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Tables of Contents for Shadows of the Mind
Chapter/Section Title
Page #
Page Count
Notes to the reader
xv
Prologue
1
6
Part I: Why We Need New Physics to Understand the Mind
The Non-Computability of Conscious Thought
Consciousness and computation
7
57
Mind and science
7
1
Can robots save this troubled world?
8
4
The A, B, C, D of computation and conscious thinking
12
4
Physicialism vs. mentalism
16
1
Computation: top-down and bottom-up procedures
17
3
Does viewpoint C violate the Church-Turing thesis?
20
1
Chaos
21
3
Analogue computation
24
2
What kind of action could be non-computational?
26
7
What of the future?
33
2
Can computers have rights or responsibilities?
35
2
`Awareness', `Understanding', `consciousness', `intelligence'
37
3
John Searle's argument
40
1
Some difficulties with the computational model
41
3
Do limitations of present-day AI provide a case for C?
44
4
The argument from Godel's theorem
48
2
Platonism or mysticism?
50
1
What is the relevance of mathematical understanding?
51
2
What has Godel's theorem to do with common-sense behaviour?
53
3
Mental visualization and virtual reality
56
3
Is mathematical imagination non-computational?
59
5
The Godelian case
64
63
Godel's theorem and Turing machines
64
2
Computations
66
1
Non-stopping computations
67
1
How do we decide that some computations do not stop?
68
4
Families of computations; the Godel-Turing conclusion G
72
5
Possible technical objections to G
77
11
Some deeper mathematical considerations
88
2
The condition of ω-consistency
90
2
Formal systems and algorithmic proof
92
3
Further possible technical objections to G
95
32
Appendix A: An explicit Godelizing Turing machine
117
10
The case for non-computability in mathematical thought
127
86
What did Godel and Turing think?
127
3
Could an unsound algorithm knowably simulate mathematical understanding?
130
2
Could a knowable algorithm unknowably simulate mathematical understanding?
132
5
Do mathematicians unwittingly use an unsound algorithm?
137
4
Can an algorithm be unknowable?
141
3
Natural selection or an act of God?
144
1
One algorithm or many?
145
2
Natural selection of unworldly esoteric mathematicians
147
3
Learning algorithms
150
2
May the environment provide a non-algorithmic external factor?
152
2
How can a robot learn?
154
2
Can a robot attain `firm mathematical beliefs'?
156
3
Mechanisms underlying robot mathematics
159
3
The basic contradiction
162
1
Ways that the contradiction might be averted
163
1
Does the robot need to believe in M?
164
3
Robot errors and robot `meanings'?
167
2
How to incorporate randomness---ensembles of robot activity
169
1
The removal of erroneous *-assertions
170
3
Only finitely many *M-assertions need be considered
173
3
Adequacy of safeguards?
176
1
Can chaos save the computational model of mind?
177
2
Reductio ad absurdum---a fantasy dialogue
179
11
Have we been using paradoxical reasoning?
190
3
Complication in mathematical proofs
193
2
Computational breaking of loops
195
4
Top-down or bottom-up computational mathematics?
199
2
Conclusions
201
12
Part II: What New Physics We Need to Understand the Mind
The Quest for a Non-Computational Physics of Mind
Does mind have a place in classical physics?
213
24
The mind and physical laws
213
1
Computability and chaos in the physics of today
214
2
Consciousness: new physics or `emergent phenomenon'?
216
1
The Einstein Tilt
217
10
Computation and physics
227
10
Structure of the quantum world
237
70
Quantum theory: puzzle and paradox
237
2
The Elitzur-Vaidman bomb-testing problem
239
1
Magic dodecahedra
240
6
Experimental status of EPR-type Z-mysteries
246
3
Quantum theory's bedrock: a history extraordinary
249
7
The basic rules of quantum theory
256
3
Unitary evolution U
259
4
State-vector reduction R
263
5
Solution of the Elitzur-Vaidman bomb-testing problem
268
2
Quantum theory of spin; the Riemann sphere
270
7
Position and momentum of a particle
277
2
Hilbert space
279
3
The Hilbert-space description of R
282
4
Commuting measurements
286
1
The quantum-mechanical `and'
287
2
Orthogonality of product states
289
1
Quantum entanglement
290
6
The magic dodecahedra explained
296
11
Appendix B: The non-colourability of the dodecahedron
300
1
Appendix C: Orthogonality between general spin states
301
6
Quantum theory and reality
307
41
Is R a real process?
307
3
Many-worlds-type viewpoints
310
2
Not taking |ψ⟩ seriously
312
4
The density matrix
316
5
Density matrices for EPR pairs
321
2
A FAPP explanation of R?
323
5
Does FAPP explain the squared modulus rule?
328
1
Is it consciousness that reduces the state vector?
329
2
Taking |ψ&rang really seriously
331
4
Gravitationally induced state-vector reduction?
335
2
Absolute units
337
2
The new criterion
339
9
Quantum theory and the brain
348
45
Large-scale quantum action in brain function?
348
4
Neurons, synapses, and computers
352
3
Quantum computation
355
2
Cytoskeletons and microtubules
357
10
Quantum coherence within microtubules?
367
2
Microtubules and consciousness
369
2
A model for a mind?
371
6
Non-computability in quantum gravity: 1
377
2
Oracle machines and physical laws
379
2
Non-computability in quantum gravity: 2
381
2
Time and conscious perceptions
383
5
EPR and time: need for a new world-view
388
5
Implications?
393
30
Intelligent artificial `devices'
393
3
Things that computers do well---or badly
396
3
Aesthetics, etc
399
2
Some dangers inherent in computer technology
401
2
The puzzling election
403
3
The physical phenomenon of consciousness?
406
5
Three worlds and three mysteries
411
12
Epilogue
423
2
Bibliography
425
22
Index
447