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

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: 8530
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History of mathematics.

Order and Organism

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: 7578
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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.

Mind and Nature

Mind and Nature

Selected Writings on Philosophy, Mathematics, and Physics

  • Author: Hermann Weyl
  • Publisher: Princeton University Press
  • ISBN: 9781400833320
  • Category: Mathematics
  • Page: 272
  • View: 887
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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.

Levels of Infinity

Levels of Infinity

Selected Writings on Mathematics and Philosophy

  • Author: Hermann Weyl
  • Publisher: Courier Corporation
  • ISBN: 0486266931
  • Category: Mathematics
  • Page: 208
  • View: 8802
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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.

Converging Realities

Converging Realities

Toward a Common Philosophy of Physics and Mathematics

  • Author: Roland Omnès
  • Publisher: Princeton University Press
  • ISBN: 9780691115306
  • Category: Mathematics
  • Page: 264
  • View: 4772
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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.

Reading Natural Philosophy

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: 1680
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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.

A History of Natural Philosophy

A History of Natural Philosophy

From the Ancient World to the Nineteenth Century

  • Author: Edward Grant
  • Publisher: Cambridge University Press
  • ISBN: 0521869315
  • Category: History
  • Page: 361
  • View: 634
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This book describes how natural philosophy and exact mathematical sciences joined together to make the Scientific Revolution possible.

Philosophy of Science

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: 8515
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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).

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

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: 7690
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Eleven distinguished historians of science explore natural philosophy and mathematics in the Middle Ages.

Three Views of Logic

Three Views of Logic

Mathematics, Philosophy, and Computer Science

  • Author: Donald W. Loveland,Richard E. Hodel,S. G. Sterrett
  • Publisher: Princeton University Press
  • ISBN: 140084875X
  • Category: Mathematics
  • Page: 344
  • View: 8497
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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

The Philosophy of Science

The Philosophy of Science

  • Author: Alexander Rosenberg
  • Publisher: Psychology Press
  • ISBN: 0415939275
  • Category: Science
  • Page: N.A
  • View: 9803
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Representing and Intervening

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: 4456
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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.

The History and Philosophy of Science

The History and Philosophy of Science

  • Author: Daniel McKaughan,Holly VandeWall
  • Publisher: Bloomsbury Publishing
  • ISBN: 1474232744
  • Category: Philosophy
  • Page: 1104
  • View: 7482
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The History and Philosophy of Science: A Reader brings together seminal texts from antiquity to the end of the nineteenth century and makes them accessible in one volume for the first time. With readings from Aristotle, Aquinas, Copernicus, Galileo, Descartes, Newton, Lavoisier, Linnaeus, Darwin, Faraday, and Maxwell, it analyses and discusses major classical, medieval and modern texts and figures from the natural sciences. Grouped by topic to clarify the development of methods and disciplines and the unification of theories, each section includes an introduction, suggestions for further reading and end-of-section discussion questions, allowing students to develop the skills needed to: § read, interpret, and critically engage with central problems and ideas from the history and philosophy of science § understand and evaluate scientific material found in a wide variety of professional and popular settings § appreciate the social and cultural context in which scientific ideas emerge § identify the roles that mathematics plays in scientific inquiry Featuring primary sources in all the core scientific fields - astronomy, physics, chemistry, and the life sciences - The History and Philosophy of Science: A Reader is ideal for students looking to better understand the origins of natural science and the questions asked throughout its history. By taking a thematic approach to introduce influential assumptions, methods and answers, this reader illustrates the implications of an impressive range of values and ideas across the history and philosophy of Western science.

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

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: 3743
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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

Philosophy of Mathematics

Structure and Ontology

  • Author: Stewart Shapiro
  • Publisher: Oxford University Press
  • ISBN: 9780198025450
  • Category: Philosophy
  • Page: 296
  • View: 2830
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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.

Phenomenology and the Natural Sciences

Phenomenology and the Natural Sciences

  • Author: Joseph J. Kockelmans
  • Publisher: Northwestern University Press
  • ISBN: 9780810106130
  • Category: Philosophy
  • Page: 520
  • View: 7532
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Concepts of Proof in Mathematics, Philosophy, and Computer Science

Concepts of Proof in Mathematics, Philosophy, and Computer Science

  • Author: Dieter Probst,Peter Schuster
  • Publisher: Walter de Gruyter GmbH & Co KG
  • ISBN: 1501502646
  • Category: Philosophy
  • Page: 384
  • View: 9062
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This book provides the reader with research arising from the Humboldt-Kolleg ‘Proof’ held in Bern in fall 2013, which gathered leading experts actively involved with the concept ‘proof’ in philosophy, mathematics and computer science. This volume aims to do justice to the breadth and depth of the subject and presents relevant current conceptions and technical advances featuring ‘proof’ in those fields.

Naturalizing Logico-Mathematical Knowledge

Naturalizing Logico-Mathematical Knowledge

Approaches from Philosophy, Psychology and Cognitive Science

  • Author: Sorin Bangu
  • Publisher: Routledge
  • ISBN: 1351998447
  • Category: Mathematics
  • Page: 306
  • View: 6936
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This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Physics, Philosophy, and the Scientific Community

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: 9702
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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 Nature of Classification

The Nature of Classification

Relationships and Kinds in the Natural Sciences

  • Author: J. Wilkins,M. Ebach
  • Publisher: Springer
  • ISBN: 1137318120
  • Category: Science
  • Page: 197
  • View: 5291
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Discussing the generally ignored issue of the classification of natural objects in the philosophy of science, this book focuses on knowledge and social relations, and offers a way to understand classification as a necessary aspect of doing science.