Isomorphism
GÖDEL
"To prove that a system is consistent, you must step outside the system. But then you are in a larger system. Is that one consistent?"
ESCHER
Order out of Chaos. Figure out of Ground.
BACH
"A fugue is a conversation between voices, where the subject is echoed, inverted, and reversed, yet remains the same."
The Eternal Golden Braid
"The two strands are distinct, yet they are one."
Part IGEB
Part IIEGB
Levels of Description, and Computer Systems
Brains and Thoughts
Minds and Thoughts
BlooP and FlooP and GlooP
On Formally Undecidable Propositions
Jumping out of the System
Self-Ref and Self-Rep
Church, Turing, Tarski, and Others
Artificial Intelligence: Retrospects
Artificial Intelligence: Prospects
Strange Loops, Or Tangled Hierarchies
"This object before us... it appears to be a mere book. A finite collection of pages."
"Ah, but look closer, my swift friend. It is not just a book. It is a Strange Loop captured in paper. It contains the instructions for its own understanding."
"And how does one enter such a loop? Must I solve a riddle?"
"Simplest thing in the world. You must merely hold the reflection. The rest will rewrite itself within you."
The Three-Part Invention
"Counterpoints in the Key of Meaning"
I Am a Strange Loop
The Sequel. Hofstadter distills the 'I' into a symbol within a formal system.
The Mind's I
The Anthology. A hall of mirrors exploring the self, soul, and machine consciousness.
Alice in Wonderland
The Precursor. Carroll's logic games create a world where meaning dissolves into play.
The Strange Loop
"Gödel, Escher, and Bach were only shadows cast in different directions by some central solid essence."
Isomorphism