New York, Raven Press, 1965.
8vo. Original full blue cloth with gilt lettering to spine in the original dust jacket. In: "The Undecidable. Basic Paper on Undecidable Propositions, Unsolvable Problems And Computable Functions". Sunning to spinem and dust-jacket price-clipped and and with a few tears. "W. V. Quine" to front free end-paper. A fine and clean copy. Pp. 41-74. [Entire volume: (6), 440 pp.].
First published English edition of Gödel's influential lecture. THE COPY HAS BELONGED TO THE GREAT LOGICIAN WILLARD ORMAN VAN QUINE and bears his signature to front free end-paper.
In 1929 Gödel had shown, in his doctorial dissertation ('Die Vollständigkeit der Axiome des logischen Funktionskalküls', published 1930), that first-order logic is complete, i.e., that every logically valid formula is provable. This was an answer to one of two important questions posed by Hilbert and Ackermann in their 'Grunzüge der theoretischen Logik' from 1928 - this work contained the first exposition ever of first-order logic, and posed the problem of its completeness and decidability ('Entscheidungsproblem'). In 1936 Alonzo Church and Allan Turing, independantly of each other, gave their answer in the negative to the later problem, i.e., that there exists no general effective algorithm which can decide the truth-value of any formula in first-order logic.