From Foundations To Philosophy Of Mathematics
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From Foundations To Philosophy Of Mathematics
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Author : Joan Roselló
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2011-10-18
From Foundations To Philosophy Of Mathematics written by Joan Roselló and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-18 with Mathematics categories.
From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Gödel. Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell’s type theory, Zermelo’s set theory and Gödel’s incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.
Philosophical Approaches To The Foundations Of Logic And Mathematics
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Author : Marcin Trepczyński
language : en
Publisher: BRILL
Release Date : 2021-01-25
Philosophical Approaches To The Foundations Of Logic And Mathematics written by Marcin Trepczyński and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-25 with Philosophy categories.
Eleven papers collected in the volume Philosophical Approaches to the Foundations of Logic and Mathematics address various aspects of the “roots”, basic concepts and the nature of logic and mathematics. Taken together, these papers reveal how many serious philosophical problems lie at the foundations of logic and mathematics. The topics discussed in this volume include: transcending anti-foundationalism and two concurrent trends of "anthropological" and "practical" understanding of the foundations of mathematics, new approaches to mathematical realism, the “roots” of logic in a genetic perspective, the primacy of truth or satisfaction, and the “effectiveness” of mathematics in terms of categorical semantics.
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
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.
Why Is There Philosophy Of Mathematics At All
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Author : Ian Hacking
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-30
Why Is There Philosophy Of Mathematics At All written by Ian Hacking 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 2014-01-30 with Mathematics categories.
Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.
Pluralism In Mathematics A New Position In Philosophy Of Mathematics
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Author : Michèle Friend
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-20
Pluralism In Mathematics A New Position In Philosophy Of Mathematics written by Michèle Friend 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 2013-11-20 with Science categories.
This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.
The Foundations Of Mathematics
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Author : Paul Carus
language : en
Publisher:
Release Date : 1908
The Foundations Of Mathematics written by Paul Carus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1908 with Geometry categories.
Philosophy Of Mathematics
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Author : Thomas Bedürftig
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-10-26
Philosophy Of Mathematics written by Thomas Bedürftig and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-26 with Mathematics categories.
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
An Historical Introduction To The Philosophy Of Mathematics A Reader
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Author : Russell Marcus
language : en
Publisher: Bloomsbury Publishing
Release Date : 2016-02-11
An Historical Introduction To The Philosophy Of Mathematics A Reader written by Russell Marcus and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Philosophy categories.
A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Reflections On The Foundations Of Mathematics
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.