geb chapter 2
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