From the Introduction. In 1931 there appeared in a German scientific periodical a relatively short paper with the forbidding title ""Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme"" (""On Formally Undecidable propositions of Principia Mathematica and Related Systems""). Its author was Kurt Godel, then a young mathematician of 25 at the University of Vienna and since 1938 a permanent member of the Institute for Advanced Study at Princeton. The paper is a milestone in the history of logic and mathematics. When Harvard University awarded Godel an honorary degree in 1952, the citation described the work as one of the most important advances in logic in modern times. At the time of its appearance, however, neither the title of Godel's paper nor its content was intelligible to most mathematicians.
A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.
What did Gödel establish, and how did he prove his results? His main conclusions are twofold. In the first place (though this is not the order of Gödel's actual argument), he showed that it is impossible to give a metamathematical proof ...
S(zp,zp) analyses the text of the proof of Gödel's result, and shows that mathematical language, like other forms of language, enjoys the full complexity of language as a process, with its embodied genesis, constitutive paradoxical forces ...
S.G. Shanker. G(-.)DEL'S THEOREM IN FOCUS PHILOSOPHERS IN FOCUS SERIES GODEUS THEOREM IN FOCUS Edited by.
"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven Pinker Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the ...
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems.
This book provides a concise and self-contained introduction to the foundations of mathematics.