The central thesis of GEB is this: what is a self? From the preface of the 20th anniversary edition:
"GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?"
It is interesting to me that the author would start at the materialist assumption. Most people take it as a “given”, but I have softened to the idea that maybe it is not a correct or complete way of viewing things.
The author's favorite topic, as described by him in the final Dialogue, is 'indirect self-reference'. This has a double meaning. Indirect self-reference can mean what it says such as Godel numbering which is a method of referring to a self indirectly but it can also mean that the whole book is an indirect way of referring to the question of 'what is a self?' He is approaching the topic of consciousness indirectly.
I disagree that most people would take materialism as a given (I think most people in the world are at least slightly religious or spiritual), nor do I think it's necessarily a correct reading to say that Hofstadter actually assumes materialism must be true (though I believe he does), rather Hofstadter starts from the premise that it is and then tries to see if that premise can be logically consistant.
"GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?"