Pluralism In Mathematics
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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.
Humanizing Mathematics And Its Philosophy
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Author : Bharath Sriraman
language : en
Publisher: Birkhäuser
Release Date : 2017-11-07
Humanizing Mathematics And Its Philosophy written by Bharath Sriraman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
Pluralism In Mathematics
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Author : Michele Friend
language : en
Publisher:
Release Date : 2013-09-30
Pluralism In Mathematics written by Michele Friend and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-30 with categories.
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.
Logic Epistemology And The Unity Of Science
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Author : Shahid Rahman
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-25
Logic Epistemology And The Unity Of Science written by Shahid Rahman 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 2004-10-25 with Philosophy categories.
This is the first volume in a series aimed at considering the scientific enterprise in light of recent developments in logic and philosophy. This work explores new ways of achieving the integration of science in all its diversity.
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.
Logical Pluralism And Logical Consequence
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Author : Erik Stei
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-30
Logical Pluralism And Logical Consequence written by Erik Stei 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 2023-03-30 with Philosophy categories.
A detailed discussion and rejection of the view that there is more than one correct logic.
New Waves In Philosophy Of Mathematics
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Author : O. Bueno
language : en
Publisher: Springer
Release Date : 2009-09-29
New Waves In Philosophy Of Mathematics written by O. Bueno and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-29 with Philosophy categories.
Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.
Multicivilizational Exchanges In The Making Of Modern Science
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Author : Arun Bala
language : en
Publisher: Springer Nature
Release Date : 2024-09-09
Multicivilizational Exchanges In The Making Of Modern Science written by Arun Bala and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Social Science categories.
This book explores how and why exchanges across civilizations have come to enrich science today. The dialogical dimension of the history of science has long been marginalized by an excessive concern on why modern science emerged in Europe, but not in any of the advanced civilizations of the East. This focus upon what has been called Joseph Needham's "Grand Comparative Question" ignores his other project, focused on showing how dialogues between civilizations have nurtured science. Needham's "Grand Dialogical Question" – if we may call it that by parity – has directly or indirectly inspired a vast body of literature showing how interconnections of civilizations over the last three thousand years, and exchanges of cosmological, mathematical, geographical, physical, biological and medical technologies, techniques, practices and knowledge, have been woven together to produce current science. Bringing together scholars whose research range across multiple civilizations and disciplines, this book investigates the scope and limits of Needham's dialogical vision for science.
The Problem Of Plurality Of Logics
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Author : Pavel Arazim
language : en
Publisher: Bloomsbury Publishing
Release Date : 2021-08-12
The Problem Of Plurality Of Logics written by Pavel Arazim and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-12 with Philosophy categories.
As the foundation of our rationality, logic has traditionally been considered fixed, stable and constant. This conception of the discipline has been challenged recently by the plurality of logics and in this book, Pavel Arazim extends the debate to offer a new view of logic as dynamic and without a definite, specific shape. The Problem of Plurality of Logics examines the origins of our standard view of logic alongside Kant's theories, the holistic view, the issue of logic's pragmatic significance and Robert Brandom's logical expressivism. Arazim then draws on proof-theoretical approaches to present a convincing argument for a dynamic version of logical inferentialism, which opens space for a new freedom to modify our own logic. He explores the scope, possibilities and limits of this freedom in order to highlight the future paths logic could take, as a motivation for further research. Marking a departure from logical monism and also from the recent doctrine of logical pluralism in its various forms, this book addresses current debates concerning the expressive role of logic and contributes to a lively area of discussion in analytic philosophy.