The chapter deals with Galen’s attack on the pulse-classification of the first-century CE Pneumatist doctor Archigenes, and examines Galen’s reasons for replacing Archigenes’ theory with his own. Galen claims that Archigenes has no idea of the proper method of determining the real species of pulse, and he castigates him for terminological failings as well. But it turns out on close analysis that Archigenes’ actual classification is very close to Galen’s own; and the terminological cavils seem fairly trivial and pedantic. So what is the real substance of Galen’s attack? The chapter suggests that the point at issue is partly simply a matter of professional rivalry, but partly also a consequence of Galen’s insistence on adhering to the properly philosophical method of conducting divisions.

Does Plato in the Republic restrict to philosophers alone the possibility of achieving happiness in this life and the next? It is often thought so. But if that were the case, the dialogue would fail on its own terms, in its task of persuading the interlocutors Glaucon and Adeimantus that they should cultivate justice, not (as Thrasymachus argues) injustice. They are not philosophers, nor envisaged as likely to achieve the level of rational understanding that is the precondition of happiness. In truth, however, there is plentiful, if scattered, evidence that an approximation to perfect happiness is available for various categories of people figuring in the Republic who have not attained what the dialogue counts as knowledge, ranging from Socrates himself, to trainee philosophers and warriors, to farmers and craftsmen. The requirement to be satisfied is the habit of respect for the law, not from fear of its punitive powers, but internalised as the way to lead a life of justice.

In his Autobiography, John Stuart Mill asserts that in 1813 he read ‘the first six dialogues (in the common arrangement) of Plato, from the Euthyphro to the Theaetetus inclusive’ (he was then seven years old; he means the Greek text). What was ‘the common arrangement’? In which edition of the text did Mill encounter it? Indeed, which editions did his father James Mill possess, and which is the one he would have chosen for his son’s introduction to Plato and Platonic Greek? The Thrasyllan arrangement familiar to modern readers from Burnet’s Oxford Text was anything but common or usual in earlier centuries. The only credible candidate is the one pioneered in Serranus’ edition of 1578, printed by Stephanus and then adopted widely, whose pagination has remained the standard Plato reference system. The Stephanus order is found in the complete Bipont Plato edition of 1781-87, whose volumes James Mill gradually acquired. Though it cannot be proved that he possessed in 1813 its opening volumes, containing the dialogues John Stuart read, these are a much likelier choice than the far less readily legible 1602 Frankfurt edition, which he almost certainly owned by that date.

Plato’s philosophical writings have over the centuries evoked widely differing styles of response. Platonist metaphysical systems have been created, as by his first successors in the Academy, down to Plotinus and later Neoplatonists and beyond; while the questioning spirit they evince was what fuelled the scepticism of Arcesilaus and Carneades in the Hellenistic period, and what most impressed James Mill and George Grote, the nineteenth-century British ‘Philosophical Radicals’. Both types of response agreed, however, in rejecting what the dialogues call ‘opinion’, the metaphysicians because it lacks the security and clarity of true knowledge, the sceptics and radicals because it leaves prevailing norms unquestioned. They all took from Plato the precept: Think for yourself, whatever opinion or the prevailing norms may be. And from the beginning they disagreed among themselves too, with Speusippus, Plato’s nephew and his successor as head of the Academy, already rejecting the dialogues’ theory of transcendent Forms. Where the theory was embraced, it was developed further than its originator ever did himself or perhaps could have done. Plato wrote for eternity, to open minds and encourage independent thought in any reader, whatever their historical circumstances.

Numenius (second century AD), the only witty Platonist after Plato himself, memorably described Plato as ‘Moses talking Attic’. He did not mean thereby to rate Eastern wisdom more highly than Platonic philosophy, as is sometimes suggested, but to recognise in the words ‘I AM THAT I AM’, spoken to Moses by the God of the Hebrews, an anticipation, unique in Eastern lore, of the conception Numenius championed of the Platonic first principle One or Good as Being itself. This paper proposes that his further exploration of that idea shows him to have construed the Timaeus account of such being as an eternal present, or in Boethius’s words ‘the complete possession all at once of an infinite life’, not as timelessness (the Timaeus interpretation advocated by Richard Sorabji). It is argued that this was both a correct interpretation of Plato’s text, and one shared in much subsequent ancient and medieval philosophy, including Plotinus, Augustine, and Aquinas. From our own human perspective, a present tense without past or future connections might be considered ‘a kind of logical torso’, a defective remnant of ordinary time. For Plato that human conception of present time is itself a mere image of eternity.

Since the arguments that Plato provides in the Republic for the thesis that the human soul consists of three parts (reason, spirit, appetite) are notoriously problematic, I propose other reasons for accepting tripartition: reasons that we too could endorse, or at least entertain with some sympathy. To wit, (a) the appetitive part of Plato’s divided soul houses desires and tendencies we have because we are animal bodies programmed to survive (as individuals and as a species) in disequilibrium with a variegated, often varying environment, (b) the spirited middle part houses status concerns that belong to us as social animals, while (c) what makes us rational animals is a faculty of reason, conceived in strikingly non-Humean terms, which determines what is best all things considered. Other psychic tendencies may then be explained in terms of the education and mutual interaction of the three parts we are ‘programmed’ for from birth.

The framework of this paper is a defence of Burnet’s construal of Apology 30b2–4. Socrates does not claim, as he is standardly translated, that virtue makes you rich, but that virtue makes money and everything else good for you. This view of the relation between virtue and wealth is paralleled in dialogues of every period, and a sophisticated development of it appears in Aristotle. My philological defence of the philosophically preferable translation extends recent scholarly work on εἶναι in Plato and Aristotle to γίγνεσθαι, which is the main verb in the disputed sentence. When attached to a subject, both verbs make a complete statement on their own, but a statement that is further completable by adding a complement. The important point is that the addition of a complement does not change the meaning of the verb from existence to the copula. Proving this is a lengthy task which takes me into some of the deeper reaches of Platonic and Aristotelian ontology, and into discussion of whether Greek ever acquired a verb that corresponds to modem verbs of existence. I conclude that even when later authors such as Philo Judaeus, Sextus Empiricus and Plotinus debate what we naturally translate as issues of existence, none of the verbs they use (εἶναι, ὑπάρχειν, ὑφεστηκέναι) can be said to have existential meaning.

A discussion of the role of character in Plato, initially focused on Thrasymachus in the Republic, and on arguing that his person is less important to Plato than his view of politics as domination of the weak by the strong. The Socrates of that and other dialogues is certainly one of the most vividly characterised figures in world literature. Nonetheless, when this unique individual speaks of philosophy and the philosopher, he directs our attention away from individuals towards a realm of abstract generalities. Once the magnetism of Socrates has established the legitimacy of philosophy (under that name), Plato has reason to make philosophy independent of his idiosyncratic central figure. Accordingly, in some later writings he relegates Socrates to the margins, and brings on stage a nameless, generic philosopher – a visitor from Elea – to discuss the paradoxes of not-being in the Sophist and political expertise in the Statesman.

A diagnosis and discussion of the trope of paternity – biological and dialectical – with which Plato plays in Republic and Philebus.

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.

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.

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.

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.

Alexander played an important role in medieval Islamic philosophy and Persian literature, serving as a vehicle for discussions of the ‘ideal king’ in Mirror for Princes literature. This chapter explores the background to one particular work, Amir Khusraw’s Mirror of Alexander (1299), in which the king consults the philosopher Plato for advice on rulership before embarking on his submarine voyage to explore the nature of the universe. Plato’s characterisation as a mystical sage is contrasted in medieval Islam with the wisdom of Aristotle, Alexander’s teacher. In Amir Khusraw as in Nizami, Alexander is as much a philosopher as a king.

In DA I.2–5, Aristotle offers a series of critical discussions of earlier Greek definitions of the soul. The status of these discussions and the role they play in the justification of Aristotle’s theory of soul in DA II–III is controversial. In contrast to a common view, I argue that these discussions are not dialectical but philosophical. I also contend that Aristotle does not consider earlier philosophical definitions of soul to be endoxa, but rather contradoxa – beliefs about which the many and the wise disagree among themselves. Through an analysis of Plato’s and Empedocles’s definitions of soul, I show that these definitions are nevertheless treated by Aristotle as potential scientific principles for explaining two of the soul’s per se attributes: causing motion and cognition in animate bodies. The main role of the critical discussions in DA I.2–5 is to show that all such earlier definitions of soul fail this explanatory task. Nevertheless, I show that these chapters are not wholly aporetic. Aristotle makes progress by solving two scientific puzzles within them: whether the soul has spatial parts, and whether ‘soul’ refers to a uniform entity across biological species.

I examine Aristotle’s reasons in DA I.3 for rejecting the claim that understanding (nous) is a magnitude (megethos), an idea Aristotle associates most explicitly with Plato, who describes nous as a self-moving circle in the Timaeus. Aristotle shows that his definition of soul, on which soul is not a magnitude or body of any kind, can explain perception, thought, and motion better than his predecessor’s materialist accounts. But unlike perception and motion, nous is not actualized through the body nor does it have a bodily organ, which makes nous a very different kind of soul capacity. Earlier thinkers, including Plato, already maintain that nous does not have a bodily organ, but they cannot explain how nous could operate or be a mover without being some sort of body itself. Even in the Timaeus, nous is described as being a kind of magnitude. But if nous were a magnitude of any kind, Aristotle claims it would not be able to think or reason. There is something about being a magnitude qua magnitude that makes reason impossible. His critique of Plato in I.3 prepares the way for his account of nous in DA III.4.