Gödel Versus Wittgenstein

Author : Mike Hockney
Publisher : Magus Books
Page : 550 pages
File Size : 48,8 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX

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Gödel Versus Wittgenstein by Mike Hockney Pdf

Perhaps nothing has been more misinterpreted than Gödel's incompleteness theorems. Stephen Hawking, adopting the popular misconception, said, "Thus mathematics is either inconsistent, or incomplete. The smart money is on incomplete." If mathematics is tautology, as Wittgenstein said, mathematics cannot be inconsistent and/or incomplete, and so Gödel's work cannot be about mathematics. If mathematics is not tautological, mathematics is mired in inconsistency and/or incompleteness, just as Stephen Hawking said, hence is unreliable. If mathematics is non-ontological, it cannot say anything about reality. If mathematics is ontological, it's the only thing that can say anything true about reality. There can't be a world where math is a bit true and a bit false. Either the world is wholly mathematical – in which case math and not science is how we must study the world – or the world isn't mathematical at all, in which case it's absurd for science to use math.

Author : Ludwig Wittgenstein
Publisher : Unknown
Page : 204 pages
File Size : 45,8 Mb
Release : 1972
Category : Mathematics
ISBN : 0262730170

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Bemerkungen Über Die Grundlagen Der Mathematik by Ludwig Wittgenstein Pdf

Author : Sebastian Sunday Grève,Jakub Mácha
Publisher : Springer
Page : 314 pages
File Size : 49,7 Mb
Release : 2016-01-26
Category : Philosophy
ISBN : 9781137472540

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Wittgenstein and the Creativity of Language by Sebastian Sunday Grève,Jakub Mácha Pdf

This volume is the first to focus on a particular complex of questions that have troubled Wittgenstein scholarship since its very beginnings. The authors re-examine Wittgenstein’s fundamental insights into the workings of human linguistic behaviour, its creative extensions and its philosophical capabilities, as well as his creative use of language. It offers insight into a variety of topics including painting, politics, literature, poetry, literary theory, mathematics, philosophy of language, aesthetics and philosophical methodology.

Author : Rebecca Goldstein
Publisher : W. W. Norton & Company
Page : 299 pages
File Size : 48,6 Mb
Release : 2006-01-31
Category : Biography & Autobiography
ISBN : 9780393327601

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Incompleteness by Rebecca Goldstein Pdf

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Author : A. Biletzki
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 54,9 Mb
Release : 2012-09-14
Category : Philosophy
ISBN : 9789400708228

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(Over)Interpreting Wittgenstein by A. Biletzki Pdf

This book tells the story of Wittgenstein interpretation during the past eighty years. It provides different interpretations, chronologies, developments, and controversies. It aims to discover the motives and motivations behind the philosophical community's project of interpreting Wittgenstein. It will prove valuable to philosophers, scholars, interpreters, students, and specialists, in both analytic and continental philosophy.

Author : Francesco Berto
Publisher : John Wiley & Sons
Page : 262 pages
File Size : 42,6 Mb
Release : 2011-09-13
Category : Philosophy
ISBN : 9781444357615

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There's Something About Gödel by Francesco Berto Pdf

Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories Written in an accessible, non-technical style

Author : Hao Wang
Publisher : Courier Corporation
Page : 292 pages
File Size : 55,8 Mb
Release : 2014-09-22
Category : Mathematics
ISBN : 9780486171043

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Popular Lectures on Mathematical Logic by Hao Wang Pdf

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.

Author : Carl Posy,Yemima Ben-Menahem
Publisher : Springer Nature
Page : 404 pages
File Size : 50,5 Mb
Release : 2023-05-05
Category : Mathematics
ISBN : 9783031216558

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Mathematical Knowledge, Objects and Applications by Carl Posy,Yemima Ben-Menahem Pdf

This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.

Author : Friedrich Stadler
Publisher : Springer Nature
Page : 615 pages
File Size : 40,7 Mb
Release : 2023-03-03
Category : Philosophy
ISBN : 9783031077890

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Wittgenstein and the Vienna Circle by Friedrich Stadler Pdf

This book offers a critical update of current Wittgenstein research on the Tractatus logico-philosophicus (TLP) and its relation to the Vienna Circle. The contributions are written by renowned Wittgenstein scholars, on the occasion of the "Wittgenstein Years" 1921/1922 with a special focus on its origin, reception, and interpretation then and now. The main topic is the mutual relation between Wittgenstein and the Vienna Circle (esp. Schlick, Waismann, Carnap, Gödel), but also Russell and Ramsey. In addition, included in this volume are new studies on Wittgenstein's life and work, on the philosophy of the TLP, and on the Wittgenstein family in philosophical and historical context. Furthermore, unpublished documents on Wittgenstein and Waismann from the archives are provided in form of edited and commented primary sources. As per the book series' usual format, a general part of this Yearbook covers a study on Neurath's economy as well as reviews of related publications.

Author : S.G. Shanker
Publisher : Routledge
Page : 373 pages
File Size : 47,8 Mb
Release : 2013-12-19
Category : Philosophy
ISBN : 9781317832041

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Wittgenstein and the Turning Point in the Philosophy of Mathematics by S.G. Shanker Pdf

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Hao Wang
Publisher : MIT Press
Page : 420 pages
File Size : 53,6 Mb
Release : 1997-02-03
Category : Philosophy
ISBN : 0262261251

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A Logical Journey by Hao Wang Pdf

Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

Author : Arthur Gibson,Niamh O'Mahony
Publisher : Springer Nature
Page : 490 pages
File Size : 47,6 Mb
Release : 2020-12-13
Category : Philosophy
ISBN : 9783030360870

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Ludwig Wittgenstein: Dictating Philosophy by Arthur Gibson,Niamh O'Mahony Pdf

In this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein’s philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter’s role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein’s fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. This collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O’Mahony joined him in co-editing and bringing this book to publication.

Author : Juliet Floyd,Felix Mühlhölzer
Publisher : Springer Nature
Page : 330 pages
File Size : 47,7 Mb
Release : 2020-08-31
Category : Mathematics
ISBN : 9783030484811

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Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics by Juliet Floyd,Felix Mühlhölzer Pdf

This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.

Author : Jaakko Hintikka
Publisher : Springer
Page : 358 pages
File Size : 52,9 Mb
Release : 2013-11-27
Category : Philosophy
ISBN : 9781402041099

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Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths by Jaakko Hintikka Pdf

IF WITI'GENSTEIN COULD TALK, COULD WE UNDERSTAND HIM? Perusing the secondary literature on Wittgenstein, I have frequently experienced a perfect Brechtean Entfremdungseffekt. This is interesting, I have felt like saying when reading books and papers on Wittgenstein, but who is the writer talking about? Certainly not Ludwig Wittgenstein the actual person who wrote his books and notebooks and whom I happened to meet. Why is there this strange gap between the ideas of the actual philosopher and the musings of his interpreters? Wittgenstein is talking to us through the posthumous publication of his writings. Why don't philosophers understand what he is saying? A partial reason is outlined in the first essay of this volume. Wittgenstein was far too impatient to explain in his books and book drafts what his problems were, what it was that he was trying to get clear about. He was even too impatient to explain in full his earlier solutions, often merely referring to them casually as it were in a shorthand notation. For one important instance, in The Brown Book, Wittgenstein had explained in some detail what name-object relationships amount to in his view. There he offers both an explanation of what his problem is and an account of his own view illustrated by means of specific examples of language-games. But when he raises the same question again in Philosophical Investigations I, sec.

Author : Hao Wang
Publisher : Bradford Books
Page : 0 pages
File Size : 50,8 Mb
Release : 1990-03-14
Category : Philosophy
ISBN : 0262730871

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Reflections on Kurt Gödel by Hao Wang Pdf

Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel's ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel's and on points of agreement develops Gödel's views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel's career - the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life. A Bradford Book.