The Logical Foundations Of Mathematics
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The Logical Foundations Of Mathematics
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Author : William S. Hatcher
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Logical Foundations Of Mathematics written by William S. Hatcher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.
The Logical Foundations Of Mathematics
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Author : William S. Hatcher
language : en
Publisher:
Release Date : 1982
The Logical Foundations Of Mathematics written by William S. Hatcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Logical Foundations Of Mathematics And Computational Complexity
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Author : Pavel Pudlák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-22
Logical Foundations Of Mathematics And Computational Complexity written by Pavel Pudlák 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 2013-04-22 with Mathematics categories.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
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.
Logical Foundations Of Mathematics For Behavioral Scientists
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Author : Abraham S. Luchins
language : en
Publisher:
Release Date : 1965
Logical Foundations Of Mathematics For Behavioral Scientists written by Abraham S. Luchins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Logic categories.
Theoretic study of the application of mathematics to experimental social psychology and behavioural science. Bibliography pp. 394 to 418.
Logicism Renewed
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Author : Paul C. Gilmore
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30
Logicism Renewed written by Paul C. Gilmore 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 2017-03-30 with Mathematics categories.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.
The Logical Foundations Of Mathematics
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Author : Richard Burdon Haldane Haldane (Viscount)
language : en
Publisher:
Release Date : 1909
The Logical Foundations Of Mathematics written by Richard Burdon Haldane Haldane (Viscount) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1909 with categories.
Mathematical Logic And The Foundations Of Mathematics
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Author : G. T. Kneebone
language : en
Publisher:
Release Date : 1963
Mathematical Logic And The Foundations Of Mathematics written by G. T. Kneebone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Logic, Symbolic and mathematical categories.
Introduction To The Foundations Of Mathematics
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Author : Raymond L. Wilder
language : en
Publisher: Courier Corporation
Release Date : 2012-01-01
Introduction To The Foundations Of Mathematics written by Raymond L. Wilder and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Mathematics categories.
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.
The Logical Foundations Of Scientific Theories
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Author : Decio Krause
language : en
Publisher: Routledge
Release Date : 2016-07-15
The Logical Foundations Of Scientific Theories written by Decio Krause and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-15 with Mathematics categories.
This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.