Godel,Escher,Bach-AnEternalGoldenBraid - (EPUB全文下载)

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Table of Contents
Part II: EGB
Introduction:
A Musico-Logical Offering
Three-Part Invention
Formal Systems
Theorems, Axioms, Rules
Inside and Outside the System
Jumping out of the System
M-Mode, I-Mode, U-Mode
Decision Procedures
or,
What the Tortoise Said to Achilles
by Lewis Carroll'
The pq-System
The Decision Procedure
Bottom-up vs. Top-down
Isomorphisms Induce Meaning
Meaningless and Meaningful Interpretations
Active vs. Passive Meanings
Double-Entendre!
Formal Systems and Reality
Mathematics and Symbol Manipulation
The Basic Laws of Arithmetic
/ // // // / /
Ideal Numbers
Euclid's Proof
Getting Around Infinity
The telephone rings; Achilles picks it up.
Primes vs. Composites
The tq-System
Capturing Compositeness
Illegally Characterizing Primes
Figure and Ground in Music
Recursively Enumerable Sets vs. Recursive Sets
Primes as Figure Rather than Ground
Implicit and Explicit Meaning
Explicit Meaning of the Contracrostipunctus
Implicit Meanings of the Contracrostipunctus
Mapping Between the Contracrostipunctus and Gödel’s Theorem
The Art of the Fugue
Problems Caused by Gödel’s Result
The Modified pq-System and Inconsistency
The History of Euclidean Geometry
The Many Faces of Noneuclid
Undefined Terms
The Possibility of Multiple Interpretations
Varieties of Consistency
Hypothetical Worlds and Consistency
Embedding of One Formal System In Another
Layers of Stability in Visual Perception
Is Mathematics the Same in Every Conceivable World?
Is Number Theory the Same In All Conceivable Worlds?
Completenes
How an Interpretation May Make or Break Completeness
Incompleteness of Formalized Number Theory
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What Is Recursion?
Pushing, Popping, and Stacks
Stacks in Music
Recursion in Language
Recursive Transition Networks
"Bottoming Out" and Heterarchies
Expanding Nodes
Diagram G and Recursive Sequences
A Chaotic Sequence
Two Striking Recursive Graphs
Recursion at the Lowest Level of Matter
Copies and Sameness
Programming and Recursion: Modularity, Loops, Procedures
Recursion in Chess Programs
Recursion and Unpredictability
When Is One Thing Not Always the Same?
Information-Bearers and Information- Revealers
Genotype and Phenotype
Exotic and Prosaic Isomorphisms
Jukeboxes and Triggers
DNA and the Necessity of Chemical Context
An Unlikely UFO
Levels of Understanding of a Message
"Imaginary Spacescape"
The Heroic Decipherers
Three Layers of Any Message
Schrodinger's Aperiodic Crystals
Languages for the Three Levels
The "Jukebox" Theory of Meaning.
Agains ............

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