguish between these two approaches for the sake of philosophical clarification and analysis. Thus the aim is not to provide a clear-cut contrast by which to classify historical interpretations of the Timaeus. For Plotinus, Porphyry, and Proclus the world of nature is the launching pad for the soul’s ascent to the intelligibles and beyond, and these philosophers were surely more occupied with the metaphysical problem of how the intelligible manages to be reflected in the sensible and in matter, than with constructing a picture of the physical world by conjecturing the contents of its paradigm. One might therefore infer that they read the Timaeus accordingly; and broadly and impressionistically this may be plausible. But Plotinus and Porphyry are not in the business of giving an extended commentary on the Timaeus, and Proclus, who is, understands his task in a way that certainly accepts the cosmology as such even though for him there is a great deal more to it than just that; and he seems to have no uneasiness in combining these different perspectives.