Why does Plato in the Republic attach such importance to mathematics? Not for its practical utility, nor for the transferable skills acquired by the mathematician, nor because of the rigour of the formal procedures of mathematical proof. It is rather that the five mathematical sciences described and explained in Book VII convert the soul from merely human perspective, and tell us how things are objectively speaking. Their content is what counts. They convey knowledge or understanding of the context-invariant truth of unqualified reality. In contrast with modern conceptions of mathematics and its relation to reality, these sciences are conceived as themselves sciences of value. Above all, they enlarge ethical understanding. Crucial here is harmonics, which incorporates principles first studied through the first four sciences that Plato specifies. Mathematical proportion is what underpins the musical structures – the concords – that form the subject matter of harmonics. Such mathematical structures, when internalised by the philosopher, function as abstract schemata for applying their knowledge of the Good in the social world. Plato values them so highly because they create and sustain unity: unity is for him the highest value.

The topic is ancient Greek terms for knowing: three main verbs, three cognate nouns, how to translate them, and how to understand the relation between translation issues and philosophical interpretation. Central are the schemas devised by John Lyons, in Structural Semantics: An Analysis of Part of the Vocabulary of Plato (Oxford, 1961). So far as Plato is concerned I favour Lyons’ original book account, as against his subsequent accommodation to the Rylean distinctions which so dominated scholarly discussion in Barnes’ and my youth. Besides the extensive texts of Plato and Aristotle, there is an account of Simplicius disagreeing with Alexander about the four knowledge verbs in the first sentence of Aristotle’s Physics. I close by elucidating Heraclitus frag. 57.

What did Plato mean when in Timaeus he characterised his account of the created world as an εἰκὼς μῦθος? The phrase is typically translated ‘a probable story’, ‘a likely tale’. Connotations that modern empiricist philosophy of science might attach to those expressions are misleading. Careful attention to the two terms Plato uses, and their resonances in previous Greek literature and thought, suggests instead the strikingly oxymoronic: ‘a rational/reasonable myth’. This is not, however, the reasonableness of deduction or of inference to the best explanation, but of the practical reasoning in which a supremely good designer would probably engage, assuming that he wanted to make his product as like himself as possible, but from materials with their own properties not of his making. Practical wisdom cannot aspire to the same standards of rigour as theoretical wisdom can. It can attempt only the most reasonable option given such constraints – as could any account of why that choice was made. Hence the importance of the Timaeus’ initial reminder of Socrates’ construction of a political order (witness the Republic), and its address to a company competent in politics as well as mathematics, interested no less in κόσμος as political order than in cosmology.

Plato’s treatment of justice in the individual in Book IV of the Republic has been heavily criticised. His radical proposal that it consists in an ordering of elements of the soul, parallel to justice in the city conceived as a social order maintained by specialisation of roles assigned to the three classes he specifies, is often seen as too remote from what anybody would recognise as ‘justice’. The criticism rests on two principal misconceptions: of the connection Plato is positing between psychic harmony and just behaviour, and of what he takes psychic harmony to consist in. First, he assumes law-abiding citizens behaving with what he like anybody else would count as justice. What harmony of the soul provides is the best explanation of their inner motivation for so behaving. Second, harmony is conceived as achieved when each element in the soul is focused as it should and will be, following good upbringing and education such as is described for the Guards in Books II and III.

This volume collects those of Myles Burnyeat’s philosophical publications from his Oxford period and in retirement that were devoted to two particular areas of his Plato scholarship. He had regularly lectured in his Cambridge days on the central books of Plato’s Republic. But it was in these later years that he was able to articulate in extended published form his multi-faceted vision of the dialogue. One highly developed but hitherto unpublished paper (‘Plato and the dairy-maids’) appeared to require only one or two small finishing touches, and is also included. In addition, two short book reviews which address further important aspects of the Republic’s philosophy or literary form are reproduced.

This chapter offers an account of the inspiration for their active advocacy of political, social, and educational reform that three key figures of the British nineteenth century found in Plato: John Stuart Mill, George Grote (author of the classic three-volume study Plato of 1865), and Benjamin Jowett (whose translation of the entire Platonic corpus of 1871 was to be hugely influential). For both Mill and Grote, the importance of the probing Socratic method portrayed in the dialogues was paramount. Grote contrasted it with the tyranny exercised over the dissenting individual by the conformism of society at large: what he called King Nomos, with his eye particularly on the Great Speech Plato puts in Protagoras’s mouth in the Protagoras. To his mind, the Republic represented a sad betrayal of the Socratic spirit. It was Jowett who was chiefly responsible for making that dialogue’s moral idealism central to the education Oxford provided for the nation’s future elite, and whose endorsement of its radical proposals for equality for women in education and in politics is particularly notable.

This is a close scrutiny of De Anima II.5, led by two questions. First, what can be learned from so long and intricate a discussion about the neglected problem of how to read an Aristotelian chapter? Second, what can the chapter, properly read, teach us about some widely debated issues in Aristotle’s theory of perception? I argue that it refutes two claims defended by Martha Nussbaum, Hilary Putnam, and Richard Sorabji: (i) that when Aristotle speaks of the perceiver becoming like the object perceived, the assimilation he has in mind is ordinary alteration of the type exemplified when fire heats the surrounding air, (ii) that this alteration stands to perceptual awareness as matter to form. Claim (i) is wrong because the assimilation that perceiving is is not ordinary alteration. Claim (ii) is wrong because the special type of alteration that perceiving is is not its underlying material realisation. Indeed, there is no mention in the text of any underlying material realisation for perceiving.

This chapter is the only detailed study available to date on the long introductory scene of the Charmides. It provides systematic analysis of the social, historical, and dramatic context, sketches the main characters, discusses their interactions and motivations, dwells on the story of Zalmoxis and the corresponding holistic conception of therapy, and assesses the method that Socrates proposes to follow in order to examine the question of whether Charmides has sôphrosynê.

This chapter discusses the section of the dialogue in which Critias advances an ingenious interpretation of the Delphic inscription ‘Know Thyself’ in order to introduce his account of temperance as self-knowledge. The analysis shows how Critias’ speech pursues ideas he has articulated earlier in the dialogue, and in particular the intuition that one cannot be both temperate and ignorant of one’s temperance – an intuition on account of which Critias abandoned the definition of temperance as ‘doing one’s own’. It is suggested that Critias’ appeal to the Delphic inscription is intended to evoke the god’s verdict about Socrates in the Apology and bring to the forefront the two competing conceptions of self-knowledge at work in the dialogue.

The main aim of this chapter is to assess Socrates’ summary of the key moves of the investigation and the criticisms that he directs against both his interlocutor and himself. The first section argues that, although some of Socrates’ criticisms against Critias’ ‘science of science’ can also raise problems for Socrates’ own philosophy and method, they serve a constructive rather than a destructive purpose: while they point to the limitations of Socratic dialectic, they do not imply that the latter is useless but only that it cannot by itself take us all the way to virtue and truth. The second section discusses Socrates’ last exchange with Charmides, while the third section offers a new interpretation of the final scene of the dialogue and wraps up the discussion of the characters’ development.

This chapter considers Charmides’ second definition of temperance as aidôs – modesty or a sense of shame. It proposes a new reconstruction of the argument, addresses the charge that the latter contains a paralogism, and discusses the social, political, and moral implications of the relation between sôphrosynê and aidôs.