: 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)

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)

This article explores in greater depth the historiographical traditions concerning Herennius Pontius, a Samnite wisdom-practitioner who is said by the Peripatetic Aristoxenus of Tarentum to have been an interlocutor of the philosophers Archytas of Tarentum and Plato of Athens. Specifically, it argues that extant speeches attributed to Herennius Pontius in the writings of Cassius Dio and Appian preserve a philosophy of “extreme proportional benefaction” among unequals. Greek theories of ethics among unequals such as those of Aristotle and Archytas of Tarentum, (...) which aim for moderation, can be distinguished from that attributed to Herennius Pontius, which is circumstantial and stipulates extreme responses to extremes. Romans, in particular Appius Claudius Caecus and Sulla, celebrate and espouse proverbial wisdom strikingly similar to the theory of “extreme proportional benefaction” associated with Herennius Pontius, and in contrast to Greek ethics of moderation. Such comparisons suggest that starting in the late fourth century BCE, Romans and Samnites may have held shared ideological principles, as defined against Greek cultural paradigms. (shrink)

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)

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)

IAMBLICHUS: ON THE PYTHAGOREAN LIFE 1 Preface. The philosophy of Pythagoras. Preliminary invocation of the gods. The usefulness and difficulty of the ...

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.

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

"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 ...

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)

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)

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)

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.

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.

Throughout its history the Game was closely allied with music, and usually proceeded according to musical or mathematical rules. One theme, two themes, or three themes were stated, elaborated, varied, and underwent a development quite similar to that of the theme in a Bach fugue or a concerto movement.… Experts and Masters of the Game freely wove the initial theme into unlimited combinations [p. 30].