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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.
With this book, Raymond Smullyan once again demonstrates his command of both logic and the English language: he understands and can explain it.
In general, each chapter begins with a brief explanation of the primary topic, followed by a set of problems exercises where the reader is expected to think their way through to the solution. Solutions to those problems are given at the end of each chapter.
Smullyan also gives a powerful existence proof of the fundamental principle that mathematics is the manipulation of symbols together with an operator, the latter being the replacing of one set of characters with another set of characters.
While doing this he illustrates some of the deepest mathematical concepts. Smullyan opens with some examples of paradoxes; in this case they are undecidable expressions.
The island of knights who always tell the truth and knaves who never tell the truth serves to set the stage for what is to come.
The concept of omega-inconsistency is covered. It is defined as the situation where for the number 1 there is a proof that 1 does not have the property, there is a separate proof that the number 2 does not have the property, and so on, continuing through all the natural numbers. But at the same time there is a separate proof that there is in fact some number n such that n has the property.
Smullyan then goes on to state that there are indeed consistent systems that are omega inconsistent. In his spare time, he reads about these things and helps his daughter in her lawn care business. Skip to main content. Search form Search. Login Join Give Shops.
Halmos - Lester R. Ford Awards Merten M. Raymond M. Publication Date:. Number of Pages:. BLL Rating:. Log in to post comments.
The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs
Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs