Pythagoreans

This chapter is about women and ancient Pythagorean philosophy. Specifically, the focus is on the letters and treatises written in the Hellenistic and Imperial Age under the name of Pythagorean female authors. Scholars have primarily raised two objections against these texts: first, they are likely to be spurious and might not have been authored by women, but rather male philosophers writing under female pseudonyms. Second, these texts are not philosophical. After a brief introduction to the role of women in Pythagoreanism (...) and overview of the authorship issue, I show that, regardless of the original authors, these texts are written for women who are considered capable of reading philosophy. As such, they establish women’s philosophical potential in two ways: on the one hand, they ascribe philosophical arguments to female authors and, on the other hand, they encourage women to pursue philosophy. This makes the texts the first case of philosophical prose ascribed to Greek women and, I argue, an early example of female philosophical protreptics. (shrink)

Diogenes Laertius ascribes the first concept of spherical Earth to both Pythagoras and Parmenides. Indeed, a major shift in cosmologies—emergence of the spherical conception of the Earth and the surrounding heaven—took place between the sixth and fifth centuries BCE. Given the poor state of preservation of early Pythagorean tradition, it is argued that primacy in formulating the notion of spherical Earth should be ascribed to Parmenides.

Die Pythagoreer.--Empodokles.--Platon.--Aristoteles.--Katharsis: ein Exkurs.

I will deal with a much-discussed passage of Aristophanes’ Birds, in which Socrates is depicted as a psuchagogos, a conjurer of souls. This is the only passage in Socratic literature in which such an activity is attributed to Socrates. In the Clouds, which was staged nine years prior to Birds, Aristophanes defines Socrates’ school as the ‘thinkery of wise souls’, and the endeavors of his pupils as a ‘taking care’ of their own souls. In the Clouds, Socrates is portrayed training (...) his pupils in natural philosophy, eristic arguments and Orphic-Pythagorean rituals: but what Socrates specifically does with the souls of his pupils is not clear at all. For this, we have to look to Birds, and in particular to verses 1553-1564, a passage I examine in detail. I first discuss the passage itself and how it relates to the comedy as a whole, I then provide a reading of parallel passages from the Clouds and Pythagorean literature, before finally returning to the verses in the Birds to draw some conclusions. (shrink)

This paper critically examines the use of the name 'Pseudo-Archytas' to refer to two aspects of the reception of Archytas of Tarentum in antiquity: the 'author-inflection' and the 'authority-inflection'. In order to make progress on our understanding of authority and authorship within the Pythagorean tradition, it attempts to reconstruct Porphyry's views on the importance of Archytas as guarantor of Pythagorean authenticity in the former's lost work On the History of the Philosophers by considering a fragment preserved in Arabic by Ibn (...) Abī Uṣaybi‘a. The article finally argues that a range of problems attend our use of the term 'pseudo-Archytas', which is not fit for purpose when considering the evidence regarding authorship and authority in the Pythagorean tradition. It recommends a more critical approach to the notion of authenticity within the Pythagorean tradition and suggests a new term, 'Archytism', as a more useful point of reference. (shrink)

Archytas of Tarentum, a contemporary and associate of Plato, was a famous Pythagorean, mathematician, and statesman of Tarentum. Although his works are lost and most of the fragments attributed to him were composed in later eras, they nevertheless contain valuable information about his thought. In particular, the fragments of On Law and Justice are likely based on a work by the early Peripatetic biographer Aristoxenus of Tarentum. The fragments touch on key themes of early Greek ethics, including: written and unwritten (...) laws; freedom and self-sufficiency; moderation of the emotions and cultivation of virtues; equality and the competence of the majority to participate in government; criticism of “rule by an individual”; a theory of the ideal “mixed constitution”; distributive and corrective justice and punishment, and of the rule of law. The fragments also contain one of the only positive accounts of democracy in ancient Greek philosophy. (shrink)

In this paper I argue that we can better understand Plato’s Phaedo, if we don’t concentrate solely on the hints of Pythagoreanism among the characters and their doctrines, as though that were the principal key to the dialogue’s dialec- tical targets. I suggest that the dialogue is intended to make us think of the meta-physics of at least one other Presocratic predecessor, besides any Pythagorean influence (which may be much less than has been thought). Not least among the thinkers of (...) whom we are reminded is Heraclitus. In the Phaedo, Plato invites us to explore the limitations of these earlier metaphysical views, and to consider how far they can or cannot make space for the capacity of the soul to direct the body, to make decisions, to grasp eternal truths and potentially to survive in perpetuity beyond the decay of the body. (shrink)

The article deals with the doctrines of Orpheus and Pythagoras about the immortality of the soul in the context of the birth of philosophy in ancient Greece. Orpheus demonstrated the closeness of heavenly (divine) and earthly (human) worlds, and Pythagoras mathematically proved their fundamental identity. Greek philosophy was “an investment in the afterlife future”, being the product of the mystical (Orpheus) and rationalist (Pythagoras) theology.

Pythagoras’s number doctrine had a great effect on the development of science. Number – the key to the highest reality, and such approach allowed Pythagoras to transform mathematics from craft into science, which continues implementation of its project of “digitization of being”. Pythagoras's project underwent considerable transformation, but it only means that the plan in knowledge is often far from result.

In Pythagorean Women, classical scholar Sarah B. Pomeroy discusses the groundbreaking principles that Pythagoras established for family life in Archaic Greece, such as constituting a single standard of sexual conduct for women and men. Among the Pythagoreans, women played an important role and participated actively in the philosophical life. While Pythagoras encouraged women to be submissive to men, his reasoning was based on the desire to preserve harmony in the home. -/- Pythagorean Women provides English translations of all the earliest (...) extant examples of literary Greek prose by Neopythagorean women, shedding light on their attitudes about marriage, the home, music, and the cosmos. Pomeroy sets the Pythagorean and Neopythagorean women vividly in their historical, ecological, and intellectual contexts, illustrated with original photographs of sites and artifacts known to these women. (shrink)

Surviving fragments of information about Pythagoras gave rise to a growing set of legends about this famous sage and his followers, whose reputations throughout Antiquity and the Middle Ages have never before been studied systematically. This book is the first to examine the unified concepts of harmony, proportion, form, and order that were attributed to Pythagoras in the millennium after his death and the important developments to which they led in art, architecture, mathematics, astronomy, music, medicine, morals, religion, law, alchemy, (...) and the occult sciences. In this profusely illustrated book, Christiane L. Joost-Gaugier sets out the panorama of Pythagoras's influence and that of Christian and Jewish thinkers who followed his ideas in the Greek, Roman, early Christian, and medieval worlds. In illuminating this tradition of thought, Joost-Gaugier shows how the influence of Pythagoreanism was far broader than is usually realized, and that it affected the development of ancient and medieval art and architecture from Greek and Roman temples to Gothic cathedrals. Joost-Gaugier demonstrates that Pythagoreanism—centered on the dim memory of a single person that endured for centuries and grew ever-greater—inspired a new language for artists and architects, enabling them to be "modern.". (shrink)

This paper traces how the dualism of body and soul, cosmic and human, is bridged in philosophical and religious traditions through appeal to the notion of ‘breath’ (πνεῦμα). It pursues this project by way of a genealogy of pneumatic cosmology and anthropology, covering a wide range of sources, including the Pythagoreans of the fifth century BCE (in particular, Philolaus of Croton); the Stoics of the third and second centuries BCE (especially Posidonius); the Jews writing in Hellenistic Alexandria in the first (...) century BCE (Philo); and the Christians of the first century CE (the gospel writers and Paul). Starting from the early Pythagoreans, ‘breath’ and ‘breathing’ function to draw analogies between cosmogony and anthropogony – a notion ultimately rejected by Plato in the Timaeus and Aristotle in his cosmological works, but taken up by the Posidonius (perhaps following the early Stoa) and expanded into a rich and challenging corporeal metaphysics. Similarly, the Post-Hellenistic philosopher and biblical exegete Philo of Alexandria, who was deeply influenced by both Platonist and Stoic physics, approaches the cosmogony and anthropogony described in Genesis (1:1–3 and 1:7) through Platonist-Stoic philosophy, in his attempt to provide a philosophically rigorous explanation for why Moses employed certain terms or phrases when writing his book of creation. Finally, the chapter sees a determined shift in the direction of rejecting pneumatic cosmology for a revised pneumatic anthropogony in the writings of the New Testament: by appeal to the ‘Holy Spirit’ or ‘Holy Breath’ (πνεῦμα ἅγιον), early Christians effectively adapted the Stoic metaphysics of ‘breath’, with its notions of divine intelligence and bonding, to the prophetic and ecclesiastical project of building a Christian community conceived of as the ‘body of Christ’. Hence, the spiritual cosmogony of the Pythagoreans, Stoics, and Philo is effectively subordinated to the spiritual anthropogony that facilitates the construction of the Christian kosmopolis, only fully realised in the form of New Jerusalem, the ‘bride’ which, in tandem with the Holy Spirit, calls to the anointed. At the end of the Christian worldview, the kosmos of Greek philosophy is supplanted by the pneumatic kosmopolis. (shrink)

When did kosmos come to mean *the* kosmos, in the sense of ‘world-order’? I venture a new answer by examining later evidence often underutilised or dismissed by scholars. Two late doxographical accounts in which Pythagoras is said to be first to call the heavens kosmos (in the anonymous Life of Pythagoras and the fragments of Favorinus) exhibit heurematographical tendencies that place their claims in a dialectic with the early Peripatetics about the first discoverers of the mathematical structure of the universe. (...) Likewise, Xenophon and Plato refer to ‘wise men’ who nominate kosmos as the object of scientific inquiry into nature as a whole and the cosmic ‘communion’ (koinônia) between all living beings, respectively. Again, later testimonies help in identifying the anonymous ‘wise men’ by associating them with the Pythagoreans and, especially, Empedocles. As Horky argues, not only is Empedocles the earliest surviving source to use kosmos to refer to a harmonic ‘world-order’ and to illustrate cosmic ‘communities’ between oppositional pairs, but also his cosmology realises the mutual correspondence of these aspects in the cycle of love and strife. Thus, if later figures posited Pythagoras as the first to refer to the universal ‘world-order’ as the kosmos, they did so because they believed Empedocles to have been a Pythagorean natural scientist, whose combined focus on cosmology and ethics exemplified a distinctively Pythagorean approach to philosophy. (shrink)

By the colours and decoration of a vase fragment one determines the period and style to which the original belonged; while its physical contours show from what part of the original it comes. The material may be insufficient for a reconstruction of the whole design. But it is often legitimate to go beyond what is actually contained in the preserved pieces.

Dominic O'Meara has produced a scholarly and sympathetic account of a most enigmatic subject, namely, the role of mathematics in late Greek Platonic thought. O'Meara traces the path of mathematical philosophy from the Neopythagoreanism of the second and third centuries A.D. through that master of Athenian Neoplatonism, Proclus. Without this study few would recognize the paradigmatic role that mathematics played in Platonic thinkers throughout this period, for mathematics became the model for many forms of philosophical inquiry--not only theology and physics, (...) but even ethics. (shrink)

According to Dicaearchus, metempsychosis was the best known among Pythagoras’ teachings. In this paper, I investigate two features of Pythagorean metempsychosis: its non-retributive character and its epistemological value. I argue that the Pythagoreans did not conceive of reincarnation as a punishment for the wicked and a reward for the virtuous, but rather as a way to gain experience, knowledge and therefore wisdom. This reading enables us to throw light on the puzzling list of Pythagoras’ past lives, which includes Aethalides son (...) of Hermes, Euphorbus the warrior, Pyrrhus the fisherman and even Alco the harlot. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

How did the ancient Greeks and Romans conceptualise order? This book answers that question by analysing the formative concept of kosmos in ancient literature, philosophy, science, art, and religion. This concept encouraged the Greeks and Romans to develop theories to explain core aspects of human life, including nature, beauty, society, politics, the individual, and what lies beyond human experience. Hence, Greek kosmos, and its Latin correlate mundus, are subjects of profound reflection by a wide range of important ancient figures, including (...) philosophers, poets and playwrights, intellectuals, and religious exegetes. By revealing kosmos in its many ancient manifestations, this book asks us to rethink our own sense of 'order', and to reflect on our place within a broader cosmic history. (shrink)

The Pythagorean Precepts by Aristotle's pupil, Aristoxenus of Tarentum, present the principles of the Pythagorean way of life that Plato praised in the Republic. They are our best guide to what it meant to be a Pythagorean in the time of Plato and Aristotle. The Precepts have been neglected in modern scholarship and this is the first full edition and translation of and commentary on all the surviving fragments. The introduction provides an accessible overview of the ethical system of the (...) Precepts and their place not only in the Pythagorean tradition but also in the history of Greek ethics as a whole. The Pythagoreans thought that human beings were by nature insolent and excessive and that they could only be saved from themselves if they followed a strictly structured way of life. The Precepts govern every aspect of life: e.g. procreation, abortion, child rearing, friendship, religion, desire and even diet. (shrink)

This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.

This volume presents the first Italian translation with commentary of the Doric Pseudo-Pythagorean texts, which are ascribed to Archytas and Brontinus and deal with metaphysical, logical, and epistemological questions. These texts probably date from the 1st century BCE and are the product of a re-emerging dogmatic interpretation of Plato's dialogues.