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细节
TURING, Alan Mathison (1912-1954). 'Systems of logic based on ordinals.' Offprint from: Proceedings of the London Mathematical Society, ser. 2, vol. 45. London: 1939.
Extremely rare offprint of Turing's doctoral disseration, and an important association copy of one of Turing's major works. In it, Turing investigates ordinal logic and Gödel's theorem. 'In a "complete ordinal logic", any theorem in arithmetic could be proved by a mixture of mechanical reasoning, and steps of "intuition". In this way [Turing] hoped to bring the Godel incompleteness under some kind of control. But he regarded the results as disappointingly negative. "Complete logics" did exist, but they suffered from the defect that one could not count the number of intuitive steps that were necessary to prove any particular theorem ... This introduced the idea of relative computability, or relative unsolvability, which opened up a new field in mathematical logic' (Hodges, p.143).
Robin Gandy met Turing at a party in 1940, but it wasn't until 1944 that the two were brought together at Hanslope Park in 1944 to work on a speech decipherment system. 'Their friendship continued after the war, back at King’s College where Turing had resumed his fellowship. Gandy took Part III of the Mathematical Tripos with distinction, then began studying for a PhD under Turing’s supervision; his successful thesis on the logical foundation of physics (On axiomatic systems in mathematics and theories in physics) was presented in 1953 and can now be seen as a bridge between his wartime expertise and later career. When Turing died in 1954 he left his mathematical books and papers to Gandy, who, in 1963, took over from Max Newman the task of editing the papers for publication' (Moschovakis & Yates, pp. 367-8). Offprints of Turing’s papers are extremely rare both in commerce and in institutional holdings. Only 3 copies of this offprint can be traced: Alan Turing Archive at King’s College Cambridge (AMT/B/15), one at St. Andrew’s, and one in the Max Newman collection at Bletchley Park.
Octavo (256 x 176mm). 68pp., 161-228. Preserving the original olive-green front wrapper (rebacked with new rear wrapper done to style, skilful restoration to upper cover, 2 insignificant faint spots to upper wrapper). Provenance: Robin Oilver Gandy (1919-1995; inscribed in pencil on front cover in his hand 'with corrections by ROG' and with some pencil and biro marginalia).
Extremely rare offprint of Turing's doctoral disseration, and an important association copy of one of Turing's major works. In it, Turing investigates ordinal logic and Gödel's theorem. 'In a "complete ordinal logic", any theorem in arithmetic could be proved by a mixture of mechanical reasoning, and steps of "intuition". In this way [Turing] hoped to bring the Godel incompleteness under some kind of control. But he regarded the results as disappointingly negative. "Complete logics" did exist, but they suffered from the defect that one could not count the number of intuitive steps that were necessary to prove any particular theorem ... This introduced the idea of relative computability, or relative unsolvability, which opened up a new field in mathematical logic' (Hodges, p.143).
Robin Gandy met Turing at a party in 1940, but it wasn't until 1944 that the two were brought together at Hanslope Park in 1944 to work on a speech decipherment system. 'Their friendship continued after the war, back at King’s College where Turing had resumed his fellowship. Gandy took Part III of the Mathematical Tripos with distinction, then began studying for a PhD under Turing’s supervision; his successful thesis on the logical foundation of physics (On axiomatic systems in mathematics and theories in physics) was presented in 1953 and can now be seen as a bridge between his wartime expertise and later career. When Turing died in 1954 he left his mathematical books and papers to Gandy, who, in 1963, took over from Max Newman the task of editing the papers for publication' (Moschovakis & Yates, pp. 367-8). Offprints of Turing’s papers are extremely rare both in commerce and in institutional holdings. Only 3 copies of this offprint can be traced: Alan Turing Archive at King’s College Cambridge (AMT/B/15), one at St. Andrew’s, and one in the Max Newman collection at Bletchley Park.
Octavo (256 x 176mm). 68pp., 161-228. Preserving the original olive-green front wrapper (rebacked with new rear wrapper done to style, skilful restoration to upper cover, 2 insignificant faint spots to upper wrapper). Provenance: Robin Oilver Gandy (1919-1995; inscribed in pencil on front cover in his hand 'with corrections by ROG' and with some pencil and biro marginalia).
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Eugenio Donadoni