Inexhaustibility A Non Exhaustive Treatment
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Inexhaustibility
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Author : Torkel Franzén
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30
Inexhaustibility written by Torkel Franzén 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. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.
Inexhaustibility
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Author : Torkel Franzén
language : en
Publisher: A K Peters/CRC Press
Release Date : 2004
Inexhaustibility written by Torkel Franzén and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with MATHEMATICS categories.
Gödel's Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough.
The History Of Philosophical And Formal Logic
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Author : Alex Malpass
language : en
Publisher: Bloomsbury Publishing
Release Date : 2017-06-29
The History Of Philosophical And Formal Logic written by Alex Malpass and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-29 with Philosophy categories.
The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages (Aristotle and The Stoics) The early modern period (Bolzano, Boole) High modern period (Frege, Peano & Russell and Hilbert) Early 20th century (Godel and Tarski) Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic.
The Epistemic Lightness Of Truth
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Author : Cezary Cieśliński
language : en
Publisher: Cambridge University Press
Release Date : 2017-12-07
The Epistemic Lightness Of Truth written by Cezary Cieśliński 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 2017-12-07 with Philosophy categories.
This volume explores the deflationary claim of the innocence of truth, taking into account recent results on axiomatic truth theories.
Alan Turing
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Author : S. Barry Cooper
language : en
Publisher: Elsevier
Release Date : 2013-03-18
Alan Turing written by S. Barry Cooper and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Mathematics categories.
In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews Affordable, key collection of the most significant papers by A.M. Turing Commentary explaining the significance of each seminal paper by preeminent leaders in the field Additional resources available online
Modes Of Truth
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Author : Carlo Nicolai
language : en
Publisher: Routledge
Release Date : 2021-03-30
Modes Of Truth written by Carlo Nicolai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-30 with Philosophy categories.
The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics. The Open Access version of this book, available at www.taylorfrancis.com, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.
Alan Turing S Systems Of Logic
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Author : Andrew W. Appel
language : en
Publisher: Princeton University Press
Release Date : 2021-10-12
Alan Turing S Systems Of Logic written by Andrew W. Appel 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 2021-10-12 with Computers categories.
A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.
Constructing The World
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Author : David J. Chalmers
language : en
Publisher: Oxford University Press
Release Date : 2012-10-04
Constructing The World written by David J. Chalmers 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 2012-10-04 with Philosophy categories.
David J. Chalmers constructs a highly ambitious and original picture of the world, from a few basic elements. He returns to Rudolf Carnap's attempt to do the same, and adopts the idea of scrutability—according to which reasoning from a limited class of basic truths yields all truths about the world—to address central themes in philosophy.
Reverse Mathematics 2001
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Author : Stephen G. Ross
language : en
Publisher: CRC Press
Release Date : 2005-09-01
Reverse Mathematics 2001 written by Stephen G. Ross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-01 with Mathematics categories.
Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting rece
Recursion Theory
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Author : Joseph R. Shoenfield
language : en
Publisher: CRC Press
Release Date : 2018-04-27
Recursion Theory written by Joseph R. Shoenfield and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Mathematics categories.
This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.