Constructibility And Mathematical Existence

Author : Charles S. Chihara
Publisher : Clarendon Press
ISBN 13 : 0191520004
Total Pages : 298 pages
Book Rating : 4.06/5 ( download)

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Download or read book Constructibility and Mathematical Existence written by Charles S. Chihara and published by Clarendon Press. This book was released on 1990-04-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Charles S. Chihara
Publisher : Oxford University Press
ISBN 13 : 0198248172
Total Pages : 299 pages
Book Rating : 4.70/5 ( download)

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Download or read book Constructibility and Mathematical Existence written by Charles S. Chihara and published by Oxford University Press. This book was released on 1990 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : K. J. Devlin
Publisher : Springer
ISBN 13 :
Total Pages : 448 pages
Book Rating : 4.79/5 ( download)

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Download or read book Constructibility written by K. J. Devlin and published by Springer. This book was released on 1984-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".

Author : Keith J. Devlin
Publisher : Springer
ISBN 13 :
Total Pages : 444 pages
Book Rating : 4.62/5 ( download)

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Download or read book Constructibility written by Keith J. Devlin and published by Springer. This book was released on 1984 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : K. J. Devlin
Publisher : Springer
ISBN 13 : 354037034X
Total Pages : 105 pages
Book Rating : 4.45/5 ( download)

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Download or read book The Axiom of Constructibility written by K. J. Devlin and published by Springer. This book was released on 2006-11-15 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Charles S. Chihara
Publisher : Clarendon Press
ISBN 13 : 0191533106
Total Pages : 395 pages
Book Rating : 4.05/5 ( download)

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Download or read book A Structural Account of Mathematics written by Charles S. Chihara and published by Clarendon Press. This book was released on 2003-11-20 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Keith J. Devlin
Publisher : Springer
ISBN 13 : 9780387065229
Total Pages : 240 pages
Book Rating : 4.29/5 ( download)

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Download or read book Aspects of Constructibility written by Keith J. Devlin and published by Springer. This book was released on 1973 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0198033990
Total Pages : 856 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by Oxford University Press. This book was released on 2005-02-10 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Author : Bonnie Gold
Publisher : MAA
ISBN 13 : 9780883855676
Total Pages : 392 pages
Book Rating : 4.74/5 ( download)

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Download or read book Proof and Other Dilemmas written by Bonnie Gold and published by MAA. This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.

Author : Charles S. Chihara
Publisher : Clarendon Press
ISBN 13 : 0199267537
Total Pages : 395 pages
Book Rating : 4.38/5 ( download)

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Download or read book A Structural Account of Mathematics written by Charles S. Chihara and published by Clarendon Press. This book was released on 2004 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 areapplied 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 howsuch 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 nominalisticoutlook 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.