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Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1966 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre Cartier
Publisher : Springer
ISBN 13 : 8132227883
Total Pages : 128 pages
Book Rating : 4.1/5 (322 download)
Download or read book Freedom in Mathematics written by Pierre Cartier and published by Springer. This book was released on 2016-04-26 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
Author : Robert Feys
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.1/5 (162 download)
Download or read book Collection de logique mathématique written by Robert Feys and published by . This book was released on 1965 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.1/5 (394 download)
Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
Author : Joseph M. Bochenski
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.:/5 (5 download)
Download or read book Précis de Logique Mathématique written by Joseph M. Bochenski and published by . This book was released on 1948 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Rusnock
Publisher : Oxford University Press
ISBN 13 : 0192556835
Total Pages : 702 pages
Book Rating : 4.1/5 (925 download)
Download or read book Bernard Bolzano written by Paul Rusnock and published by Oxford University Press. This book was released on 2019-04-25 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernard Bolzano (1781-1850) is increasingly recognized as one of the greatest nineteenth-century philosophers. A philosopher and mathematician of rare talent, he made ground-breaking contributions to logic, the foundations and philosophy of mathematics, metaphysics, and the philosophy of religion. Many of the larger features of later analytic philosophy (but also many of the details) first appear in his work: for example, the separation of logic from psychology, his sophisticated understanding of mathematical proof, his definition of logical consequence, his work on the semantics of natural kind terms, or his anticipations of Cantor's set theory, to name but a few. To his contemporaries, however, he was best known as an intelligent and determined advocate for reform of Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a program for the non-violent reform of the authoritarian institutions of the Hapsburg Empire, a program which he himself helped to set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. Persecuted in his lifetime by secular and ecclesiastical authorities, long ignored or misunderstood by philosophers, Bolzano's reputation has nevertheless steadily increased over the past century and a half. Much discussed and respected in Central Europe for over a century, he is finally beginning to receive the recognition he deserves in the English-speaking world. This book provides a comprehensive and detailed critical introduction to Bolzano, covering both his life and works.
Author : Yvon Gauthier
Publisher : Birkhäuser
ISBN 13 : 331922087X
Total Pages : 193 pages
Book Rating : 4.3/5 (192 download)
Download or read book Towards an Arithmetical Logic written by Yvon Gauthier and published by Birkhäuser. This book was released on 2015-09-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.
Author : J. Barwise
Publisher : Elsevier
ISBN 13 : 0080933645
Total Pages : 1179 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Mathematical Logic written by J. Barwise and published by Elsevier. This book was released on 1982-03-01 with total page 1179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.
Author : G. D. Bowne
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112318412
Total Pages : 160 pages
Book Rating : 4.1/5 (123 download)
Download or read book The Philosophy of Logic written by G. D. Bowne and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "The Philosophy of Logic".
Author : Y. Gauthier
Publisher : Springer Science & Business Media
ISBN 13 : 9401700834
Total Pages : 276 pages
Book Rating : 4.4/5 (17 download)
Download or read book Internal Logic written by Y. Gauthier and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.
Author : Mark Amadeus Notturno
Publisher : BRILL
ISBN 13 : 9004451528
Total Pages : 512 pages
Book Rating : 4.0/5 (44 download)
Download or read book Perspectives on Psychologism written by Mark Amadeus Notturno and published by BRILL. This book was released on 2023-03-13 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kurt R. Jankowsky
Publisher : John Benjamins Publishing
ISBN 13 : 9027276374
Total Pages : 402 pages
Book Rating : 4.0/5 (272 download)
Download or read book History of Linguistics 1993 written by Kurt R. Jankowsky and published by John Benjamins Publishing. This book was released on 1995-07-13 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 32 papers of this volume were selected from 78 papers read at ICHoLS VI, were contributed by linguists from 16 countries of Europe, Asia, and the Americas. They are presented in six sections:1. General Concerns 2. Oriental Linguistics and Related Issues 3. From the Early Middle Ages to the End of the 17th Century 4. On 19th-century European Linguistics 5. On the Verge of Modernity: From the 19th to the 20th Century 6. Contemporary IssuesIndividual topics range from dealing with overriding concerns of linguistic historiography to focusing on specific fields of inquiry within a limited frame and involving a large variety of topical areas. Most of the papers are written in English. The exceptions are one French and two German contributions.
Author : A. Heyting
Publisher : Elsevier
ISBN 13 : 1483278158
Total Pages : 645 pages
Book Rating : 4.4/5 (832 download)
Download or read book Philosophy and Foundations of Mathematics written by A. Heyting and published by Elsevier. This book was released on 2014-05-12 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.
Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0190287535
Total Pages : 856 pages
Book Rating : 4.1/5 (92 download)
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 : J.M. Bochenski
Publisher : Springer Science & Business Media
ISBN 13 : 9401705925
Total Pages : 109 pages
Book Rating : 4.4/5 (17 download)
Download or read book A Precis of Mathematical Logic written by J.M. Bochenski and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German (Grund riss der Logistik, F. Schoningh, Paderborn). In making my translation I have used both editions. For the most part I have followed the original French edition, since I thought there was some advantage in keeping the work as short as possible. However, I have included the more extensive historical notes of Dr. Menne, his bibliography, and the two sections on modal logic and the syntactical categories (§ 25 and 27), which were not in the original. I have endeavored to correct the typo graphical errors that appeared in the original editions and have made a few additions to the bibliography. In making the translation I have profited more than words can tell from the ever-generous help of Fr. Bochenski while he was teaching at the University of Notre Dame during 1955-56. OTTO BIRD Notre Dame, 1959 I GENERAL PRINCIPLES § O. INTRODUCTION 0. 1. Notion and history. Mathematical logic, also called 'logistic', ·symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last century with the aid of an artificial notation and a rigorously deductive method.
Author : J.W. Addison
Publisher : Elsevier
ISBN 13 : 1483275345
Total Pages : 513 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Theory of Models written by J.W. Addison and published by Elsevier. This book was released on 2014-05-27 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Author : A.A. Fraenkel
Publisher : Elsevier
ISBN 13 : 0080887058
Total Pages : 415 pages
Book Rating : 4.0/5 (88 download)
Download or read book Foundations of Set Theory written by A.A. Fraenkel and published by Elsevier. This book was released on 1973-12-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
