Set Theory And Its Philosophy
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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.
Set Theory And Its Philosophy
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Author : Michael D. Potter
language : en
Publisher: Clarendon Press
Release Date : 2004
Set Theory And Its Philosophy written by Michael D. 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 with Mathematics categories.
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
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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
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.
Set Theory And Its Logic
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Author : Willard Van Orman Quine
language : en
Publisher: Harvard University Press
Release Date : 1969
Set Theory And Its Logic written by Willard Van Orman Quine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
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.
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.
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.
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.
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.
The Palgrave Companion To The Philosophy Of Set Theory
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Author : Neil Barton
language : en
Publisher: Palgrave Macmillan
Release Date : 2024-08-27
The Palgrave Companion To The Philosophy Of Set Theory written by Neil Barton and has been published by Palgrave Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-27 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.