Godel, Escher & Bach - Introduction

Hofstadter made a beautiful introduction to "Godel, Escher, Bach". He introduces us to three geniuses and how they represented the strange loops:

• Bach, a musician whose Canons represent a strange loop.
  
• Escher, artist, whose drawings represent the impossible geometry (strange loops)
• Godel; logician, mathematician and philosopher that questioned the foundation of mathematics introducing his "incompleteness theorems"

In order to give some kind of notion of what a strange loop is, I'll post an example that Hofstadter gives in the introduction:

The following sentence is false.
The preceding sentence is true.

So here we have a sense of infinity, of something that won't stop. Something that can't be measurable. That's where I got interested in how that makes us "mediocre" as humans beings searching for truth in a system which we have created, but how can we prove that system outside that system? Are we really understanding reality if our minds are the beginning and ending point?