Kurt Gödel: Collected Works: Volume II

Publications 1938-1974

Author: Kurt Gödel

Publisher: Oxford University Press

ISBN: 9780195039726

Category: Mathematics

Page: 407

View: 7079


This second volume of a comprehensive edition of Kurt Godel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in historical context.

Philosophical Explorations of the Legacy of Alan Turing

Turing 100

Author: Juliet Floyd,Alisa Bokulich

Publisher: Springer

ISBN: 3319532804

Category: Science

Page: 361

View: 4066


This volume presents an historical and philosophical revisiting of the foundational character of Turing’s conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing’s work. The centennial of Turing’s birth in 2012 led to the highly celebrated “Alan Turing Year”, which stimulated a world-wide cooperative, interdisciplinary revisiting of his life and work. Turing is widely regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert’s famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing’s breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing’s work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering.

Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman

Lecture Notes in Logic 15

Author: Wilfried Sieg,Richard Sommer,Carolyn Talcott

Publisher: CRC Press

ISBN: 1439863768

Category: Mathematics

Page: 450

View: 7984


Solomon Feferman has shaped the field of foundational research for nearly half a century. These papers, most of which were presented at the symposium honoring him at his 70th birthday, reflect his broad interests as well as his approach to foundational research, which places the solution of mathematical and philosophical problems at the top of his agenda. The contributions range from historical to technical to philosophical topics, with emphasis on proof theory and computational aspects.

The Oxford Handbook of The History of Analytic Philosophy

Author: Michael Beaney

Publisher: OUP Oxford

ISBN: 0191662674

Category: Philosophy

Page: 1184

View: 6336


During the course of the twentieth century, analytic philosophy developed into the dominant philosophical tradition in the English-speaking world. In the last two decades, it has become increasingly influential in the rest of the world, from continental Europe to Latin America and Asia. At the same time there has been deepening interest in the origins and history of analytic philosophy, as analytic philosophers examine the foundations of their tradition and question many of the assumptions of their predecessors. This has led to greater historical self-consciousness among analytic philosophers and more scholarly work on the historical contexts in which analytic philosophy developed. This historical turn in analytic philosophy has been gathering pace since the 1990s, and the present volume is the most comprehensive collection of essays to date on the history of analytic philosophy. It contains state-of-the-art contributions from many of the leading scholars in the field, all of the contributions specially commissioned. The introductory essays discuss the nature and historiography of analytic philosophy, accompanied by a detailed chronology and bibliography. Part One elucidates the origins of analytic philosophy, with special emphasis on the work of Frege, Russell, Moore, and Wittgenstein. Part Two explains the development of analytic philosophy, from Oxford realism and logical positivism to the most recent work in analytic philosophy, and includes essays on ethics, aesthetics, and political philosophy as well as on the areas usually seen as central to analytic philosophy, such as philosophy of language and mind. Part Three explores certain key themes in the history of analytic philosophy.

Turing's Legacy

Developments from Turing's Ideas in Logic

Author: Rod Downey

Publisher: Cambridge University Press

ISBN: 1107043484

Category: Computers

Page: 539

View: 6746


A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.

Introduction to Mathematical Logic, Fourth Edition

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 9780412808302

Category: Mathematics

Page: 440

View: 6379


The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Peirce and Spencer-Brown

History and Synergies in Cybersemiotics

Author: Louis Kauffman,Soren Brier

Publisher: N.A

ISBN: 9781845401054

Category: Computers

Page: 159

View: 3783


This special double issue of Cybernetics and Human Knowing is comprised of a collection of papers devoted to the cybernetics and mathematics of Charles Sanders Peirce with a special focus on its synergies with George Spencer-Brown's thinking. Peirce was a truly original American philosopher and logician working in the late 1800s and early 1900s; Spencer-Brown is an English polymath, best known as the author of Laws of Form. The contributions reflect the extraordinary richness of Peirce's work and his relevance to present concerns in cybernetics. The similarities in the focus on some of the deep foundational subjects are astonishing, amongst those especially the concept of the void or Firstness and the continuity of mind and matter.


Author: N.A

Publisher: N.A


Category: Logic, Symbolic and mathematical

Page: N.A

View: 5816



Computing Anticipatory Systems

CASYS'07 - Eighth International Conference

Author: D. Dubois

Publisher: American Inst. of Physics

ISBN: 9780735405790

Category: Computers

Page: 428

View: 4423


These proceedings deal with a selection of papers presented at the 8th International Conference CASYS’07, on COMPUTING ANTICIPATORY SYSTEMS, 6-11 August 2007, held at HEC Management School - University of Liege, Liège, Belgium. The content of these proceedings deals with the most recent Research & Development in the area of theoretical developments and applications in the modelling and computing of anticipation in any fields of natural and artificial systems. A computing anticipatory system is a system that computes its current states in taking into account its past and present states but also its potential future states. Strong anticipation refers to an anticipation of events built by or embedded in a system. Weak anticipation refers to an anticipation of events predicted or forecasted from a model of a system. This volume contains the first invited lecture “Neural Approach to Machine Consciousness”, by Prof. Dr Igor Aleksander, FREng (UK) who received the CHAOS AWARD, and the second invited lecture “Quantum Mechanics, Pattern Recognition, and the Mammalian Brain”, by Dr George Chapline (USA) who received the CASYS AWARD. The peer reviewed papers that received a BEST PAPER AWARD at CASYS’07, and some invited papers are included in these proceedings. Adel F. Antippa (Canada) and Daniel M. Dubois (Belgium) presented the continuation of their original research project on discrete physics with their third fundamental paper “Synchronous Discrete Harmonic Oscillator” that also appears in these proceedings. The interdisciplinary outstanding topics of these proceedings are readable by researchers and scientists with a university background.