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Andrew W. Appel, Alan Turing's System of Logic: The Princeton Thesis, Princeton UP, 2012

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The Essential Turing

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On 23 September 1936 Turing left England on a vessel bound for New York. His destination was Princeton University, where the Mathematics Department and the Institute for Advanced Study combined to make Princeton a leading centre for mathematics. Turing had applied unsuccessfully for a Visiting Fellowship to Princeton in the spring of 1935. When a year later he learned of Church’s work at Princeton on the Entscheidungsproblem, which paralleled his own (see ‘Computable Numbers: A Guide’), Turing ‘decided quite definitely’ to go there. He planned to stay for a year. In mid-1937 the offer of a Visiting Fellowship for the next academic year persuaded him to prolong his visit, and he embarked on a Ph.D. thesis. Already advanced in his academic career, Turing was an unusual graduate student (in the autumn of 1937, he himself was appointed by Cambridge University to examine a Ph.D. thesis). By October 1937 Turing was looking forward to his thesis being ‘done by about Christmas’. It took jus...

Logicians are usually philosophically or mathematically minded. Why, then, would they be so interested in problems that belong to computer science, like the explication of the notions of algorithm, effective procedure, and suchlike? The reason for their interest is presumably this. Such problems are interdisciplinary, and modern mathematics, logic and analytic philosophy have much in common, going hand in hand. For instance, the classical decision problem (Entscheidungsproblem) was tremendously popular among logicians. Kurt Gödel, for one, worked on it. Thus I first provide in Section 1 a brief summary of Gödel’s famous incompleteness results. In the summary I use a current technical vernacular. That is, I use terms like ‘algorithm’, ‘effective procedure’, ‘recursive axiomatization’, etc. These terms were not used in the time when Gödel was pursuing his research on (un)decidability, because the study of these modern notions was triggered, inter alia, just by Gödel’s incompleteness r...

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Turing historical article of 1936 is the result of a special endeavor focused around the factuality of a general process for algorithmic computation. The Turing machine as a universal feasibility test for computing procedures is applied up to closely examining what are considered to be the limits of computation itself. In this regard he claims to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the enumeration of the computable sequences. This article closely examines the original 1936 argument, displaying how it cannot be considered a demontration, and that there is indeed no evidence of such a defined number that is not computable.

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Alan Turing's Systems of Logic: The Princeton Thesis (Chapter 1) (reference to archive.org)

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(Princeton University Press) Alan Turing (1912-1954) broke the German Enigma code during World War II, and was the British founder of computer science and artificial intelligence. Though less well known than his other work, Turing’s 1938 Princeton Ph.D. thesis, “Systems of Logic Based on Ordinals,” which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance. Appel is Eugene Higgins Professor and Chairman of the Department of Computer Science at Princeton.

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Alan Turing’s Systems of Logic: The Princeton Thesis

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.

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• Preface ix The Birth of Computer Science at Princeton in the 1930s Andrew W. Appel 1 Turing's Thesis Solomon Feferman 13 Notes on the Manuscript 27 Systems of Logic Based on Ordinals Alan Turing 31 A Remarkable Bibliography 141 Contributors 143.
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Alan turing's systems of logic: the princeton thesis.

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This well produced facsimile edition of Alan Turing's Princeton thesis with notes by Solomon Fefferman will be of interest mainly to historians of logic and computer science.

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Alan Turing's Systems of Logic: The Princeton Thesis

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A facsimile edition of Alan Turing's influential Princeton thesis 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.

• ISBN-10 0691155747
• ISBN-13 978-0691155746
• Publisher Princeton University Press
• Publication date May 27, 2012
• Language English
• Dimensions 7.25 x 0.5 x 10 inches
• Print length 160 pages
• See all details

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"For me, this is the most interesting of Alan Turing's writings, and it is a real delight to see a facsimile of the original typescript here. The work is packed with ideas that have turned out to be significant for all sorts of current research areas in computer science and mathematics." --Barry Cooper, University of Leeds

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• Publisher ‏ : ‎ Princeton University Press (May 27, 2012)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 160 pages
• ISBN-10 ‏ : ‎ 0691155747
• ISBN-13 ‏ : ‎ 978-0691155746
• Item Weight ‏ : ‎ 1.12 pounds
• Dimensions ‏ : ‎ 7.25 x 0.5 x 10 inches
• #374 in Computer Programming Logic
• #537 in Logic (Books)
• #860 in Computing Industry History

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