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On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
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Book Synopsis On Formally Undecidable Propositions of Principia Mathematica and Related Systems by : Kurt Gödel
Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Book Synopsis On Formally Undecidable Propositions of Principia Mathematica and Related Systems by : Kurt Gödel
Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 1992-01-01 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Download or read book Godel's Proof written by Ernest Nagel and published by Routledge. This book was released on 2012-11-12 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Book Synopsis An Introduction to Gödel's Theorems by : Peter Smith
Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Book Synopsis Incompleteness by : Rebecca Goldstein
Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Download or read book Godel's Proof written by Ernest Nagel and published by Lulu.com. This book was released on 2018-09-14 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
Book Synopsis Undecidable Theories by : Alfred Tarski
Download or read book Undecidable Theories written by Alfred Tarski and published by Dover Books on Mathematics. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Download or read book The Undecidable written by Martin Davis and published by Courier Corporation. This book was released on 2004-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics "Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study. The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.
Book Synopsis Godel's Incompleteness Theorems by : Raymond M. Smullyan
Download or read book Godel's Incompleteness Theorems written by Raymond M. Smullyan and published by Oxford University Press. This book was released on 1992-08-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
Book Synopsis A Concise Introduction to Mathematical Logic by : Wolfgang Rautenberg
Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer. This book was released on 2010-07-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
Book Synopsis Numbers, Sets and Axioms by : A. G. Hamilton
Download or read book Numbers, Sets and Axioms written by A. G. Hamilton and published by Cambridge University Press. This book was released on 1982 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Book Synopsis Beyond Art: A Third Culture by : Peter Weibel
Download or read book Beyond Art: A Third Culture written by Peter Weibel and published by Springer Science & Business Media. This book was released on 2005-05-17 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new theory of culture presented with a new method achieved by comparing closely the art and science in 20th century Austria and Hungary. Major achievements that have influenced the world like psychoanalysis, abstract art, quantum physics, Gestalt psychology, formal languages, vision theories, and the game theory etc. originated from these countries, and influence the world still today as a result of exile nurtured in the US. A source book with numerous photographs, images and diagrams, it opens up a nearly infinite horizon of knowledge that helps one to understand what is going on in today’s worlds of art and science.
Book Synopsis Logic, Semantics, Metamathematics by : Alfred Tarski
Download or read book Logic, Semantics, Metamathematics written by Alfred Tarski and published by Hackett Publishing. This book was released on 1983-01-01 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Blackwell Guide to Philosophical Logic by : Lou Goble
Download or read book The Blackwell Guide to Philosophical Logic written by Lou Goble and published by Wiley-Blackwell. This book was released on 2001-08-30 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts. The chapters, written especially for this volume by internationally distinguished logicians, philosophers, computer scientists and linguists, provide comprehensive studies of the concepts, motivations, methods, formal systems, major results and applications of their subject areas. The Blackwell Guide to Philosophical Logic engages both general readers and experienced logicians and provides a solid foundation for further study.
Book Synopsis Hilbert's Programs and Beyond by : Wilfried Sieg
Download or read book Hilbert's Programs and Beyond written by Wilfried Sieg and published by Oxford University Press. This book was released on 2013-01-24 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.
Book Synopsis Incompleteness and Computability by : Richard Zach
Download or read book Incompleteness and Computability written by Richard Zach and published by Createspace Independent Publishing Platform. This book was released on 2017-06-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.
Book Synopsis Continuous Geometry by : John von Neumann
Download or read book Continuous Geometry written by John von Neumann and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
