Godel,Escher,BachAnEternalGoldenBraid

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 ......