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geb chapter 2 [ea30b619]

Tags: Hofstadter - Godel, Escher, Bach

  • Axiom schema are the framework for axioms
  • Any formal system that lets you make longer theorems from shorter ones requires a decision procedure, which leads to halting problem
  • any constructions of an isomorphism induces meaning, because if there is a way to transform the information without losing it, then there is inherent meaning in the information

  • interpretation vs meaning

    • intepretation - what the symbol represents
    • meaning - the underlying thing
  • systems can take on multipl;e passive meanings
  • do formal systems always need to map onto reality?
  • how do we "prove" isomorphism?
  • numbers misbehave, although people have an innate sense that they do not
  • euclid's theorem
  • Proofs can be broken down into discontinous jumps that never make sense until zoomed out