Mathematics And Philosophy
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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.
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.
The Oxford Handbook Of Philosophy Of Mathematics And Logic
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 2005-02-10
The Oxford Handbook Of Philosophy Of Mathematics And Logic written by Stewart Shapiro and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-10 with Mathematics categories.
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
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.
The Philosophy Of Mathematical Practice
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Author : Paolo Mancosu
language : en
Publisher: OUP Oxford
Release Date : 2008-06-19
The Philosophy Of Mathematical Practice written by Paolo Mancosu and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-19 with Philosophy categories.
Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.
Philosophy Of Mathematics
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Author : Paul Benacerraf
language : en
Publisher: Cambridge University Press
Release Date : 1983
Philosophy Of Mathematics written by Paul Benacerraf 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 1983 with Mathematics categories.
Seminal articles in the philosophy of mathematics by Russell, Quine, Gödel and other major thinkers.
The Adventure Of Reason
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Author : Paolo Mancosu
language : en
Publisher: OUP Oxford
Release Date : 2014-01-09
The Adventure Of Reason written by Paolo Mancosu and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Philosophy categories.
Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.
Philosophy Of Mathematics
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Author : AHMET. CEVIK
language : en
Publisher: CRC Press
Release Date : 2021-11-10
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 2021-11-10 with categories.
The philosophy of mathematics is an exciting subject. This book explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians into thinking 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.
Frege
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Author : Michael Dummett
language : en
Publisher: Harvard University Press
Release Date : 1991
Frege written by Michael Dummett 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 1991 with Mathematics categories.
No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.
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.