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-1 DOUGLAS R. HOFSTA DTER
godel,escher,bach
I ANETERNALGOLDEN BRAID
■): i
A METAPHORIC'AL FUGL E ON MIN DS A N E> M AC HIN ES
, IN THE SPIRIT OF LEWIS CARROLL
Contents
Overview viii
List of Illustrations xiv
Words of Thanks xix
Part I: GEB
Introduction: A Musico-Logical Offering 3
Three-Part Invention 29
Chapter I: The MU-puzzle 33
Two-Part Invention 43
Chapter II: Meaning and Form in Mathematics 46
Sonata for Unaccompanied Achilles 61
Chapter III: Figure and Ground 64
Contracrostipunctus 75
Chapter IV: Consistency, Completeness, and Geometry 82
Little Harmonic Labyrinth 103
Chapter V: Recursive Structures and Processes 127
Canon by Intervallic Augmentation 153
Chapter VI: The Location of Meaning 158
Chromatic Fantasy, And Feud 177
Chapter VII: The Propositional Calculus 181
Crab Canon 199
Chapter VIII: Typographical Number Theory 204
A Mu Offering 231
Chapter IX: Mum on and Godel 246
Contents
VI
Part II EGB
Prelude ... 275
Chapter X: Levels of Description, and Computer Systems 285
Ant Fugue 311
Chapter XI: Brains and Thoughts 337
English French German Suit 366
Chapter XII: Minds and Thoughts 369
Aria with Diverse Variations 391
Chapter XIII: BlooP and FlooP and GlooP 406
Air on G's String 431
Chapter XIV: On Formally Undecidable Propositions of TNT
and Related Systems 438
B irthday Cantatatata ... 461
Chapter XV: Jumping out of the System 465
Edifying Thoughts of a Tobacco Smoker 480