Gödel's Theorem: An Incomplete Guide to its Use and Abuse

Citation

Howard, W.R. (2006), "Gödel's Theorem: An Incomplete Guide to its Use and Abuse", Kybernetes, Vol. 35 No. 5, pp. 763-764. https://doi.org/10.1108/03684920610679036

There remains a great deal of interest in the incompleteness theorems of Kurt Gödel. Obviously, this is primarily by mathematicians who regard them as such an important part of the development of their field but also by others who still meet to discuss their implications. This is not the place to either criticise or comment about the many interpretations and, indeed we are told, their exploitation. Here, however, an opportunity is provided by the author for the non‐mathematician, and dare we say, lay person who is especially interested, in finding out about the theorems and what they may imply.

This is a well‐written book that aims to inform with clarity what the theorems actually say and what the author believes they do not say or imply. To do this the text's chapters flow continuously and in good teaching style, repeat and discuss important points.

The text includes: Chapter 1. Gives the background to the theorems and to Gödel himself. Chapter 2. The concepts needed to help understand the theorems. Chapter 3. Looks at computability, formal systems and incompleteness. Chapter 4. Applications of the incompleteness theorems and general discussions. Chapter 7. Explanation of Gödel's completeness theorem. Chapter 8. Considers Gregory Chaitin's philosophical claims about randomness and complexity.

Mathematicians are also catered for in the Appendix which provides more formal statements of the theorem.

This is a book well worth reading and one that lives up to the sub‐title – “An incomplete guide to its use and abuse”. Anyone who browses the web will be aware of the continued interest in Gödel's theorem as well as his life and contributions. Torkel Franzen's guide may be incomplete, but in reality it provides an excellent source for study which will help the readers decide what is good use of the theorem and what is indeed abuse.