Predicative Arithmetic Mn 32

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Predicative Arithmetic. (MN-32)

Author : Edward Nelson
Publisher : Princeton University Press
ISBN 13 : 1400858925
Total Pages : 199 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Predicative Arithmetic. (MN-32) by : Edward Nelson

Download or read book Predicative Arithmetic. (MN-32) written by Edward Nelson and published by Princeton University Press. This book was released on 2014-07-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Understanding the Infinite

Author : Shaughan Lavine
Publisher : Harvard University Press
ISBN 13 : 0674265335
Total Pages : 262 pages
Book Rating : 4.6/5 (742 download)

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Book Synopsis Understanding the Infinite by : Shaughan Lavine

Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 2009-06-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice

The Oxford Handbook of Philosophy of Mathematics and Logic

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0190287535
Total Pages : 856 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis The Oxford Handbook of Philosophy of Mathematics and Logic by : Stewart Shapiro

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.

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)

Author : William G. Faris
Publisher : Princeton University Press
ISBN 13 : 1400865255
Total Pages : 257 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) by : William G. Faris

Download or read book Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) written by William G. Faris and published by Princeton University Press. This book was released on 2014-09-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Perspectives of Systems Informatics

Author : Manfred Broy
Publisher : Springer Science & Business Media
ISBN 13 : 3540208135
Total Pages : 587 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Perspectives of Systems Informatics by : Manfred Broy

Download or read book Perspectives of Systems Informatics written by Manfred Broy and published by Springer Science & Business Media. This book was released on 2004-01-13 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed postconference proceedings of the 5th International Andrei Ershov Memorial Conference, PSI 2003, held in Akademgorodok, Novosibirsk, Russia in July 2003. The 55 revised full papers presented were carefully reviewed and selected from 110 submissions during two rounds of evaluation and improvement. The papers are organized in topical sections on programming, software engineering, software education, program synthesis and transformation, graphical interfaces, partial evaluation and supercompilation, verification, logic and types, concurrent and distributed systems, reactive systems, program specification, verification and model checking, constraint programming, documentation and testing, databases, and natural language processing.

Mathematics, Science and Epistemology: Volume 2, Philosophical Papers

Author : Imre Lakatos
Publisher : Cambridge University Press
ISBN 13 : 9780521280303
Total Pages : 302 pages
Book Rating : 4.2/5 (83 download)

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Book Synopsis Mathematics, Science and Epistemology: Volume 2, Philosophical Papers by : Imre Lakatos

Download or read book Mathematics, Science and Epistemology: Volume 2, Philosophical Papers written by Imre Lakatos and published by Cambridge University Press. This book was released on 1980-10-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics together with some critical essays on contemporary philosophers of science.

Logical Syntax of Language

Author : Rudolf Carnap
Publisher : Routledge
ISBN 13 : 1317830601
Total Pages : 368 pages
Book Rating : 4.3/5 (178 download)

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Book Synopsis Logical Syntax of Language by : Rudolf Carnap

Download or read book Logical Syntax of Language written by Rudolf Carnap and published by Routledge. This book was released on 2014-06-23 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Mathematics for Computer Science

Author : Eric Lehman
Publisher :
ISBN 13 : 9789888407064
Total Pages : 988 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematics for Computer Science by : Eric Lehman

Download or read book Mathematics for Computer Science written by Eric Lehman and published by . This book was released on 2017-03-08 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

The Arché Papers on the Mathematics of Abstraction

Author : Roy T. Cook
Publisher : Springer Science & Business Media
ISBN 13 : 1402042655
Total Pages : 454 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Arché Papers on the Mathematics of Abstraction by : Roy T. Cook

Download or read book The Arché Papers on the Mathematics of Abstraction written by Roy T. Cook and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.

A Book of Set Theory

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Set Theory by : Charles C Pinter

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Varieties of Continua

Author : Geoffrey Hellman
Publisher : Oxford University Press
ISBN 13 : 019871274X
Total Pages : 219 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Varieties of Continua by : Geoffrey Hellman

Download or read book Varieties of Continua written by Geoffrey Hellman and published by Oxford University Press. This book was released on 2018 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be composed of points, to the now standard, point-based frameworks for analysis and geometry found in modern mainstream mathematics (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-tolate-twentieth century revival of pre-limit methods in analysis and geometry using infinitesimals including non-standard analysis (due to Abraham Robinson), and the more radical smooth infinitesimal analysis that uses intuitionistic logic. Hellman and Shapiro present a systematic comparison of these and related alternatives (including constructivist and predicative conceptions), weighing various trade-offs, helping articulate a modern pluralist perspective, and articulate a modern pluralist perspective on continuity. The main creative work of the book is the development of rigorous regions-based theories of classical continua, including Euclidean and non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics.

The Autonomy of Mathematical Knowledge

Author : Curtis Franks
Publisher : Cambridge University Press
ISBN 13 : 0521514371
Total Pages : 229 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis The Autonomy of Mathematical Knowledge by : Curtis Franks

Download or read book The Autonomy of Mathematical Knowledge written by Curtis Franks and published by Cambridge University Press. This book was released on 2009-10-08 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.

The Logical Syntax of Language

Author : Rudolf Carnap
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Logical Syntax of Language by : Rudolf Carnap

Download or read book The Logical Syntax of Language written by Rudolf Carnap and published by . This book was released on 1937 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

School Education

Author :
Publisher :
ISBN 13 :
Total Pages : 760 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis School Education by :

Download or read book School Education written by and published by . This book was released on 1909 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Limits of Logic

Author : Stewart Shapiro
Publisher : Routledge
ISBN 13 : 1351886665
Total Pages : 352 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis The Limits of Logic by : Stewart Shapiro

Download or read book The Limits of Logic written by Stewart Shapiro and published by Routledge. This book was released on 2016-12-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.

Books in Series

Author :
Publisher :
ISBN 13 :
Total Pages : 1404 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Books in Series by :

Download or read book Books in Series written by and published by . This book was released on 1985 with total page 1404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1980- issued in three parts: Series, Authors, and Titles.

An Introduction to Mathematical Reasoning

Author : Peter J. Eccles
Publisher : Cambridge University Press
ISBN 13 : 9780521597180
Total Pages : 366 pages
Book Rating : 4.5/5 (971 download)

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Book Synopsis An Introduction to Mathematical Reasoning by : Peter J. Eccles

Download or read book An Introduction to Mathematical Reasoning written by Peter J. Eccles and published by Cambridge University Press. This book was released on 1997-12-11 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.