A Non-Exhaustive Treatment

Author: Torkel Franzén

Publisher: Cambridge University Press

ISBN: 1108641636

Category: Mathematics

Page: 251

View: 3631


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: 7095


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: 3031


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: 4807


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.


Lecture Notes in Logic 22

Author: Reinhard Kahle

Publisher: CRC Press

ISBN: 1439864306

Category: Mathematics

Page: 280

View: 4008


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.


Webster’s Timeline History, 1869 - 2004

Author: Icon Group International

Publisher: ICON Group International

ISBN: 9780546476439


Page: N.A

View: 7809


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


Category: Mathematics

Page: 408

View: 7994


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: 5415


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: 2818


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.

Laudato si

Die Umwelt-Enzyklika des Papstes

Author: Franziskus (Papst),

Publisher: Verlag Herder GmbH

ISBN: 345180736X

Category: Religion

Page: 288

View: 8329


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.

In die Wildnis

Allein nach Alaska

Author: Jon Krakauer

Publisher: Piper Verlag

ISBN: 3492957773

Category: Biography & Autobiography

Page: 304

View: 1839


Im August 1992 wurde die Leiche von Chris McCandless im Eis von Alaska gefunden. Wer war dieser junge Mann, und was hatte ihn in die gottverlassene Wildnis getrieben? Jon Krakauer hat sein Leben erforscht, seine Reise in den Tod rekonstruiert und ein traurig-schönes Buch geschrieben über die Sehnsucht, die diesen Mann veranlasste, sämtliche Besitztümer und Errungenschaften der Zivilisation hinter sich zu lassen, um tief in die wilde und einsame Schönheit der Natur einzutauchen.– Verfilmt von Sean Penn mit Emile Hirsch.

Kurt Gödel

Jahrhundertmathematiker und großer Entdecker

Author: Rebecca Goldstein

Publisher: N.A

ISBN: 9783492249607


Page: 312

View: 6535


Die Freude des Evangeliums

Author: Franziskus (Papst),

Publisher: Verlag Herder GmbH

ISBN: 3451801507

Category: Religion

Page: 320

View: 5931


"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

Mein Kampf

Author: Adolf Hitler

Publisher: N.A

ISBN: 9781911417682


Page: N.A

View: 9418


Als glUckliche Bestimmung gilt es mir heute, da das Schicksal mir zum Geburtsort gerade Braunau am Inn zuwies. Liegt doch dieses StAdtchen an der Grenze jener zwei deutschen Staaten, deren Wiedervereinigung mindestens uns JUngeren als eine mit allen Mitteln durchzufUhrende Lebensaufgabe erscheint! DeutschOsterreich mu wieder zurUck zum groen deutschen Mutterlande, und zwar nicht aus GrUnden irgendwelcher wirtschaftlichen ErwAgungen heraus. Nein, nein: Auch wenn diese Vereinigung, wirtschaftlich gedacht, gleichgUltig, ja selbst wenn sie schAdlich wAre, sie mUte dennoch stattfinden. Gleiches Blut gehOrt in ein gemeinsames Reich. Das deutsche Volk besitzt solange kein moralisches Recht zu kolonialpolitischer TAtigkeit, solange es nicht einmal seine eigenen SOhne in einem gemeinsamen Staat zu fassen vermag. Erst wenn des Reiches Grenze auch den letzten Deutschen umschliet, ohne mehr die Sicherheit seiner ErnAhrung bieten zu kOnnen, ersteht aus der Not des eigenen Volkes das moralische Recht zur Erwerbung fremden Grund und Bodens. Der Pflug ist dann das Schwert, und aus den TrAnen des Krieges erwAchst fUr die Nach welt das tAgliche Brot. So scheint mir dieses kleine GrenzstAdtchen das Symbol einer groen Aufgabe zu sein.