Set Theory and Its Philosophy

Author: Michael D. Potter
Publisher: Clarendon Press
ISBN: 9780199269730
Category : Mathematics
Languages : en
Pages : 345

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

The Philosophy of Set Theory

Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 0486138550
Category : Mathematics
Languages : en
Pages : 258

Book Description
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

Quine, New Foundations, and the Philosophy of Set Theory

Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 110715250X
Category : History
Languages : en
Pages : 221

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

Philosophical Introduction to Set Theory

Author: Stephen Pollard
Publisher: Courier Dover Publications
ISBN: 0486797147
Category : Mathematics
Languages : en
Pages : 196

Book Description
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.

Defending the Axioms

Author: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199596182
Category : Mathematics
Languages : en
Pages : 161

Book Description
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.

Universality in Set Theories

Author: Manuel Bremer
Publisher: Walter de Gruyter
ISBN: 3110326108
Category : Philosophy
Languages : en
Pages : 125

Book Description
The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

Conceptions of Set and the Foundations of Mathematics

Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255

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

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
Category : Mathematics
Languages : en
Pages : 196

Book Description
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 the Theory of Sets

Author: Joseph Breuer
Publisher: Courier Corporation
ISBN: 0486154874
Category : Mathematics
Languages : en
Pages : 130

Book Description
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Lectures on the Philosophy of Mathematics

Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350

Book Description
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.