The Philosophy Of Set Theory
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The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
The Philosophy Of Set Theory written by Mary Tiles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.
Set Theory And Its Philosophy
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Author : Michael D. Potter
language : en
Publisher:
Release Date : 2004
Set Theory And Its Philosophy written by Michael D. Potter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Set theory categories.
Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. This is a comprehensive philosophical introduction to the field offering a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates.
Quine New Foundations And The Philosophy Of Set Theory
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Author : Sean Morris
language : en
Publisher: Cambridge University Press
Release Date : 2018-12-13
Quine New Foundations And The Philosophy Of Set Theory written by Sean Morris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-13 with History categories.
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Defending The Axioms
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Author : Penelope Maddy
language : en
Publisher: Oxford University Press
Release Date : 2011-01-27
Defending The Axioms written by Penelope Maddy and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-27 with Mathematics categories.
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.
Set Theory And The Continuum Hypothesis
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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
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.
Universality In Set Theories
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Author : Manuel Bremer
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-02
Universality In Set Theories written by Manuel Bremer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Philosophy categories.
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?
Badiou S Being And Event And The Mathematics Of Set Theory
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Author : Burhanuddin Baki
language : en
Publisher: Bloomsbury Publishing
Release Date : 2014-11-20
Badiou S Being And Event And The Mathematics Of Set Theory written by Burhanuddin Baki and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-20 with Philosophy categories.
Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Gödel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.
A Logical Foundation For Potentialist Set Theory
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Author : Sharon Berry
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-17
A Logical Foundation For Potentialist Set Theory written by Sharon Berry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Mathematics categories.
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Conceptions Of Set And The Foundations Of Mathematics
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Author : Luca Incurvati
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Conceptions Of Set And The Foundations Of Mathematics written by Luca Incurvati and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with History categories.
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Set Theory
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Author : John P. Burgess
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10
Set Theory written by John P. Burgess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Philosophy categories.
Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.