Set Theory and its Philosophy PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Set Theory and its Philosophy PDF full book. Access full book title Set Theory and its Philosophy by Michael Potter. Download full books in PDF and EPUB format.
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362
Get Book Here
Book Description
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.
Author: Michael D. Potter
Publisher: Clarendon Press
ISBN: 9780199269730
Category : Mathematics
Languages : en
Pages : 345
Get Book Here
Book Description
A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 0486138550
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
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
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 110715250X
Category : History
Languages : en
Pages : 221
Get Book Here
Book Description
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
Get Book Here
Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: John P. Burgess
Publisher: Cambridge University Press
ISBN: 9781108986915
Category : Philosophy
Languages : en
Pages : 75
Get Book Here
Book Description
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.
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362
Get Book Here
Book Description
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.
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 1108604536
Category : Philosophy
Languages : en
Pages : 221
Get Book Here
Book Description
Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.
Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108834310
Category : Mathematics
Languages : en
Pages : 249
Get Book Here
Book Description
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Author: Carolin Antos
Publisher: Birkhäuser
ISBN: 3319629352
Category : Mathematics
Languages : en
Pages : 277
Get Book Here
Book Description
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015
Author: Stuart Brock
Publisher: Routledge
ISBN: 1317494261
Category : Philosophy
Languages : en
Pages : 226
Get Book Here
Book Description
There are a bewildering variety of ways the terms "realism" and "anti-realism" have been used in philosophy and furthermore the different uses of these terms are only loosely connected with one another. Rather than give a piecemeal map of this very diverse landscape, the authors focus on what they see as the core concept: realism about a particular domain is the view that there are facts or entities distinctive of that domain, and their existence and nature is in some important sense objective and mind-independent. The authors carefully set out and explain the different realist and anti-realist positions and arguments that occur in five key domains: science, ethics, mathematics, modality and fictional objects. For each area the authors examine the various styles of argument in support of and against realism and anti-realism, show how these different positions and arguments arise in very different domains, evaluate their success within these fields, and draw general conclusions about these assorted strategies. Error theory, fictionalism, non-cognitivism, relativism and response-dependence are taken as the most important positions in opposition to the realist and these are explored in depth. Suitable for advanced level undergraduates, the book offers readers a clear introduction to a subject central to much contemporary work in metaphysics, epistemology and philosophy of language.
