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A Mathematical Prelude to the Philosophy of Mathematics

Author : Stephen Pollard

Publisher : Springer

Page : 206 pages

File Size : 47,48 MB

Release : 2014-05-12

Category : Science

ISBN : 3319058169

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Book Description

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.



The Adventure of Reason

Author : Paolo Mancosu

Publisher : OUP Oxford

Page : 632 pages

File Size : 47,88 MB

Release : 2014-01-09

Category : Philosophy

ISBN : 0191021997

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Book Description

Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.



Philosophy of Mathematics

Author : Paul Benacerraf

Publisher : Cambridge University Press

Page : 604 pages

File Size : 33,63 MB

Release : 1984-01-27

Category : Science

ISBN : 1107268133

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Book Description

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.



An Introduction to the Philosophy of Mathematics

Author : Mark Colyvan

Publisher : Cambridge University Press

Page : 199 pages

File Size : 20,40 MB

Release : 2012-06-14

Category : Mathematics

ISBN : 0521826020

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Book Description

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



Mathematical Thought

Author : E.W. Beth

Publisher : Springer Science & Business Media

Page : 220 pages

File Size : 35,44 MB

Release : 2013-06-29

Category : Science

ISBN : 9401722072

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Book Description

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.



From Mathematics to Philosophy (Routledge Revivals)

Author : Hao Wang

Publisher : Routledge

Page : 445 pages

File Size : 13,21 MB

Release : 2016-06-10

Category : Philosophy

ISBN : 1134884338

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Book Description

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.



Prelude to Mathematics

Author : W. W. Sawyer

Publisher : Courier Corporation

Page : 228 pages

File Size : 32,94 MB

Release : 2012-04-19

Category : Mathematics

ISBN : 0486152774

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Book Description

This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.



Philosophical Introduction to Set Theory

Author : Stephen Pollard

Publisher : Courier Dover Publications

Page : 196 pages

File Size : 22,18 MB

Release : 2015-07-20

Category : Mathematics

ISBN : 0486805824

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Book Description

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.



An Historical Introduction to the Philosophy of Mathematics: A Reader

Author : Russell Marcus

Publisher : Bloomsbury Publishing

Page : 849 pages

File Size : 29,62 MB

Release : 2016-02-11

Category : Philosophy

ISBN : 1472529480

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Book Description

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.



Introducing Philosophy of Mathematics

Author : Michèle Friend

Publisher : Routledge

Page : 224 pages

File Size : 17,5 MB

Release : 2007

Category : Mathematics

ISBN :

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Book Description

This volume introduces the central debates in the philosophy of mathematics and examines the standard theories of mathematics: platonism and realism, logicism, formalism, constructivism and structuralism.