Inexhaustibility

A Non-Exhaustive Treatment

Author: Torkel Franzén

Publisher: Cambridge University Press

ISBN: 1108641636

Category: Mathematics

Page: 251

View: 4286

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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

Alan Turing: His Work and Impact

Author: S. Barry Cooper,J. van Leeuwen

Publisher: Elsevier

ISBN: 0123870127

Category: Mathematics

Page: 944

View: 2147

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In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews Affordable, key collection of the most significant papers by A.M. Turing Commentary explaining the significance of each seminal paper by preeminent leaders in the field Additional resources available online

The History of Philosophical and Formal Logic

From Aristotle to Tarski

Author: Alex Malpass,Marianna Antonutti Marfori

Publisher: Bloomsbury Publishing

ISBN: 1472505255

Category: Philosophy

Page: 256

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The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages (Aristotle and The Stoics) The early modern period (Bolzano, Boole) High modern period (Frege, Peano & Russell and Hilbert) Early 20th century (Godel and Tarski) Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic.

Alan Turing's Systems of Logic

The Princeton Thesis

Author: Andrew W. Appel

Publisher: Princeton University Press

ISBN: 0691164738

Category: Computers

Page: 160

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Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Intensionality

Lecture Notes in Logic 22

Author: Reinhard Kahle

Publisher: CRC Press

ISBN: 1439864306

Category: Mathematics

Page: 280

View: 4879

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A compilation of articles about Intensionality in philosophy, logic, linguistics, and mathematics. The articles approach the concept of Intensionality from different perspectives. Some articles address philosophical issues raised by the possible worlds approach to intensionality; others are devoted to technical aspects of modal logic. The volume highlights the particular interdisciplinary nature of intensionality with articles spanning the areas of philosophy, linguistics, mathematics, and computer science.

Laudato si

Die Umwelt-Enzyklika des Papstes

Author: Franziskus (Papst),

Publisher: Verlag Herder GmbH

ISBN: 345180736X

Category: Religion

Page: 288

View: 716

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Mit großer Spannung wurde sie erwartet, auch von Nicht-Katholiken: Die Umwelt-Enzyklika von Papst Franziskus nimmt die heute entscheidenden Themen in den Blick; es geht um die geht um soziale, ökologische und politische Zusammenhänge. Wohl selten war ein päpstliches Schreiben so aktuell und brisant und vor allem relevant für alle Gesellschaftsschichten und Menschen weltweit. Mit "Laudato si" beweist Franziskus, dass die Kirche nach wie vor eine unverzichtbare Stimme im Diskurs zur Gestaltung der modernen Welt ist. Wer verstehen will, wie Papst und Kirche die großen Herausforderungen unserer Zeit bestehen wollen, kommt an diesem Werk nicht vorbei. Ein Muss für jeden, der an den drängenden Fragen unserer Zeit interessiert ist.

Der Gödelsche Beweis

Author: Ernest Nagel,James R. Newman

Publisher: de Gruyter Oldenbourg

ISBN: 9783486597264

Category:

Page: 110

View: 6801

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Spätestens seit Douglas R. Hofstadters "Gödel, Escher, Bach" ist der Name Gödel auch bei Nichtmathematikern bekannt geworden. 1931 hatte Kurt Gödel unter dem Titel "Über formal unterscheidbare Sätze der Principia Mathematica und verwandter Systeme" seinen Unvollständigkeitssatz publiziert. Nagel und Newman haben das Wesentliche an Gödels Ergebnissen für Nichtfachleute dargestellt. Die vorliegende 9. Auflage ist ein unveränderter Nachdruck der längst klassisch gewordenen Ausgabe von 1958.

Inexhaustibility

Webster’s Timeline History, 1869 - 2004

Author: Icon Group International

Publisher: ICON Group International

ISBN: 9780546476439

Category:

Page: N.A

View: 8771

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Die Freude des Evangeliums

Author: Franziskus (Papst),

Publisher: Verlag Herder GmbH

ISBN: 3451801507

Category: Religion

Page: 320

View: 4355

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"Ich weiß sehr wohl, dass heute die Dokumente nicht dasselbe Interesse wecken wie zu anderen Zeiten und schnell vergessen werden. Trotzdem betone ich, dass das, was ich hier zu sagen beabsichtige, eine programmatische Bedeutung hat und wichtige Konsequenzen beinhaltet ... Ich wünsche mir eine arme Kirche für die Armen." Papst Franziskus Das vollständige Dokument plus Einführung und Themenschlüssel

Überwachen und Strafen

die Geburt des Gefängnisses

Author: Michel Foucault

Publisher: N.A

ISBN: 9783518387719

Category: Bürgerliche Gesellschaft - Disziplinierung - Geschichte

Page: 396

View: 619

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Das andere Geschlecht

Sitte und Sexus der Frau

Author: Simone de Beauvoir

Publisher: Rowohlt Verlag GmbH

ISBN: 3644051615

Category: Social Science

Page: 944

View: 4495

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Das berühmte Standardwerk von Simone de Beauvoir. Die universelle Standortbestimmung der Frau, die aus jahrtausendealter Abhängigkeit von männlicher Vorherrschaft ausgebrochen ist, hat nichts an Gültigkeit eingebüßt. Die Scharfsichtigkeit der grundlegenden Analyse tritt in der Neuübersetzung noch deutlicher hervor.

Die feinen Unterschiede

Kritik der gesellschaftlichen Urteilskraft

Author: Pierre Bourdieu

Publisher: N.A

ISBN: 9783518576250

Category: Aesthetics, French

Page: 877

View: 4139

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Die Analyse des kulturellen Konsums ist für alle von Interesse, die geneigt sind, ihre eigenen, meist als selbstverständlich aufgefassten kulturellen Vorlieben und Praktiken zu prüfen. Der Reiz und das Verdienst des Buches liegen darin, dass der Autor immer im Kontakt zum konkreten Alltag bleibt. Die Lektüre der Feinen Unterschiede wird ein spannender Selbsterfahrungsprozess.

Das wilde Denken

Author: Claude Lévi-Strauss

Publisher: N.A

ISBN: 9783518276143

Category: Totemismus - Strukturalismus

Page: 333

View: 5755

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Mein Kampf

Author: Adolf Hitler

Publisher: Createspace Independent Publishing Platform

ISBN: 9781983638206

Category:

Page: 822

View: 5023

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Published in the German language, this is the infamous Main Kampf, by Adolf Hitler.