I admire McCarthy a lot, but I'm with you there in being a bit disappointed. As for humans being able to know truths that cannot be discovered computationally, there is some evidence [1] supporting the hypothesis that animal brains do what they do using analogue information processing. So it may be that there are "thruths" which can only be "known" using analogue processes, in which case, as digital reasoners, computers would always remain at a disadvantage when compared against humans in terms of "intelligence".
[1] Spivey, M., Grosjean, M. & Knoblich, G. (2005). Continuous attraction toward phonological competitors. Proceedings of the National Academy of Sciences, 102(29), 10393-10398.
Hypothetically speaking, if we develop a sufficient understanding of analogue information processing, couldn't we build either (a) some kind of analog co-processor that operates in this manner and interfaces with the computer, or even (b) a sufficiently precise digital simulation of a system that can use analogue processes?
Maybe we can. I hope we'll invest in finding out, and soon. Then again, John McCarthy doesn't seem to agree, as this answer suggests:
Q. Is there anything in principle that would prevent a computer from thinking as a human would?
A. No
IOW, there's still no recognition today, on the side of the purveyors of "classical" AI, that anything except digital processing might be needed for a computer to think "as a human would". So the big money is likely to continue being thrown at attempts to emulate animal brains using purely digital means. And I suspect that these funds might largely be better spent elsewhere.
I tried to find a free PDF version of that paper, but no such luck. However, I found an earlier one by Michael Spivey and Rick Dale, ON THE CONTINUITY OF MIND: TOWARD A
DYNAMICAL ACCOUNT OF COGNITION (59 pages, <http://www.cogstud.cornell.edu/spiveylab/PLM.pdf>;).
[1] Spivey, M., Grosjean, M. & Knoblich, G. (2005). Continuous attraction toward phonological competitors. Proceedings of the National Academy of Sciences, 102(29), 10393-10398.