**Author**: Hermann Weyl,Frank Wilczek

**Publisher:** Princeton University Press

**ISBN:** 9780691141206

**Category:** Mathematics

**Page:** 311

**View:** 7988

History of mathematics.

Eleven distinguished historians of science explore natural philosophy and mathematics in the Middle Ages.

What is now needed is a way of thinking about the physical that is realistic in outlook but which departs radically from the mechanistic post-Galilean tradition. Since it seems clear that we can no longer take for granted the certainty and absolute objectivity of scientific knowledge, any alternative view must be able to do full justice to subjective modes of knowing. Order and Organism shows how Alfred North Whitehead's thought can reconcile some of the most insistent demands of common sense with the esoteric results of modern physics and mathematics. Whitehead shows a way to resolve the perennial puzzle of why mathematics works. Under his view, it is possible to account for the necessity and uniqueness of mathematical theories without denying the fact that such theories often arise from the mathematician's essentially aesthetic interest in various kinds of pattern.

The mysterious beauty, harmony, and consistency of mathematics once caused philosopher Hilary Putnam to term its existence a "miracle." Now, advances in the understanding of physics suggest that the foundations of mathematics are encompassed by the laws of nature, an idea that sheds new light on both mathematics and physics. The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject. Based on a simple but powerful idea, it shows that the axioms needed for the mathematics used in physics can also generate practically every field of contemporary pure mathematics. It also provides a foundation for current investigations in string theory and other areas of physics. This approach to the nature of mathematics is not really new, but it became overshadowed by formalism near the end of nineteenth century. The debate turned eventually into an exclusive dialogue between mathematicians and philosophers, as if physics and nature did not exist. This unsatisfactory situation was enforced by the uncertain standing of physical reality in quantum mechanics. The recent advances in the interpretation of quantum mechanics (as described in Quantum Philosophy, also by Omnès) have now reconciled the foundations of physics with objectivity and common sense. In Converging Realities, Roland Omnès is among the first scholars to consider the connection of natural laws with mathematics.

This broad and insightful book presents current scholarship in important subfields of philosophy of science and addresses an interdisciplinary and multidisciplinary readership. It groups carefully selected contributions into the four fields of I) philosophy of physics, II) philosophy of life sciences, III) philosophy of social sciences and values in science, and IV) philosophy of mathematics and formal modeling. Readers will discover research papers by Paul Hoyningen-Huene, Keizo Matsubara, Kian Salimkhani, Andrea Reichenberger, Anne Sophie Meincke, Javier Suárez, Roger Deulofeu, Ludger Jansen, Peter Hucklenbroich, Martin Carrier, Elizaveta Kostrova, Lara Huber, Jens Harbecke, Antonio Piccolomini d’Aragona and Axel Gelfert. This collection fosters dialogue between philosophers of science working in different subfields, and brings readers the finest and latest work across the breadth of the field, illustrating that contemporary philosophy of science has successfully broadened its scope of reflection. It will interest and inspire a wide audience of philosophers as well as scholars of the natural sciences, social sciences and the humanities. The volume shares selected contributions from the prestigious second triennial conference of the German Society for Philosophy of Science/ Gesellschaft für Wissenschaftsphilosophie (GWP.2016, March 8, 2016 – March 11, 2016).

Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.

For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics.

In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

In three volumes, a distinguished group of scholars from a variety of disciplines in the natural and social sciences, the humanities and the arts contribute essays in honor of Robert S. Cohen, on the occasion of his 70th birthday. The range of the essays, as well as their originality, and their critical and historical depth, pay tribute to the extraordinary scope of Professor Cohen's intellectual interests, as a scientist-philosopher and a humanist, and also to his engagement in the world of social and political practice. The essays presented in Physics, Philosophy, and the Scientific Community (Volume I of Essays in Honor of Robert S. Cohen) focus on philosophical and historical issues in contemporary physics: on the origins and conceptual foundations of quantum mechanics, on the reception and understanding of Bohr's and Einstein's work, on the emergence of quantum electrodynamics, and on some of the sharp philosophical and scientific issues that arise in current scientific practice (e.g. in superconductivity research). In addition, several essays deal with critical issues within the philosophy of science, both historical and contemporary: e.g. with Cartesian notions of mechanism in the philosophy of biology; with the language and logic of science - e.g. with new insights concerning the issue of a `physicalistic' language in the arguments of Neurath, Carnap and Wittgenstein; with the notion of `elementary logic'; and with rational and non-rational elements in the history of science. Two original contributions to the history of mathematics and some studies in the comparative sociology of science round off this outstanding collection.

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

A collection of American poems written for children or traditionally enjoyed by children, by such authors as Longfellow, Poe, Eugene Field, Langston Hughes, Dr. Seuss, and Jack Prelutsky.

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

The articles in this collection were all selected from the first five volumes of the Journal of Dialectics of Nature published by the Chinese Academy of Sciences between 1979 and 1985. The Journal was established in 1979 as a comprehensive theoretical publication concerning the history, philosophy and sociology of the natural sciences. It began publication as a response to China's reform, particularly the policy of opening to the outside world. Chinese scholars began to undertake distinctive, original research in these fields. This collection provides a cross-section of their efforts during the initial phase. To enable western scholars to understand the historical process of this change in Chinese academics, Yu Guangyuan's `On the Emancipation of the Mind' and Xu Liangying's `Essay on the Role of Science and Democracy in Society' have been included in this collection. Three of the papers included on the philosophy of science are discussions of philosophical issues in cosmology and biology by scientists themselves. The remaining four are written by philosophers of science and discuss information and cognition, homeostasis and Chinese traditional medicine, the I Ching (Yi Jing) and mathematics, etc. Papers have been selected on the history of both classical and modern science and technology, the most distinctive of which are macro-comparisons of the development of science in China and the west. Some papers discuss the issue of the demarcation of periods in the history of science, the history of ancient Chinese mathematics, astronomy, metallurgy, machinery, medicine, etc. Others discuss the history of modern physics and biology, the history of historiography of science in China and the history of regional development of Chinese science and technology. Also included are biographies of three post-eighteenth-century Chinese scholars, Li Shanlan (1811-1882), Hua Hengfang (1833–1902), and Cai Yuanpei (1868–1940), who contributed greatly to the introduction of western science and scholarship to China. In addition, three short papers have been included introducing the interactions between Chinese scholars and three great western scientists, Niels Bohr, Norbert Wiener, and Robert A. Millikan.

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.

Modern philosophy has benefited immensely from the intelligence and sensitivity, the creative and critical energies, and the lucidity of Polish scholars. Their investigations into the logical and methodological founda tions of mathematics, the physical and biological sciences, ethics and esthetics, psychology, linguistics, economics and jurisprudence, and the social sciences - all are marked by profound and imaginative work. To the centers of empiricist philosophy of science in Vienna, Berlin and Cambridge during the first half of this century, one always added the great school of analytic and methodological studies in Warsaw and Lw6w. To the world centers of Marxist theoretical practice in Berlin, Moscow, Paris, Rome and elsewhere, one must add the Poland of the same era, from Ludwig Krzywicki (1859-1941) onward. (From our preface to Wiatr [1979p. Other movements also have been distinctive in Poland. Phenomenology was developed in the impressive school of Roman Ingarden at Cracow, semiotics from the early work of the philosopher and psychologist Kazimierz Twardowski at Lw6w in the 1890's, with masterful develop ment by his disciples Kotarbinski and Ajdukiewicz onward, conceptual foundations of physics in the incisive methodological reflections of Marian Smoluchowski, and mathematical logic from Jan I:.ukasiewicz and Stanislaw Lesniewski to Tarski, Mostowski, and many others.

This volume presents a selection of papers from the Poincaré Project of the Center for the Philosophy of Science, University of Lisbon, bringing together an international group of scholars with new assessments of Henri Poincaré's philosophy of science—both its historical impact on the foundations of science and mathematics, and its relevance to contemporary philosophical inquiry. The work of Poincaré (1854-1912) extends over many fields within mathematics and mathematical physics. But his scientific work was inseparable from his groundbreaking philosophical reflections, and the scientific ferment in which he participated was inseparable from the philosophical controversies in which he played a pre-eminent part. The subsequent history of the mathematical sciences was profoundly influenced by Poincaré’s philosophical analyses of the relations between and among mathematics, logic, and physics, and, more generally, the relations between formal structures and the world of experience. The papers in this collection illuminate Poincaré’s place within his own historical context as well as the implications of his work for ours.

This volume collects papers presented at the Founding Conference of the European Philosophy of Science Association meeting, held November 2007. It provides an excellent overview of the state of the art in philosophy of science in different European countries.