A study of James Mill’s engagement with Plato. It focuses on two hostile reviews of Thomas Taylor’s Neoplatonist Plato, one published by him in 2004 in The Literary Journal, a short-lived periodical that he himself edited, and another in 2009 in The Edinburgh Review, a much more prestigious and enduring forum of opinion, for which he wrote regularly for some years. It celebrates Mill as a pioneer, who had the good fortune to make his first approach to Plato from the vantage point of the scepticism of Cicero’s Academica, and very likely exerted influence on the interpretation of Plato in George Grote’s great study of 1865, which portrays an exploratory thinker, not a system builder.

This short book review discusses the philosophical appropriation by Plato and Aristotle of the Greek institution, at once social, political, and religious, of theoria, ‘spectating’. Pythagoras was alleged to have classified those who travelled to the Olympic Games as competitors, traders, or spectators: symbolising the pursuit in human life of honour, economic gain, and wisdom. Plato and Aristotle are often taken accordingly to be committed to what is sometimes labelled ‘the spectator theory of knowledge’, with knowledge of ultimate principles construed as non-discursive intuition or ‘instant ocularity’. But the vision they have in mind is actually the ‘seeing’ constituted by grasp of an explanation of how a whole complex of things hangs together, achieved only after much preparatory, exploratory thought.

Why would a fourth-century BC Atomist – Anaxarchus – express his scepticism about knowing the truth of things by imaging these as scene-painting? The comparison seems already to have been made by Democritus and Anaxagoras, who according to Vitruvius had been impressed by something an Athenian painter named Agatharchus had written on perspective. This chapter offers a detailed scrutiny of a range of texts that have a bearing on the interpretation of Vitruvius’ claim. It argues that Agatharchus was probably author of a pioneering treatise on stage-building, which included a section on scene-painting lauding its power to create the illusion of a whole three-dimensional world. Anaxagoras will have taken this claim as cue for his dictum: ‘Appearances are a sight of things unseen’ – in the sense that there is no break between the macroscopic world of ordinary observation and the microscopic world which explains it. The Atomist Democritus will no doubt have imparted a quite different spin to Anaxagoras’ slogan in praising it. But it is unlikely that either Presocratic was prompted to a mathematical interest in perspective by reading Agatharchus. It is only with the Hellenistic philosophers, and especially Epicurus, that optics begins to leave its trace on general epistemology.

It is often said that in the Republic Plato proposes to ban art and poetry from his ideal society. The truth is that poetry – the right sort of poetry – will be a pervasive presence in the life of the warrior class whose upbringing and education are discussed in Books 2 and 3 of the Republic. What Plato develops here is a systematic anti-democratic programme for reforming music, i.e. musical poetry, incorporating dance as well as song. There are four stages in the programme: first, purging poetic content; second, placing severe restrictions on the manner of performance and on those permitted to engage in it, and particularly on the extent of mimesis or impersonation deemed allowable in performance, on account of its influence on character; third, placing similarly severe restrictions on musical technique, particular on the musical modes composers are allowed to employ in constructing melodies; and fourth, ensuring that the material and social settings in which musical poetry is performed are also designed with a gracefulness and beauty that will work their appropriate effect on the performers, providing the ideal conditions for them to fall in love, homoerotically conceived.

This paper is detective work. I aim to show that the brilliant Pythagorean mathematician Archytas of Tarentum was the founder of ancient Greek mathematical optics. The evidence is indirect. (1) A fragment of Aristotle preserved in Iamblichus is one of two doxographical notices to mention Pythagorean work in optics. (2) Apuleius credits Archytas with a theory of visual rays which saves the principle that the angle of reflection is equal to the angle of incidence. I argue that the source from which Apuleius got this information was the Catoptrics of Archimedes, the genuineness of which I defend against Knorr’s hypothesis that it is the Euclidean Catoptrics, which had been misattributed to Archimedes. (3) The omission of optics from the mathematical curriculum in Plato’s Republic, and the Timaeus’ wholly physical account of mirror images, can be explained as polemical, for it is well attested that optics was practised in the Academy. The reason Plato does not mention optics is that he objected to Archytas using mathematics to understand the physical world rather than to transcend it.

The construal of Apology 30b2–4 which in JHS 123 (2003) I attributed to John Bumet had appeared in print sixteen years before his edition of Euthyphro, Apology, and Crito. I now suggest that it probably originated in the mind of J. A. Smith, who was an undergraduate contemporary of Burnet’s at Balliol College, Oxford, and later Waynflete Professor of Moral and Metaphysical Philosophy. The unexpected construal, transmitted by Balliol tradition, is typical of Smith’s cast of mind.

What does Aquinas mean when he speaks of ‘spiritual’ change in explaining sense perception? This chapter is partly exegesis of that notion, partly explication of the author’s own previous invocation of ‘spiritual’ change to characterise the way perception for Aristotle takes on sensible form without matter, and partly explanation of why in philosophy since Descartes it is so difficult to understand how for Aristotle and Aquinas perception is both physical and mental. For both thinkers, it is an ‘unordinary’ physical alteration. That does not make it a ‘mental’ event in any sense that contrasts with ‘physical’. In sight the eye is coloured by the sensible form of red conceived not as a natural form, but as what Aquinas calls an intentio. The notion of intentio here expresses the idea of cognitive awareness, or of sensible form causing knowledge in a being which has the power of cognition. Aquinas calls sight the ‘most spiritual’ of the senses because, whereas with the operation of the other senses ordinary natural processes are required either as causal antecedents or concomitant effects, in sight there is no similar natural change at all. In its power of cognition alone we reach the end of explanation.

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.