Foundations Logic Language And Mathematics
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Foundations Logic Language And Mathematics
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Author : Hugues Leblanc
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Foundations Logic Language And Mathematics written by Hugues Leblanc 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 2013-04-17 with Science categories.
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.
Foundations
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Author :
language : en
Publisher:
Release Date : 1984
Foundations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Language and languages categories.
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.
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 Language And Mathematics
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Author : Alexander Miller
language : en
Publisher: Oxford University Press
Release Date : 2020-06-17
Logic Language And Mathematics written by Alexander Miller and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-17 with Philosophy categories.
Crispin Wright is widely recognised as one of the most important and influential analytic philosophers of the twentieth and twenty-first centuries. This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics. It comprises specially written chapters by a group of internationally renowned thinkers, as well as four substantial responses from Wright. In these thematically organized replies, Wright summarizes his life's work and responds to the contributory essays collected in this book. In bringing together such scholarship, the present volume testifies to both the enormous interest in Wright's thought and the continued relevance of Wright's seminal contributions in analytic philosophy for present-day debates;
Essays On The Foundations Of Mathematics And Logic
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Author : Giandomenico Sica
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2005
Essays On The Foundations Of Mathematics And Logic written by Giandomenico Sica and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
W V O Quine
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Author : Alex Orenstein
language : en
Publisher: Routledge
Release Date : 2014-12-18
W V O Quine written by Alex Orenstein and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-18 with Philosophy categories.
The most influential philosopher in the analytic tradition of his time, Willard Van Orman Quine (1908-2000) changed the way we think about language and its relation to the world. His rejection of the analytic/synthetic distinction, his scepticism about modal logic and essentialism, his celebrated theme of the indeterminacy of translation, and his advocacy of naturalism have challenged key assumptions of the prevailing orthodoxy and helped shape the development of much of recent philosophy. This introduction to Quine's philosophical ideas provides philosophers, students and generalists with an authoritative analysis of his lasting contributions to philosophy. Quine's ideas throughout are contrasted with more traditional views, as well as with contemporaries such as Frege, Russell, Carnap, Davidson, Field, Kripke and Chomsky, enabling the reader to grasp a clear sense of the place of Quine's views in twentieth-century philosophy and the important criticisms of them.
Foundations Of Artificial Intelligence And Robotics
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Author : Wendell H. Chun
language : en
Publisher: CRC Press
Release Date : 2024-12-24
Foundations Of Artificial Intelligence And Robotics written by Wendell H. Chun and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-24 with Computers categories.
Artificial intelligence (AI) is a complicated science that combines philosophy, cognitive psychology, neuroscience, mathematics and logic (logicism), economics, computer science, computability, and software. Meanwhile, robotics is an engineering field that compliments AI. There can be situations where AI can function without a robot (e.g., Turing Test) and robotics without AI (e.g., teleoperation), but in many cases, each technology requires each other to exhibit a complete system: having "smart" robots and AI being able to control its interactions (i.e., effectors) with its environment. This book provides a complete history of computing, AI, and robotics from its early development to state‐of‐the‐art technology, providing a roadmap of these complicated and constantly evolving subjects. Divided into two volumes covering the progress of symbolic logic and the explosion in learning/deep learning in natural language and perception, this first volume investigates the coming together of AI (the mind) and robotics (the body), and discusses the state of AI today. Key Features: Provides a complete overview of the topic of AI, starting with philosophy, psychology, neuroscience, and logicism, and extending to the action of the robots and AI needed for a futuristic society Provides a holistic view of AI, and touches on all the misconceptions and tangents to the technologies through taking a systematic approach Provides a glossary of terms, list of notable people, and extensive references Provides the interconnections and history of the progress of technology for over 100 years as both the hardware (Moore’s Law, GPUs) and software, i.e., generative AI, have advanced Intended as a complete reference, this book is useful to undergraduate and postgraduate students of computing, as well as the general reader. It can also be used as a textbook by course convenors. If you only had one book on AI and robotics, this set would be the first reference to acquire and learn about the theory and practice.
W V Quine
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Author : Alex Orenstein
language : en
Publisher: Princeton University Press
Release Date : 2002-04-14
W V Quine written by Alex Orenstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-14 with Philosophy categories.
The most influential philosopher in the analytic tradition of his time, Willard Van Orman Quine (1908-2000) changed the way we think about language and its relation to the world. His rejection of the analytic/synthetic distinction, his scepticism about modal logic and essentialism, his celebrated theme of the indeterminacy of translation, and his advocacy of naturalism have challenged key assumptions of the prevailing orthodoxy and helped shape the development of much of recent philosophy. This introduction to Quine's philosophical ideas provides philosophers, students, and generalists with an authoritative analysis of Quine's lasting contributions to philosophy. The major themes covered include the adaptation of the language of modern logic to formulate a criterion of ontological commitment; Quine's own ontological commitments; Duhemian-Holistic empiricism and the attendant rejection of a priori knowledge; the nature and grounds of logical truth; Quine's criticisms of such notions as meaning, synonymy, analyticity, and necessity; the conjecture of the indeterminacy of translation; modal logic; propositional attitudes; and Quine's work on naturalized epistemology. Quine's ideas throughout are contrasted with more traditional views, as well as with contemporaries such as Frege, Russell, Carnap, Davidson, Field, Kripke, and Chomsky, enabling the reader to grasp a clear sense of the place of Quine's views in twentieth-century philosophy and the important criticisms of them.
Logic Language Ontology
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Author : Urszula B. Wybraniec-Skardowska
language : en
Publisher: Springer Nature
Release Date : 2022-12-01
Logic Language Ontology written by Urszula B. Wybraniec-Skardowska and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.
How should we think about the meaning of the words that make up our language? How does reference of these terms work, and what is their referent when these are connected to abstract objects rather than to concrete ones? Can logic help to address these questions? This collection of papers aims to unify the questions of syntax and semantics of language, which span across the fields of logic, philosophy and ontology of language. The leading motif of the presented selection is the differentiation between linguistic tokens (material, concrete objects) on the one hand and linguistic types (ideal, abstract objects) on the other. Through a promenade among articles that span over all of the Author’s career, this book addresses the complex philosophical question of the ontology of language by following the crystalline conceptual tools offered by logic. At the core of Wybraniec-Skardowska’s scholarship is the idea that language is an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. The application throughout the book of tools of classical logic and set theory results fosters the emergence of a general formal logical theory of syntax, semantics and of the pragmatics of language, which takes into account the duality token-type in the understanding of linguistic expressions. Via a functional approach to language itself, logic appears as ontologically neutral with respect to existential assumptions relating to the nature of linguistic expressions and their extra-linguistic counterparts. The book is addressed to readers both at the graduate and undergraduate level, but also to a more general audience interested in getting a firmer grip on the interplay between reality and the language we use to describe and understand it.