: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

For the first English edition of his distinguished study, Weisheit und Wissenschaft: Studien zu Pythagoras, Philoloas und Platon, Mr. Burkert has extensively ...

This book publishes and discusses a hitherto unedited text from one of Renaissance Florence's most tumultuous periods, the Savonarolan era of the end of the ...

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. Mathematical platonists claim that at least some of the objects which are the subject matter of pure mathematics (e.g. numbers, sets, groups) actually exist. Furthermore, they claim that these objects differ radically from the concrete objects (trees, cats, stars, molecules) which inhabit the material world. We take the standard platonistic position to include the claim that platonic objects lack spatio-temporal location and causal powers. Many (perhaps most) mathematical platonists subscribe to this view.1 But some who call themselves (or might be called) mathematical platonists.. (shrink)

En el mundo occidental, la primera figura que encarna el arquetipo del mediador sapiencial entre la comunidad humana y lo divino es, sin duda, Pitágoras de Samos. Las implicaciones de las doctrinas de este chamán en la historia de las ideas son enormes, pues sus invenciones abarcan todos los campos del saber: matemáticas, astronomía, filosofía, retórica, política, adivinación, medicina y religión. Nada escapa a este sabio griego, al que se atribuye un famoso teorema matemático, las escalas musicales y la idea (...) de la inmortalidad del alma. La primera parte del libro se ocupa de estudiar a Pitágoras como figura carismática y legendaria, la colección de sus enseñanzas, sus aspectos mánticos y políticos y, finalmente, la tradición pitagórica entre la realidad y la falsificación. En la segunda parte se presenta por primera vez, en una nueva traducción anotada, una recopilación de todas las biografías del filósofo: las escritas por Porfirio de Tiro, Jámblico de Calcis y Diógenes Laercio, y, como novedad, la más antigua que se conserva, redactada por el historiador griego Diodoro de Sicilia (s. I a.C.), y la del patriarca Focio de Constantinopla (s. IX). Todo ello, junto a la colección de máximas pitagóricas de origen tardío, llamada Versos de oro, así como el epítome de la enciclopedia bizantina Suda (s. X), forma el presente corpus biográfico-doctrinal de Pitágoras, que era una labor pendiente en el panorama bibliográfico español. David Hernández de la Fuente (Madrid, 1974) es escritor y profesor universitario, especializado en religión griega, antigüedad tardía e historia del platonismo. Doctor en filología clásica y sociología, es autor de los ensayos Oráculos griegos (Alianza) y Bakkhos Anax (CSIC), así como de numerosos artículos en revistas académicas y ediciones de autores clásicos, y ha coordinado la obra colectiva New Perspectives on Late Antiquity (Cambridge Scholars Pub.). Como autor de narrativa ha publicado Las puertas del sueño (Premio de Arte Joven 2005 de la Comunidad de Madrid), Continental (2007) y A cubierto (Premio Diputación de Valencia 2010). Memoria mundi 59 Isbn: 978-84-938466-6-4 440 páginas. (shrink)

This book investigates the link Kant discerned between our experience of beauty and our experience of the moral law. By examining Kant's relation to Greek philosophy, to Plato and Pythagoras, as found in Kant's own writings, the author sheds new light on one the most intriguing and mysterious doctrines of Kant's third Critique.

Intent upon harmonizing doctrines of their predecessors, some Neoplatonic commentators are faced with a problem of resolving doctrinal discrepancies so as to restore the συµφωνία in the history of philosophy. This article considers a particular example of this attempt ats harmonization: how Simplicius reconciles Aristotle's Categories with the Neopythagorean doctrine of the Pseudo-Archytas. The chronological inversion introduced by the counterfeiter produces remarkable effects on the late Platonic doctrine about general terms, to the extent that a commentator such as Simplicius works (...) to reduce the dissonance between Archytas' and Aristotle's words. This paper has three aims: to restore the general grid that Simplicius uses for reading and commenting on Archytas through Aristotle; to identify the exegetical strategies aimed at a doctrinal reconciliation; to consider a specific case, provided by the doctrine of weight, which engenders a new physical theory by Simplicius. (shrink)

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's "relations of uncertainty." The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one solution with (...) the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty. (shrink)

Into the forge -- Of measured multitude -- Remainders -- Disproportions -- Ciphers -- Temperaments -- Of measureless magnitude.

Intended for general readers, The Illustrated To Think Like God explores how philosophy became a speculative science, tracing its origins to the Greek colonies of southern Italy, from the late sixth century to the mid-fifth century BCE. In this lavishly illustrated full-color work, Arnold Hermann tells the story of the sage Pythagoras, the poet Xenophanes, and the lawmaker Parmenides, describing how each in his own way believed that true insight belonged only to the gods. With a sympathetic and critical eye, (...) Hermann investigates how the Pythagoreans tried to discover otherworldly knowledge by studying numerical relationships, believing that these govern the universe. He shows that the difficulties of their quest were further aggravated by cultism, political conspiracies, and bloody uprisings. Numbers were not the key to the divine that everyone had hoped for. The real challenge, Hermann argues, came from Xenophanes, who argued that divine or absolute truth was beyond the reach of mortals. Even if a human being should happen to state exactly what was the case, he had no reliable way of knowing that he did. Hermann convinces readers that this dilemma certainly would have concerned a legislative mind like that of Parmenides, and he examines how Parmenides introduced techniques for testing the truth of statements. Parmenides�2 unparalleled approach was not based on physical evidence of the experience of our five senses. Instead, they relied on the faculty we humans share with the gods--our ability to reason. Handsome illustrations, created by the same designers responsible for Stephen Hawking�2s Universe in a Nutshell, accompany Hermann�2s text, illuminating and expanding its complex ideas. Incisive, thought-provoking, and certain to engage the intellectually curious, The Illustrated To Think Like God reveals Parmenides to be the true father of theoretical science. As the philosopher who taught us that truth is not about claims but about proof, Parmenides ironically gave birth to the discipline in the process of trying to plumb the depths of the mind of god. "Figures from Anaximander to Zeno, the ruins where they lived and thought, and the paradoxes and thought-experiments they proposed are depicted among the [many] well-chosen color illustrations. �5lovingly written, lavishly laid-out�5making it engaging enough to draw in readers to whom it has not been assigned." - Publisher's Weekly "To Think Like God is a highly ambitious book . . . Hermann's approach deserves to be taken seriously as an alternative to standard interpretations." - Richard D. McKirahan, Jr., Edwin Clarence Norton Professor of Classics and Professor of Philosophy, Pomona College "Arnold Hermann brings fresh life into the specialists' debates . . . a blow of wind that dissipates much fog." - Walter Burkert, Professor Emeritus of Classical Philology, University of Zurich. (shrink)

This fascinating and thought-provoking book provides much-needed philosophical background for counselors, therapists, and healthcare workers looking for broader, deeper foundations in the struggle to help and make sense of others. While examining the best among 20th century philosophy it shows the wealth of inspiration of earlier centuries, and demonstrates with remarkable clarity the way in which the ideas of, and the relations between, these philosophers can inspire, inform, and underpin much of counseling and psychotherapy.

Archytas of Tarentum was a central figure in fourth-century Greek life and thought and the last great philosopher in the early Pythagorean tradition. He solved a famous mathematical puzzle, saved Plato from the tyrant of Syracuse, led a powerful Greek city state, and was the subject of three books by Aristotle. This first extensive study of Archytas' work in any language presents a radically new interpretation of his significance for fourth-century Greek thought and his relationship to Plato, as well as (...) a full commentary on all the fragments and testimonia. (shrink)

This is the first comprehensive study for nearly 200 years of what remains of the writings of the Presocratic philosopher Philolaus of Croton (470-390 B.C.). Professor Huffman presents the fragments and testimonia with accompanying translations and introductory chapters and interpretive commentary. He produces further arguments for the authenticity of much that used to be neglected, and undertakes a critique of Aristotle's testimony, opening the way for a quite new reading of fifth-century Pythagoreanism in general and of Philolaus in particular.

Two conflicting tendencies may be discerned in Pythagorean ethics as applied to the environment: on the one hand, a sense of reverence for nature and kinship with all life that opposed killing and other forms of interference in the natural world, and on the other hand, a doctrine of the separability of soul and body which denigrates the body and the external world of which it is apart. The prescriptive content of Pythagorean ethics includes prohibitions against taking life, even in (...) sacrifices to the gods, and against eating anything that has been killed. Pollution of certain kinds is forbidden. These strictures were based on an organic, cyclical view of the world, emphasizing its harmony and balance. The Pythagoreans investigated some questions that would today be called ecological. Perhaps most importantly, they evinced a genuine respect for living things, deriving in part from the belief that animals and plants contain the reborn souls of human beings. These doctrines may have been derived from the attitudes and practices of ancestral hunters and gatherers in southeast Europe, with traditional Greek religion serving as the means of transmission from tribaI cultures to c1assical philosophy. The followers of Pythagoras split into two schools: a “scientific” school that neglected biology and therefore ecology, and a “religious” school that emphasized purity of soul and rejected any concern with physical nature. The more “environmentalist”teachings were gradually abandoned as the Pythagoreans accommodated themselves to the general attitudes of Greco-Roman culture. For instance, the objections to animal sacrifice, and to most plants as food, were dropped. The divorce of body and soul in later Pythagorean thought, wherever its influence was strong, brought with it indifference not only to the body, but to all the rest of the natural environment. (shrink)

The Pythagorean Life is the most extensive surviving source on Pythagoreanism, and has wider interest as an account of the religious aspirations of late antiquity. "...admirably clear translation and sensible introduction"--The Classical ...

A review essay about Carl Huffman's recent edition of the fragments of Archytas of Tarentum, along with translations of dubious material rejected by Huffman.

A review of Carl Huffman's new edition of the fragments of Archytas of Tarentum. Praises the extensive commentary on four fragments, but argues that at least two dubious works not included in the edition ("On Law and Justice" and "On Wisdom") deserve further consideration and contain important information for the interpretation of Archytas. Provides a complete translation for the fragments of those works.

"In this illustrated book, Christiane L. Joost-Gaugier sets out the panorama of Pythagoras's influence and that of Christian and Jewish thinkers who followed ...

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

My personal odyssey -- Tripping the night fantastic. Who-and what-am I? -- The journey home. Take me to the river-- -- The being human -- White crows : mystics, savants, and other harbingers of human potential. Mystic mind (or how to crack open the cranium) -- Wake up! Greek philosophy breaks the trance -- The ultimate cage match : philosophy, science, and religion (or togas, Bibles, and microscopes : why can't we all just get along?) -- Homo anxious : I (...) think, therefore I worry. Mindfulness walk : "being" without thinking -- Why philosophy matters-and how it just might save your life! Am I a neuron in the mind of God? -- Reality bites -- The physical world : the tip of the reality iceberg. More to reality than meets the eye -- Real deal reality : beyond sense and beyond reason. Beyond logic : riddles and paradoxes. Pyramids, togas, and cosmic consciousness -- Pythagoras squared : who was this mystic mathemagician? Infinity : the ultimate mind trip -- Good vibrations : Pythagoras and the big beat. The cosmic symphony : music from the universal orchestra -- Escaping Plato's cave -- Plato's retreat-from the material world. the universe as one big thought -- On the nature of change : the more things change--. Change : the great illusion -- Death : the new birth. Incubation (or how death can transform your life) -- Yes, but what does it all mean? -- New science and old wisdom -- Musings from my dissertation -- Some final thoughts. (shrink)

The aim -- The journey -- The goal -- The view -- The endless joy.

This is the first book to analyze systematically crucial aspects of ancient Greek philosophy in their original context of mystery, religion, and magic. The author brings to light recently uncovered evidence about ancient Pythagoreanism and its influence on Plato, and reconstructs the fascinating esoteric transmission of Pythagorean ideas from the Greek West down to the alchemists and magicians of Egypt, and from there into the world of Islam.

Recent developments in astrophysical cosmology have revived support for the design argument among a growing clique of astrophysicists. I show that the scientific/mathematical evidence cited in support of intelligent design of the universe is infected with a mathematical sharp practice: the concepts of two numbers being of the same order of magnitude, and of being within an order of each other, have been stretched from their proper meanings so as to doctor the numbers evidentially. This practice started with A. S. (...) Eddington and P. A. M. Dirac in the 1920s and 1930s, but it is still very much alive today. 1 Introduction 2 The birth of a sharp practice 3 High tide for the anthropic principle 4 How not to do things with numbers 5 The recalcitrant sloppiness of crud 6 How excited can excited carbon-12 be? 7 Is a pile of doubts a doubtful pile? 8 Conclusion. (shrink)