Set Theory And Its Philosophy

Set Theory And Its Philosophy Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Set Theory And Its Philosophy book. This book definitely worth reading, it is an incredibly well-written.

Set Theory and its Philosophy

Michael Potter
Set Theory and its Philosophy Book PDF

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 47,8 Mb
Release : 2004-01-15
Category : Philosophy
ISBN : 9780191556432

Get Book

Set Theory and its Philosophy by Michael Potter Pdf

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

Michael D. Potter
Set Theory and Its Philosophy Book PDF

Author : Michael D. Potter
Publisher : Clarendon Press
Page : 345 pages
File Size : 45,7 Mb
Release : 2004
Category : Mathematics
ISBN : 0199269734

Get Book

Set Theory and Its Philosophy by Michael D. Potter Pdf

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

Mary Tiles
The Philosophy of Set Theory Book PDF

Author : Mary Tiles
Publisher : Courier Corporation
Page : 258 pages
File Size : 42,6 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486138558

Get Book

The Philosophy of Set Theory by Mary Tiles Pdf

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

Stephen Pollard
Philosophical Introduction to Set Theory Book PDF

Author : Stephen Pollard
Publisher : Courier Dover Publications
Page : 196 pages
File Size : 46,6 Mb
Release : 2015-07-15
Category : Mathematics
ISBN : 9780486797144

Get Book

Philosophical Introduction to Set Theory by Stephen Pollard Pdf

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

Sean Morris
Quine New Foundations and the Philosophy of Set Theory Book PDF

Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 52,5 Mb
Release : 2018-12-13
Category : History
ISBN : 9781107152502

Get Book

Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris Pdf

Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Defending the Axioms

Penelope Maddy
Defending the Axioms Book PDF

Author : Penelope Maddy
Publisher : Oxford University Press
Page : 161 pages
File Size : 52,5 Mb
Release : 2011-01-27
Category : Mathematics
ISBN : 9780199596188

Get Book

Defending the Axioms by Penelope Maddy Pdf

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.

Lectures on the Philosophy of Mathematics

Joel David Hamkins
Lectures on the Philosophy of Mathematics Book PDF

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 43,8 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9780262542234

Get Book

Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

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.

Conceptions of Set and the Foundations of Mathematics

Luca Incurvati
Conceptions of Set and the Foundations of Mathematics Book PDF

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 48,6 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824

Get Book

Conceptions of Set and the Foundations of Mathematics by Luca Incurvati Pdf

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Universality in Set Theories

Manuel Bremer
Universality in Set Theories Book PDF

Author : Manuel Bremer
Publisher : Walter de Gruyter
Page : 125 pages
File Size : 54,7 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110326109

Get Book

Universality in Set Theories by Manuel Bremer Pdf

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?

A Logical Foundation for Potentialist Set Theory

Sharon Berry
A Logical Foundation for Potentialist Set Theory Book PDF

Author : Sharon Berry
Publisher : Cambridge University Press
Page : 249 pages
File Size : 53,6 Mb
Release : 2022-02-17
Category : Science
ISBN : 9781108834315

Get Book

A Logical Foundation for Potentialist Set Theory by Sharon Berry Pdf

A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.

Set Theory, Logic and Their Limitations

Moshe Machover
Set Theory Logic and Their Limitations Book PDF

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 45,8 Mb
Release : 1996-05-23
Category : Mathematics
ISBN : 0521479983

Get Book

Set Theory, Logic and Their Limitations by Moshe Machover Pdf

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.

Set Theory and the Continuum Hypothesis

Paul J. Cohen
Set Theory and the Continuum Hypothesis Book PDF

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 41,7 Mb
Release : 2008-12-09
Category : Mathematics
ISBN : 9780486469218

Get Book

Set Theory and the Continuum Hypothesis by Paul J. Cohen Pdf

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.

Set Theory and Its Logic

Willard Van Orman Quine
Set Theory and Its Logic Book PDF

Author : Willard Van Orman Quine
Publisher : Harvard University Press
Page : 384 pages
File Size : 45,7 Mb
Release : 1969
Category : Mathematics
ISBN : 0674802071

Get Book

Set Theory and Its Logic by Willard Van Orman Quine Pdf

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.

More Precisely: The Math You Need to Do Philosophy - Second Edition

Eric Steinhart
More Precisely The Math You Need to Do Philosophy Second Edition Book PDF

Author : Eric Steinhart
Publisher : Broadview Press
Page : 250 pages
File Size : 45,9 Mb
Release : 2017-11-21
Category : Philosophy
ISBN : 9781554813452

Get Book

More Precisely: The Math You Need to Do Philosophy - Second Edition by Eric Steinhart Pdf

More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.

Badiou's Being and Event and the Mathematics of Set Theory

Burhanuddin Baki
Badiou s Being and Event and the Mathematics of Set Theory Book PDF

Author : Burhanuddin Baki
Publisher : Bloomsbury Publishing
Page : 283 pages
File Size : 43,6 Mb
Release : 2014-11-20
Category : Philosophy
ISBN : 9781472578716

Get Book

Badiou's Being and Event and the Mathematics of Set Theory by Burhanuddin Baki Pdf

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.