Godel's Incompleteness Theorems

by Raymond M. Smullyan

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

Genres: Mathematics, Logic, Science, Philosophy, Textbooks, Nonfiction

160 pages, Hardcover

First published January 1, 1992

About the author

Raymond M. Smullyan was a logician, musician, Zen master, puzzle master, and writer.

Reviews

[Bill Hammack · Rating 5 out of 5]

I could not sleep last night, so I read Smullyan's GODEL'S INCOMPLETENESS THEOREM (Oxford). Once or twice a year I'll read a math book for pure enjoyment. Somehow it takes me out of my element, it diverts me completely. I've got great joy over the years from reading his THEORY OF FORMAL SYSTEMS and
Davis' COMPUTABILITY AND UNDECIDABILITY - I first read them in 1986ish.

[Brandon Hopkins · Rating 5 out of 5]

Best introduction to Godel's incompleteness theorems, hands down.

[Barney Beck · Rating 5 out of 5]

Gödel’s incompleteness theorems three times differently.

[DJ]

recommended by Scott Aaronson when I asked if there had been any investigation into why truth is such a mathematically strange concept.

[Brian · Rating 5 out of 5]

What can I say that countless people have not already said? Godel was a genius.