"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems.
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
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.
This book provides a concise and self-contained introduction to the foundations of mathematics.
A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.
S.G. Shanker. G(-.)DEL'S THEOREM IN FOCUS PHILOSOPHERS IN FOCUS SERIES GODEUS THEOREM IN FOCUS Edited by.
... the basis of the sole assumption that TNT is (simply) consistent. Rosser's result is therefore a strengthening of Godel's. We aren't particularly interested in the technical details of Rosser's Theorem, but some hint is appropriate.
This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a.
The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to ...
This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student...