Alan Turing s Systems of Logic

Author: Alan Mathison Turing
Publisher:
ISBN: 0691155747
Release Date: 2012
Genre: Computers

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.

Alan Turing s Systems of Logic

Author: Andrew W. Appel
Publisher: Princeton University Press
ISBN: 9780691164731
Release Date: 2014-11-16
Genre: Computers

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.

Philosophical Explorations of the Legacy of Alan Turing

Author: Juliet Floyd
Publisher: Springer
ISBN: 9783319532806
Release Date: 2017-05-29
Genre: Science

This volume presents an historical and philosophical revisiting of the foundational character of Turing’s conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing’s work. The centennial of Turing’s birth in 2012 led to the highly celebrated “Alan Turing Year”, which stimulated a world-wide cooperative, interdisciplinary revisiting of his life and work. Turing is widely regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert’s famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing’s breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing’s work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering.

The soul of a university

Author: Brink, Chris
Publisher: Policy Press
ISBN: 9781529200355
Release Date: 2018-07-01
Genre: Education

What is the role of a university in society? In this innovative book, Chris Brink offers the timely reminder that it should have social purpose, as well as achieve academic excellence. The current obsession with rankings and league tables has perpetuated inequality and is preventing social mobility. This book shows how universities can – and should - respond to societal challenges and promote positive social change.

Engineering Trustworthy Software Systems

Author: Jonathan P. Bowen
Publisher: Springer
ISBN: 9783319568416
Release Date: 2017-05-31
Genre: Computers

This volume contains a record of some of the lectures and seminars delivered at the Second International School on Engineering Trustworthy Software Systems (SETSS 2016), held in March/April 2016 at Southwest University in Chongqing, China. The six contributions included in this volume provide an overview of leading-edge research in methods and tools for use in computer system engineering. They have been distilled from six courses and two seminars on topics such as: modelling and verification in event-B; parallel programming today; runtime verification; Java in the safety-critical domain; semantics of reactive systems; parameterized unit testing; formal reasoning about infinite data values; and Alan Turing and his remarkable achievements. The material is useful for postgraduate students, researchers, academics, and industrial engineers, who are interested in the theory and practice of methods and tools for the design and programming of trustworthy software systems.

The Essential Turing

Author: B. Jack. Copeland
Publisher: Clarendon Press
ISBN: 0191520284
Release Date: 2004-09-10
Genre: Science

Alan Turing, pioneer of computing and WWII codebreaker, is one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight. An introduction by leading Turing expert Jack Copeland provides the background and guides the reader through the selection. About Alan Turing Alan Turing FRS OBE, (1912-1954) studied mathematics at King's College, Cambridge. He was elected a Fellow of King's in March 1935, at the age of only 22. In the same year he invented the abstract computing machines - now known simply as Turing machines - on which all subsequent stored-program digital computers are modelled. During 1936-1938 Turing continued his studies, now at Princeton University. He completed a PhD in mathematical logic, analysing the notion of 'intuition' in mathematics and introducing the idea of oracular computation, now fundamental in mathematical recursion theory. An 'oracle' is an abstract device able to solve mathematical problems too difficult for the universal Turing machine. In the summer of 1938 Turing returned to his Fellowship at King's. When WWII started in 1939 he joined the wartime headquarters of the Government Code and Cypher School (GC&CS) at Bletchley Park, Buckinghamshire. Building on earlier work by Polish cryptanalysts, Turing contributed crucially to the design of electro-mechanical machines ('bombes') used to decipher Enigma, the code by means of which the German armed forces sought to protect their radio communications. Turing's work on the version of Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as 'Fish'. Based on binary teleprinter code, Fish was used during the latter part of the war in preference to morse-based Enigma for the encryption of high-level signals, for example messages from Hitler and other members of the German High Command. It is estimated that the work of GC&CS shortened the war in Europe by at least two years. Turing received the Order of the British Empire for the part he played. In 1945, the war over, Turing was recruited to the National Physical Laboratory (NPL) in London, his brief to design and develop an electronic computer - a concrete form of the universal Turing machine. Turing's report setting out his design for the Automatic Computing Engine (ACE) was the first relatively complete specification of an electronic stored-program general-purpose digital computer. Delays beyond Turing's control resulted in NPL's losing the race to build the world's first working electronic stored-program digital computer - an honour that went to the Royal Society Computing Machine Laboratory at Manchester University, in June 1948. Discouraged by the delays at NPL, Turing took up the Deputy Directorship of the Royal Society Computing Machine Laboratory in that year. Turing was a founding father of modern cognitive science and a leading early exponent of the hypothesis that the human brain is in large part a digital computing machine, theorising that the cortex at birth is an 'unorganised machine' which through 'training' becomes organised 'into a universal machine or something like it'. He also pioneered Artificial Intelligence. Turing spent the rest of his short career at Manchester University, being appointed to a specially created Readership in the Theory of Computing in May 1953. He was elected a Fellow of the Royal Society of London in March 1951 (a high honour).

Historische Notizen zur Informatik

Author: Friedrich L. Bauer
Publisher: Springer Science & Business Media
ISBN: 9783540857891
Release Date: 2009-01-08
Genre: Computers

Die Informatik selbst ist eine junge Wissenschaft, ihre Wurzeln aber reichen weit in die Vergangenheit zurück. Der Autor zeigt dies auf unterhaltsame Weise und gleichzeitig mit mathematischer Strenge anhand zahlreicher Facetten aus der Geschichte der Informatik. Die Beiträge sind über viele Jahre in der Zeitschrift Informatik Spektrum erschienen und erscheinen nun erstmals gesammelt als Buch.

Principia Mathematica

Author: Alfred North Whitehead
Publisher:
ISBN: STANFORD:36105039675058
Release Date: 1984-01
Genre: Logic, Symbolic and mathematical


Grundz ge der theoretischen Logik

Author: David Hilbert
Publisher: Springer-Verlag
ISBN: 9783662119327
Release Date: 2013-12-14
Genre: Mathematics

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der formalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet für die Logik eine ähnliche Formel sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebräuchlich ist. In der Mathematik würde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewöhnlichen Sprache bedienen. Die großen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum wesentlichen Teil mit dadurch bedingt, daß es gelang, einen brauchbaren und leistungsfähigen Formalismus zu finden. - Was durch die Formel sprache in der Mathematik erreicht wird, das soll auch in der theoretischen Logik durch diese erzielt werden, nämlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten können. Der Übergang zu logischen Folgerungen, wie er durch das Schließen geschieht, wird in seine letzten Elemente zerlegt und erscheint als formale Umgestaltung der Ausgangsformeln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem Logikkalkül. Dieser Kalkül macht die erfolgreiche Inangriffnahme von Problemen möglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehört z. B.

Alan Turing Enigma

Author: Andrew Hodges
Publisher: Springer
ISBN: 370915832X
Release Date: 2013-11-13
Genre: Computers

Alan Turing, Enigma ist die Biographie des legendären britischen Mathematikers, Logikers, Kryptoanalytikers und Computerkonstrukteurs Alan Mathison Turing (1912-1954). Turing war einer der bedeutendsten Mathematiker dieses Jahrhunderts und eine höchst exzentrische Persönlichkeit. Er gilt seit seiner 1937 erschienenen Arbeit "On Computable Numbers", in der er das Prinzip des abstrakten Universalrechners entwickelte, als der Erfinder des Computers. Er legte auch die Grundlagen für das heute "Künstliche Intelligenz" genannte Forschungsgebiet. Turings zentrale Frage "Kann eine Maschine denken?" war das Motiv seiner Arbeit und wird die Schlüsselfrage des Umgangs mit dem Computer werden. Die bis 1975 geheimgehaltene Tätigkeit Turings für den britischen Geheimdienst, die zur Entschlüsselung des deutschen Funkverkehrs führte, trug entscheidend zum Verlauf und Ausgang des Zweiten Weltkriegs bei.

Die Rechenmaschine und das Gehirn

Author: John von Neumann
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783486819663
Release Date: 1991-01-01
Genre: Computers

"The Computer and the Brain" war der Titel von John von Neumanns letzter hinterlassener Arbeit, in der er den wechselseitigen Beziehungen zwischen der Rechenmaschine und dem menschlichen Denk- und Nervensystem nachgeht. Diese Arbeit gibt ein zusammengefaßtes Zeugnis seiner eindringlichen und unorthodoxen Denkweise. John von Neumann gilt heute als einer der Pioniere der modernen Rechentechnik.

Der Turing Omnibus

Author: A.K. Dewdney
Publisher: Springer-Verlag
ISBN: 9783642788727
Release Date: 2013-03-12
Genre: Computers

Der Turing Omnibus macht in 66 exzellent geschriebenen Beiträgen Station bei den interessantesten Themen aus der Informatik, der Computertechnologie und ihren Anwendungen.

Erfahrung Mathematik

Author: P.J. Davis
Publisher: Springer-Verlag
ISBN: 9783034850407
Release Date: 2013-09-03
Genre: Science

ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.