Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 29,61 MB
Release : 2018-12-13
Category : History
ISBN : 110715250X
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 34,8 MB
Release : 2020-01-23
Category : History
ISBN : 1108497829
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 28,39 MB
Release : 2018-12-13
Category : Philosophy
ISBN : 1108604536
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 : Willard Van Orman Quine
Publisher : Harvard University Press
Page : 384 pages
File Size : 14,59 MB
Release : 1969
Category : Mathematics
ISBN : 9780674802070
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.
Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 15,17 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432
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 : L. Decock
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 13,78 MB
Release : 2002-09-30
Category : Philosophy
ISBN : 9781402008658
Willard Van Orman Quine (1908-2000) was probably the most influential American philosopher of the twentieth century. In Trading Ontology for Ideology Lieven Decock offers an insightful analysis of the development of Quine's ontological views from his first texts in the early thirties onwards. The importance of Quine's work in logic and set theory for his ontology is highlighted. Decock argues that the tenet of extensionalism is at least as important as naturalism, and assesses the relation between the two. The other focus of the work is the relation between ontology, i.e. what there is, and ideology, i.e. what can be expressed by means of words. Decock shows that the interplay between ontology and ideology is far more complicated and interesting than has generally been assumed.
Author : Alfred North Whitehead
Publisher :
Page : 688 pages
File Size : 28,67 MB
Release : 1910
Category : Logic, Symbolic and mathematical
ISBN :
Author : Abraham Adolf Fraenkel
Publisher :
Page : 297 pages
File Size : 17,34 MB
Release : 1968
Category :
ISBN :
Author : John P. Burgess
Publisher : Cambridge University Press
Page : 253 pages
File Size : 30,85 MB
Release : 2008-02-21
Category : Science
ISBN : 113947054X
John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.
Author : Manuel Bremer
Publisher : Walter de Gruyter
Page : 125 pages
File Size : 43,50 MB
Release : 2013-05-02
Category : Philosophy
ISBN : 3110326108
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?
