Constructibility And Mathematical Existence
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Constructibility And Mathematical Existence
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Author : Charles S. Chihara
language : en
Publisher: Clarendon Press
Release Date : 1990-04-12
Constructibility And Mathematical Existence written by Charles S. Chihara and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-12 with Mathematics categories.
This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
Constructibility And Mathematical Existence
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Author : Charles S. Chihara
language : en
Publisher: Oxford University Press
Release Date : 1990
Constructibility And Mathematical Existence written by Charles S. Chihara and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Law categories.
Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.
Constructibility
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Author : K. J. Devlin
language : en
Publisher: Springer
Release Date : 1984-06
Constructibility written by K. J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-06 with Mathematics categories.
This book is intended to give a fairly comprehensive account of the theory of constructible sets at an advanced level. The intended reader is a graduate mathe matician with some knowledge of mathematical logic. In particular, we assume familiarity with the notions of formal languages, axiomatic theories in formal languages, logical deductions in such theories, and the interpretation oflanguages in structures. Practically any introductory text on mathematical logic will supply the necessary material. We also assume some familiarity with Zermelo-Fraenkel set theory up to the development or ordinal and cardinal numbers. Any number of texts would suffice here, for instance Devlin (1979) or Levy (1979). The book is not intended to provide a complete coverage of the many and diverse applications of the methods of constructibility theory, rather the theory itself. Such applications as are given are there to motivate and to exemplify the theory. The book is divided into two parts. Part A ("Elementary Theory") deals with the classical definition of the La-hierarchy of constructible sets. With some prun ing, this part could be used as the basis of a graduate course on constructibility theory. Part B ("Advanced Theory") deals with the fa-hierarchy and the Jensen "fine-structure theory".
Constructibility
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Author : Keith J. Devlin
language : en
Publisher: Springer
Release Date : 1984
Constructibility written by Keith J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
A Structural Account Of Mathematics
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Author : Charles S. Chihara
language : en
Publisher: Clarendon Press
Release Date : 2003-11-20
A Structural Account Of Mathematics written by Charles S. Chihara and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-20 with Philosophy categories.
Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.
The Axiom Of Constructibility
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Author : K. J. Devlin
language : en
Publisher: Springer
Release Date : 2006-11-15
The Axiom Of Constructibility written by K. J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Aspects Of Constructibility
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Author : K. J. Devlin
language : en
Publisher: Springer
Release Date : 2006-11-15
Aspects Of Constructibility written by K. J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book aims to collect together most of the existing information on constructibility, much of which is fairly recent.
The Axiom Of Constructibility
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Author : K. J. Devlin
language : en
Publisher:
Release Date : 2014-09-01
The Axiom Of Constructibility written by K. J. Devlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Aspects Of Constructibility
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Author : Keith J. Devlin
language : en
Publisher: Springer
Release Date : 1973
Aspects Of Constructibility written by Keith J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Constructibility (Set theory) categories.
Naturalism In Mathematics
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Author : Penelope Maddy
language : en
Publisher: Clarendon Press
Release Date : 1997-11-13
Naturalism In Mathematics written by Penelope Maddy and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-13 with Philosophy categories.
Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.