# Search Results for "philosophy-of-mathematics-and-natural-science"

## Philosophy of Mathematics and Natural Science

**Author**: Hermann Weyl,Frank Wilczek**Publisher:**Princeton University Press**ISBN:**9780691141206**Category:**Mathematics**Page:**311**View:**2154

History of mathematics.

## Mind and Nature

*Selected Writings on Philosophy, Mathematics, and Physics*

**Author**: Hermann Weyl**Publisher:**Princeton University Press**ISBN:**9781400833320**Category:**Mathematics**Page:**272**View:**3730

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

## Reading Natural Philosophy

*Essays in the History and Philosophy of Science and Mathematics*

**Author**: David B. Malament**Publisher:**Open Court Publishing**ISBN:**9780812695076**Category:**Philosophy**Page:**424**View:**4996

In this book, 13 leading philosophers of science focus on the work of Professor Howard Stein, best known for his study of the intimate connection between philosophy and natural science. Also included is a comprehensive bibliography of Howard Stein's writings.

## Levels of Infinity

*Selected Writings on Mathematics and Philosophy*

**Author**: Hermann Weyl**Publisher:**Courier Corporation**ISBN:**0486266931**Category:**Mathematics**Page:**208**View:**2588

Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.

## Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages

*Essays in Honour of Marshall Clagett*

**Author**: Edward Grant,John Emery Murdoch**Publisher:**Cambridge University Press**ISBN:**052132260X**Category:**Science**Page:**337**View:**3765

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

## Philosophy of Science

*Between the Natural Sciences, the Social Sciences, and the Humanities*

**Author**: Alexander Christian,David Hommen,Nina Retzlaff,Gerhard Schurz**Publisher:**Springer**ISBN:**3319725777**Category:**Philosophy**Page:**274**View:**1632

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).

## The Philosophy of Science

**Author**: Alexander Rosenberg**Publisher:**Psychology Press**ISBN:**0415939275**Category:**Science**Page:**N.A**View:**5929

## Order and Organism

*Steps Toward a Whiteheadian Philosophy of Mathematics and the Natural Sciences*

**Author**: Murray Code**Publisher:**SUNY Press**ISBN:**9780873959513**Category:**Mathematics**Page:**265**View:**4778

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.

## Converging Realities

*Toward a Common Philosophy of Physics and Mathematics*

**Author**: Roland Omnès**Publisher:**Princeton University Press**ISBN:**9780691115306**Category:**Mathematics**Page:**264**View:**3561

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.

## Physics, Philosophy, and the Scientific Community

*Essays in the philosophy and history of the natural sciences and mathematics In honor of Robert S. Cohen*

**Author**: Kostas Gavroglu,John Stachel,Marx W. Wartofsky**Publisher:**Springer Science & Business Media**ISBN:**9401726582**Category:**Science**Page:**388**View:**8413

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.

## Representing and Intervening

*Introductory Topics in the Philosophy of Natural Science*

**Author**: Ian Hacking**Publisher:**Cambridge University Press**ISBN:**110726815X**Category:**Science**Page:**N.A**View:**2920

This 1983 book is a lively and clearly written introduction to the philosophy of natural science, organized around the central theme of scientific realism. It has two parts. 'Representing' deals with the different philosophical accounts of scientific objectivity and the reality of scientific entities. The views of Kuhn, Feyerabend, Lakatos, Putnam, van Fraassen, and others, are all considered. 'Intervening' presents the first sustained treatment of experimental science for many years and uses it to give a new direction to debates about realism. Hacking illustrates how experimentation often has a life independent of theory. He argues that although the philosophical problems of scientific realism can not be resolved when put in terms of theory alone, a sound philosophy of experiment provides compelling grounds for a realistic attitude. A great many scientific examples are described in both parts of the book, which also includes lucid expositions of recent high energy physics and a remarkable chapter on the microscope in cell biology.

## Structures and Algorithms

*Mathematics and the Nature of Knowledge*

**Author**: Jens Erik Fenstad**Publisher:**Springer**ISBN:**3319729748**Category:**Philosophy**Page:**134**View:**3861

This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.

## The Concept and the Role of the Model in Mathematics and Natural and Social Sciences

*Proceedings of the Colloquium sponsored by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences organized at Utrecht, January 1960*

**Author**: Hans Freudenthal**Publisher:**Springer**ISBN:**9027700176**Category:**Science**Page:**204**View:**2701

Proceedings of the Colloquium sponsored by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences organized at Utrecht, January 1960.

## Philosophy of Mathematics

*Structure and Ontology*

**Author**: Stewart Shapiro**Publisher:**Oxford University Press**ISBN:**9780198025450**Category:**Philosophy**Page:**296**View:**2485

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.

## The Nature of Mathematical Knowledge

**Author**: Philip Kitcher**Publisher:**Oxford University Press on Demand**ISBN:**0195035410**Category:**Mathematics**Page:**287**View:**8303

This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledgeand its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.

## Philosophy, Mathematics and Modern Physics

*A Dialogue*

**Author**: Enno Rudolph,Ion-Olimpiu Stamatescu**Publisher:**Springer Science & Business Media**ISBN:**3642788084**Category:**Science**Page:**244**View:**2359

In recent times a new dialogue has begun between the natural sciences and the humanities. This is particularly true of physics and philosophy, whose sphere of mutual interest expanded significantly with the advent of quantum mechanics. Among other topics, the discussion covers the evolution of theories, the role of mathematics in the physical sciences, the perception and cognition of nature and definitions of space and time. In contrast to the custom of the last two centuries, mathematics - the language of physics - is once again finding a respected place in the discourse of philosophers. The interdisciplinary communication between philosophers, mathematicians and physicists will be given new impetus by the thoughtful and wide-ranging contributions to this book.

## Symmetries of Nature

*A Handbook for Philosophy of Nature and Science*

**Author**: Klaus Mainzer**Publisher:**Walter de Gruyter**ISBN:**3110886936**Category:**Philosophy**Page:**694**View:**3396

## Proof and Other Dilemmas

*Mathematics and Philosophy*

**Author**: Roger Simons**Publisher:**MAA**ISBN:**9780883855676**Category:**Mathematics**Page:**346**View:**6194

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.

## Chinese Studies in the History and Philosophy of Science and Technology

**Author**: Fan Dainian,Robert S. Cohen**Publisher:**Springer Science & Business Media**ISBN:**9401587175**Category:**Science**Page:**483**View:**4952

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.

## Phenomenology, Logic, and the Philosophy of Mathematics

**Author**: Richard L. Tieszen**Publisher:**Cambridge University Press**ISBN:**9780521837828**Category:**Mathematics**Page:**357**View:**5894

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