Gödel, Escher, Bach #2

What is a formal system?

• It does not have content, it only has symbols which are related to other symbols. 
• You can fill in these symbols with whatever information you want (you play with them).
• These symbols have to be coherent. 
• All elements are defined and have rules to guide them (simplified representation of something with rules). 
• Example: Chess. 
• Each term has a specific meaning, you can´t interchange the meaning of terms. 

Isomorphism:

• Something that can't be explained formally but explained pragmatically.
• We have to experience it to know what it is. 
• We have to start by practice and move on step by step until we reach a formal explanation. 
• Its when we give a word a meaning (Ex: the word APPLE is associated with an actual apple; the number 1 represents a cuantity)