The Private Finance Initiative (PFI) is a specific example of health care privatization within the British National Health Service. In this essay, I critically assess the ways in which various Private Finance Initiatives have increased health care efficiency and effectiveness, as well as encouraged medical innovation. Indeed, as the analysis will demonstrate, significant empirical evidence supports the conclusion that Private Finance Initiatives are a driving force of innovation within the British Health Care System.

In ancient tradition, Pythagoras emerges as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. This volume offers a comprehensive study of Pythagoras, Pythagoreanism, and the early Pythagoreans through an analysis of the many representations of the individual and his followers.

The Pythagorean idea that numbers are the key to understanding reality inspired philosophers in late Antiquity (4th and 5th centuries A.D.) to develop theories in physics and metaphysics based on mathematical models. This book draws on some newly discovered evidence, including fragments of Iamblichus's On Pythagoreanism, to examine these early theories and trace their influence on later Neoplatonists (particularly Proclus and Syrianus) and on medieval and early modern philosophy.

Kahn tries to do justice to the contribution Pythagoras and his followers might have had for Greek science. Thus he downplays the religious figure so prominent with Burkert's groundbreaking study "Lore and Science". He sees the transformation Pythagorean ideas may have undergone in Plato's Academy as pivotal for the developments of Pythagoreanism in later antiquity as well as in Renaissance speculation, e. g. Kepler. The book offers a good overview for the history of Pythagoreanism from its founder to modern (...) times. (shrink)

A new form of the Hyperbolic Pythagorean Theorem, which has a striking intuitive appeal and offers a strong contrast to its standard form, is presented. It expresses the square of the hyperbolic length of the hypotenuse of a hyperbolic right-angled triangle as the “Einstein sum” of the squares of the hyperbolic lengths of the other two sides, Fig. 1, thus completing the long path from Pythagoras to Einstein. Following the pioneering work of Varičak it is well known that relativistic (...) velocities are governed by hyperbolic geometry in the same way that prerelativistic velocities are governed by Euclidean geometry. Unlike prerelativistic velocity composition, given by the ordinary vector addition, the composition of relativistic velocities, given by the Einstein addition, is neither commutative nor associative due to the presence of Thomas precession. Following the discovery of the mathematical regularity that Thomas precession stores, it is now possible to extend Thomas precession by abstraction, (i) allowing hyperbolic geometry to be studied by means of analogies that it shares with Euclidean geometry; and, similarly (ii) allowing velocities and accelerations in relativistic mechanics to be studied by means of analogies that they share with velocities and accelerations in classical mechanics. The abstract Thomas precession, called the Thomas gyration, gives rise to gyrovector space theory in which the prefix gyro is used extensively in terms like gyrogroups and gyrovector spaces, gyroassociative and gyrocommutative laws, gyroautomorphisms, gyrotranslations, etc. We demonstrate the superiority of our gyrovector space formalism in capturing analogies by deriving the Hyperbolic Pythagorean Theorem in a form fully analogous to its Euclidean counterpart, thus contrasting it with the standard form in which the Hyperbolic Pythagorean Theorem is known in the literature. The hyperbolic metric, which supports the Hyperbolic Pythagorean Theorem, has a dual metric. We show that the dual metric does not support a Pythagorean theorem but, instead, it supports the π-Theorem according to which the sum of the three dual angles of a hyperbolic triangle is π. (shrink)

Fiction and truth : ancient stories about Pythagoras -- In search of the historical Pythagoras -- The Pythagorean secret society -- Thinkers influenced by Pythagoras and his pupils.

A fascinating portrait of the Pythagorean tradition, including a substantial account of the Neo-Pythagorean revival, and ending with Johannes Kepler on the threshold of modernism.

The timeless brilliance of this exhaustive survey of the best classical writers of antiquity on Pythagoras was first published in 1687 in Thomas Stanley's massive tome, The History of Philosophy. It remains as contemporary today as it was over three hundred years ago. The text of the 1687 book has been reset and modernized to make it more accessible to the modern reader. Spelling has been regularized, obsolete words not found in a modern dictionary have been replaced, and contemporary (...) conventions of punctuation have been used. Biographical sketches of Thomas Stanley and Pythagoras by Manly Palmer Hall, founder of the Philosophical Research Society, have been included, along with a profound overview of Pythagorean philosophy by Platonic scholar Dr. Henry L. Drake. The extensive Greek language references throughout the text have been corrected and contextualized, and reset in a modern Greek font. Each quotation has been verified with the source document in Greek. An extensive annotated appendix of these classical sources is included. A complete bibliography details all the reference works utilized, and a small Glossary defines a number of terms, especially those from musical theory, which may be unfamiliar to the non-technical reader. (shrink)

The influence which the Pythagorean society and its leading doctrines exercised upon Athenian intellectual and political developments in the late fifth century leads us to seek in Pythagoras a figure of greater stature and more clear-cut features than modern scholarship is prepared to allow. To us he is a great name but little more, the large body of detailed information about his life which is available in later writers being dismissed as fabulous. This scepticism was reasonable enough when the (...) reader was faced with the garbled hotchpotch of an Iamblichus or a Porphyry. But since the task has been put in hand of determining what portions of this tradition can safely be attributed to the various authorities who concerned themselves with the Pythagorean story in the fourth century, and of considering the respective historical value of these authorities, the scepticism of, for example, Burnet's account becomes unjustified. It is now possible to present a fairly detailed account of Pythagoras' activity, which has at least as much claim to credence as a great deal of what we now readily accept as ancient history, and is furthermore consistent with the general picture of the man that emerges from a careful scrutiny of classical sources. Not only for its own sake, but in the context of the increasingly fruitful investigation of fifth-century Athenian movements, I feel that it may be useful to put together such an account of Pythagoras. It will certainly be regarded by some as mere fiction, but may nevertheless provide others with a convenient summary of what the fifth- and fourth-century writers thought and believed about a man and a movement that had profound influence upon their times. I hope at the same time to suggest some links between what Pythagoras thought and did and the main tradition of Greek social behaviour. If Pythagoras was, as I believe, not so much an innovator as a reformer and developer of some of the central institutions of Greek life, the possibility will be opened of regarding various phenomena in mainland Greece which we have been asked to call Pythagorean, e.g. the Socratic phrontisterion as it appears in the Clouds, not as deriving from Pythagoras but as a parallel growth to the Pythagorean synedria and nourished by the same root. (shrink)

In this book, Christiane L. Joost-Gaugier offers the first systematic study of Pythagoras and his influence on mathematics, astronomy, philosophy, religion, medicine, music, the occult, and social life-as well as on architecture and art-in the late medieval and early modern eras. Following the threads of admiration for this ancient Greek sage from the fourteenth century to Kepler and Galileo in the seventeenth, this book demonstrates that Pythagoras's influence in intellectual circles-Christian, Jewish, and Arab-was more widespread than has previously (...) been acknowledged. Joost-Gaugier shows that during this period Pythagoras was respected by many intellectuals in different areas of Europe. She also shows how this admiration was reflected in ideas that were applied to the visual arts by a number of well known architects and artists who sought, through the use of a visual language inspired by the memory of Pythagoras, to obtain perfect harmony in their creations. Among these were Alberti, Bramante, Leonardo da Vinci, Michelangelo, and Raphael. Thus did, she suggests, some of the greatest art works in the Western world owe their modernity to an inspirational force that, paradoxically, had been conceived in the distant past. (shrink)

The author clarifies the thesis of the social constructivists and shows how it is overlapping with some ideas of its critics. Based on established agreement between social constructivism and evolutionary epistemology, she argues that the conceptual elements of mathematical knowledge are social constructs.

Introduction: The poetic topos of the doctrine of transmigration -- Genealogy of the doctrine of transmigration -- Beyond mysticism and science : symbolism and philosophical magic -- The emergence of mystic cults and the immortal soul -- Philolaus and the question of pythagorean harmony -- The alleged critique of Pythagoras by Parmenides -- Between the earth and the sky : on the pythagorean divine -- The pythagorean bios and the doctrine of transmigration -- The path of the event -- (...) The path of remembrance or return -- The platonic rupture : writing and difference -- Plotinus : the ascent of the soul toward the one -- Plotinus as neoplatonic mystic : letter to Flaccus -- Epilogue: The fate of the doctrine of transmigration. (shrink)

Apart from his teachings, wonders and scientific discoveries, Pythagoras was also known for his wide-ranging journeys. Ancient authors alleged that he visited many countries and nations from Egypt to India, stayed with the Phoenicians and the Ethiopians and talked to the Persian Magi and Gallic Druids. However, he never went to the North. If, nevertheless, he was eventually associated with the northern inhabitants, it is only because they themselves came into close contact with him. The first of them was (...) Zalmoxis, a deity of a Thracian tribe, the Getae, who guaranteed them immortality after death. Having described a blood ritual that the Getae practised to become immortal, Herodotus relates a story he heard from the Hellespontine and Pontic Greeks. It goes that Zalmoxis was not adaimōnbut a former slave of Pythagoras on Samos and, having adopted the doctrine of immortality from him, he returned to Thrace and converted his tribesmen to it with a cunning trick. He invited the most prominent of them to a men's hall for entertainment and told them that neither he nor they or their descendants would die, but would live eternally. Then, having constructed a secret underground chamber, he suddenly disappeared from the eyes of the Getae and hid in his shelter for three full years, being lamented as dead. Then he showed himself again to the Getae, thus persuading them of the truth of his promises. (shrink)

Die vorliegende Sammlung von Aufsatzen einiger der weltbesten Spezialisten der antiken griechischen Philosophie konzentriert sich auf die philosophischen Texte, die wahrend der hellenistischen und kaiserlichen Zeit Pythagoras und den Pythagoreern zugeschrieben wurden. Ihre unbekannten Verfasser behaupten, die Positionen der ursprunglichen pythagoreischen Schule zur Metaphysik, Theologie, Zahlenphilosophie, Physik, Logik, politischen Philosophie, Ethik und zur richtigen Lebensweise zu vermitteln. Die kuhnsten unter ihnen prasentieren sich als die Quellen, aus denen Platon und Aristoteles die Inspiration fur den Timaios und die Kategorien geschopft (...) haben. Da sie von den meisten antiken Denkern als massgebend angesehen wurden, fuhrte dies zu einer Renaissance der platonischen und pythagoreischen Tradition. (shrink)

Our purpose on the present occasion is to evaluate some ideas the biographers of late antiquity held about the origins of European thought. Speaking about this period we are no longer dealing with the question of transferring of the archaic practices: these practices are indeed long dead. What we encounter can be better defined as the import of ideas. Equally important is a study of the changing attitudes of our authors: rather than passive witnesses, they became active participants of this (...) import. The process is truly fascinating and we hope that the following examples, mostly from Hippolytus, will elucidate this. The best, almost a paradigmatic example is Pythagoras, who in late antiquity had many faces. His biography is an interesting instance of general change of attitude to ancient wisdom, typical for the source utilized by Hippolytus. Looking at a number of peculiar features of Hippolytus’ report which, we hope, will help us to see why the image of Pythagoras and his philosophy, formed by Hippolytus, is somewhat untypical for the period. We will see that Hippolytus’ biographic report, however garbled, shows no signs of so-called ‘Neopythagorean’ biographic development. Admittedly, the later authors frequently combine their sources to make them suitable to their needs, polemical or apologetic. Do we still have a reason to believe that these stories, however doubtful from the historical point of view, may contain the germs of truth? (shrink)

Too often the historians of philosophy tend to relegate a philosopher to a meaningless anonymity by rigidly classifying his thought into one particular category. De Vogel feels that this has been done to Pythagoras and the Pythagorean tradition. He claims that because philosophical scholars have relied chiefly on Platonic and Aristotelian accounts of Pythagoras, two misleading effects have ensued: 1. We have lost sight of the man Pythagoras and his charismatic influence on the people of Croton and (...) Magna Graecia; 2. Pythagoras, cosmic theory of numerical ratios has been emphasized to the neglect of, and in separation from, his political and social teachings. De Vogel hopes to remedy these two impressions by returning to "neglected evidence" and reconstructing the life of Pythagoras. He hopes to remove Pythagoras from that vague classification as one of the οἱ φυσικοί into which Aristotle had placed all the pre-Socratic thinkers. Furthermore, the author wants to show the essential unity of Pythagoras' cosmic, social, and political thinking. The neglected evidence on which De Vogel bases his reconstruction is mainly the testimony of Timaeus, an historian of Southern Italy and Sicily; Aristoxenus, a follower of Pythagoras; and Dicaearchus, a writer of cultural history. In addition to these last mentioned sources, the author cites the testimony of coins and quotes leading archaeologists; he refers to the many historians and biographers of Pythagoras; and especially, he draws from the four speeches of Pythagoras that are recorded by Iamblichus. With these source materials, De Vogel reconstructs a Pythagoras who is a charismatic preacher-moralist; one who gives precepts of life governing justice, friendship, love, health, education, rhetoric, and medicine. What is more, all of these social and political teachings are shown to be integrated with the cosmic theory of numbers which De Vogel removes from the realm of abstract and idle theory. Pythagoras emerges as a leading figure in Croton and throughout Magna Graecia. All in all, this volume is an excellent contribution to Pythagorean scholarship.--J. J. R. (shrink)

Too often the historians of philosophy tend to relegate a philosopher to a meaningless anonymity by rigidly classifying his thought into one particular category. De Vogel feels that this has been done to Pythagoras and the Pythagorean tradition. He claims that because philosophical scholars have relied chiefly on Platonic and Aristotelian accounts of Pythagoras, two misleading effects have ensued: 1. We have lost sight of the man Pythagoras and his charismatic influence on the people of Croton and (...) Magna Graecia; 2. Pythagoras, cosmic theory of numerical ratios has been emphasized to the neglect of, and in separation from, his political and social teachings. De Vogel hopes to remedy these two impressions by returning to "neglected evidence" and reconstructing the life of Pythagoras. He hopes to remove Pythagoras from that vague classification as one of the οἱ φυσικοί into which Aristotle had placed all the pre-Socratic thinkers. Furthermore, the author wants to show the essential unity of Pythagoras' cosmic, social, and political thinking. The neglected evidence on which De Vogel bases his reconstruction is mainly the testimony of Timaeus, an historian of Southern Italy and Sicily; Aristoxenus, a follower of Pythagoras; and Dicaearchus, a writer of cultural history. In addition to these last mentioned sources, the author cites the testimony of coins and quotes leading archaeologists; he refers to the many historians and biographers of Pythagoras; and especially, he draws from the four speeches of Pythagoras that are recorded by Iamblichus. With these source materials, De Vogel reconstructs a Pythagoras who is a charismatic preacher-moralist; one who gives precepts of life governing justice, friendship, love, health, education, rhetoric, and medicine. What is more, all of these social and political teachings are shown to be integrated with the cosmic theory of numbers which De Vogel removes from the realm of abstract and idle theory. Pythagoras emerges as a leading figure in Croton and throughout Magna Graecia. All in all, this volume is an excellent contribution to Pythagorean scholarship.--J. J. R. (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)

Mathematician. Philosopher. World traveler. Pythagoras was an intelligent and curious scholar and teacher. While he¿s best-known for the Pythagorean theorem, he shared ideas about numbers, animals, and many other areas of knowledge with his students. Since none of his writings were left behind, it¿s not always easy for historians to know what¿s true about Pythagoras and what may be legendary. What does seem apparent is that he was a vegetarian but not a trendy dresser. Some people saw him (...) as godlike. Others felt he made false claims about things. No matter what, Pythagoras¿s curiosity and willingness to grapple with complex issues have helped further the knowledge of mathematics and philosophy for thousands of years. (shrink)

The early years -- The traveling student -- Egypt and Babylon -- A return to Greece -- The Pythagorean school -- Pythagorean thought -- Pythagoras' legacy.

AëtiusPlacita1.3.8, in the chapterOn Principles, provides a systematic overview of Pythagorean thought, which can be instructively compared with ps.-ArchytasOn Principles, provided both fragments of the latter are kept together.

Growing up in Ionia -- Travels far and wide -- Settling in Croton -- Pythagorean beliefs -- A lasting legacy.

Pythagoras von Samos (ca. 570-510 v.Chr.) war in den antiken Uberlieferungen nicht nur als Naturphilosoph, sondern auch als religioser Experte und Wundertater bekannt. Diesen Wundererzahlungen rund um Pythagoras widmet sich Stephan Scharinger in der vorliegenden Studie. Basis seiner Uberlegungen sind Analyse und Auswertung des einschlagigen Quellenmaterials, beginnend mit den altesten schriftlichen Quellen, die in die Lebenszeit des Pythagoras zuruckreichen, bis hin zu den Pythagorasviten der romischen Kaiserzeit. Darauf aufbauend und mithilfe der historischen Kontextualisierung des Pythagoras (Pythagoreismus (...) und Orphik, Pythagoras und die "Sieben Weisen", Schamanismus) klassifiziert Scharinger die pythagoreischen Wundertaten in Abhangigkeit von der griechisch-romischen Umwelt (ethnische Religionen, altindische und alttestamentarisch-fruhkirchliche Vorstellungen). Die Wundertraditionen in den pythagoreischen Uberlieferungen werden schliesslich in einem zweifachen Vergleich beleuchtet. Der "interne" Vergleich zeigt Parallelen und Unterschiede zwischen den Wunderberichten bei Diogenes Laertios, Porphyrios von Tyros und Iamblichos von Chalkis auf, wahrend der "externe" Vergleich die pythagoreischen Wundertaten mit den Berichten rund um andere Wundertater der antiken Mittelmeerwelt in einen grosseren Zusammenhang stellt. Uberlegungen zum religionshistorischen Umfeld, zur Diskussion um Pythagoras als theios aner sowie zur Klassifikation der Wundertaten als "magische" oder "religiose" Wunder runden die Arbeit ab. (shrink)