Founding Mathematics On Semantic Conventions
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Founding Mathematics On Semantic Conventions
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Author : Casper Storm Hansen
language : en
Publisher: Springer Nature
Release Date : 2021-11-04
Founding Mathematics On Semantic Conventions written by Casper Storm Hansen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Mathematics categories.
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Language And Philosophical Problems
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Author : Sören Stenlund
language : en
Publisher: Taylor & Francis
Release Date : 2013-01-11
Language And Philosophical Problems written by Sören Stenlund and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Philosophy categories.
Language and Philosophical Problems investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, Sren Stenlund demonstrates a strategy for tracing out and resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many prima facie different kinds of problems are shown to have common roots, and should thus be dealt and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem.
The Cognitive Science Of Belief
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Author : Julien Musolino
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-17
The Cognitive Science Of Belief written by Julien Musolino 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 2022-11-17 with Psychology categories.
Beliefs play a central role in our lives. They lie at the heart of what makes us human, they shape the organization and functioning of our minds, they define the boundaries of our culture, and they guide our motivation and behavior. Given their central importance, researchers across a number of disciplines have studied beliefs, leading to results and literatures that do not always interact. The Cognitive Science of Belief aims to integrate these disconnected lines of research to start a broader dialogue on the nature, role, and consequences of beliefs. It tackles timeless questions, as well as applications of beliefs that speak to current social issues. This multidisciplinary approach to beliefs will benefit graduate students and researchers in cognitive science, psychology, philosophy, political science, economics, and religious studies.
Logic Mathematics Philosophy Vintage Enthusiasms
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Author : David DeVidi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-23
Logic Mathematics Philosophy Vintage Enthusiasms written by David DeVidi 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 2011-03-23 with Philosophy categories.
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.
The Philosophy Of Mathematics Education
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Author : Paul Ernest
language : en
Publisher: Routledge
Release Date : 2002-11-01
The Philosophy Of Mathematics Education written by Paul Ernest and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-01 with Education categories.
Although many agree that all teaching rests on a theory of knowledge, there has been no in-depth exploration of the implications of the philosophy of mathematics for education. This is Paul Ernest's aim. Building on the work of Lakatos and Wittgenstein it challenges the prevalent notion that mathematical knowledge is certain, absolute and neutral, and offers instead an account of mathematics as a social construction. This has profound educational implications for social issues, including gender, race and multiculturalism; for pedagogy, including investigations and problem solving; and challenges hierarchical views of mathematics, learning and ability. Beyond this, the book offers a well-grounded model of five educational ideologies, each with its own epistemology, values, aims and social group of adherents. An analysis of the impact of these groups on the National Curriculum results in a powerful critique, revealing the questionable assumptions, values and interests upon which it rests. The book finishes on an optimistic note, arguing that pedagogy, left unspecified by the National Curriculum, is the way to achieve the radical aims of educating confident problem posers and solvers who are able to critically evaluate the social uses of mathematics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Lexicon Grammaticorum
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Author : Harro Stammerjohann
language : en
Publisher: Walter de Gruyter
Release Date : 2009-06-02
Lexicon Grammaticorum written by Harro Stammerjohann and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-02 with Language Arts & Disciplines categories.
Lexicon Grammaticorum is a biographical and bibliographical reference work on the history of all the world's traditions of linguistics. Each article consists of a short definition, details of the life, work and influence of the subject and a primary and secondary bibliography. The authors include some of the most renowned linguistic scholars alive today. For the second edition, twenty co-editors were commissioned to propose articles and authors for their areas of expertise. Thus this edition contains some 500 new articles by more than 400 authors from 25 countries in addition to the completely revised 1.500 articles from the first edition. Attention has been paid to making the articles more reader-friendly, in particular by resolving abbreviations in the textual sections. Key features: essential reference book for linguists worldwide 500 new articles over 400 contributors of 25 countries
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
Logic And Philosophy In The Lvov Warsaw School
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Author : Jan Wolenski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic And Philosophy In The Lvov Warsaw School written by Jan Wolenski 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 2012-12-06 with Science categories.
The Lvov-Warsaw School was active in all spheres of philosophy. Its members worked in the border area between philosophy and disci plines such as psychology, linguistics, and literary theory. But its most important achievements were without doubt in logic and philosophical analysis based on logic. The present book is concerned with fields to which the Lvov-Warsaw School made its most important and famous contributions. Data on the School as a whole are included only in the first and last part of the book. This work is based on my monograph (1985), which appeared in Polish. But it is not merely a translation, because some fragments of the Polish version have been omitted (e. g., the chapter on ethics), and some have been revised. Many persons helped me in my work on the book in Polish as well as on the present edition. I must first mention the late Izydora D~mbska, to whom this book is dedicated. On various detailed issues I have availed myself of advice and information given to me by Stefan Amsterdamski, Zdzislaw Augustynek, Kazimierz Czarnota, Henryk Hii, Boleslaw Iwanus, Jacek Jadacki, Jacek KabziIiski, Stanislaw Kiczuk, Tomasz Komendzinski, Janina Kotarbinska, Czeslaw Lejewski, Jerzy Perzanowski, Marian Przet~cki, the late Jerzy Slupecki, Klemens Szaniawski, Stefan Zamecki, Zbigniew Zwinogrodzki i Jan Zygmunt. I am indebted to Jaakko Hintikka for suggesting that my book be trans lated into English and published by Reidel. Olgierd Wojtasiewicz helped me to prepare the English text.
Mathematics Of Program Construction
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Author : Ekaterina Komendantskaya
language : en
Publisher: Springer Nature
Release Date : 2022-09-21
Mathematics Of Program Construction written by Ekaterina Komendantskaya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Computers categories.
This book constitutes the refereed proceedings of the 14th International Conference on Mathematics of Program Construction, MPC 2022, held in Tbilisi, Georgia, in September 2022. The 9 revised full papers presented together with three invited papers were carefully reviewed and selected from 14 submissions. The papers deal with mathematical principles and techniques for constructing computer programs.