An Historical Introduction To The Philosophy Of Mathematics A Reader

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An Historical Introduction to the Philosophy of Mathematics: A Reader

Russell Marcus,Mark McEvoy
An Historical Introduction to the Philosophy of Mathematics A Reader Book PDF

Author : Russell Marcus,Mark McEvoy
Publisher : Bloomsbury Publishing
Page : 896 pages
File Size : 50,7 Mb
Release : 2016-02-11
Category : Philosophy
ISBN : 9781472529480

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An Historical Introduction to the Philosophy of Mathematics: A Reader by Russell Marcus,Mark McEvoy Pdf

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.

An Historical Introduction to the Philosophy of Mathematics

Russell Marcus
An Historical Introduction to the Philosophy of Mathematics Book PDF

Author : Russell Marcus
Publisher : Createspace Independent Publishing Platform
Page : 318 pages
File Size : 43,6 Mb
Release : 2017-07-22
Category : Electronic
ISBN : 1973776375

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An Historical Introduction to the Philosophy of Mathematics by Russell Marcus Pdf

An Historical Introduction to the Philosophy of Mathematics By Russell Marcus

An Historical Introduction to the Philosophy of Mathematics: A Reader

Russell Marcus,Mark McEvoy
An Historical Introduction to the Philosophy of Mathematics A Reader Book PDF

Author : Russell Marcus,Mark McEvoy
Publisher : Bloomsbury Publishing
Page : 849 pages
File Size : 51,9 Mb
Release : 2016-02-11
Category : Philosophy
ISBN : 9781472525345

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An Historical Introduction to the Philosophy of Mathematics: A Reader by Russell Marcus,Mark McEvoy Pdf

As the first comprehensive collection of historical readings in the philosophy of mathematics, this much-needed introduction reveals the rich history of the subject. Focusing on the philosophy of mathematics before the 20th-century, An Historical Introduction to the Philosophy of Mathematics: A Readerbrings together an impressive collection of primary sources from ancient, medieval 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 Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with modern thinkers. While a selection of recent texts offering insights the current state of the discipline, clearly illustrate the development of the subject. Presenting historical background essential to understanding contemporary trends, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates studying the philosophy of mathematics.

An Introduction to the Philosophy of Mathematics

Mark Colyvan
An Introduction to the Philosophy of Mathematics Book PDF

Author : Mark Colyvan
Publisher : Cambridge University Press
Page : 199 pages
File Size : 46,6 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780521826020

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An Introduction to the Philosophy of Mathematics by Mark Colyvan Pdf

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Introduction to Mathematical Philosophy

Bertrand Russell
Introduction to Mathematical Philosophy Book PDF

Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 40,8 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240

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Introduction to Mathematical Philosophy by Bertrand Russell Pdf

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

Set Theory and its Philosophy

Michael Potter
Set Theory and its Philosophy Book PDF

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 44,6 Mb
Release : 2004-01-15
Category : Philosophy
ISBN : 9780191556432

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Set Theory and its Philosophy by Michael Potter Pdf

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Historical Introduction to Mathematical Literature

G a Miller
Historical Introduction to Mathematical Literature Book PDF

Author : G a Miller
Publisher : Legare Street Press
Page : 0 pages
File Size : 45,8 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 1022022806

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Historical Introduction to Mathematical Literature by G a Miller Pdf

Gain insight into the world of mathematical literature with this informative guide. Published in 1916, this book covers the history and development of mathematics, as well as the major themes and trends in mathematical literature up to that time. An essential resource for anyone interested in the history and philosophy of mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Wittgenstein on Mathematics

Severin Schroeder
Wittgenstein on Mathematics Book PDF

Author : Severin Schroeder
Publisher : Routledge
Page : 238 pages
File Size : 44,7 Mb
Release : 2020-12-29
Category : Philosophy
ISBN : 9781000318272

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Wittgenstein on Mathematics by Severin Schroeder Pdf

This book offers a detailed account and discussion of Ludwig Wittgenstein’s philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege’s logicist attempt to provide arithmetic with a foundation and Wittgenstein’s criticisms of it, followed by sketches of Wittgenstein’s early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein’s mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity — calculation — rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein’s provocative views on Hilbert’s Formalism and the quest for consistency proofs and on Gödel’s incompleteness theorems.

History and Philosophy of Modern Mathematics

William Aspray,Philip Kitcher
History and Philosophy of Modern Mathematics Book PDF

Author : William Aspray,Philip Kitcher
Publisher : U of Minnesota Press
Page : 396 pages
File Size : 46,8 Mb
Release : 1988
Category : Mathematics
ISBN : 9780816615674

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History and Philosophy of Modern Mathematics by William Aspray,Philip Kitcher Pdf

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Philosophical and Mathematical Logic

Harrie de Swart
Philosophical and Mathematical Logic Book PDF

Author : Harrie de Swart
Publisher : Springer
Page : 539 pages
File Size : 52,6 Mb
Release : 2018-11-28
Category : Philosophy
ISBN : 9783030032555

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Philosophical and Mathematical Logic by Harrie de Swart Pdf

This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo

The Best Writing on Mathematics 2016

Mircea Pitici
The Best Writing on Mathematics 2016 Book PDF

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 408 pages
File Size : 55,8 Mb
Release : 2017-02-14
Category : Mathematics
ISBN : 9781400885602

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The Best Writing on Mathematics 2016 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Thinking about Mathematics

Stewart Shapiro
Thinking about Mathematics Book PDF

Author : Stewart Shapiro
Publisher : OUP Oxford
Page : 323 pages
File Size : 50,7 Mb
Release : 2000-07-13
Category : Philosophy
ISBN : 9780192893062

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Thinking about Mathematics by Stewart Shapiro Pdf

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Philosophy of Mathematics

Øystein Linnebo
Philosophy of Mathematics Book PDF

Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 55,8 Mb
Release : 2020-03-24
Category : Mathematics
ISBN : 9780691202297

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Philosophy of Mathematics by Øystein Linnebo Pdf

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

The Philosophy of Set Theory

Mary Tiles
The Philosophy of Set Theory Book PDF

Author : Mary Tiles
Publisher : Courier Corporation
Page : 258 pages
File Size : 50,6 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486138558

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The Philosophy of Set Theory by Mary Tiles Pdf

DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Mathematics: A Concise History and Philosophy

W.S. Anglin
Mathematics A Concise History and Philosophy Book PDF

Author : W.S. Anglin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461208754

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Mathematics: A Concise History and Philosophy by W.S. Anglin Pdf

This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.