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.
The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Courier Corporation
Release Date : 2012-03-08
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 2012-03-08 with Mathematics categories.
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
Set Theory And Its Philosophy
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Author : Michael Potter
language : en
Publisher: Clarendon Press
Release Date : 2004-01-15
Set Theory And Its Philosophy written by Michael Potter and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-15 with Philosophy categories.
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.
The Palgrave Companion To The Philosophy Of Set Theory
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Author : Carolin Antos
language : en
Publisher: Palgrave Macmillan
Release Date : 2025-04-18
The Palgrave Companion To The Philosophy Of Set Theory written by Carolin Antos and has been published by Palgrave Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Mathematics categories.
This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity. Key features of this volume: • Explores new and interesting connections between philosophy, set theory, and the study of infinity. • Considers questions intended to appeal to a wider audience in both philosophy and mathematical logic. • Examines three key areas of study: Epistemology, Formal Theories, and Ontology. The book provides a key reference text for future debates and is ideal for both newcomers to the philosophy of set theory and established researchers in the field.
The Palgrave Companion To The Philosophy Of Set Theory
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Author : Carolin Antos
language : en
Publisher: Springer Nature
Release Date : 2025-04-17
The Palgrave Companion To The Philosophy Of Set Theory written by Carolin Antos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-17 with Mathematics categories.
This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity. Key features of this volume: • Explores new and interesting connections between philosophy, set theory, and the study of infinity. • Considers questions intended to appeal to a wider audience in both philosophy and mathematical logic. • Examines three key areas of study: Epistemology, Formal Theories, and Ontology. The book provides a key reference text for future debates and is ideal for both newcomers to the philosophy of set theory and established researchers in the field.
Philosophical Introduction To Set Theory
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Author : Stephen Pollard
language : en
Publisher: Courier Dover Publications
Release Date : 2015-07-20
Philosophical Introduction To Set Theory written by Stephen Pollard and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-20 with Mathematics categories.
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.
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.
Philosophical Introduction To Set Theory
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Author : Stephen Pollard
language : en
Publisher: Courier Dover Publications
Release Date : 2015-07-15
Philosophical Introduction To Set Theory written by Stephen Pollard and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
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.
The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Wiley-Blackwell
Release Date : 1989
The Philosophy Of Set Theory written by Mary Tiles and has been published by Wiley-Blackwell this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.