Inexhaustibility

A Non-Exhaustive Treatment
Author: Torkel Franzén
Publisher: Cambridge University Press
ISBN: 1108641636
Category: Mathematics
Page: 251
View: 7438
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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: 7491
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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
View: 4240
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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
View: 409
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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: 3797
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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.

The Bulletin of Symbolic Logic


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
View: 5364
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Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5530
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Inexhaustibility

Webster’s Timeline History, 1869 - 2004
Author: Icon Group International
Publisher: ICON Group International
ISBN: 9780546476439
Category:
Page: N.A
View: 8139
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The Logica Yearbook


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
View: 3458
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Mengenlehre und ihre Logik


Author: Willard van Orman Quine
Publisher: Springer-Verlag
ISBN: 3322859436
Category: Mathematics
Page: 264
View: 3800
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Die Lage der arbeitenden Klasse in England


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Great Britain
Page: N.A
View: 4957
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Laudato si

Die Umwelt-Enzyklika des Papstes
Author: Franziskus (Papst),
Publisher: Verlag Herder GmbH
ISBN: 345180736X
Category: Religion
Page: 288
View: 5556
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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.

Logic Colloquium 2000

proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in Paris, France, July 23-31, 2000
Author: René Cori
Publisher: A K Peters Ltd
ISBN: N.A
Category: Mathematics
Page: 408
View: 8826
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This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.

Reverse mathematics 2001


Author: Stephen George Simpson
Publisher: A K Peters Ltd
ISBN: 9781568812632
Category: Mathematics
Page: 401
View: 8333
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Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic.

Logicism renewed

logical foundations for mathematics and computer science
Author: Paul Carl Gilmore
Publisher: A K Peters Ltd
ISBN: 9781568812755
Category: Mathematics
Page: 230
View: 6838
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Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In Logicism Renewed, the author revisits this concept in light of advances in mathematical logic and the need for languages that can be understood by both humans and computers that require distinguishing between the intension and extension of predicates. Using Intensional Type Theory (ITT) the author provides a unified foundation for mathematics and computer science, yielding a much simpler foundation for recursion theory and the semantics of computer programs than that currently provided by category theory.

Der Gödelsche Beweis


Author: Ernest Nagel,James R. Newman
Publisher: de Gruyter Oldenbourg
ISBN: 9783486597264
Category:
Page: 110
View: 642
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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.

Die Freude des Evangeliums


Author: Franziskus (Papst),
Publisher: Verlag Herder GmbH
ISBN: 3451801507
Category: Religion
Page: 320
View: 1035
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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: 2654
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Der Mensch und seine Symbole


Author: Carl G. Jung
Publisher: N.A
ISBN: 9783843602945
Category:
Page: 320
View: 6539
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