Philosophical Introduction To Set Theory
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Author |
: Michael Potter |
Publisher |
: Clarendon Press |
Total Pages |
: 362 |
Release |
: 2004-01-15 |
ISBN-10 |
: 9780191556432 |
ISBN-13 |
: 0191556432 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Set Theory and its Philosophy by : Michael Potter
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 |
: Stephen Pollard |
Publisher |
: Courier Dover Publications |
Total Pages |
: 196 |
Release |
: 2015-07-15 |
ISBN-10 |
: 9780486797144 |
ISBN-13 |
: 0486797147 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard
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 |
: Penelope Maddy |
Publisher |
: Oxford University Press |
Total Pages |
: 161 |
Release |
: 2011-01-27 |
ISBN-10 |
: 9780199596188 |
ISBN-13 |
: 0199596182 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Defending the Axioms by : Penelope Maddy
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 |
: Luca Incurvati |
Publisher |
: Cambridge University Press |
Total Pages |
: 255 |
Release |
: 2020-01-23 |
ISBN-10 |
: 9781108497824 |
ISBN-13 |
: 1108497829 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author |
: Mary Tiles |
Publisher |
: Courier Corporation |
Total Pages |
: 258 |
Release |
: 2012-03-08 |
ISBN-10 |
: 9780486138558 |
ISBN-13 |
: 0486138550 |
Rating |
: 4/5 (58 Downloads) |
Synopsis The Philosophy of Set Theory by : Mary Tiles
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 |
: Paul J. Cohen |
Publisher |
: Courier Corporation |
Total Pages |
: 196 |
Release |
: 2008-12-09 |
ISBN-10 |
: 9780486469218 |
ISBN-13 |
: 0486469212 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Set Theory and the Continuum Hypothesis by : Paul J. Cohen
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 |
Total Pages |
: 350 |
Release |
: 2021-03-09 |
ISBN-10 |
: 9780262542234 |
ISBN-13 |
: 0262542234 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins
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 |
: Mark Colyvan |
Publisher |
: Cambridge University Press |
Total Pages |
: 199 |
Release |
: 2012-06-14 |
ISBN-10 |
: 9780521826020 |
ISBN-13 |
: 0521826020 |
Rating |
: 4/5 (20 Downloads) |
Synopsis An Introduction to the Philosophy of Mathematics by : Mark Colyvan
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Author |
: Patrick Suppes |
Publisher |
: Courier Corporation |
Total Pages |
: 340 |
Release |
: 2012-07-12 |
ISBN-10 |
: 9780486138053 |
ISBN-13 |
: 0486138054 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Introduction to Logic by : Patrick Suppes
Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
Author |
: George Englebretsen |
Publisher |
: A&C Black |
Total Pages |
: 209 |
Release |
: 2011-03-24 |
ISBN-10 |
: 9781441119117 |
ISBN-13 |
: 1441119116 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Philosophical Logic by : George Englebretsen
Introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols.