Author : Michael D. Potter
Publisher : Clarendon Press
Page : 345 pages
File Size : 48,33 MB
Release : 2004
Category : 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.
Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 41,17 MB
Release : 2018-12-13
Category : History
ISBN : 110715250X
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author : Mary Tiles
Publisher : Courier Corporation
Page : 258 pages
File Size : 26,43 MB
Release : 2012-03-08
Category : 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
Author : Penelope Maddy
Publisher : Oxford University Press
Page : 161 pages
File Size : 46,11 MB
Release : 2011-01-27
Category : 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.
Author : Stephen Pollard
Publisher : Courier Dover Publications
Page : 196 pages
File Size : 22,48 MB
Release : 2015-07-15
Category : 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.
Author : Manuel Bremer
Publisher : Walter de Gruyter
Page : 125 pages
File Size : 22,19 MB
Release : 2013-05-02
Category : Philosophy
ISBN : 3110326108
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?
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 23,95 MB
Release : 2020-01-23
Category : History
ISBN : 1108497829
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author : Joseph Breuer
Publisher : Courier Corporation
Page : 130 pages
File Size : 12,66 MB
Release : 2012-08-09
Category : Mathematics
ISBN : 0486154874
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.
Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 20,51 MB
Release : 2021-03-09
Category : 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.
Author : Willard Van Orman Quine
Publisher : Harvard University Press
Page : 384 pages
File Size : 17,12 MB
Release : 1969
Category : Mathematics
ISBN : 9780674802070
This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
