A Beginner's Guide to Mathematical Logic

by Raymond M. Smullyan

Overview

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems.
Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.

Product Details

ISBN-13:	9780486492377
Publisher:	Dover Publications
Publication date:	07/16/2014
Pages:	288
Product dimensions:	6.10(w) x 9.10(h) x 0.70(d)

About the Author

Raymond Smullyan received his PhD from Princeton University and taught at Dartmouth, Princeton, Indiana University, and New York's Lehman College. Best known for his mathematical and creative logic puzzles and games, he was also a concert pianist and a magician. He wrote over a dozen books of logic puzzles and texts on mathematical logic.
Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919–2017), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years.

In the Author's Own Words:
"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini."

"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'" — Raymond Smullyan

Table of Contents

Part I General Background

Chapter 1 Genesis 3

Chapter 2 Infinite Sets 17

Chapter 3 Some Problems Arise! 29

Chapter 4 Further Background 37

Part II Prepositional Logic

Chapter 5 Beginning Propositions! Logic 61

Chapter 6 Propositional Tableaux 81

Chapter 7 Axiomatic Propositional Logic 101

Part III First-Order Logic

Chapter 8 Beginning First-Order Logic 133

Chapter 9 First-Order Logic: Main Topics 149

Part IV The Incompleteness Phenomenon

Chapter 10 Incompleteness in a General Setting 171

Chapter 11 Elementary Arithmetic 191

Chapter 12 Formal Systems 219

Chapter 13 Peano Arithmetic 235

Chapter 14 Further Topics 251

References 263

Index 265