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The ancients offered a huge range of therapeutic exercises. Some ward off future emotion, some deal with emotion that has already arisen from a past occurrence. Chrysippus' emphasis on re-evaluating situations is a therapy for emotions, whereas Posidonius' reversion to Plato would have helped with moods as well. Pythagoreans, Democritus, Epicureans, Cynics, Aristo of Ceos (Aristotelian), Plutarch, and Galen all make contributions. The poet Ovid parodies the philosophers' therapies. All this is echoed in Christianity, but the Stoics are outstanding, Epictetus the ex-slave sterner, Seneca the aristocrat more adapted to ordinary discomforts. In recent times, Epictetus enabled Admiral Stockdale to withstand torture and solitary confinement, and his account shows how even the sterner therapies could work in practice.

According to Seneca, the arts, including tragedy and music, can only produce first movements. So Aristotle's claim that tragedy and comedy produce catharsis by arousing emotion is wrong, as is Posidonius' belief in wordless music changing emotion without changing judgements. But, pace Seneca, there is a residue of cases of genuine emotion about the content of the play or about the melody, and a better defence of Stoicism in these cases would be that the relevant judgements are there. But when wordless music changes emotion, Posidonius prefers to say that the emotion is non-judgemental; Philodemus, his Epicurean contemporary, says that the emotion persists and one is merely distracted. The debate involved Pythagoreans, the Stoics Zeno and Diogenes of Babylon, and later Augustine.

This chapter discusses how all the Pythagorean theories of the soul known to us are different. Only Simmias and Echecrates, the pupils of Philolaus, held identical views. The similarity among some of these theories can sometimes be explained by direct influence (Alcmaeon and Hippon, Alcmaeon, and Philolaus), but most often by the fact that many Pythagoreans shared the interpretation of the soul as the source of motion, which was the most widespread view amongst the Presocratics. It is also shown that there is neither a clear formulation of number doctrine, nor tangible examples of it, in ancient Pythagoreanism. It transpires that the theory which was taken to be the essence of Pythagorean philosophy, a theory backed by the authority of Aristotle as the source and as a historian of philosophy, is, like many other elements of the ancient tradition about the Pythagoreans, a retrospective projection.

This chapter first considers the estimates of how great the contribution of the Pythagoreans was to Plato's philosophy and how these views diverge substantially, and which vary across the range from ‘decisive’ to ‘insignificant’. It shows that Platonists were characterized by a benevolent attitude to Pythagoras and the Pythagoreans and an interest in their scientific, philosophical, and religious theories. Number doctrine is found in the testimonies of all three Platonists, but there is in them no picture of a Pythagorean philosophy even remotely reminiscent of number doctrine. The Platonists reacted, not to a common Pythagorean doctrine, but to various theories of Pythagoras and his successors: Philolaus, Archytas, Ecphantus and Hicetas, et al. The chapter then considers Aristotle's reports on the Pythagoreans in his surviving works.

This chapter reviews references to Pythagoras by the authors of the pre-Platonic period. It shows that in the course of the fourth century, studies in mathematics, particularly geometry and arithmetic, became a constant element of the tradition of Pythagoras; astronomy and harmonics are less frequently mentioned. Mathematics did not displace metempsychosis and wonders, nor did the tradition of Pythagoras the politician which emerged concurrently with it, yet they did edge them aside, completing the ambivalent, contradictory image of Pythagoras, which was retained by his Neoplatonic biographers and passed from them into modern scholarship. It concludes that Pythagoras the mathematician is as little a product of the Academy as Pythagoras the philosopher.

This chapter discusses the Pythagorean ‘symbols’ and their custodians, the mathematici and the acusmatici. The ‘symbols’ are short sayings divided into three kinds according to the question they answer. The first kind answer the question, ‘What is...?’ The second kind answers the question, ‘What is most...?’ The third and most important kind contains precepts and prohibitions. In its application of the ‘symbols’, the following question is addressed: was there in the history of ancient Pythagoreanism a period in which the precepts and taboos they contain were observed to the letter, and, if there was, then what circle of persons was affected?

This chapter picks up a claim made in the previous chapter—that a term like philosophos would have been coined in response to certain sorts of unusual activity. It accumulates the earliest evidence that the Pythagoreans would have been excellent targets of this term. This is because their public face was politically notorious and influential, with their cohesion and even efficacy seeming to depend on their pedagogical and research exercises. The chapter thereby develops Walter Burkert's acknowledgment of the organized political side of their existence. Additional evidence comes from what looks to be Aristotle's support of Heraclides' account, if Iamblichus' late citations of Aristotle can be reconstructed correctly. Burkert asserts that Pythagoras was not really a philosopher; what concerns this chapter is only the beliefs that observers had about him and the names that they had reason to call him—since, for his contemporaries, philosophos hardly meant what academic philosophers now mean by “philosopher.”

This chapter presents an English translation of the ascetic corpus writing of Evagrius of Pontus about gnomic sayings. The gnomic sayings in this piece are closely related to other earlier collections including those of Sextus, Clitarchus and the Pythagoreans. There are also nine instances in which there appears to be an intentional adaptation of the pre-existing saying in the direction of Christian or even Evagrian teaching. The dependency on the older collections of sayings and proverbs is most evident in the first part of this work and least evident in the third.

The Pythagoreans are presented by Aristotle in Chapter 5 as a sort of bridge between the physicists and the Platonists. They resemble the physicists in treating their principles as material, although with the striking innovation that these are conceived in mathematical terms; and they talk less obscurely than their predecessors about principles as such. The ontology presupposed by their thesis that ‘numbers are primary in nature’ and ‘constitute the whole heaven’ can be reconstructed from elsewhere in Aristotle and Alexander of Aphrodisias. No less importantly, however, they anticipate the direction in which Socrates and Plato will take philosophy. Their principles — limit and unlimited — are not natures like fire or earth, but substances in their own right of the things of which they are predicated; and they made attempts, albeit superficial and confused, at definitions.

In chapter 6 Aristotle introduces Plato's views on the first principles. In the first part Aristotle offers a plausible account on how Plato came to develop the doctrine of the Forms. The second part, on the relation between numbers and Forms and on the ultimate principles of whatever exists (the One and the Great and the Small) , has inspired numerous speculations on the ‘unwritten’ doctrine of Plato Notwithstanding some misgivings we may have about Aristotle's transposition of Plato's doctrine in his own format, chapter 6 occupies within the composition of Alpha a central place as Aristotle expounds here how he understands the views, not of some remote predecessor, but of the philosopher who had the greatest influence on the formation of his own thought and who kept dominating and haunting the Academy to which Aristotle still intellectually belonged. Although his insistence on similarities with the Pythagoreans may have led him to integrate too easily the doctrine of the Forms and numbers — probably because in the Academy this Pythagorizing current was dominant — he recognizes Plato's essential contribution in the search for the first principles. Plato, is indeed, the first to have developed the doctrine of a formal cause, which is also central in Aristotle's explaining of the world. It is also Plato who first developed a notion of a material principle that is quite different from the material cause of the natural philosophers, a purely receptive principle that can only functions when ‘given form’ by the Forms. It is not without reason that this chapter set for centuries the perspective to understand Plato.

In chapter A 8, Aristotle looks once more into the theories of Empedocles, Anaxagoras and the so-called Pythagoreans, this time in order to evaluate their views on principles for his own search for wisdom. In the case of Empedocles, Aristotle acknowledges the realization of both the material and the moving cause but he criticises the division of the former into four elements and of the latter into the two forces of love and strife. Although Anaxagoras theory about a primal mixture appears to be untenable, the opposition between nous and mixture contains a potential modernity that foreshadows Plato's theory of principles. The so-called Pythagoreans, on the one hand, correctly include intelligible causes into their theory, but, on the other, apply them insufficiently.

This chapter provides the commentary on Aristotle's On the Heavens (De Caelo). It begins with an introduction detailing the important distinction between the cosmos as a whole and the several elements that compose it, namely earth, water, air, and fire. It also details Aristotle's move from the talk of bodies, the plurality of things in the world, to body, which is considered a generic or logical sense. On the several meanings of phusis or nature, 'nature', the chapter highlights how Aristotle presents his own conception of nature by defining it as anarchê kinêseôs (principle of movement). It explores Aristotle's indication of the importance of 'right' and 'left' to thinkers when he included the terms in the 'table of opposites' used by the Pythagoreans.

This book aims to resolve an important philosophical and historical problem about the making of sexual morality in Western culture. There are three main reasons why many scholars emphasize apparent connections between Greek moral philosophy and Christian sexual morality at the expense of the disparities. The work directly complements the social history of early Christian sexual asceticism and related didactic ideology. It examines the arguments that Plato, the Stoics, and the Pythagoreans offer to support their respective conceptions of justifiable and unjustifiable sexual conduct. The book also focuses on the Septuagint's sexual laws and on the normative sexual poetics of the Pentateuch and Prophets. It then demonstrates how the Greek philosophical and biblical sexual principles are reworked in three very different sectors of patristic Christian thought: the sexually encratite, the proto-orthodox, and the more libertine positions. The problems with fornication are described.

This chapter provides a discussion on the reproductive technology of the Pythagoreans. It also addresses the Greek and Roman sources on procreationism that are not part of Hellenistic Judaism or Christianity. Aristoxenus's Pythagoreans believed that all acts of heterosexual copulation ought to be procreationist in purpose and method. Charondas assumes that each man has or should have a wife and that the married couple should reproduce. Charondas's unconditional procreationism is far more inflexible than Plato's use of the regulation in the Laws. Ocellus presumes the key Pythagorean tenet that sexual relations are motivated either for the production of children or for pleasure. Seneca advocates procreationism in its Neopythagorean version. Charondas, Ocellus, Seneca, and Musonius appear to have been somewhat distanced from the older Pythagorean eugenics that originally motivated procreationism. However, they show neither Plato's reflective modification of the procreationist principle nor the vestigial ambiguity of Aristoxenus.

This chapter argues that Philo's religious sexual ethic is an innovative synthesis which combines the Pentateuchal laws and sexual poetics of spiritual fornication with the sexual-reform plans of the Pythagoreans and Plato. Despite the differences in the specific laws of Plato and Moses, Philo and the Christian Platonists such as Clement found it irresistible to regard Moses' Law and Plato's Laws as part one and part two of the same dispensation. Philo appropriates the Stoic terminology of the passions to recast the biblical danger of spiritual fornication in psychological terms. The chapter indicates that Philo develops a forceful new program against sexual desire through his synthesis of Hellenistic Jewish and Platonic ideas about wrongful desire. Philo's limited synthesis of his criteria of impermissible sexual activity is covered. Philo also lays the ground for a paradigm shift in biblical sexual norms, but he remains relatively conservative himself.

This chapter focuses on the traditions of thoughts in ancient Greece, labeled as “Pythagorean,” that also contained multiple theories of rebirth. Pythagoras, like similar figures in religious history, is simultaneously an historical and mythic persona such that it makes little sense to differentiate the two. Pythagoras is a construction of Pythagoreanism, that is, the tradition of thought built on the work of a mythic founder. There does not seem to be the slightest doubt that Pythagoras believed in reincarnation, and to demonstrate it this chapter focuses on the Pythagoreans. References to Pythagoras, across genres, indicate that this rebirth eschatology entailed animal rebirths, which therefore explains the strong injunction against consuming flesh. The tradition of a vegetarian diet was also pronounced although some accommodations were made to the popular Greek cuisine of the sacrifice. Pythagoras received ridicule from Greek thinkers and intense reverence from believers, followers, and intellectual admirers. He refined his capacity for retrocognition to the extent of recollecting past lives. Pythagoras was considered the founder of Greek mathematics and a “philosopher.”

This chapter describes the kinds of Pythagoreans who may have existed from the sixth through fourth centuries bce and their philosophical activities based on the evidence preserved by Aristotle. It identifies the characteristics that distinguished the mathematical Pythagorean pragmateia from the pragmateia of the rival acousmatic Pythagorean brotherhood in Magna Graecia. It argues that Aristotle establishes this distinction by appeal to the divergent philosophical methodologies of each group. The mathematical Pythagoreans, who are the same as the “so-called Pythagoreans” in Metaphysics A, employ superordinate mathematical sciences in establishing something that approximates demonstrations that explain the “reason why” they hold their philosophical positions, whereas the acousmatic Pythagoreans, who are distinguished from the “so-called” Pythagoreans in Metaphysics A, appeal to basic, empirically derived “fact” in defense of their doctrines.

This chapter examines the fragmentary evidence derived from Timaeus' history of the city-states of Sicily and Southern Italy, with special attention to the account of a certain Apollonius preserved by Iamblichus in his work On the Pythagorean Way of Life. The analysis introduces the term, “exoteric” Pythagoreans, which appears to correspond with the mathematical Pythagoreans, on the grounds that both were considered heretical for having published/demonstrated the doctrines of Pythagoras—an act that corresponded with the advent of a “democratic” type of Pythagoreanism. A comparative analysis of Timaean and Peripatetic histories of Pythagoreanism yields an account of how the “publication” of the doctrines of Pythagoras corresponds with the “democratization” of philosophical knowledge, an activity that serves as a model for the public use of reason in order to resolve disputes.

This chapter elucidates the ways Plato camouflages his critical responses to Pythagoreanism by using mythological figures to refer to Pythagorean philosophical invention in the middle and later dialogues, especially Republic, Timaeus, and Philebus. The theme of “discovery” takes on Pythagorean overtones, and the exploration of the various culture heroes (“first-discoverers”) in these dialogues shows that Plato ensconced his responses to the mathematical Pythagoreans by narrating the stories of mythological philanthropists who suffered punishment for their transgressions, such as Prometheus and Palamedes.