geb chapter 2

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