Chapter 10 explores the range of love in Plotinus, going from human earthly (including sexual) loves up to the One/Good as itself love. Plotinus takes over Plato’s interest in love and makes it into a feature of reality in general. Human love – the desire to unite with the beloved, the feeling of need – anticipates aspects of higher levels of love, soul’s love which brings it to union with transcendent Intellect, Intellect being itself love of the One. I discuss the special sense in which the One can be said to be love and self-love.

Chapter 24: the theme of the harmony of the spheres appears already in Plato and is criticized (as a Pythagorean theory) in Aristotle: if there is such a harmony, why is it that we do not hear it? Despite Aristotle’s criticism, various attempts were made in Antiquity to provide an answer to the question. In Chapter 24 I present an answer to be found in Simplicius which, I argue, goes back to Iamblichus: Pythagoras alone can hear the celestial harmony, whereas we in general cannot; this is because Pythagoras has a faculty corresponding to and able to sense this harmony, an astral vehicle of the soul which is pure, as compared to the impure accretions our souls accumulate in our descent to the body and which prevent us from hearing the celestial music. I describe this music, how Pythagoras educated himself in hearing it and how he composed audible music imaging it for the moral education of his followers.

Chapter 4 discusses the protreptic structure of Iamblichus’ De communi mathematica scientia and of Proclus’ revision of this text in the First Prologue to his commentary on Euclid’s Elements. I note rhetorical patterns and styles of argumentation used by Iamblichus, which mean, for example, that the same arguments can be made both in support of the study of philosophy (in the Protrepticus) and in support of the study of mathematics (in the De communi mathematica scientia). I note Proclus’ use of Syrianus’ commentary on Aristotle’s Metaphysics in his revision of Iamblichus’ book and suggest that Iamblichus may have been influenced by the prolegomena of Ptolemy’s Syntaxis.

Chapter 5 explores some relations between rhetorical models for speeches in praise of the gods and Platonist texts relating to metaphysics, or ‘theology’, the science of divine first principles. As rhetoric distinguishes different modes and styles in discourse about the gods, so do the Platonists, both in their own works and in those of their ancient authorities (Pythagoras and Plato), distinguish in corresponding ways between different modes of teaching in theology. And as rhetoric prescribes, for speeches about the gods, genealogies of the gods, their actions and benefactions, so too do Platonist theological texts expound the metaphysical genealogy of first principles, a hierarchy of causes and their effects. But speech expresses the limitations of human souls: to approach what is divine and transcendent, which is ineffable, is to be silent, to practice the silence of Pythagoras and of Socrates.

Chapter 25 introduces Alexander of Aphrodisias’ systematic reading of Aristotle’s Metaphysics. I show how Syrianus took over Alexander’s reading of Aristotle, combining it with Plato’s references to a supreme knowledge, ‘dialectic’, and explaining the possibility of scientific knowledge of the objects of metaphysics – transcendent divine first principles – in terms of concepts innate in the soul which both image these first principles and are available to discursive reasoning as sources of knowledge of these principles. The primary text for metaphysics, according to the Platonists, was Plato’s Parmenides. I show how Proclus’ interpretation of the Parmenides, inspired by Syrianus, underlies the composition of Proclus’ metaphysical masterpiece, the Elements of Theology. Finally, Damascius is shown to have brought out to the fullest extent the limits of human reasonings about transcendent divine principles, reasonings which incessantly lead to contradictions and impasses, the aporetical ‘birth-pangs’ of the reasoning soul where it meets what transcend it.

Olympiodorus provided his students in Alexandria in the sixth century with a handy summary of political science which I discuss and develop in Chapter 14. The following themes are introduced: the domain of political science (the realm of praxis, the life of soul in the material world, in the state or city, where political science directs other subordinate expertises); law (the primacy of law in an ideal city for humans); practical wisdom (its use of theoretical wisdom and difference from it); the goal (‘political’ happiness, involving the political virtues and preparing for a higher life); earthly and heavenly cities; the place of the philosopher in the city; Platonist texts concerning political science.

In Chapter 7 I discuss the consequences, as regards the theory of virtue, of Plotinus’ denial that ‘spirit’ (thumos) and ‘desire’ (epithumia) are parts of the nature of soul. This denial contrasts with Plato’s tripartition of the soul (which includes spirit and desire) in the Republic, where the tripartition serves to define the four cardinal virtues. However, Plotinus defines these ‘political’ virtues in a different way, as the knowledge and the measure and order brought by rational soul to the affects which arise in the living body. Plotinus introduces furthermore a higher level of virtues, the ‘greater’ virtues. I discuss the relation between these two levels of virtue, in particular as regards the nature of this scale. I argue that in Plotinus the lower (‘political’) virtues are imperfect if possessed without the greater virtues

Chapter 16 provides an analysis of an important passage in Simplicius’ Commentary on Epictetus’ Manual. What functions can the (true) philosopher have in political and social life? Simplicius answers this question as concerning either a state or city which is good or one which is evil. In general, the philosopher should look to the moral wellbeing of others, seeking to ‘humanize’ them (i.e., to promote the virtues, the political virtues, of a good human being). With this in view, in a good state the philosopher will assume leadership functions, as described in Plato’s concept of political science. In a morally corrupt state there will be no place for the philosopher in politics. To preserve his integrity, the philosopher may have to go into exile, as Epictetus did, and Simplicius himself. Or if exile is not possible, the philosopher will try to act in a more limited (probably domestic) sphere, but without compromise.

Only two complete works on the philosophy of mathematics survive from Antiquity, Iamblichus’ De communi mathematica scientia and Proclus’ commentary on Euclid’s Elements Book I. Chapter 21 lists works by Proclus concerning mathematics and the sources he used in these works. Concentrating on Proclus’ commentary on Euclid, I describe his conception of the ontological status of the objects with which mathematics is concerned: these objects are originally concepts innate in human soul, forming part of its very nature, concepts which the mathematician then seeks to articulate, project, construct through various methods so as to constitute an elaborated science. I present also the distinctions made between the mathematical sciences and their methods, the importance of mathematics for other sciences (both superior and inferior to it), and Proclus’ relations with other mathematicians of his time.

Chapter 19 shows that the ideas described in Chapter 18 can be found in the writings of Julian the Emperor. Julian speaks of a hierarchy of laws, going down from divine paradigmatic laws to the laws of nature and to human laws (both universal and regional). I also describe Julian’s concept of the ideal legislator, how it relates to Iamblichus’ views, and I give an example of Julian’s legislation, that concerning funeral processions, and describe how this legislation is explained by Julian as relating to metaphysical principles.

The way in which Proclus’ Elements of Theology exemplifies metaphysical science as understood by Late Antique Platonists and as expressed in Proclus’ commentary on Plato’s Parmenides is examined in Chapter 27, which proposes an analysis of the propositions and demonstrations which open the book. I stress the idea that these metaphysical reasonings were regarded as ‘exercises’ of the rational soul, a training leading to a greater proximity to divine first principles.

Chapter 2 discusses fragments surviving from Iamblichus’ correspondence. This correspondence, which includes open letters destined for a wider readership, seems to have been collected for use in the philosophical schools. The collection contains letters which originally, I argue, were of different types. One type is that of an exhortation (a ‘protreptic’) to the study of a science, in this case dialectic. I compare this protreptic with that to be found in Iamblichus’ De communi mathematica scientia; both protreptics correspond to the rhetorical model for the praise of a science. Another type of open letter is that which proposes a ‘Mirror of Princes’ for the edification of people in power and their entourage. A third type to be found in the letters is a monograph which discusses a difficult philosophical question: the relation between fate and freedom. If addressed to a well-educated professional, perhaps a former student of Iamblichus, this letter could have had a wider circulation.

Chapter 26 discusses in more detail the concepts innate in the soul whereby soul can reason about what transcends reasoning. I describe the relations between words, concepts and things (in this case transcendent realities), as the later Platonists saw these relations, and argue that the rational soul does not simple ‘look’ at metaphysical concepts, as it were, but that they are known as part of the dynamic, productive operations of rational thought.

Plotinus provided an explanation of evil which was original and philosophically challenging. While deriving everything from one source, the absolute transcendent Good, Plotinus does not trivialize the phenomenon of evil or reduce it to human moral deviation, as do other philosophical and religious approaches, but traces evil back to a metaphysical principle, matter, the source of evil in the world and in human souls. In Chapter 11 I present Plotinus’ account of evil and discuss to what extent it can be defended against a series of criticisms formulated by Plotinus’ successors, in particular by Proclus.

In Chapter 3, the first book of Iamblichus’ work On Pythagoreanism, a book entitled On the Pythagorean Life, is placed in the context of Iamblichus’ advocacy of a revival of the ancient roots of Platonism in Pythagoreanism. An analysis of the book suggests that Iamblichus makes free use of rhetorical models of two kinds of speeches of praise, that of a hero (Pythagoras) and that of a science (Pythagorean philosophy). The work invites the reader to a study of Pythagorean philosophy by showing the exceptional nature of Pythagoras’ contribution to human welfare and the value of the sciences which he revealed. This protreptic function would be carried on in the second book, the Protrepticus, an exhortation to study philosophy in general and Pythagorean philosophy in particular; and in the third, the De communi mathematica scientia, a protreptic to mathematics. The following books introduced the four mathematical sciences, arithmetic, geometry, music and astronomy, and related arithmetic to physics, ethics and theology.

Chapter 6 gives a survey of ethical themes in Plotinus. It begins with happiness (eudaimonia) as life at its highest degree, the life of intellect of which human soul is capable. The affairs of bodily existence have no part in this life of intellect, which is a perfect, joyful, peaceful state. To reach this state, virtue is required. Two sorts of virtue are distinguished: the ‘political’ virtues and the ‘higher’ (or ‘greater’) virtues, as stages in assimilation to the divine life of transcendent Intellect. The affairs of our bodily life concern us as souls which have a need, a natural ‘appropriation’, to take care of bodily lives, ours and that of others. Action in this bodily existence should be guided by practical wisdom, a wisdom guided by ‘premises’, i.e., norms derived from theoretical wisdom. Finally, I indicate the variety of texts composed by Plotinus’ Platonist successors where ethical themes may be found.