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LASSEGUE, Jean - TURING, Alan
Turing.
Coll. "Figures du Savoir", Paris, éd. Les Belles Lettres, 2003, 2e tirage, in-8, cartonnage souple, couv. ill. coul. sur fond noir éd., 210 pp., bibliographie, table des matières, "Alan Turing (1912-1954), mathematicien et logicien, est considere comme le pere de l'informatique et de l'intelligence artificielle. Il etait aussi theoricien de la biologie et philosophe: lui revient le merite d'avoir mis en rapport la logique et la biologie. On essaye ici de retracer l'itineraire exceptionnel de ce savant qui fut aussi un homme d'action: pendant la seconde guerre mondiale, alors que les sous-marins allemands faisaient le blocus de l'Angleterre il decrypte les messages codes par la machine Enigma envoyes par radio de Berlin; malgre la penurie d'apres-guerre, il a concu le projet de l'ordinateur et l'a rendu operationnel; il avait, des 1945, le projet de "construire un cerveau"... Ce livre, presentant pour la premiere fois en francais l'ensemble de l'oeuvre de Turing, vise a mieux faire comprendre le monde de la techno-science dans lequel nous vivons aujourd'hui et que Turing a contribue a engendrer." Très bon état
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5 book(s) with the same title
Systems of Logic based on Ordinals. [Received 31 May, 1938. - Read 16 June, 1938.]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 45]. - [TURING'S PH.D.-THESIS]
London, Hodgson & Son, 1939. Royal8vo. In a recent nice red full cloth binding with gilt lettering to spine. Entire volume 45 of ""Proceedings of the London Mathematical Society. Second Series"". Small white square paper label pasted on to lower part of spine, covering year of publication stating: ""A Gift / From /Anna Wheeler"". A very nice and clean copy without any institutional stamps. Pp. 161-240. [Entire volume: (4), 475 pp.].
The rare first printing of Turing's Ph.D.-thesis, which ""opened new fields of investigation in mathematical logic"". This seminal work constitutes the first systematic attempt to deal with the Gödelian incompleteness theorem as well as the introduction to the notion of relative computing. After having studied at King's College at Cambridge from 1931 to 1934 and having been elected a fellow here in 1935, Turing, in 1936 wrote a work that was to change the future of mathematics, namely his seminal ""On Computable Numbers"", in which he answered the famous ""Entscheidungsproblem"", came up with his ""Universal Machine"" and inaugurated mechanical and electronic methods in computing. This most famous theoretical paper in the history of computing caught the attention of Church, who was teaching at Princeton, and in fact he gave to the famous ""Turing Machine"" its name. It was during Church's work with Turing's paper that the ""Church-Turing Thesis"" was born. After this breakthrough work, Newman, under whom Turing had studied at Cambridge, urged him to spend a year studying with Church, and in September 1936 he went to Princeton. It is here at Princeton, under the guidance of Church, that Turing in 1938 finishes his thesis [the present paper] and later the same year is granted the Ph.D. on the basis of it. The thesis was published in ""Proceedings of the London Mathematical Society"" in 1939, and after the publication of it, Turing did no more on the topic, leaving the actual breakthroughs to other generations. In his extraordinary Ph.D.-thesis Turing provides an ingenious method of proof, in which a union of systems prove their own consistency, disproving, albeit shifting the problem to even more complicated matters, Gödel's incompleteness theorem. It would be many years before the ingenious arguments and striking partial completeness result that Turing obtained in the present paper would be thoroughly investigated and his line of research continued. The present thesis also presents other highly important proofs and hypotheses that came to influence several branches of mathematics. Most noteworthy of these is the idea that was later to change the face of the general theory of computation, namely the attempt to produce an arithmetical problem that is not number-theoretical (in his sense). Turing's result is his seminal ""o-machines"""" he here introduces the notion of relative computing and augments the ""Turing Machines"" with so-called oracles (""o""), which allowed for the study of problems that could not be solved by the Turing machine. Turing, however, made no further use of his seminal o-machine, but it is that which Emil Post used as the basis for his theory of ""Degrees of Unsolvability"", crediting Turing with the result that for any set of natural numbers there is another of higher degree of unsolvability. This transformed the notion of computability from an absolute notion into a relative one, which led to entirely new developments and in turn to vastly generalized forms of recursion theory. ""In 1939 Turing published ""Systems of Logic Based on Ordinals,""... This paper had a far-reaching influence"" in 1942 E.L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing's ideas to use ordinal logics in predicative mathematics."" (D.S.B. XIII:498). A part from these groundbreaking points, which Turing never returned to himself, he here also considers intuition versus technical ingenuity in mathematical reasoning, does so in an interesting and provocative manner and comes to present himself as one of the most important thinkers of modern mathematical as well as philosophical logic.""Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (1938), which then appeared as ""Systems of Logic based on Ordinals"" (Turing 1939). It is generally the view, as expressed by Feferman (1988), that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 198), there are 'formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.' Turing's theory of 'ordinal logics' was an attempt to 'avoid as far as possible the effects of Gödel's theorem' by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.In his investigation, Turing introduced the idea of an 'oracle' capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some 'black box' component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 1998). An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined 'oracle-machines' as Turing machines with an additional configuration in which they 'call the oracle' so as to take an uncomputable step. But these oracle-machines are not purely mechanical. They are only partially mechanical, like Turing's choice-machines. Indeed the whole point of the oracle-machine is to explore the realm of what cannot be done by purely mechanical processes...Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity."" (SEP).Following an oral examination in May, in which his performance was noted as ""Excellent,"" Turing was granted his PhD in June 1938.
[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Post:] Finite combinatory processes-formulation... - [LANDMARK VOLUME IN THE HISTORY OF LOGIC]
[No place], The Association for Symbolic Logic, 1936 & 1937. Royal8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 1 & 2 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 16 pages. A very fine copy. [Church:] Pp. 40-1" Pp. 101-2. [Post:] Pp. 103-5. [Turing:] Pp. 153-163" 164. [Entire volume: (4), 218, (2), IV, 188 pp.]
First edition of this collection of seminal papers within mathematical logic, all constituting some of the most important contributions mathematical logic and computional mathematics. A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) CORRECTION TO A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) REVIEW OF ""A. M. TURING. ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM"":First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) Church coined in his review of Turing's paper the phrase 'Turing machine'.FINITE COMBINATORY PROCESSES-FORMULATION I: The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post corresponds exactly to those performed by a Turing machine, and Church, who edited the Journal of Symbolic Logic, felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and asserting that ""the present article ... although bearing a later date, was written entirely independently of Turing's"". (Hook & Norman: Origins of Cyberspace, 356).COMPUTABILITY AND LAMBDA-DEFINABILITY (+) THE Ø-FUNCTION IN LAMBDA-K-CONVERSION: The volume also contains Turing's influential ""Computability and lambda-definability"" in which he proved that computable functions ""are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene"". (Hook & Norman: Origins of Cyberspace, 395).
Finite Combinatory Processes-Formulation 1. [In: The Journal of Symbolic Logic, Vol. 1, Number 3, Sept. 1936]. - [A SIMULTANEOUS VERSION OF THE ""TURING MACHINE""]
[No place], 1936. 8vo. Extract, unbound, unstapled. Pp. 103-105.
The uncommon first printing of Post's seminal paper, in which he, simultaneously with but independently of Turing, describes a logic automaton, which very much resembles the Turing machine. The Universal Turing Machine, which is presented for the first time in Turing's seminal paper in the Proceedings of the London Mathematical Society for 1936 (same year as the present paper), is considered one of the most important innovations in the theory of computation and constitutes the most famous theoretical paper in the history of computing. ""Post [in the present paper] suggests a computation scheme by which a ""worker"" can solve all problems in symbolic logic by performing only machinelike ""primitive acts"". Remarkably, the instructions given to the ""worker"" in Post's paper and to a Universal Turing Machine were identical."" (A Computer Perspective, p. 125). ""The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, indepently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper [the paper offered]. Post's paper was intended to fill a conceptual gap in Alonzo Churchs' paper on ""An unsolvable problem of elementary number theory"" (Americ. Journ. of Math. 58, 1936). Church's paper had answered in the negative Hilbert's question as to whether a definite method existed for proving the truth or falsity of any mathematical statement (the Entscheidungsproblem), but failed to provide the assertion that any such definite method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be written in the form of instructions to a mindless worker operating on an infinite line of ""boxes"" (equivalent to Turing's machine's ""tape""). The worker would be capable only of reading the instructions and performing the following tasks... This range of tasks corresponds exactly to those performed by a Turing machine, and Church, who edited the ""Journal of Symbolic Logic"", felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and ascertaining that ""the present article... although bearing a later date, was written entirely independently of Turing's"" (p. 103)."" (Origins of Cyberspace, pp. 111-12).Hook & Norman, Origins of Cyberspace, 2002: 355.Charles & Ray Eames, A Computer Perspective, 1973: 125.
A Method for the Calculation of the Zeta-Function. [Received 7 March, 1939. - Read 16 March, 1939]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 48]. - [TURING'S FIRST WORK ON THE ZETA-FUNCTION]
London, Hodgson & Son, 1945. Royal 8vo. Entire volume 48 of ""Proceedings of the London Mathematical Society. Second Series"" bound WITH ALL THE SIX ORIGINAL FRONT-WRAPPERS for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris (""Belford College. Univ. London"") to spine. Very minor bumping to extremities. Overall in excellent, very nice, clean, and fresh condition in- as well as ex-ternally. Small circle-stamp to pasted-down front free end-paper and to title-page (""Bedford College for Women""). Book-plate stating that the book was presented to the Library of Bedford College by ""Professor H. Simpson./ 1945"" + discreet library-markings to upper margin of pasted-down front free end-paper. Pp. 180-197. [Entire volume: (4),477, (1) pp + 1 plate (balance sheet)].
The very rare first printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous ""Zeta-function Machine"", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. ""Turing had ideas for the design of an ""analogue"" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides."" (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking ""A Method for the Calculation of the Zeta-Function"", which constitutes his first printed contribution to the subject.""After the publication of his paper ""On computable Numbers,"" Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers... Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]..."" (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).
A Method for the Calculation of the Zeta-Function. [Received 7 March, 1939. - Read 16 March, 1939]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 48]. - [TURING'S FIRST WORK ON THE ZETA-FUNCTION]
London, Hodgson & Son, 1945. Royal 8vo. Entire volume 48 of ""Proceedings of the London Mathematical Society. Second Series"" bound in a nice contemporary blue full cloth binding with gilt ex-libris (""Sir John Cass College"") to front board and gilt title-label and year to spine. Very minor wear to extremities. Nicely re-enforced at inner hinges. A very nice, clean, and tight copy. Large library-book-plate to inside of front board (stating that the volume was presented by ""Dr. A.E.R. Church""), with ""withdrawn""-stamp. Also ""withdrawn""-stamp to title-page and to final page, and a library-stamp to p. (1). Otherwise a nice and clean copy with no markings, etc. Pp. 180-197. [Entire volume: (4),477, (1) pp.
The very rare first printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous ""Zeta-function Machine"", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. ""Turing had ideas for the design of an ""analogue"" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides."" (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking ""A Method for the Calculation of the Zeta-Function"", which constitutes his first printed contribution to the subject.""After the publication of his paper ""On computable Numbers,"" Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers... Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]..."" (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).
