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In this powerful re-examination of the purpose and direction of philosophy for the next century, Anthony O'Hear engages with our most pressing questions: Is there knowledge outside of science? Does religion still have meaning and coherence today? What is beauty, and why do so few contemporary artists believe in it? Contemporary philosophy mostly divides into the technical approach of the Anglo-Americans, which is inaccessible to most, and the oracular obscurantism of the Continental approach, which does violence to sense and reason. O'Hear argues that philosophy should work with the grain of tradition and commonsense to understand politics, religion, aesthetics, and the vast number of ethical questions that will continue to arise as the scientific and technical revolution accelerates. Giving up philosophy's special position means giving up our best chances of thinking and acting wisely. In making a strong case for the relevance of philosophy, Anthony O'Hear presents a coherent and compelling vision for recovering wisdom in our time.
In this powerful re-examination of the purpose and direction of philosophy for the next century, Anthony O'Hear engages with our most pressing questions: Is there knowledge outside of science? Does religion still have meaning and coherence today? What is beauty, and why do so few contemporary artists believe in it? Contemporary philosophy mostly divides into the technical approach of the Anglo-Americans, which is inaccessible to most, and the oracular obscurantism of the Continental approach, which does violence to sense and reason. O'Hear argues that philosophy should work with the grain of tradition and commonsense to understand politics, religion, aesthetics, and the vast number of ethical questions that will continue to arise as the scientific and technical revolution accelerates. Giving up philosophy's special position means giving up our best chances of thinking and acting wisely. In making a strong case for the relevance of philosophy, Anthony O'Hear presents a coherent and compelling vision for recovering wisdom in our time.
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Connolly investigates the realities of sin through reflection on different biblical and literary texts. Writers as varied as Sophocles, Graham Greene, Gabriel Garcia Marquez and Irvine Welsh help illuminate different models of sin. Physical evil, law and morality, alienation and existence, power and money, spiritual love and failure are some of the ever-compelling themes that are scrutinized. In Dostoevsky's novels, sin is the rejection of life and love and a refusal to commit oneself to destiny. This book rediscovers a truly relational understanding of sin and moves toward a more adult conception of the mystery of sin and forgiveness.
Puzzles about time - about past, present and future, and the nature of becoming - have concerned philosophers from the ancient Greeks to the present day. Yet few have been as radical in their thinking as Friedrich Nietzsche. Time and Becoming in Nietzsche's Thought explores Nietzsche's approach to temporality, showing that his metaphorical and literary presentations lend themselves, in surprising detail, to the debates that have engaged other thinkers. Like Heraclitus, Nietzsche is a philosopher of becoming who sees reality as a continual flow of change. Time is an interpretation of becoming, designed to enable its tensions and fluctuations to be grasped conceptually by our minds. From this starting point, Robin Small explores the emergence of sharply contrasting models of temporality which express differing forms of life. The book concludes with a return to Nietzsche's Dionysian vision of playful participation in becoming as a never-ending creation and destruction. Time and Becoming in Nietzsche's Thought reveals Nietzsche as a major contributor to our thinking about temporality and its significance for human life.
Kenny, a philosopher by profession, struggles with the intellectual problems of theism and the possibility of believing in god, especially in an intellectual climate dominated by Logical Positivism. Here he revisits the Five Ways of Aquinas and argues that they are not so much proofs as definitions of God. He is also in constant dialogue with Wittgenstein for, Kenny writes, no man in recent years has surpassed him in devotion of sharp intelligence to the demarcation of the boundary between sense and nonsense.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
The Effective Teaching of Religious Education provides an accessible yet intellectually rigorous resource for all those involved in the teaching of RE in schools today. Written with the needs of specialist and non-specialist teachers in mind, in both the primary and secondary sectors, it successfully integrates theory and practice, encouraging debate and reflection on a broad range of issues in what is often regarded as a complex and often controversial subject area. The second edition has been written with the collaboration of a new co-author, Penny Thompson and has been thoroughly updated, revised and extended to include: A new chapter on the place of Christianity in RE New material on the purpose of RE and on the relationship of RE to other subjects A new Appendix on tackling assessment and syllabus requirements A new companion website at www.pearsoned.co.uk/watson-thompson including an overview of the use of ICT in RE teaching, web links and practical resources for use in the classroom.
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.