But it seems (to me) that logic doesn't capture all of what we call intelligence, and that the effort to recapitulate the human mind solely on the basis of discrete logic machines is almost certainly going to fail. But I think that failure will be valuable, and that we should not avoid the attempt to make a sculpture of the mind.
Babbage had an automaton, the Silver Lady, that could imitate the dancing of a ballerina. We might be able to make "Silver Minds" that imitate the outward manifestations of the human personality, and so learn more about the nature and essence of thinking, as the Silver Lady must have of dancing. Certainly the craftsman who made her must have known a thing or two about ballet and physiology?
There are enormous gaps in reasoning that you just have to gloss over to go from the current state of the world to a post-singularity one, that you are expected to accept, on faith.
I personally think it's about as likely as the return of the Messiah in our lifetimes. That is to say, it is not.
As with everything in nature, there are diminishing returns. It is not clear that any significant leaps in 'intelligence' are possible. At least to the extent proposed by 'singularity' advocates. Or that such an intelligence would be able to completely outclass humans, either in the current form, or augumented by tech.