Cantorian Set Theory and Limitation of Size 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 Cantorian Set Theory and Limitation of Size PDF full book. Access full book title Cantorian Set Theory and Limitation of Size by Michael Hallett. Download full books in PDF and EPUB format.
Author: Michael Hallett
Publisher: Oxford University Press
ISBN: 9780198532835
Category : Mathematics
Languages : en
Pages : 372
Get Book
Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Michael Hallett
Publisher: Oxford University Press
ISBN: 9780198532835
Category : Mathematics
Languages : en
Pages : 372
Get Book
Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Moshe Machover
Publisher: Cambridge University Press
ISBN: 9780521479981
Category : Mathematics
Languages : en
Pages : 304
Get Book
Book Description
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.
Author: Mirosław Szatkowski
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311133256X
Category :
Languages : de
Pages : 844
Get Book
Book Description
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 1108604536
Category : Philosophy
Languages : en
Pages :
Get Book
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: Barnaby Sheppard
Publisher: Cambridge University Press
ISBN: 1107058317
Category : Mathematics
Languages : en
Pages : 498
Get Book
Book Description
This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.
Author: Burt Hopkins
Publisher: Routledge
ISBN: 1317401271
Category : Philosophy
Languages : en
Pages : 346
Get Book
Book Description
The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.
Author: William Ewald
Publisher: Springer-Verlag
ISBN: 3540694447
Category : Mathematics
Languages : de
Pages : 1062
Get Book
Book Description
The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.
Author: Felix Hausdorff
Publisher: Springer-Verlag
ISBN: 3540768076
Category : Mathematics
Languages : de
Pages : 1010
Get Book
Book Description
Der Mathematiker Hausdorff hat in seinem 1914 erschienen Buch „Mengenlehre" erstmals den damals aktuellen Stand auf dem Gebiet der deskriptiven Mengenlehre dargestellt. Neben diesem Werk, das von Experten sorgfältig kommentiert wurde, präsentiert der 3. Band der Hausdorff-Edition seine veröffentlichten Arbeiten zur deskriptiven Mengenlehre und Topologie sowie zahlreiche Studien aus dem Nachlass. Darunter u. a. seine originelle Vorlesung im Sommersemester 1933 über algebraische Topologie.
Author: Gabriele Lolli
Publisher: Springer
ISBN: 3319104349
Category : Philosophy
Languages : en
Pages : 336
Get Book
Book Description
This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
Author: Andrew Gibson
Publisher: OUP Oxford
ISBN: 0191525901
Category : Literary Criticism
Languages : en
Pages : 340
Get Book
Book Description
Beckett and Badiou offers a provocative new reading of Samuel Beckett's work on the basis of a full, critical account of the thought of Alain Badiou. Badiou is the most eminent of contemporary French philosophers. His devotion to Beckett's work has been lifelong. Yet for Badiou philosophy must be integrally affirmative, whilst Beckett apparently commits his art to a work of negation. Beckett and Badiou explores the coherences, contradictions, and extreme complexities of the intellectual relationship between the two oeuvres. It examines Badiou's philosophy of being, the event, truth, and the subject and the importance of mathematics within his system. It considers the major features of his politics, ethics, and aesthetics and provides an explanation, interpretation, critique, and radical revision of his work on Beckett. It argues that, once revised, Badiou's version of Beckett offers an extraordinarily powerful tool for understanding his work. Badiou and Beckett are instances of a vestigial or melancholic modernism; that is, in the teeth of a contemporary culture that dreams ever more ambitiously of plenitude, they commit themselves to a rigorous concept of limit and intermittency. Truth and value are occasional and rare. It is seldom that the chance event arrives to disturb the inertia of the world. For Badiou, however, it is the event and its consequences alone that matter. Beckett rather insists on the common experience of intermittency as destitution. His art is a series of limit-figures, exquisitely subtle and nuanced forms for a world whose state of seemingly rigid paralysis is also always volatile, delicately balanced.
