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.

It is familiar that, in Phaedo 95e ff., Plato argues that causation requires Forms and that Forms are causes. According to the standard and mainstream view, Plato’s argument for this view relies on the view that Forms are self-predicative (i.e., the Form of F is itself F) and that the cause transmits its character to the effect. The chapter demonstrates that Plato’s argument depends on neither of these views. It shows that what the argument relies on is the view that, first, Forms are essences (i.e,. the Form of F is what it is to be F), and, secondly, causation/explanation is uniform (i.e., same cause if, and only if, same effect).

The chapter considers why, and in what sense, Plato thinks that Forms are separate from sense-perceptible things. It argues that the notion of separation Plato operates with is not a purely modal notion, but rather, an essentialist notion: A is separate from B, if, and only if, What A is makes no reference to B, but what B is makes reference to A. It demonstrates that, for Plato, Forms are, in this sense, separate from sense-perceptible things, because what the primary Forms are, such as oneness or likeness, does not have to make reference to sense-perceptible things.

The chapter considers the relation, in Plato's Phaedo, between knowledge and enquiry. It argues that Plato's account of knowledge is not independent of his account of enquiry and that certain reatures of his account of knoweldge are based on his account of enquiry.

The chapter considers why Plato thinks that Forms are unitary and changeless. It argues that this follows from Plato's supposition that Forms are essences and that the definition of essences must conform to certain requirements.

The chapter considers why Plato thinks that Forms are distinct from sense-perceptible things. It focuses on Phaedo 74 and Republic 478-480. It argues against the standard view that, for Plato, sense-perceptible things are subject to co-presence of opposites. Plato's view is rather that sense-perceptible things, in so far as they are simply perceived by the senses, are subject to co-presence of opposites.

The chapter is dedicated to the Sun Analogy in Republic. It shows that, for Plato, mind and world are co-ordinate: neither is prior to the other; and this is because both mind and world are co-explained by a single ultimate principle, which is super-ordinate to both mind and world: the Idea of the Good.

The chapter considers why, in Republic VII. 523-525, Plato associates Forms with judgements about sense-perceptible things. It argues that he does so because he argues that judgements about sense-peceptible things, if they are to conform to the principle of non-contradiction, must use certain Forms, and especially the Form of oneness or unity, to individuate sense-perceptible things.

The chapter considers Plato's claim, in Parmenides 135, that thinking about things requires Forms. It locates Plato's argument for this claim in 132 and, especially, in the second part of the dialogue (142ff.). It shows that the second part of the dialogue is just as much about thinking as it is about being.

This is the Conclusion, and it shows that that upshot of this project is that Forms simply are essences, not things that have an essence.

The chapter argues that Plato, in the Hippias Major gives due consideration to the question whether, for some qualities F, such as beauty, it is possible to give an account of what F is by pointing to an example-and-exemplar. He takes seriously, and gives cogent reasons in defense of, an affirmative answer to this question in a manner comparable to Geach – although he argues that these reasons lead to inconsistency, if combined with the view that it is possible to make comparisons in regard to F among significantly different examples-and-exemplars of a thing that is F.