The Philosophy Of Mathematics And Natural Laws

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The Philosophy Of Mathematics And Natural Laws

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Author : Noel Curran
language : en
Publisher: Routledge
Release Date : 2019-07-23

The Philosophy Of Mathematics And Natural Laws written by Noel Curran and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Philosophy categories.

First published in 1997, this title is a sequel to Dr Noel Curran's first book The Logical Universe: The Real Universe (published by Ashgate under the Avebury imprint, 1994). The philosophy of mathematics in this book is based on ideas of Sir William Rowan Hamilton on the ordinal character of numbers, the real numbers, the measure numbers, scalar numbers and the extension to vectors. The final extension is to Hamilton’s quaternions. This algebra is interpreted as the mathematics of spin. This led to a a new theory of time and space which is Euclidian. The motion of spin is absolute, no frame of reference is required. If time is assumed to have a beginning it would be asymmetric with an arrow. This concept is applied to the laws of nature, which are symmetrical. This is another Copernican Revolution in three aspects: absolute time is restored, time has an arrow - is asymmetric, and thirdly the theory is based on the motion of spin which is absolute and more fundamental than the motion of translation. This opens the way to the final unification of physics.

Philosophy Of Mathematics And Natural Science

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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 2009-05-17

Philosophy Of Mathematics And Natural Science written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-17 with Mathematics categories.

History of mathematics.

The Applicability Of Mathematics As A Philosophical Problem

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Author : Mark Steiner
language : en
Publisher: Harvard University Press
Release Date : 2009-07-01

The Applicability Of Mathematics As A Philosophical Problem written by Mark Steiner and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Mathematics categories.

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions. The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.

Mind And Nature

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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 2009-03-31

Mind And Nature written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-31 with Mathematics categories.

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.

Introduction To Mathematical Philosophy

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Author : Bertrand Russell
language : en
Publisher: Courier Corporation
Release Date : 1993-01-01

Introduction To Mathematical Philosophy written by Bertrand Russell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

An Introduction To The Philosophy Of Mathematics

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Author : Mark Colyvan
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14

An Introduction To The Philosophy Of Mathematics written by Mark Colyvan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Philosophy Of Mathematics

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Author : Øystein Linnebo
language : en
Publisher: Princeton University Press
Release Date : 2020-03-24

Philosophy Of Mathematics written by Øystein Linnebo and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-24 with Mathematics categories.

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

The Argument Of Mathematics

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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01

The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Thinking About Mathematics

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Author : Stewart Shapiro
language : en
Publisher: OUP Oxford
Release Date : 2000-07-13

Thinking About Mathematics written by Stewart Shapiro and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-13 with Philosophy categories.

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques