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The Incompleteness Phenomenon
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Book Synopsis The Incompleteness Phenomenon by : Martin Goldstern
Download or read book The Incompleteness Phenomenon written by Martin Goldstern and published by CRC Press. This book was released on 2018-10-08 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.
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.
Book Synopsis Can Mathematics Be Proved Consistent? by : Jan von Plato
Download or read book Can Mathematics Be Proved Consistent? written by Jan von Plato and published by Springer Nature. This book was released on 2020-07-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906–1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren’t. The result is known as Gödel’s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödel’s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödel’s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.
Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Book Synopsis Intelligent Design and Religion as a Natural Phenomenon by : John S. Wilkins
Download or read book Intelligent Design and Religion as a Natural Phenomenon written by John S. Wilkins and published by Routledge. This book was released on 2017-03-02 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade a strident public debate has arisen about the nature and origin of religions. Controversies include how exactly religion evolved, whether by individual or group selection, if it is adaptive, and if not, whether and how it is a side effect of evolution. This volume focuses on the issue of naturalizing religion: on the ways in which cognitive science and social sciences have treated religion as a natural phenomenon. It questions whether religious behaviour, institutions, and experiences can be explained in natural terms. The editor brings together some of the best published work on the definition of 'religion', intelligent design and the evolution of religion.
Download or read book Goedel's Way written by Gregory Chaitin and published by CRC Press. This book was released on 2011-10-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8
Book Synopsis Incomplete Nature: How Mind Emerged from Matter by : Terrence W. Deacon
Download or read book Incomplete Nature: How Mind Emerged from Matter written by Terrence W. Deacon and published by W. W. Norton & Company. This book was released on 2012 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the emergent processes that bridge the gap between organisms that think and have consciousness and those that do not and discusses the origins of life, information, and free will.
Author :Anna-Teresa Tymieniecka Publisher :Springer Science & Business Media ISBN 13 :940172525X Total Pages :484 pages Book Rating :4.4/5 (17 download)
Book Synopsis Paideia by : Anna-Teresa Tymieniecka
Download or read book Paideia written by Anna-Teresa Tymieniecka and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The education of humanity is the key to the next century's culture, its social and practical life. The main concerns of education are perennial, but the continuous flood of inventions, the technological innovations that re-shape life, calls for a radically new appraisal of the situation, such as only philosophy can provide. Answering the call of humanity for the measure, sense of proportion and direction that could re-orient present and future education, the phenomenology of life - integral and scientific, in a dialogue with the arts, the sciences, and the humanities - proposes an ontopoietic model of life's unfolding as the universal paradigm for this re-orientation. Taking the Human Creative Condition as its Archimedean point, it offers a unique context for a fresh investigation of the concerns of education, both perennial and immediate.
Book Synopsis Landmark Writings in Western Mathematics 1640-1940 by : Ivor Grattan-Guinness
Download or read book Landmark Writings in Western Mathematics 1640-1940 written by Ivor Grattan-Guinness and published by Elsevier. This book was released on 2005-02-11 with total page 1040 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field
Book Synopsis Limits Of Mathematical Modeling In The Social Sciences, The: The Significance Of Godel's Incompleteness Phenomenon by : Doria Francisco Antonio
Download or read book Limits Of Mathematical Modeling In The Social Sciences, The: The Significance Of Godel's Incompleteness Phenomenon written by Doria Francisco Antonio and published by World Scientific. This book was released on 2017-05-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through Gödel's two incompleteness theorems, and in doing so demonstrates how influential Gödel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while Gödel's theorems are able to predict their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science.
Download or read book Proven Impossible written by Dan Gusfield and published by Cambridge University Press. This book was released on 2023-12-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic – and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training – all you need is the discipline to follow logical arguments and a pen in your hand.
Book Synopsis Gödel's Disjunction by : Leon Horsten
Download or read book Gödel's Disjunction written by Leon Horsten and published by Oxford University Press. This book was released on 2016 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Book Synopsis Philosophy of Mathematics by : Ahmet Cevik
Download or read book Philosophy of Mathematics written by Ahmet Cevik and published by CRC Press. This book was released on 2021-11-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
Book Synopsis Forever Undecided by : Raymond M. Smullyan
Download or read book Forever Undecided written by Raymond M. Smullyan and published by Knopf. This book was released on 2012-07-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!
Book Synopsis Information and Randomness by : Cristian S. Calude
Download or read book Information and Randomness written by Cristian S. Calude and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.
Book Synopsis Modelling Critical and Catastrophic Phenomena in Geoscience by : Pratip Bhattacharyya
Download or read book Modelling Critical and Catastrophic Phenomena in Geoscience written by Pratip Bhattacharyya and published by Springer. This book was released on 2006-09-10 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or applied mathematics.
Book Synopsis What Is Mathematics, Really? by : Reuben Hersh
Download or read book What Is Mathematics, Really? written by Reuben Hersh and published by Oxford University Press. This book was released on 1997-08-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
