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Index
Preface
Acknowledgments
1 Introduction
2 Language Paradoxes
2.1 Liar! Liar!
2.2 Self-Referential Paradoxes
2.3 Naming Numbers
3 Philosophical Conundrums
3.1 Ships, People, and Other Objects
3.2 Hangin’ with Zeno and Gödel
3.3 Bald Men, Heaps, and Vagueness
3.4 Knowing about Knowing
4 Infinity Puzzles
4.1 Sets and Sizes
4.2 Infinite Sets
4.3 Anything Larger?
4.4 Knowable and Unknowable
5 Computing Complexities
5.1 Some Easy Problems
5.2 Some Hard Problems
5.3 They’re All Connected
5.4 Almost Solving Hard Problems
5.5 Even Harder Problems
6 Computing Impossibilities
6.1 Algorithms, Computers, Machines, and Programs
6.2 To Halt or Not to Halt?
6.3 They’re All Connected
6.4 A Hierarchy of the Unknown
6.5 Minds, Brains, and Computers
7 Scientific Limitations
7.1 Chaos and Cosmos
7.2 Quantum Mechanics
7.3 Relativity Theory
8 Metascientific Perplexities
8.1 Philosophical Limitations of Science
8.2 Science and Mathematics
8.3 The Origin of Reason
9 Mathematical Obstructions
9.1 Classical Limits
9.2 Galois Theory
9.3 Harder Than Halting
9.4 Logic
9.5 Axioms and Independence
10 Beyond Reason
10.1 Summing Up
10.2 Defining Reason
10.3 Peering Beyond
Notes
Bibliography
Index
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