Gödel's Disjunction

The scope and limits of mathematical knowledge

Author: Leon Horsten,Philip Welch

Publisher: Oxford University Press

ISBN: 0191077690

Category: Mathematics

Page: 288

View: 6235

The logician Kurt Gödel 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 Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
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Physical Perspectives on Computation, Computational Perspectives on Physics

Author: Michael E. Cuffaro,Samuel C. Fletcher

Publisher: Cambridge University Press

ISBN: 1316767396

Category: Science

Page: N.A

View: 4600

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.
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Die Grundlagen der Arithmetik

eine logisch-mathematische untersuchung über den begriff der zahl

Author: Gottlob Frege

Publisher: Georg Olms Verlag

ISBN: 9783487400280

Category:

Page: 119

View: 8774

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The Encyclopaedia Britannica

A Dictionary of Arts, Sciences and General Literature

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Encyclopedias and dictionaries

Page: N.A

View: 2431

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Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 1878

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The Century Dictionary

An Encyclopedic Lexicon of the English Language

Author: William Dwight Whitney

Publisher: N.A

ISBN: N.A

Category: Encyclopedias and dictionaries

Page: 7076

View: 8085

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Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 6592

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Data mining

praktische Werkzeuge und Techniken für das maschinelle Lernen

Author: Ian H. Witten,Eibe Frank

Publisher: N.A

ISBN: 9783446215337

Category:

Page: 386

View: 1765

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Wahrscheinlichkeitsrechnung (Ars Conjectandi)

Author: Jakob Bernoulli

Publisher: Wentworth Press

ISBN: 9780270072112

Category:

Page: 170

View: 8193

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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Theaitetos

Author: Platon

Publisher: Jazzybee Verlag

ISBN: 384961803X

Category:

Page: 89

View: 2725

Die Serie "Meisterwerke der Literatur" beinhaltet die Klassiker der deutschen und weltweiten Literatur in einer einzigartigen Sammlung für Ihren eBook Reader. Lesen Sie die besten Werke großer Schriftsteller,Poeten, Autoren und Philosophen auf Ihrem Reader. Dieses Werk bietet zusätzlich * Eine Biografie/Bibliografie des Autors. Der Theaitetos (griechisch Θεαίτητος, eingedeutscht auch Theaetet oder Theätet) ist eines der mittleren bis späteren Werke des Philosophen Platon. Es gehört zusammen mit den Dialogen Kratylos, Sophistes und dem Politikos zur zweiten Tetralogie der platonischen Werke. Neben Sokrates treten darin Theodoros von Kyrene und der namensgebende Theaitetos auf. Der Dialog diskutiert drei verschiedene Konzepte des Wissens, ohne dabei eine definitive Antwort zu finden. (aus wikipedia.de)
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Menon

Author: Platon

Publisher: BoD – Books on Demand

ISBN: 3843062064

Category: Philosophy

Page: 52

View: 861

Platon: Menon Entstanden etwa zwischen 393 und 388 v. Chr. Erstdruck (in lateinischer Übersetzung durch Marsilio Ficino) in: Opera, Florenz o. J. (ca. 1482/84). Erstdruck des griechischen Originals in: Hapanta ta tu Platônos, herausgegeben von M. Musoros, Venedig 1513. Erste deutsche Übersetzung durch Friedrich Gedike in: Vier Dialogen des Platon, Berlin 1780. Der Text folgt der Übersetzung durch Ludwig von Georgii von 1860. Vollständige Neuausgabe mit einer Biographie des Autors. Herausgegeben von Karl-Maria Guth. Berlin 2016. Textgrundlage ist die Ausgabe: Platon: Sämtliche Werke. Berlin: Lambert Schneider, [1940]. Die Paginierung obiger Ausgabe wird in dieser Neuausgabe als Marginalie zeilengenau mitgeführt. Umschlaggestaltung von Thomas Schultz-Overhage unter Verwendung des Bildes: Raffael, Die Schule von Athen (Detail). Gesetzt aus der Minion Pro, 11 pt.
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Schule des Denkens

vom Lösen mathematischer Probleme

Author: George Pólya

Publisher: N.A

ISBN: 9783772006081

Category:

Page: 266

View: 2912

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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 2045

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Theorien und Dinge

Author: Willard van Orman Quine

Publisher: N.A

ISBN: 9783518285602

Category:

Page: 256

View: 1373

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