The Philosophy Of Mathematics
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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.
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.
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.
Lectures On The Philosophy Of Mathematics
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Author : Joel David Hamkins
language : en
Publisher: MIT Press
Release Date : 2021-03-09
Lectures On The Philosophy Of Mathematics written by Joel David Hamkins and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Mathematics categories.
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Introducing Philosophy Of Mathematics
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Author : Michele Friend
language : en
Publisher: Routledge
Release Date : 2014-12-05
Introducing Philosophy Of Mathematics written by Michele Friend and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Philosophy categories.
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
Philosophy Of Mathematics
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Author : Ahmet Cevik
language : en
Publisher: CRC Press
Release Date : 2021-11-09
Philosophy Of Mathematics written by Ahmet Cevik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-09 with Mathematics categories.
The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
New Directions In The Philosophy Of Mathematics
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Author : Thomas Tymoczko
language : en
Publisher: Princeton University Press
Release Date : 1998-02
New Directions In The Philosophy Of Mathematics written by Thomas Tymoczko 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 1998-02 with Mathematics categories.
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.
Philosophy Of Mathematics
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Author : James Robert Brown
language : en
Publisher: Psychology Press
Release Date : 1999
Philosophy Of Mathematics written by James Robert Brown and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Philosophy of Mathematics is an excellent introductory text for philosophy of mathematics. Clear and engaging, it moves at a good pace, is easy to understand and student friendly.
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.
Philosophy Of Mathematics
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Author : James Robert Brown
language : en
Publisher: Psychology Press
Release Date : 1999
Philosophy Of Mathematics written by James Robert Brown and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.