In a series of recent papers, Randall and Foulis have developed a generalized theory of probability (operational statistics) which is based on the notion of a physical operation. They have shown that the quantum logic description of quantum mechanics can be naturally imbedded into this generalized theory of probability. In this paper we shall investigate the role of entropy (in the sense of Shannon's theory of information) in operational statistics. We shall find that there are several related entropy concepts in (...) operational statistics. We shall examine the relationships between these different entropy concepts and examine their implications for the foundations of quantum theory. We shall also examine the extension of the Jaynes inference scheme to the operational statistics formalism, and apply the latter to the case of quantum statistical mechanics. (shrink)

In a series of recent papers, Randall and Foulis report the development of a generalized theory of probability which is based on the concept of a physical operation. A central concept in this theory is that of a generalized sample space. In this paper, we introduce a generalized sample space, which for historial reasons we shall call the Poincaré sphere sample space. We investigate the relationship between this nonclassical sample space and its classical analogs, and find that the key to (...) this relationship is found in the use of idealized (Gedanken) experiments. The Poincaré sphere sample space is seen to describe a “photon” description of polarization, and the classical analogs represent different classical descriptions. We also discuss superposition and entropy for the Poincaré sphere sample space and its classical analogs, and we comment on the application of this generalized theory of probability to problems in the foundations of quantum theory. (shrink)

In _The History of the Race Idea: From Ray to Carus,_ Eric Voegelin places the rise of the race idea in the context of the development of modern philosophy. The history of the race idea, according to Voegelin, begins with the postChristian orientation toward a natural system of living forms. In the late seventeenth century, philosophy set about a new task--to oppose the devaluation of man's physical nature. By the middle of the eighteenth century the effort of philosophy was to (...) place man, with his variety of physical manifestations throughout the world, within a systemic order of nature. Voegelin perceives the problem of race as the epitome of the difficulties presented by this new theoretical approach. Part I covers the development of race theories from the English naturalist John Ray to Blumenbach and Kant. Voegelin, anticipating fairly recent genetic insights, explains that human beings must be seen as one speciesdifferent races must not be interpreted as emerging from separate species. In Part II, Voegelin discusses the evolution of the concepts of the body, the organism, and the person. The finite image of the person as a body-mind unit in which body is equal to mind in value provides the basis for Carl Gustav Carus' theory of race, the first significant racial ideology, in Voegelin's estimation. Voegelin's complex analysis levels a scathing critique at Nazi pretensions. He writes: "Compared to its classical form, the current condition of race theory is one of decay.... [T]hese men, with no eyes for the brilliance of the German spirit, want to interfere in human relations and ultimately presume to explicate the German nation to us and to the world--an undertaking with evil consequences.... [The] great thinkers of the past would have been orrified at somebody finding in himself all the traits of the Nordic race with the help of a book on anthropology and then imagining himself to be somebody special who does not have to do anything else. "Let us now take a look at contemporary race theory--we will see an image of destruction.... It is a nightmare to think that we should recognize the people whom we follow and whom we allow to come near us not by their looks, their words, and their gestures, but by their cranial index." Ultimately, Voegelin dismisses any attempt to reduce the human being--his existence, appearance, or actionsto a lower level: "Man as mind-body and historical substance cannot be 1explained' by an element that is less than man himself.". (shrink)

This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, (...) music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle Ages and Renaissance. (shrink)

Archytas of Tarentum is one of the three most important philosophers in the Pythagorean tradition, a prominent mathematician, who gave the first solution to the famous problem of doubling the cube, an important music theorist, and the leader of a powerful Greek city-state. He is famous for sending a trireme to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC. This 2005 study was the first extensive enquiry into Archytas' work in any language. It (...) contains original texts, English translations and a commentary for all the fragments of his writings and for all testimonia concerning his life and work. In addition there are introductory essays on Archytas' life and writings, his philosophy, and the question of authenticity. Carl A. Huffman presents an interpretation of Archytas' significance both for the Pythagorean tradition and also for fourth-century Greek thought, including the philosophies of Plato and Aristotle. (shrink)

This is the first comprehensive study for nearly 200 years of what remains of the writings of the Presocratic philosopher Philolaus of Croton. These fragments are crucial to our understanding of one of the most influential schools of ancient philosophy, the Pythagoreans; they also show close ties with the main lines of development of Presocratic thought, and represent a significant response to thinkers such as Parmenides and Anaxagoras. Professor Huffman presents the fragments and testimonia with accompanying translations and introductory chapters (...) and interpretive commentary. He not only produces further argument for the authenticity of much that used to be neglected, but also 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. Philolaus is revealed as a serious natural philosopher. (shrink)

For theorists in search of a political theology that is more responsive to the challenges now facing Western democracies, this book tenders a new political economy anchored in a theory of value. The political theology of the future, Carl Raschke argues, must draw on a powerful, hidden impetus--the "force of God"--to frame a new value economy. It must also embrace a radical, "faith-based" revolutionary style of theory that reconceives the power of the "theological" in political thought and action. Raschke (...) ties democracy's retreat to the West's failure to confront its decadence and mobilize its vast spiritual resources. Worsening debt, rising unemployment, and gross income inequality have led to a crisis in political representation and values that twentieth-century theorists never anticipated. Drawing on the thought of Hegel and Nietzsche as well as recent work by Michel Foucault, Jacques Derrida, Jean-Joseph Goux, Giorgio Agamben, and Alain Badiou, among others, Raschke recasts political theology for a new generation. He proposes a bold, uncompromising critical theory that acknowledges the enduring significance of Marx without his materialism and builds a vital, more spiritually grounded relationship between politics and the religious imaginary. (shrink)

Publication of The Alchemy of the Word in 1979 brought the deconstructive philosophy of Jacques Derrida into the arena of theological discourse & marked the end of theology as it had been understood by many. This work, revised & reissued as The End of Theology, is an important contribution to understanding the possibilities of a creative postmodern secular theology. The first chapter examines the aims & the shortcomings of language analysis as used in the examination of religious & theological statements. (...) The second chapter investigates the broader spectrum of modern theories about the nature of language. The third chapter recapitulates the rudiments of Heidegger's thought. The fourth chapter moves out of Heidegger & toward a resolution of the problems of meaning & interpretation in proposing a "radical hermeneutics." The fifth chapter discusses the way in which a radical hermeneutics must undermine conventional theological procedures & secure a view of religious speech that is prior to "God-language" or to the "Word of God." Such a view is directed to what Heidegger takes as the "ordinary" logos that is both a pre-Christian & a post-Christian context of "revelation." The final chapter criticizes Heidegger's own "mystifications" about language & endeavors to take his thought one major step beyond. Carl Raschke is professor of religious studies at the University of Denver & senior editor of the Journal for Cultural & Religious Theory. His major books include The End of Theology, Fire & Roses: Postmodernity & the Thought of the Body, The Engendering God, Painted Black & Theological Thinking. (shrink)

At a certain stage of advance in any science it may be well to re-examine and perhaps to rearrange its fundamentals. One seeks an ideal, logical order of development, which may or may not be the best pedagogical order. Many a high school beginner in physics has become acquainted with “force” as something that gets in between two bodies of matter and pulls them together or pushes them apart, like himself between two carts or like “magnetism” between two magnets. Whether (...) or not this might ever be a proper view, the mature student of today will consider that for him, a knowledge of accelerations and strains, inter alia, is prerequisite to a knowledge of force. (shrink)

The prestige of science, derived from its claims to certainty, has adversely affected the humanities. There is, in fact, a “politics of certainty”. Our ability to predict events in a limited sphere has been idealized, engendering dangerous illusions about our power to control nature and eliminate time. In addition, the perception and propagation of science as a bearer of certainty has served to legitimate harmful forms of social, sexual, and political power. Yet, as Ilya Prigogine has argued, renewed attention to (...) the irreducible reality of time has brought us to “the end of certainty”. As we enter the age of uncertainty, there is disagreement about how science should be understood and communicated. Some scientists cling to the ideal of certainty, while others emphasize the creative potential of spontaneity, novelty, and surprise. (shrink)

Absolutely no one still believes that every physical interactionconsists of material bodies bumping into each other. Those who have tried to work out a completely mechanistic physics have been unable to explain common phenomena like liquidity, gravitation and magnetism. In fact, there is great reason to doubt that such a physics could ever account for attractive forces in general.

In a long note in his epoch-making book on ancient Pythagoreanism Walter Burkert raised some grave doubts about the authenticity of Archytas Fr. 1 which have recently been challenged in an article by A. C. Bowen. In this paper I have two goals. First, I will evaluate Burkert's doubts and the success of some of Bowen's arguments against them. Second, I will present a further consideration that both clarifies the text of the fragment and also removes the most serious problem (...) raised by Burkert. The upshot of both these points is to increase the likelihood that the fragment is authentic. I reproduce the text of just the first part of the fragment as given in DK followed by the text as it appears in the two primary sources, Nicomachus and Porphyry. (shrink)

In a long note in his epoch-making book on ancient Pythagoreanism Walter Burkert raised some grave doubts about the authenticity of Archytas Fr. 1 which have recently been challenged in an article by A. C. Bowen. In this paper I have two goals. First, I will evaluate Burkert's doubts and the success of some of Bowen's arguments against them. Second, I will present a further consideration that both clarifies the text of the fragment and also removes the most serious problem (...) raised by Burkert. The upshot of both these points is to increase the likelihood that the fragment is authentic. I reproduce the text of just the first part of the fragment as given in DK followed by the text as it appears in the two primary sources, Nicomachus and Porphyry. (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)