Mathematics And Metaphilosophy

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Mathematics and Metaphilosophy

Author : Justin Clarke-Doane
Publisher : Cambridge University Press
ISBN 13 : 1009002295
Total Pages : 105 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Mathematics and Metaphilosophy by : Justin Clarke-Doane

Download or read book Mathematics and Metaphilosophy written by Justin Clarke-Doane and published by Cambridge University Press. This book was released on 2022-06-30 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to the Philosophy of Mathematics

Author : Mark Colyvan
Publisher : Cambridge University Press
ISBN 13 : 0521826020
Total Pages : 199 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to the Philosophy of Mathematics by : Mark Colyvan

Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Morality and Mathematics

Author : Justin Clarke-Doane
Publisher : Oxford University Press
ISBN 13 : 0192556800
Total Pages : 208 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Morality and Mathematics by : Justin Clarke-Doane

Download or read book Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press. This book was released on 2020-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together — and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophy of Mathematics

Author :
Publisher : Elsevier
ISBN 13 : 0080930581
Total Pages : 735 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Philosophy of Mathematics by :

Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Philosophy of Mathematics

Author : James Robert Brown
Publisher : Routledge
ISBN 13 : 1134806442
Total Pages : 181 pages
Book Rating : 4.1/5 (348 download)

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Book Synopsis Philosophy of Mathematics by : James Robert Brown

Download or read book Philosophy of Mathematics written by James Robert Brown and published by Routledge. This book was released on 2005-08-09 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

Philosophy of Mathematics

Author : Paul Benacerraf
Publisher : Cambridge University Press
ISBN 13 : 1107268133
Total Pages : 604 pages
Book Rating : 4.1/5 (72 download)

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Book Synopsis Philosophy of Mathematics by : Paul Benacerraf

Download or read book Philosophy of Mathematics written by Paul Benacerraf and published by Cambridge University Press. This book was released on 1984-01-27 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Thinking about Mathematics

Author : Stewart Shapiro
Publisher : OUP Oxford
ISBN 13 : 0192893068
Total Pages : 323 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Thinking about Mathematics by : Stewart Shapiro

Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Thomas Bedürftig
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110470772
Total Pages : 474 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Philosophy of Mathematics by : Thomas Bedürftig

Download or read book Philosophy of Mathematics written by Thomas Bedürftig and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-10-26 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection

Why Is There Philosophy of Mathematics At All?

Author : Ian Hacking
Publisher : Cambridge University Press
ISBN 13 : 1107729823
Total Pages : 307 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Why Is There Philosophy of Mathematics At All? by : Ian Hacking

Download or read book Why Is There Philosophy of Mathematics At All? written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

The Foundations of Mathematics

Author : Paul Carus
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Foundations of Mathematics by : Paul Carus

Download or read book The Foundations of Mathematics written by Paul Carus and published by . This book was released on 1908 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Philosophy of Mathematics and Natural Science

Author : Hermann Weyl
Publisher : Princeton University Press
ISBN 13 : 0691141207
Total Pages : 332 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Philosophy of Mathematics and Natural Science by : Hermann Weyl

Download or read book Philosophy of Mathematics and Natural Science written by Hermann Weyl and published by Princeton University Press. This book was released on 2009-05-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: History of mathematics.

New Waves in Philosophy of Mathematics

Author : O. Bueno
Publisher : Springer
ISBN 13 : 0230245196
Total Pages : 330 pages
Book Rating : 4.2/5 (32 download)

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Book Synopsis New Waves in Philosophy of Mathematics by : O. Bueno

Download or read book New Waves in Philosophy of Mathematics written by O. Bueno and published by Springer. This book was released on 2009-09-29 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Thought

Author : E.W. Beth
Publisher : Springer Science & Business Media
ISBN 13 : 9401722072
Total Pages : 220 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Mathematical Thought by : E.W. Beth

Download or read book Mathematical Thought written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.

Philosophy of Mathematics

Author : Øystein Linnebo
Publisher : Princeton University Press
ISBN 13 : 0691161402
Total Pages : 214 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Philosophy of Mathematics by : Øystein Linnebo

Download or read book Philosophy of Mathematics written by Øystein Linnebo and published by Princeton University Press. This book was released on 2017-05-30 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but 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 yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

An Historical Introduction to the Philosophy of Mathematics: A Reader

Author : Russell Marcus
Publisher : Bloomsbury Publishing
ISBN 13 : 1472529480
Total Pages : 849 pages
Book Rating : 4.4/5 (725 download)

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Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus

Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Metaphilosophy

Author : Nicholas Rescher
Publisher : Lexington Books
ISBN 13 : 0739199781
Total Pages : 256 pages
Book Rating : 4.7/5 (391 download)

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Book Synopsis Metaphilosophy by : Nicholas Rescher

Download or read book Metaphilosophy written by Nicholas Rescher and published by Lexington Books. This book was released on 2014-10-23 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive mission of metaphilosophy is to facilitate an understanding of how philosophy works—the aim of the enterprise, the instrumental and procedural resources for its work, and the prospect of its success. Nicholas Rescher unites two facets of metaphilosophy to show that historical perspective and forward-thinking normative, or systematic, metaphilosophy cannot be independent of one another. The descriptive, or historical, metaphilosophy provides an account of what has been thought regarding the conduct of philosophical inquiry, and the prescriptive, or normative, metaphilosophy which deliberates about what is to be thought regarding the conduct of philosophizing. Rescher argues that metaphilosophy forms a part of philosophy itself. This is a unique feature of the discipline since the philosophy of biology is not a part of biology and the philosophy of mathematics is not a part of mathematics. Ultimately, the salient features of philosophizing in general—including the inherently controversial and discordant nature of philosophical doctrines—are also bound to afflict metaphilosophy. Thus, only by a careful analysis of the central issues can a plausible view of the enterprise be developed. Metaphilosophy: Philosophy in Philosophical Perspective challenges the static, compartmentalized view of metaphilosophy, providing insight for scholars and students of all areas of philosophy.