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Set Theory And Its Philosophy
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Book Synopsis Set Theory and its Philosophy by : Michael Potter
Download or read book Set Theory and its Philosophy written by Michael Potter and published by Clarendon Press. This book was released on 2004-01-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard
Download or read book Philosophical Introduction to Set Theory written by Stephen Pollard and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Philosophy of Set Theory by : Mary Tiles
Download or read book The Philosophy of Set Theory written by Mary Tiles and published by Courier Corporation. This book was released on 2012-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Quine, New Foundations, and the Philosophy of Set Theory by : Sean Morris
Download or read book Quine, New Foundations, and the Philosophy of Set Theory written by Sean Morris and published by Cambridge University Press. This book was released on 2018-12-13 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Book Synopsis Defending the Axioms by : Penelope Maddy
Download or read book Defending the Axioms written by Penelope Maddy and published by Oxford University Press. This book was released on 2011-01-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Universality in Set Theories by : Manuel Bremer
Download or read book Universality in Set Theories written by Manuel Bremer and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Book Synopsis Set Theory, Logic and Their Limitations by : Moshe Machover
Download or read book Set Theory, Logic and Their Limitations written by Moshe Machover and published by Cambridge University Press. This book was released on 1996-05-23 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Book Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Book Synopsis Set Theory and the Continuum Hypothesis by : Paul J. Cohen
Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Set Theory and Its Logic by : Willard Van Orman Quine
Download or read book Set Theory and Its Logic written by Willard Van Orman Quine and published by Harvard University Press. This book was released on 1969 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski
Download or read book Set Theory for the Working Mathematician written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 1997-08-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Download or read book Set Theory written by John P. Burgess and published by Cambridge University Press. This book was released on 2022-02-28 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Logical Foundation for Potentialist Set Theory by : Sharon Berry
Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Book Synopsis Principia Mathematica by : Alfred North Whitehead
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Set Theory and Logic by : Robert R. Stoll
Download or read book Set Theory and Logic written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Book Synopsis Notes on Set Theory by : Yiannis Moschovakis
Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
