‎"SMULLYAN, RAYMOND M.‎
‎Languages in which Self-reference is Possible. - [THE CONTEMPORARY UNDERSTANDING OF GÖDEL'S THEOREM]‎

‎(No place), The Association for Symbolic Logic, Inc., 1957. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 22. Barcode label pasted on to back boards. Small library stamp to lower part of 5 pages and a tear to p. 61. A very fine copy. Pp. 55-67. [Entire volume: VI, 442 pp.]‎

Reference : 50560

‎First printing of Smullyan's exceedingly influential paper in which he showed that Gödelian incompleteness held for formal systems considerably more elementary than that of Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this paper which Smullyan wrote while being a Ph.D. student. Raymond Smullyan (1919 -), New York, earned his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church.The present volume also contains Jaakko Hintikka's famous ""Vicious Circle Principles and the Paradoxes"" which (together with ""Identity, Variables, and Impredicative Definitions"" published in 1956) constitute Hintikka's attempt to cope with Wittgenstein's elimination of identity as proposed in the ""Tractatus"". With the translation rules that Hintikka here put forward, he is the first to try to carry out Wittgenstein's suggestions systematically. ‎