Mathematical Pluralism
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Mathematical Pluralism
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Author : Graham Priest
language : en
Publisher: Cambridge University Press
Release Date : 2024-04-30
Mathematical Pluralism written by Graham Priest 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 2024-04-30 with Philosophy categories.
Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.
Mathematical Pluralism
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Author : Graham Priest
language : en
Publisher:
Release Date : 2024-04-16
Mathematical Pluralism written by Graham Priest and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-16 with Philosophy categories.
Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.
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
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.
Mathematics And Metaphilosophy
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Author : Justin Clarke-Doane
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-30
Mathematics And Metaphilosophy written by Justin Clarke-Doane 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 2022-06-30 with Science categories.
This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
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
Companions In Guilt Arguments In Metaethics
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Author : Christopher Cowie
language : en
Publisher: Routledge
Release Date : 2019-09-24
Companions In Guilt Arguments In Metaethics written by Christopher Cowie and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Philosophy categories.
Comparisons between morality and other ‘companion’ disciplines – such as mathematics, religion, or aesthetics – are commonly used in philosophy, often in the context of arguing for the objectivity of morality. This is known as the ‘companions in guilt’ strategy. It has been the subject of much debate in contemporary ethics and metaethics. This volume, the first full length examination of companions in guilt arguments, comprises an introduction by the editors and a dozen new chapters by leading authors in the field. They examine the methodology of companions in guilt arguments and their use in responding to the moral error theory, as well as specific arguments that take mathematics, epistemic norms, or aesthetics as a ‘companion’, and the use of the companions in guilt strategy to vindicate claims to moral knowledge. Companions in Guilt Arguments in Metaethics is essential reading for advanced students and researchers working in moral theory and metaethics, as well as those in epistemology and philosophy of mathematics concerned with the intersection of these subjects with ethics.
Explorations In Ethics
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Author : David Kaspar
language : en
Publisher: Springer Nature
Release Date : 2020-09-01
Explorations In Ethics written by David Kaspar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Philosophy categories.
Explorations in Ethics is a collection of essays with a speculative bent. Its twelve contributors attempt to take ethics thinking in new directions. Ethics is fundamentally a speculative discipline. We sometimes lose sight of that because of our current scholarly practices, which include reliance on a set of traditional works in ethics, deferring to the scholarly literature, drawing from the evidential sources afforded us. This volume breaks the mold. It is committed, first and foremost, to exploring new ground in a methodologically sound way whilst respecting and building on the literature where needed. The contributors range from world renowned ethicists to early-career scholars. The ethical standpoints represented are various and the overall aim of this collection is to stimulate fresh thinking.
The International Science And Evidence Based Education Isee Assessment
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Author : UNESCO MGIEP
language : en
Publisher: UNESCO MGIEP
Release Date : 2022-03-22
The International Science And Evidence Based Education Isee Assessment written by UNESCO MGIEP and has been published by UNESCO MGIEP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-22 with Education categories.
The International Science and Evidence Based Education (ISEE) Assessment is an initiative of the UNESCO Mahatma Gandhi Institute of Education for Peace and Sustainable Development (MGIEP), and is its contribution to the Futures of Education process launched by UNESCO Paris in September 2019. In order to contribute to re-envisioning the future of education with a science and evidence based report, UNESCO MGIEP embarked on the first-ever large-scale assessment of knowledge of education.
Abstract Objects
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Author : José L. Falguera
language : en
Publisher: Springer Nature
Release Date : 2020-05-08
Abstract Objects written by José L. Falguera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-08 with Philosophy categories.
This volume examines the question “Do abstract objects exist?”, presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word "exist” and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered. Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume provides a variety of samples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters.