Raymond Smullyan
Knopf | 1987 | 257 páginas | rar - epub | 2 Mb
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This book provides an introduction to Kurt Godel's theorems through a collection of puzzles interspersed with an account of symbolic logic. Godel's argument has been transferred from the formal domain of mathematical systems in an attempt to make its essential ideas more accessible to the general reader. The primary emphasis is on belief systems and how they are related to systems of mathematics. This leads to the subject of possible world semantics which plays a role in computer science and artificial intelligence.
Contents
Part I YOU MIGHT BE SURPRISED!
1 A Diabolical Puzzle
2 Surprised?
Part II THE LOGIC OF LYING AND TRUTH TELLING
3 The Census Taker
4 In Search of Oona
5 An Interplanetary Tangle
Part III KNIGHTS, KNAVES, AND PROPOSITIONAL LOGIC
6 A Bit of Propositional Logic
7 Knights, Knaves, and Propositional Logic
8 Logical Closure and Consistency
Part IV LET’S BE CAREFUL!
9 Paradoxical?
10 The Problem Deepens
Part V THE CONSISTENCY PREDICAMENT
11 Logicians Who Reason About Themselves
12 The Consistency Predicament
13 Gödelian Systems
14 More Consistency Predicaments
Part VI SELF-FULFILLING BELIEFS AND LÖB’S THEOREM
15 Self-Fulfilling Beliefs
16 The Rajah’s Diamond
17 Löb’s Island
Part VIIIN DEEPER WATERS
18 Reasoners of Type G
19 Modesty, Reflexivity, and Stability
Part VIII CAN’T DECIDE!
20 Forever Undecided
21 More Indecisions!
Part IXPOSSIBLE WORLDS
22 It Ain’t Necessarily So!
23 Possible Worlds
24 From Necessity to Provability
Part X THE HEART OF THE MATTER
25 A Gödelized Universe
26 Some Remarkable Logic Machines
27 Modal Systems Self-Applied
Part X IFINALE
28 Modal Systems, Machines, and Reasoners
29 Some Strange Reasoners!
30 In Retrospect
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