[joe_the_user]

You are correct that Hofstadter doesn't have grand assertions at the level of The Singularity but there is still something like a "Hofstadter" mix - say all the ideas in Godel, Esther and Bach with the implication that these are related and important. One might reasonably say this a somewhat grandiose admixture.

All that said, I think Hofstadter's "mixture of good ideas and rubbish" description isn't a good characterization of the thinking behind The Singularity. Rather, Singularity thinking is extrapolation of growth trends which might easily be false but since it is made on a broad level, it is not easy to formulate why it is false. And Kurzweil, in particular is popularizer of the singularity with a particular version of it.

One could argue there are limitations to the expansions that Singularians have been extrapolating from but characterizing these limitations is itself quite a tricky problem.

I think the best refutation to the Singularity idea is the argument of Paul Allen, that software and the understanding of intelligence simply haven't been amenable to increased computing power.

http://www.technologyreview.com/view/425733/paul-allen-the-s...

It's a good argument but I feel the tone isn't quite fair, the sense that you could more fairly say the singularity looks plausible until you really focus on the software barrier.