Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

Published: 2015-07-15

Total Pages: 196

ISBN-13: 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.


Set Theory and Its Philosophy

Set Theory and Its Philosophy

Author: Michael D. Potter

Publisher: Clarendon Press

Published: 2004

Total Pages: 345

ISBN-13: 9780199269730

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A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.


Defending the Axioms

Defending the Axioms

Author: Penelope Maddy

Publisher: Oxford University Press

Published: 2011-01-27

Total Pages: 161

ISBN-13: 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.


Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics

Author: Joel David Hamkins

Publisher: MIT Press

Published: 2021-03-09

Total Pages: 350

ISBN-13: 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.


Set Theory and the Continuum Hypothesis

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen

Publisher: Courier Corporation

Published: 2008-12-09

Total Pages: 196

ISBN-13: 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.


An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

Published: 2012-06-14

Total Pages: 199

ISBN-13: 0521826020

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


The Philosophy of Set Theory

The Philosophy of Set Theory

Author: Mary Tiles

Publisher: Courier Corporation

Published: 2012-03-08

Total Pages: 258

ISBN-13: 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


Philosophical Devices

Philosophical Devices

Author: David Papineau

Publisher: OUP Oxford

Published: 2012-10-04

Total Pages: 224

ISBN-13: 0191656259

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This book is designed to explain the technical ideas that are taken for granted in much contemporary philosophical writing. Notions like 'denumerability', 'modal scope distinction', 'Bayesian conditionalization', and 'logical completeness' are usually only elucidated deep within difficult specialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists. The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Gödel's theorem. Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.


More Precisely: The Math You Need to Do Philosophy - Second Edition

More Precisely: The Math You Need to Do Philosophy - Second Edition

Author: Eric Steinhart

Publisher: Broadview Press

Published: 2017-11-21

Total Pages: 250

ISBN-13: 155481345X

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More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.