[PDF] The Philosophy Of Set Theory eBook

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 49,26 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Author : Mary Tiles
Publisher : Courier Corporation
Page : 258 pages
File Size : 20,91 MB
Release : 2012-03-08
Category : Mathematics
ISBN : 0486138550

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DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 49,1 MB
Release : 2018-12-13
Category : History
ISBN : 110715250X

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Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 30,71 MB
Release : 2020-01-23
Category : History
ISBN : 1108497829

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Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author : Penelope Maddy
Publisher : Oxford University Press
Page : 161 pages
File Size : 35,7 MB
Release : 2011-01-27
Category : Mathematics
ISBN : 0199596182

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Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 29,74 MB
Release : 1996-05-23
Category : Mathematics
ISBN : 9780521479981

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This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Author : Stephen Pollard
Publisher : Courier Dover Publications
Page : 196 pages
File Size : 42,37 MB
Release : 2015-07-15
Category : Mathematics
ISBN : 0486797147

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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.

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 38,23 MB
Release : 2008-12-09
Category : Mathematics
ISBN : 0486469212

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This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 32,89 MB
Release : 2021-03-09
Category : Mathematics
ISBN : 0262542234

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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.

Author : John P. Burgess
Publisher : Cambridge University Press
Page : 75 pages
File Size : 43,68 MB
Release : 2022-02-28
Category : Philosophy
ISBN : 9781108986915

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Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.