I'm not sure why anyone would consider it out-dated. None of the concepts are really things that are 'datable'.
That said, you'll probably find that you need to read it more than once to glean everything from it.
That said, you'll probably find that you need to read it more than once to glean everything from it.
Category theory and Type theory are replacing Set theory as the fundamental basis of Math, or at least it's fashionable to try to do so, and the book revolves around the Whitehead and Russel set theoretic work and Godel's deconstruction thereof. Which isn't to say that Category theory or whatever are immune to Godel's theorems, I have no idea how those would translate, and my gut tells me that they would have roughly the same outcome.
But yeah, anyways, wonderful exposition of the kind of extremely bare-bones framework fundamental mathematicians operate in, magnificient demonstration of what recursive and self-referential structures imply, and overall a great read.
Thats the only thing that comes to mind and it's only a minor quibble.
Contrast "good old-fashioned AI" with "machine learning", where the representations are as minimalistic and low-level as possible, because the only important thing is that when you update them a few billion times the right results emerge statistically.
I don't see it as a problem that this part of GEB is "dated", though, because I find GOFAI to be an interesting topic. It involves trying to think about how you think and formalize it, which rarely happens in modern AI.
Imagine a world where brute-force alpha-beta search was just not good enough to beat humans at chess; a world where advances in chess-playing computers would require chessmasters to encode their expertise in interesting data structures. This is the world that might have been, and it's the world GEB describes when it talks about AI. It's dated, but it's interesting.