# geb chaper 4 (consistency, completeness, and geometry)

Tags: Hofstadter - Godel, Escher, Bach

More complexity of isomorphism -> the more software is required ot extract meaning

Language uses isomorphisms to generate meaning, the symbols are imbued with meaning

Example: two objects collide in a vaccum, noise is not created, noise a function of the medium, not the collision

Music -> level one meaning of the grooves on a viynl

level two depends on a chain of isomorphisms

godel’s incompleteness theorem

- no formal system can reproduce every single statement of theorems
- truth transcends all formal systems

eculid’s elements

- founder of rigor in mathematics
- 4 posutlate geometry vs 5th postulate gemoetry
- attempts at proving geometry with 4 postulates creates non-euclidian geometry, ellipital vs hyperbolic geometry

Consistency

- consistency is not a product of hte systems but of the interpreations we put on it
- internal vs external consistencies

Completeness

- everything produced by a system is true
- if a system is consistent but incomplete, that means that meanings we interpret from it are wrong