Mathematics in Philosophy
Mathematics in Philosophy

Author: Charles D. Parsons

Publisher: Cornell University Press

Published: 2018-08-06

Total Pages: 367

ISBN-13: 1501729322

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This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.

18 Unconventional Essays on the Nature of Mathematics
18 Unconventional Essays on the Nature of Mathematics

Author: Reuben Hersh

Publisher: Springer Science & Business Media

Published: 2006-01-16

Total Pages: 346

ISBN-13: 0387298312

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Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

New Perspectives on Mathematical Practices
New Perspectives on Mathematical Practices

Author: Bart Van Kerkhove

Publisher: World Scientific

Published: 2009

Total Pages: 248

ISBN-13: 9812812237

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This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.

Mathematics and Its Logics
Mathematics and Its Logics

Author: Geoffrey Hellman

Publisher: Cambridge University Press

Published: 2021-02-04

Total Pages: 296

ISBN-13: 1316999602

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In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.

The Reason's Proper Study
The Reason's Proper Study

Author: Bob Hale

Publisher: Oxford University Press

Published: 2003

Total Pages: 470

ISBN-13: 0199266328

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Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the most powerful presentation yet of a neo-Fregean program.

New Directions in the Philosophy of Mathematics
New Directions in the Philosophy of Mathematics

Author: Thomas Tymoczko

Publisher: Princeton University Press

Published: 1998-02

Total Pages: 458

ISBN-13: 9780691034980

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The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Humanizing Mathematics and its Philosophy
Humanizing Mathematics and its Philosophy

Author: Bharath Sriraman

Publisher: Birkhäuser

Published: 2017-11-07

Total Pages: 357

ISBN-13: 331961231X

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This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

The Philosophy of Mathematics
The Philosophy of Mathematics

Author: Stephan Körner

Publisher:

Published: 1968

Total Pages: 198

ISBN-13: 9780090566419

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Concise, accessible sketches of the views of Plato, Aristotle, Leibniz, and Kant highlight this study of the general structure and foundation of pure and applied mathematics. Author Stephan Korner dedicates two chapters apiece -- one expository and one critical -- to each of the three main modern schools of thought on mathematical philosophy: the formalists, the logicists, and the intuitionists. After critically examining the propositions and theories of each philosophy, Korner presents a new position concerning the relation between mathematical theories, empirical data, and philosophical presuppositions. The "Review of Metaphysics" praised this volume as "a lucid and stimulating essay which combines accuracy and sophistication with a minimum of technical language." Compact but comprehensive, this nontechnical introduction will appeal to professionals, students, and other readers interested in the intersection of philosophical problems with pure and applied mathematics.

Philosophy of Mathematics in the Twentieth Century
Philosophy of Mathematics in the Twentieth Century

Author: Charles Parsons

Publisher: Harvard University Press

Published: 2014-03-10

Total Pages: 365

ISBN-13: 0674419499

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In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.