Logic Foundations Of Mathematics And Computability Theory
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Logic Foundations Of Mathematics And Computability Theory
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Author : Robert E. Butts
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic Foundations Of Mathematics And Computability Theory written by Robert E. Butts and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.
Logic Foundations Of Mathematics And Computability Theory
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Author : Robert E. Butts
language : en
Publisher:
Release Date : 1977-10-31
Logic Foundations Of Mathematics And Computability Theory written by Robert E. Butts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-10-31 with categories.
Proceedings Logic Foundations Of Mathematics And Computability Theory
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Author : Robert E. Butts
language : en
Publisher:
Release Date : 1977
Proceedings Logic Foundations Of Mathematics And Computability Theory written by Robert E. Butts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Computable functions categories.
The Art Of The Intelligible
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Author : J. Bell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Art Of The Intelligible written by J. Bell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.
The Foundations Of Computability Theory
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Author : Borut Robič
language : en
Publisher: Springer Nature
Release Date : 2020-11-13
The Foundations Of Computability Theory written by Borut Robič and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Computers categories.
This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Existence And Explanation
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Author : W. Spohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Existence And Explanation written by W. Spohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
This collection of essays is dedicated to 'Joe' Karel Lambert. The contributors are all personally affected to Joe in some way or other, but they are definitely not the only ones. Whatever excuses there are - there are some -, the editors apologize to whomever they have neglected. But even so the collection displays how influential Karel Lambert has been, personally and through his teaching and his writings. The display is in alphabetical order - with one exception: Bas van Fraassen, being about the earliest student of Karel Lambert, opens the collection with some reminiscences. Naturally, one of the focal points of this volume is Lambert's logical thinking and (or: freed of) ontological thinking. Free logic is intimately connected with description theory. Bas van Fraassen gives a survey of the development of the area, and Charles Daniels points to difficulties with definite descriptions in modal contexts and stories. Peter Woodruff addresses the relation between free logic and supervaluation semantics, presenting a novel condition which recovers desirable metatheoretic properties for free logic under that semantics. Terence Parsons shows how free logic can be utilized in interpreting sentences as purporting to denote events (true ones succeed and false ones fail) and how this helps to understand natural language.
Experiencing Nature
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Author : P. Theerman
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-30
Experiencing Nature written by P. Theerman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-30 with History categories.
This volume, honoring the renowned historian of science, Allen G Debus, explores ideas of science - `experiences of nature' - from within a historiographical tradition that Debus has done much to define. As his work shows, the sciences do not develop exclusively as a result of a progressive and inexorable logic of discovery. A wide variety of extra-scientific factors, deriving from changing intellectual contexts and differing social millieus, play crucial roles in the overall development of scientific thought. These essays represent case studies in a broad range of scientific settings - from sixteenth-century astronomy and medicine, through nineteenth-century biology and mathematics, to the social sciences in the twentieth-century - that show the impact of both social settings and the cross-fertilization of ideas on the formation of science. Aimed at a general audience interested in the history of science, this book closes with Debus's personal perspective on the development of the field. Audience: This book will appeal especially to historians of science, of chemistry, and of medicine.
Consciousness And Intentionality Models And Modalities Of Attribution
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Author : D. Fisette
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Consciousness And Intentionality Models And Modalities Of Attribution written by D. Fisette and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Philosophy categories.
Philosophy of mind has been one of the most active fields in philosophy for the past three decades. One of the most significant factors in the development of this discipline has been the emergence of cognitive science and the interest philosophers have taken in the empirical study of mind. Another equally important factor has been the "naturalistic tum" brought about by W. V. Quine. His proposal that normative epistemology be replaced by empirical psychology marked a radical departure from the Fregean "anti psychologism" and "apriorism" that had characterized much of the analytic tradition in philosophy. But while Quine's program of naturalization called the attention of philosophers to empirical psychology, his conception of psychology was inspired by an austere behaviorism which shunned the mentalism of intentional psychology in the Brentanian and phenomenological tradition. Thus, while agreeing with Brentano that the "intentional idiom" could not be reduced to that of the natural sciences, Quine argued that it is of a piece with the indeterminacy of translation. Most contributors of this col lection share the cognitivist stance and believe that the mind needs to be explained rather than eliminated. Three main questions are actually confronting current philosophers of mind, each addressed by one or another of the contributors to the present collection.
Computability Theory And Its Applications
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Author : Peter Cholak
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Computability Theory And Its Applications written by Peter Cholak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).
Mathematics And Its Logics
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Author : Geoffrey Hellman
language : en
Publisher: Cambridge University Press
Release Date : 2021-02-04
Mathematics And Its Logics written by Geoffrey Hellman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-04 with Mathematics categories.
The essays in this volume present a sustained case for a healthy pluralism in mathematics and its logics.