Model Theory And The Philosophy Of Mathematical Practice
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Model Theory And The Philosophy Of Mathematical Practice
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Author : John T. Baldwin
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Model Theory And The Philosophy Of Mathematical Practice written by John T. Baldwin 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 2018-01-25 with Mathematics categories.
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
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.
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
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.
One True Logic
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Author : Owen Griffiths
language : en
Publisher: Oxford University Press
Release Date : 2022
One True Logic written by Owen Griffiths 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 2022 with Language Arts & Disciplines categories.
One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the challenge from logical pluralism, according to which there is more than one correct logic.
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.
Physics Of Complex Systems
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Author : Dragutin T. Mihailović
language : en
Publisher: CRC Press
Release Date : 2023-09-01
Physics Of Complex Systems written by Dragutin T. Mihailović and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-01 with Science categories.
This book analyses the physics of complex systems to elaborate the problems encountered in teaching and research. Inspired by the of Kurt Gödel (including his incompleteness theorems) it considers the concept of time, the idea of models and the concept of complexity before trying to assess the state of physics in general. Using both general and practical examples, the idea of information is discussed, emphasizing its physical interpretation, debates ideas in depth using examples and evidence to provide detailed considerations on the topics. Based on the authors’ own research on these topics, this book puts forward the idea that the application of information measures can provide new results in the study of complex systems. Helpful for those already familiar with the concepts who wish to deepen their critical understanding, Physics of Complex Systems will be extremely valuable both for people that are already involved in complex systems and also readers beginning their journey into the subject. This work will encourage readers to follow and continue these ideas, enabling them to investigate the various topics further.
Human Interface And The Management Of Information Information Rich And Intelligent Environments
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Author : Sakae Yamamoto
language : en
Publisher: Springer Nature
Release Date : 2021-07-03
Human Interface And The Management Of Information Information Rich And Intelligent Environments written by Sakae Yamamoto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-03 with Computers categories.
The two-volume set LNCS 12765-12766 constitutes the refereed proceedings of the thematic area Human Interface and the Management of Information, HIMI 2021, which was held as part of HCI International 2021 and took place virtually during July 24-29, 2021. The total of 1276 papers and 241 posters included in the 39 HCII 2021 proceedings volumes was carefully reviewed and selected from 5222 submissions. The papers included in the HCII-HIMI volume set were organized in topical sections as follows: Part I: Information presentation; visualization and decision making support; information in VR and multimodal user interfaces; Part II: Learning in information-rich environments; supporting work, collaboration and design; intelligent information environments.
Philosophy And Model Theory
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Author : Tim Button
language : en
Publisher: Oxford University Press
Release Date : 2018-03-09
Philosophy And Model Theory written by Tim Button 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 2018-03-09 with Philosophy categories.
Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.
Philosophy Of Science
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Author : William Marias Malisoff
language : en
Publisher: University of Chicago Press
Release Date : 1993
Philosophy Of Science written by William Marias Malisoff and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.