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ISBN: 9780195139303

ID: 9780195139303

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. Books, [PU: Oxford University Press]

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2000, ISBN: 0195139305

ID: 30028990573

[EAN: 9780195139303], Neubuch, [SC: 0.0], [PU: OXFORD UNIV PR Sep 2000], SCIENCE; MATHEMATICS / HISTORY & PHILOSOPHY; SCIENCE PHILOSOPHY SOCIAL ASPECTS; LOGIC, Neuware - Do numbers, sets, and so forth exist What do mathematical statements mean Are they literally true or false, or do they lack truth values altogether Addressing these questions that have attracted lively debate in recent years, Stewart Shapiro argues that standard realist and antirealist accounts of mathematics are both problematic. To resolve this dilemma, he articulates a 'structuralist' approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers, existing independently, but simply a natural structure, the pattern common to any system that follows the general laws of addition. Shapiro concludes by showing how his approach can be applied to wider philosophical questions such as the nature of an object. Clear, compelling, and tautly argued it will be of deep interest to both philosophers and mathematicians. 296 pp. Englisch

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ISBN: 9780195139303

ID: 978019513930

Do numbers, sets, and so forth exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing these questions that have attracted lively debate in recent years, Stewart Shapiro argues that standard realist and antirealistaccounts of mathematics are both problematic. To resolve this dilemma, he articulates a structuralist approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers, existing independently, but simply a natural structure, the pattern common to any system thatfollows the general laws of addition. Shapiro concludes by showing how his approach can be applied to wider philosophical questions such as the nature of an object. Clear, compelling, and tautly argued it will be of deep interest to both philosophers and mathematicians. Stewart Shapiro, Books, Religion and Spirituality, Philosophy of Mathematics: Structure and Ontology Books>Religion and Spirituality, Oxford University Press

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ISBN: 9780195139303

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Do numbers, sets, and so forth exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing these questions that have attracted lively debate in recent years, Stewart Shapiro argues that standard realist and antirealist accounts of mathematics are both problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers, existing independently, but simply a natural structure, the pattern common to any system that follows the general laws of addition. Shapiro concludes by showing how his approach can be applied to wider philosophical questions such as the nature of an object. Clear, compelling, and tautly argued it will be of deep interest to both philosophers and mathematicians. Philosophy of Mathematics: Structure and Ontology Shapiro, Stewart, Oxford University Press, USA

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ISBN: 9780195139303

Paperback, [PU: Oxford University Press Inc], A structuralist approach to mathematical theory in which Shapiro argues that both realist and anti-realist accounts of mathematics are problematic . He claims that mathematical theory is not a fixed domain of numbers that exist independent of one another, but a natural structure with an initial object and successor relation., Philosophy: Logic, Philosophy Of Mathematics, History Of Mathematics, Philosophy Of Science

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** Details of the book - Philosophy of Mathematics: Structure and Ontology**

EAN (ISBN-13): 9780195139303

ISBN (ISBN-10): 0195139305

Paperback

Publishing year: 2000

Publisher: OXFORD UNIV PR

296 Pages

Weight: 0,431 kg

Language: eng/Englisch

Book in our database since 27.01.2007 10:33:44

Book found last time on 15.10.2018 10:02:50

ISBN/EAN: 0195139305

ISBN - alternate spelling:

0-19-513930-5, 978-0-19-513930-3

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