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.

The Continuum Concept introduces the idea that in order to achieve optimal physical, mental and emotional development, human beings - especially babies - require the kind of instinctive nurturing as practiced by our ancient relatives. It is a true ‘back to basics’ approach to parenting. Author Jean Liedloff spent two and-a-half years in the jungle deep in the heart of South America living with indigenous tribes and was astounded at how differently children are raised outside the Western world. She came to the realisation that essential child-rearing techniques such as touch, trust and community have been undermined in modern times, and in this book suggests practical ways to regain our natural well-being, for our children and ourselves.

The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection

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.

Volume four of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.

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.