### Synopses & Reviews

These brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.

The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Mathematician and stage magician Smullyan offers this amusing puzzlebook full of word games, paradoxes, and logical sleights of hand. Written in a conversational style for an audience with no more thanhigh school education, the first part of the book introduces the puzzles with bets over petty cash and kisses. Infinity, induction,and self-reference are gently introduced and tied to the puzzles, and logical symbols are gradually incorporated. The second part ismore technical and gives dense proofs of proposals related to provability and the famous Gödel theorem. The book is not indexed.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Synopsis

These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic is necessary.

### Table of Contents

Part I Puzzles, Paradoxes, Infinity and other Curiosities I A Chatty Personal Introduction II Some Curious Adventures III The Strange Island of Musica IV Four Metapuzzles V Certified Knights and Knaves VI Paradoxical? VII Infinity and Induction VIII Introducing Self-Reference IX Fixed Point Puzzles X Some Curious Systems XI How to Stump a Decision Machine XII Some Additional Godelian Puzzles Part II XIII Truth and Provability XIV Syntactic Incompleteness Theorems XV Provability in Stages XVI Formal Systems and Recursion XVII Incompleteness and Undecidability XVIII First-Order Arithmetic XIX Arithmetic Truth is Not Formalizable XX The Incompleteness of Peano Arithmetic References