Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory
Author: Stephen Pollard
Publisher: Courier Dover Publications
Total Pages: 196
Release: 2015-07-15
Genre: Mathematics
ISBN: 0486797147

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
Total Pages: 345
Release: 2004
Genre: Mathematics
ISBN: 9780199269730

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
Total Pages: 161
Release: 2011-01-27
Genre: Mathematics
ISBN: 0199596182

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
Total Pages: 350
Release: 2021-03-09
Genre: Mathematics
ISBN: 0262542234

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
Total Pages: 196
Release: 2008-12-09
Genre: Mathematics
ISBN: 0486469212

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.

Introduction to Logic

Introduction to Logic
Author: Patrick Suppes
Publisher: Courier Corporation
Total Pages: 340
Release: 2012-07-12
Genre: Mathematics
ISBN: 0486138054

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.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics
Author: Mark Colyvan
Publisher: Cambridge University Press
Total Pages: 199
Release: 2012-06-14
Genre: Mathematics
ISBN: 0521826020

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
Total Pages: 258
Release: 2012-03-08
Genre: Mathematics
ISBN: 0486138550

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

Discovering Modern Set Theory. I: The Basics

Discovering Modern Set Theory. I: The Basics
Author: Winfried Just
Publisher: American Mathematical Soc.
Total Pages: 230
Release: 1996
Genre: Mathematics
ISBN: 0821802666

This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.