Naturalism in Mathematics

Author: Penelope Maddy

Publisher: Oxford University Press

ISBN: 9780198235736

Category: Mathematics

Page: 254

View: 9877

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Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress inwork on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view--realism--is assessed and finally rejected in favour of another--naturalism--which attends less tometaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomaticstatus in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
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Platonism, Naturalism, and Mathematical Knowledge

Author: James Robert Brown

Publisher: Routledge

ISBN: 1136580379

Category: Philosophy

Page: 194

View: 2274

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This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.
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Naturalism in Mathematics

Author: Penelope Maddy

Publisher: Oxford University Press on Demand

ISBN: 9780198250753

Category: Philosophy

Page: 254

View: 4915

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Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favour of another approach--naturalism--which attends more closely to practical considerations drawn from within mathematics itself. Penelope Maddy defines naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original discussion is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
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Philosophy of Mathematics: Oxford Bibliographies Online Research Guide

Author: Oxford University Press

Publisher: Oxford University Press, USA

ISBN: 9780199808939

Category: Philosophy

Page: 26

View: 8858

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This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
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Truth in Mathematics

Author: Harold G. Dales,Gianluigi Oliveri

Publisher: Oxford University Press

ISBN: 9780198514763

Category: Mathematics

Page: 376

View: 4936

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The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines.
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Naturalized Epistemology and Philosophy of Science

Author: Chienkuo Mi,Ruey-lin Chen

Publisher: Rodopi

ISBN: 9042021985

Category: Philosophy

Page: 196

View: 704

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Much has happened in the field of contemporary epistemology since Quine's “Epistemology Naturalized” was published in 1969. Even before Ronald Giere published his article “Philosophy of Science Naturalized,” naturalized philosophy of science had been influenced by the so-called historical approach. Kuhm, Lakatos, Feyerabend and Laudan all contributed importantly to this trend. In this light it has emerged, without a doubt, that philosophy of science is closely related to epistemology. This volume explores some of the relevant relations and will be of interest to epistemologists and philosophers of science.
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The Development of Mathematics

Author: E. T. Bell

Publisher: Courier Corporation

ISBN: 0486152286

Category: Mathematics

Page: 656

View: 7791

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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.
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The Philosophy of Mathematics Today

Author: Matthias Schirn

Publisher: Oxford University Press

ISBN: 9780199262625

Category: Philosophy

Page: 638

View: 1383

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The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert'sand Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.
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An Introduction to Philosophical Methods

Author: Christopher Daly

Publisher: Broadview Press

ISBN: 1460401174

Category: Philosophy

Page: 258

View: 6182

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An Introduction to Philosophical Methods is the first book to survey the various methods that philosophers use to support their views. Rigorous yet accessible, the book introduces and illustrates the methodological considerations that are involved in current philosophical debates. Where there is controversy, the book presents the case for each side, but highlights where the key difficulties with them lie. While eminently student-friendly, the book makes an important contribution to the debate regarding the acceptability of the various philosophical methods, and so it will also be of interest to more experienced philosophers.
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