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Author : W. Buchholz,S. Feferman,W. Pohlers,W. Sieg
Publisher : Springer
Page : 389 pages
File Size : 44,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386490
Author : W. Buchholz,S. Feferman,W. Pohlers
Publisher : Unknown
Page : 392 pages
File Size : 50,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662167190
Author : Wilfried Buchholz
Publisher : Springer Verlag
Page : 383 pages
File Size : 54,9 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0387111700
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,8 Mb
Release : 1982
Category : Electronic
ISBN : 999175122X
Author : Jeffery I. Zucker
Publisher : Unknown
Page : 300 pages
File Size : 49,6 Mb
Release : 1971
Category : Induction (Mathematics)
ISBN : STANFORD:36105002027774
Author : Gerhard Jäger,Wilfried Sieg
Publisher : Springer
Page : 551 pages
File Size : 50,6 Mb
Release : 2018-04-04
Category : Mathematics
ISBN : 9783319633343
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.
Author : Toshiyasu Arai
Publisher : Springer Nature
Page : 327 pages
File Size : 55,5 Mb
Release : 2020-08-11
Category : Philosophy
ISBN : 9789811564598
This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.
Author : Gaisi Takeuti
Publisher : Courier Corporation
Page : 514 pages
File Size : 52,7 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9780486320670
This comprehensive monograph presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
Author : Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga
Publisher : Springer Nature
Page : 293 pages
File Size : 50,6 Mb
Release : 2022-09-17
Category : Mathematics
ISBN : 9783030777999
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Author : Hugues Leblanc,Elliott Mendelson,A. Orenstein
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 49,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401715928
The more traditional approaches to the history and philosophy of science and technology continue as well, and probably will continue as long as there are skillful practitioners such as Carl Hempel, Ernest Nagel, and th~ir students. Finally, there are still other approaches that address some of the technical problems arising when we try to provide an account of belief and of rational choice. - These include efforts to provide logical frameworks within which we can make sense of these notions. This series will attempt to bring together work from all of these approaches to the history and philosophy of science and technology in the belief that each has something to add to our understanding. The volumes of this series have emerged either from lectures given by authors while they served as honorary visiting professors at the City College of New York or from conferences sponsored by that institution. The City College Program in the History and Philosophy of Science and Technology oversees and directs these lectures and conferences with the financial aid of the Association for Philosophy of Science, Psychotheraphy, and Ethics. MARTIN TAMNY RAPHAEL STERN PREFACE The papers in this collection stem largely from the conference 'Foun dations: Logic, Language, and Mathematics' held at the Graduate Center of the City University of New York on 14-15 November 1980.
Author : Peter Aczel,Harold Simmons,Stanley S. Wainer
Publisher : Cambridge University Press
Page : 320 pages
File Size : 49,5 Mb
Release : 1992
Category : Computers
ISBN : 052141413X
The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists.
Author : J.J. Cohen,J. Los,H. Pfeiffer,K.-P. Podewski
Publisher : Elsevier
Page : 871 pages
File Size : 52,7 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 9780080960302
Logic, Methodology and Philosophy of Science VI presents the results of recent research into the foundations of science. The volume contains invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.
Author : S.R. Buss
Publisher : Elsevier
Page : 823 pages
File Size : 46,8 Mb
Release : 1998-07-09
Category : Mathematics
ISBN : 9780080533186
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Author : Stefania Centrone,Sara Negri,Deniz Sarikaya,Peter M. Schuster
Publisher : Springer Nature
Page : 375 pages
File Size : 46,7 Mb
Release : 2019-10-25
Category : Philosophy
ISBN : 9783030204471
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Author : Ralf Schindler
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 46,5 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110324907
On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.