Why The Cantor Diagonal Argument Is Not Valid

Author : Pravin Johri,Alisha Johri
Publisher : Createspace Independent Publishing Platform
Page : 98 pages
File Size : 43,6 Mb
Release : 2018-06-10
Category : Electronic
ISBN : 1720899770

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Why the Cantor Diagonal Argument Is Not Valid by Pravin Johri,Alisha Johri Pdf

The Cantor Diagonal Argument (CDA) is the quintessential result in Cantor's infinite set theory. This is one procedure that almost everyone who studies this subject finds astounding. However, mathematicians maintain that the CDA is absolutely correct and that the "countless" people trying to repudiate the CDA are not only wrong but are seemingly "irrational" enough to challenge such a widely accepted result.This book outlines all the different issues with the CDA. And, there are many.This book does not attempt to disprove the CDA by finding fault with it. Since the mathematical community has not bought into any of the tens of counterarguments it likely will ignore yet one more.Instead, assuming the CDA is correct, we create a situation where the CDA produces results when it really shouldn't and use the CDA itself to discredit the CDA.Cantor's infinite set theory is largely based on arbitrary rules, confounding axioms, and logic that defies intuition and common sense. Our previous books explain exactly what is wrong and why. The theory is hopelessly flawed because the starting assumption - the axiom of infinity - is wrong. There is no such thing as an infinite set. But mathematicians stubbornly stick to their belief that everything is correct.Hopefully this is the straw that breaks the camel's back!

Author : Richard J. Lipton,Kenneth W. Regan
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 49,7 Mb
Release : 2013-12-11
Category : Computers
ISBN : 9783642414220

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People, Problems, and Proofs by Richard J. Lipton,Kenneth W. Regan Pdf

People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.

Author : Kip K. Sewell
Publisher : Rond Books
Page : 828 pages
File Size : 48,5 Mb
Release : 2023-08-01
Category : Philosophy
ISBN : 9798988123804

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Forever Finite by Kip K. Sewell Pdf

INFINITY IS NOT WHAT IT SEEMS… Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes in a divine Creator infinite in knowledge, power, and benevolence. According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, Forever Finite offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology.

Author : Anonim
Publisher : Elsevier
Page : 878 pages
File Size : 42,9 Mb
Release : 2012-01-24
Category : Mathematics
ISBN : 9780080930664

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Sets and Extensions in the Twentieth Century by Anonim Pdf

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights

Author : Anthony C. Patton
Publisher : Algora Publishing
Page : 200 pages
File Size : 42,8 Mb
Release : 2018-07-01
Category : Philosophy
ISBN : 9781628943412

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The End of Infinity by Anthony C. Patton Pdf

Author : Detlef D. Spalt
Publisher : Springer Nature
Page : 265 pages
File Size : 46,6 Mb
Release : 2022-08-02
Category : Mathematics
ISBN : 9783031006500

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A Brief History of Analysis by Detlef D. Spalt Pdf

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

Author : Howard DeLong
Publisher : Courier Corporation
Page : 322 pages
File Size : 46,8 Mb
Release : 2012-09-26
Category : Mathematics
ISBN : 9780486139159

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A Profile of Mathematical Logic by Howard DeLong Pdf

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Author : Policy and Global Affairs,Office of Scientific and Engineering Personnel,Committee on Skill Transferability in Engineering Labor Markets
Publisher : National Academies Press
Page : 181 pages
File Size : 40,6 Mb
Release : 1990-02-01
Category : Education
ISBN : 9780309042765

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Fostering Flexibility in the Engineering Work Force by Policy and Global Affairs,Office of Scientific and Engineering Personnel,Committee on Skill Transferability in Engineering Labor Markets Pdf

Author : Clark Glymour
Publisher : MIT Press
Page : 471 pages
File Size : 42,9 Mb
Release : 2015-04-10
Category : Philosophy
ISBN : 9780262527200

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Thinking Things Through, second edition by Clark Glymour Pdf

The second edition of a unique introductory text, offering an account of the logical tradition in philosophy and its influence on contemporary scientific disciplines. Thinking Things Through offers a broad, historical, and rigorous introduction to the logical tradition in philosophy and its contemporary significance. It is unique among introductory philosophy texts in that it considers both the historical development and modern fruition of a few central questions. It traces the influence of philosophical ideas and arguments on modern logic, statistics, decision theory, computer science, cognitive science, and public policy. The text offers an account of the history of speculation and argument, and the development of theories of deductive and probabilistic reasoning. It considers whether and how new knowledge of the world is possible at all, investigates rational decision making and causality, explores the nature of mind, and considers ethical theories. Suggestions for reading, both historical and contemporary, accompany most chapters. This second edition includes four new chapters, on decision theory and causal relations, moral and political theories, “moral tools” such as game theory and voting theory, and ethical theories and their relation to real-world issues. Examples have been updated throughout, and some new material has been added. It is suitable for use in advanced undergraduate and beginning graduate classes in philosophy, and as an ancillary text for students in computer science and the natural sciences.

Author : Loke Hagberg
Publisher : BoD - Books on Demand
Page : 156 pages
File Size : 40,5 Mb
Release : 2023-11-22
Category : Mathematics
ISBN : 9789180575706

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Collected papers on finitist mathematics and phenomenalism by Loke Hagberg Pdf

This is a clarification of and development upon my previous work. It includes a rework of "Concerning the weakest coherent formalization of methodological skepticism as a Bayesian updater" and "On the finitist Wolfram physics model", then there is an outline of finite content theory and mathematical notes in various areas. Digital phenomenology itself is the study of a finitist (and therefore discrete) phenomenalism. It also includes my work on predictive liquid democracy, where liquid democracy is combined with prediction markets. The system allows for local satisfaction of Condorcet's jury theorem extended to multiple alternatives. See the part about predictive liquid democracy.

Author : Lech T. Polkowski
Publisher : Springer Nature
Page : 489 pages
File Size : 47,5 Mb
Release : 2023-11-04
Category : Computers
ISBN : 9783031420344

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Logic: Reference Book for Computer Scientists by Lech T. Polkowski Pdf

The book gives all interested in computer science, a deep review of relevant aspects of logic. In its scope are classical and non-classical logics. The content will be valid as well for those interested in linguistic, philosophy and many other areas of research both in humane and technical branches of science as logic permeates all genuine realms of science. The book contains a substantial part of classical results in logic like those by Gödel, Tarski, Church and Rosser as well as later developments like many-valued logics, logics for knowledge engineering, first-order logics plus inductive definitions. The exposition is rigorous yet without unnecessary abstractionism, so it should be accessible to readers from many disciplines of science. Each chapter contains a problem section, and problems are borrowed from research publications which allows for passing additional information, and it allows readers to test their skills. Extensive bibliography of 270 positions directs readers to research works of importance.

Author : Paul Gochet
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400989498

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Outline of a Nominalist Theory of Propositions by Paul Gochet Pdf

1. IMPORTANCE OF THE SUBJECT In 1900, in A Critical Exposition of the Philosophy of Leihniz, Russell made the following assertion: "That all sound philosophy should begin with an analysis of propositions is a truth too evident, perhaps, to demand a proof". 1 Forty years later, the interest aroused by this notion had not decreased. C. J. Ducasse wrote in the Journal of Philosophy: "There is perhaps no question more basic for the theory of knowledge than that of the nature of 2 propositions and their relations to judgments, sentences, facts and inferences". Today, the great number of publications on the subject is proof that it is still of interest. One of the problems raised by propositions, the problem of deter mining whether propositions, statements or sentences are the primary bearers of truth and falsity, is even in the eyes of Bar-Hillel, "one of the major items that the future philosophy oflanguage will have to discuss". 3 gave a correct summary of the situation when he wrote in his Ph. Devaux Russell (1967): Since Peano and Schroder who, in fact, adhered more faithfully to Boole's logic of classes, the logical and epistemological status of the proposition together with its analysis have not ceased to be the object of productive philosophical controversies. And especially so since the establishment of contemporary symbolic logic, the foundations 4 of which have been laid out by Russell and Whitehead. * 2.

Author : Joseph Wayne Smith,Graham Lyons,Gary Sauer-Thompson
Publisher : Springer
Page : 202 pages
File Size : 54,6 Mb
Release : 2016-07-27
Category : Business & Economics
ISBN : 9781349275694

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The Bankruptcy of Economics: Ecology, Economics and the Sustainability of the Earth by Joseph Wayne Smith,Graham Lyons,Gary Sauer-Thompson Pdf

We live in times of uncertainty and insecurity, at a personal, national and global level. Writers such as Samuel P. Huntington and Robert D. Kaplan, respectively, have spoken of an emerging 'clash of civilizations' and of 'coming anarchy'. This book is also concerned with the future of civilization, in particular with the conflict between economic growth and the sustainability of the biophysical lifesupport systems of the planet, arguing that the flawed system of orthodox neo-classical economics has justified the modernist belief in the necessity of unending economic growth and the ceaseless exploitation of nature.

Author : Raymond Nickerson
Publisher : Psychology Press
Page : 628 pages
File Size : 55,7 Mb
Release : 2011-02-25
Category : Psychology
ISBN : 9781136945380

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Mathematical Reasoning by Raymond Nickerson Pdf

The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Author : Eric Lemaire
Publisher : Walter de Gruyter
Page : 150 pages
File Size : 45,6 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110321845

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Wittgenstein: Issues and Debates by Eric Lemaire Pdf

The work of L. Wittgenstein addresses a huge variety of topics. The spectrum ranges from mathematics to the analysis of ethical problems. These issues have generated many important philosophical discussions and the aim of this book is to examine a the broad range of philosophical problems. Michael Le Du investigates the relevance of the problems and solutions proposed by Wittgenstein in his philosophy of social sciences. Sabine Plaud explores the synoptic views vs. the primal phenomena in Wittgenstein on Goethe’s Morphology. Eric Lemaire makes several critical remarks on Wittgenstein’s anti-metaphyscial readings. Ay?egül Çakal asks what the repudiation of private language means in Wittgenstein’s Philosophy. Alejandro Tomasini Bassols looks into Wittgenstein and the myth of hinge propositions. Lars Hertzberg discusses P.M.S. Hacker’s point of view about Wittgenstein’s meaning of “concept”. Jesús Padilla Gálvez analyzes Wittgenstein’s criticism against Gödel’s project of metalogic.