I recently heard someone say that the book Gödel, Escher, Bach tries to explain consciousness. I hadn't heard that before. I had always thought the book was essentially saying that Gödel, Escher and Bach all incorporated recursion into their work, and that recursion was cool.
So I got the book, and I read the preface. In the preface, the author does indeed claim that there is a connection between Gödel, Escher, Bach and consciousness. In particular, that the sortof strange paradoxical recursion found in Gödel's incompleteness theorem is essentially the building block of meaning, self-awareness, and consciousness.
I've had some related thoughts.
In a previous post, I drew an artsy half-baked doodle labeled "meaning of meaning". This doodle was inspired by a paper I wrote for a philosophy class in grad school, which talks about the Liar paradox and the halting problem, which I think are both essentially the same as Gödel's proof. The core idea of the paper is that meaning and truth require an interpreter. If you want to know what a statement means, then say it to someone that knows the language of the statement, and see what they do. Whatever they do is the meaning of the statement. If you want to know whether a statement is true, you must ask an interpreter of the statement whether it is true, where the word "true" itself is part of the language of the statement. A statement is not true in an of itself, since it has no meaning in and of itself, and neither does the word "true" have meaning in and of itself.
I've also written a post exploring the idea of interpretation as a candidate for understanding consciousness in a similar vien to the way Hofstadter suggests that consciousness arises from strange recursive loops, like the Gödel sentence.
However, I feel like the Gödel sentence is not enough to explain consciousness. I understand that the Gödel sentence is sortof self-aware of itself and the system it is in, and our human consciousness is sortof self-aware of ourselves and the environment we are in. I've even subjectively felt more conscious at those times when I have understood something more recursively.
But, I've also felt more conscious at those times when I've seen a beautiful landscape, or held hands with a beautiful girl. I feel like the common thread between these situations is input -- stuff to be aware of and interpret -- and recursive thinking also generates a lot of input, but it is not the only thing that does.
This is the thought I was exploring in this previous post, which suggests that there is a difference between consciousness and intelligence. I feel like recursion is a powerful tool for intelligent thought, but I'm not sure it is the building block for consciousness.
Of course, it might be. These thoughts are all a bit muddled for me, but I feel like they're related. I also feel like the notion of infinity -- explored a bit in this post -- should be in this discussion. Note that even that post mentions Gödel's paradox, but it places lower on the continuum of mathematical strangeness than higher order infinities.