Thesis (M.A.)--Boston University / This thesis examines the relation of Indian thought to Pythagoreanism. Two scholars, in particular, have dealt at length with this subject. Richard Garbe has maintained that Indian thought has had important influence on Pythagoreanism. Sir Arthur B. Keith has argued that this is not so. This thesis investigates the relation of Indian thought to Pythagoreanism in terms of a critique of thesetwo positions and in the light of more recent studies. After an introductory chapter, the arguments affirming general Indian-Greek influence are examined in Chapter Two. Chapter Three deals with the relation of Indian thought to Pythagoreanism. A concluding chapter evaluates the positions taken in regard to the problem of parallel doctrines.

The sixth-century-BCE Pythagorean communities included both male and female members. This thesis focuses on the Pythagorean women and aims to explore what reasons lie behind the prominence of women in Pythagoreanism and what roles women played in early Pythagorean societies and thought. In the first chapter, I analyse the social conditions of women in Southern Italy, where the first Pythagorean communities were founded. In the second chapter, I compare Pythagorean societies with ancient Greek political clubs and religious sects. Compared to mainland Greece, South Italian women enjoyed higher legal and socio-political status. Similarly, religious groups included female initiates, assigning them authoritative roles. Consequently, the fact that the Pythagoreans founded their communities in Croton and further afield, and that in some respects these communities resembled ancient sects helps to explain why they opened their doors to the female gender to begin with. The third chapter discusses Pythagoras’ teachings to and about women. Pythagorean doctrines did not exclusively affect the followers’ way of thinking and public activities, but also their private way of living. Thus, they also regulated key aspects of the female everyday life, such as marriage and motherhood. I argue that the Pythagorean women entered the communities as wives, mothers and daughters. Nonetheless, some of them were able to gain authority over their fellow Pythagoreans and engage in intellectual activities, thus overcoming the female traditional domestic roles. The fourth chapter argues that another contributing factor to the status of the Pythagorean women is the doctrine of metempsychosis. This belief led the Pythagoreans to adopt similar behaviours towards other ensouled beings. Therefore, since men and women were believed to have the same souls, they were treated with the same respect and received the same education. Finally, the fifth chapter explores how the Pythagorean views on women are taken up and developed in Plato’s Republic. I argue that, although the Pythagoreans never went as far as to have philosopher-queens and abolish private families, they took the first step towards Plato’s ‘gender equality’ theory. Overall, that of women in Pythagoreanism is the first documented case of female engagement with ancient philosophy: Pythagorean men and women lived together according to the same lifestyle, were educated on the same doctrines and played equally integral roles in the intellectual community.

Made available in DSpace on 2016-04-27T17:26:52Z (GMT). No. of bitstreams: 1 Guilherme Magalhaes Oliveira.pdf: 689794 bytes, checksum: 9f5057f96f879fa225b4f24f6f1b8b1e (MD5) Previous issue date: 2010-11-05 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Our object of study is the relation between music and cosmology in Pythagoreanism, specifically in the fragments by Philolaus of Croton (470-385 b.C.), a pythagorean philosopher who influenced both Platonic and Aristotelian philosophy. This investigation is divided into four parts: (1) Music in Ancient Greece, where we briefly examine the meaning of the word mousike and its relation to Greek culture, from Homer up until the Lyrical Poets. (2) Pythagoras and Pythagoreanism, where we discuss who was Pythagoras and his community. (3) Philolaus Pythagoreanism, where we analyze Philolaus fragments and explain the principles of his cosmology. Here, the meaning of limited (peras) and unlimited (apeira), his two cosmological principles, are discussed. Then we investigate the concept of harmony, understood here as a third principle, which serves the purpose of uniting in good proportion the first two principles in order to form an ordered whole (kosmos). As we look into the meaning of harmony, we also analyze the importance of the number, or arithmos, in Philolaus philosophy, since it is directly related to the concept of harmony. (4) In Music and the Cosmos, after we have explained Philolaus fundamental concepts, we demonstrate how they are linked to music, i.e. to the numeric ratios that are considered to be musical (or sound) intervals and the formation of the diatonic scale. According to Philolaus and the Pythagoreans, this scale presents a specific mathematical/musical structure, which is an image or imitation of the structure of the kosmos. Finally, we show that Philolaus diatonic scale is also used by Plato, on his Timeu / Nosso objeto de estudo é a relação entre música e cosmologia no pitagorismo, mais especificamente nos fragmentos de Filolau de Crotona (470-385 a.C.), filósofo pitagórico que exerceu influência na filosofia platônica e aristotélica. Esta investigação está dividida em quatro partes: (1) Música na Grécia Antiga, onde investigamos brevemente o significado da palavra mousike e sua relação com a cultura grega de Homero até os Poetas Líricos. (2) Pitágoras e o Pitagorismo, onde investigamos quem foi Pitágoras e sua comunidade. (3) O Pitagorismo de Filolau, onde analisaremos os fragmentos de Filolau e explicaremos os princípios de sua cosmologia. Será abordado o significado de limitado (peras) e ilimitado (apeira), seus dois princípios cosmológicos. Em segundo lugar, investigaremos o significado de harmonia, aqui entendida como um terceiro princípio, que possui o papel de unir em boa proporção os dois primeiros princípios para formar um todo ordenado (kosmos). Ao investigarmos o significado de harmonia, também apresentaremos a importância do número, ou arithmos, na filosofia de Filolau, já que este está diretamente relacionado com a harmonia. (4) A Música e o Cosmos, última parte de nosso trabalho que, após termos explicado os conceitos fundamentais de Filolau, mostraremos como eles estão vinculados com a música, ou seja, com as razões numéricas entendidas como intervalos musicais (de sons) e com a formação da escala diatônica que, segundo Filolau e os pitagóricos, possui uma estrutura matemático-musical específica, que é uma imagem ou imitação da estrutura do kosmos. Por último, mostraremos que essa escala de Filolau é a mesma usada por Platão, no Timeu

Athanasius Kircher’s Musurgia universalis (1650) was one of the largest and most widely circulated works of music theory in the seventeenth century. Although his reputation has waned over the centuries, Kircher was a leading intellectual figure of his day, authoring dozens of treatises on a multitude of topics and corresponding with scholars from around the world. Kircher’s central place within the world of learning resulted in a unique perspective on music theory and musical practice within the seventeenth century. The present study investigates a number of topics from Kircher’s music treatise and provides context from within the intellectual discourse of the time. The first chapter explores the seventeenth-century conception of encyclopedias, as well as the possible meanings associated with an encyclopedia musica, a novel term Kircher uses in his preface to describe Musurgia. Kircher’s attempt to describe all that was known about music, from highly speculative theories to the most utilitarian compositional tools, results in a complex blend of philosophical and practical elements. The middle chapters disentangle a few strands from this web of ideas, tracing the development of Pythagorean traditions and speculative music theory, as well as changing attitudes regarding empirical and occult methodologies in the early modern period. The final chapter concerns Kircher’s central goal for Musurgia, an algorithmic method based on the ars combinatoria and the emerging mathematical field of combinatorics that would allow anyone to compose musical settings, including the setting of texts in any poetic meter and in any language. Kircher’s arca musurgica—a device that contained tables to generate music—was in effect a distillation of the rules of harmony and counterpoint in the seventeenth century. Its underlying syntax of standard four-part progressions stands at the juncture between old and new ideologies of music theory and composition. / Music

A presente tese explora, como solução para o controvertido quadro geral da moderna história da crítica sobre Pitágoras e seu movimento, a definição do pitagorismo como categoria historiográfica. Superando tanto o dilema entre ceticismo e confiança nas fontes, como a pretensão de alcançar uma única chave hermenêutica que permita resolver a questão pitagórica, procura percorrer a história da tradição em busca de uma imagem suficientemente plural a ponto de possibilitar a compreensão do pitagorismo em sua irredutível articulação de bíos e theoría e não apesar dela. A configuração da comunidade e de seu bíos é percebida como elemento central de identificação do pitagorismo. A análise das duas teorias que mais decididamente contribuíram para a definição do pitagorismo ao longo da história, a transmigração da alma imortal e a doutrina dos números, procura definir as condições de possibilidade de atribuí-las ao pitagorismo mais antigo e as formas pelas quais ambas teriam contribuído, ao longo da história, para a definição do pitagorismo como categoria historiográfica. As fontes pré-socráticas, a platonização do pitagorismo, o testemunho aristotélico sobre os assim chamados pitagóricos, a literatura pseudoepigráfica helenística e o pitagorismo de época imperial são entendidos como momentos de um percurso histórico que resulta em uma imagem poliédrica de um dos maiores fenômenos intelectuais da história ocidental. / This thesis explores the definition of Pythagoreanism as historiographical category, seen as solution for the controversial general framework of modern history of criticism about Pythagoras and his movement. Overcoming both the dilemma between skepticism and faith in the sources and the claim to achieve a single hermeneutical key to solve the Pythagorean question, in it searches are made throughout the history of tradition looking for an image sufficiently plural in order to understand Pythagoreanism in accordance with its irreducible articulation of bíos and theoría, not despite it. The setting of the community and its bíos is understood as central element for Pythagorean identification. An analysis of the two theories that more decisively contributed to the definition of Pythagoreanism throughout history, the transmigration of the immortal soul and the doctrine of numbers, attempts to define the conditions of possibility to assign them to the earlier Pythagoreanism and the ways in which these have contributed throughout history to the definition of Pythagoreanism as historiographical category. Presocratic sources, the platonization of Pythagoreanism, Aristotle\'s testimony about the \"so-called\" Pythagoreans, the hellenistic Pseudoepigrapha and Pythagoreanism in imperial age are understood as moments of an historical route resulting in a polyhedral image of one of the greatest intellectual phenomena in Western history.

A presente tese explora, como solução para o controvertido quadro geral da moderna história da crítica sobre Pitágoras e seu movimento, a definição do pitagorismo como categoria historiográfica. Superando tanto o dilema entre ceticismo e confiança nas fontes, como a pretensão de alcançar uma única chave hermenêutica que permita resolver a questão pitagórica, procura percorrer a história da tradição em busca de uma imagem suficientemente plural a ponto de possibilitar a compreensão do pitagorismo em sua irredutível articulação de bíos e theoría e não apesar dela. A configuração da comunidade e de seu bíos é percebida como elemento central de identificação do pitagorismo. A análise das duas teorias que mais decididamente contribuíram para a definição do pitagorismo ao longo da história, a transmigração da alma imortal e a doutrina dos números, procura definir as condições de possibilidade de atribuí-las ao pitagorismo mais antigo e as formas pelas quais ambas teriam contribuído, ao longo da história, para a definição do pitagorismo como categoria historiográfica. As fontes pré-socráticas, a platonização do pitagorismo, o testemunho aristotélico sobre os assim chamados pitagóricos, a literatura pseudoepigráfica helenística e o pitagorismo de época imperial são entendidos como momentos de um percurso histórico que resulta em uma imagem poliédrica de um dos maiores fenômenos intelectuais da história ocidental. / This thesis explores the definition of Pythagoreanism as historiographical category, seen as solution for the controversial general framework of modern history of criticism about Pythagoras and his movement. Overcoming both the dilemma between skepticism and faith in the sources and the claim to achieve a single hermeneutical key to solve the Pythagorean question, in it searches are made throughout the history of tradition looking for an image sufficiently plural in order to understand Pythagoreanism in accordance with its irreducible articulation of bíos and theoría, not despite it. The setting of the community and its bíos is understood as central element for Pythagorean identification. An analysis of the two theories that more decisively contributed to the definition of Pythagoreanism throughout history, the transmigration of the immortal soul and the doctrine of numbers, attempts to define the conditions of possibility to assign them to the earlier Pythagoreanism and the ways in which these have contributed throughout history to the definition of Pythagoreanism as historiographical category. Presocratic sources, the platonization of Pythagoreanism, Aristotle\'s testimony about the \"so-called\" Pythagoreans, the hellenistic Pseudoepigrapha and Pythagoreanism in imperial age are understood as moments of an historical route resulting in a polyhedral image of one of the greatest intellectual phenomena in Western history.

It has been said that Pythagoras discovered the perfect musical intervals by chance when he heard sounds of hammers striking an anvil at a nearby smithy. The sounds corresponded to the same intervals Pythagoras had been studying. He experimented with various instruments and apparatus to confirm what he heard. Math, and in particular, numbers are connected to music, he concluded. The discovery of musical intervals and the icon of the musical blacksmith have been familiar tropes in history, referenced in literary, musical, and visual arts. Countless authors since Antiquity have written about the story of the discovery, most often found in theoretical texts about music. However, modern scholarship has judged the narrative as a myth and a fabrication. Its refutation of the story is peculiar because modern scholarship has failed to disprove the nature of Pythagoras’s discovery with valid physical explanations. This report examines the structural elements of the story and traces its evolution since Antiquity to the early modern period to explain how an author interprets the narrative and why modern scholarship has deemed it a legend. The case studies of Nicomachus of Gerasa, Claudius Ptolemy, Boethius, and Marin Mersenne reveal not only how the story about Pythagoras’s discovery functions for each author, but also how the alterations in each version uncover an author’s views on music. / text

Basée sur l’idée de progrès, la science moderne, d’inspiration cartésienne, est perçue par Simone Weil comme la principale cause de la crise moderne des valeurs. Sous-tendue par le mouvement droit, elle a perdu le principe d’analogie et s’est, de la sorte, dessaisie du monde ambiant des réalités quotidiennes. Aussi apparaît-elle non seulement comme à la source du scientisme, de la croyance en une raison scientifique autonome et du culte rendu aux applications techniques, mais aussi à l’origine du capitalisme industriel, du communisme révolutionnaire, du totalitarisme, de l’effondrement de l’ordre axiologique universel traditionnel concomitant à la crise de la civilisation. Les conséquences issues de ce mouvement de déracinement n’ont pas seulement conduit à l’oppression prolétarienne et coloniale ou au modernisme comme primat des valeurs d’innovation sur les valeurs de tradition, mais surtout à l’oppression généralisée et à l’oubli des structures axiologiques primordiales universelles que sont l’Etre, la Nécessité, le Passé, le Surnaturel. Fondé sur une dialectique structurelle déracinement-enracinement, pesanteur-grâce, le discours philosophique de Simone Weil sur la modernité poursuit un double enjeu. Sans se démarquer de la raison philosophique immanente, elle s’attelle à la fois à la dénonciation des propensions et défaillances qu’offrent les valeurs illusoires modernes d’argent, d’algèbre, de machinisme, d’impérialisme, de révolution, de démocratie, qu’à la conception d’une philosophie de la médiation des valeurs apte à contribuer à la renaissance d’une culture d’attention au capital axiologique de l’humanité. En effet, la modernité n’apparaissant plus que comme synonyme de crise des valeurs, il convient de tirer au clair ce piège qui fait de l’homme l’esclave de ses propres productions en y entreprenant une herméneutique ouverte non seulement au principe ontologique de nécessité, au-delà de toute projection avant-gardiste, mais surtout à une herméneutique des civilisations inspiratrices de l’humanité, en dehors de tout misonéisme passéiste, où le Surnaturel s’atteste dans sa plénitude comme critérium des valeurs authentiques et principe de médiation témoignant de l’enracinement de toutes choses dans l’être. Sans être en opposition avec les impératifs de découverte, d’invention et de développement, la philosophie weilienne de la médiation des valeurs se dévoile dans sa posture et sa validité comme une philosophie d’inspiration universelle à l’enracinement des peuples, des cultures et des nations, attentive à une pensée permanente des rapports entre la tradition et l’innovation, l’universalité et l’historicité. / Based on the idea of progress, the modern science, inspired by Descartes, is seen by Simone Weil as the primary cause of the modern crisis of values. Sustained by a linear movement, this science has lost the principle of analogy and, by consequent, it has lost its bindings with the surrounding world of everyday reality. Also, this science shows itself not only as the source of scientism, this belief in an independent scientific reason and the cult of the technical applications, but also as the source of industrial capitalism, of the revolutionary communism, of the totalitarianism, of the collapse of the traditional axiological order simultaneously to the crisis of civilization. Theses consequences resulting from the movement of uprooting not only led to the proletarian and the colonial oppression and to the modernism as the priority of the values of innovation on the values of tradition, but especially to a generalized oppression and the forgetting of the primordial universal axiological structures: the Being, the Need, the Past and the Supernatural.Based on a structural dialectic, the dislocation and the rooting, the fall and salvation, the philosophical discourse on modernity of Simone Weil seeks a double stake. Without a delimitation of the reason of the immanent philosophy, she is equally attached to the denunciation of the propensities and the failures of the modern illusory values of the money, of the algebra, of the machinery, of the imperialism, of the revolution, of the democracy, and to the conception of a philosophy of the mediation of values able to contribute to the rebirth of a culture attentive to the axiological capital of the humanity. Indeed, if the modernity appears no more as a synonym of the crisis of values, we must clarify this trap that makes the man the slave of his own productions by a hermeneutic open not only to the ontological principle of necessary, beyond any avant-garde projection, but principally a hermeneutic of the inspired civilizations of the humanity, without any outdated misoneism, where the Supernatural is attested in its fullness as criterion of the authentic values and as a principle of mediation reflecting the roots of all things in the Being. Without being in a conflict with the requirements of the discovery, of the invention, of the progress, the weilian philosophy of values mediation reveals itself as a philosophy of universal inspiration, founding the rooting of peoples, of cultures and of nations, paying permanent attention to the relationship between the tradition and the innovation, between the universality and the historicity.