I respectfully disagree, Doc: that they are generally related (though each is specifically different) can be seen in that each points to a limit in what the human mind can know at a particular instance. Each in its own way says that reality is "non-Boolean": That is, it is not completely reducible to simple and/or, if/then logical statements, but that there are occasions where "both statements" are simultaneously valid; e.g., a set is both a member and not a member if itself. FWIW.
No, not even close. What Russell's paradox actually shows is that informal usage of "set membership" doesn't work. This states nothing about the human mind, only about the problam of correct specification.
Likewise for the Heisenberg relations; they have nothing to do with what can be known; only with what can be measured, by a human or otherwise.
they are generally related (though each is specifically different)*
It's been shown through brain scans that the senses split things up to do analysis (e.g., for vision, color is processed one place and shape another) and then construct a perception. So there is a deconstructive process and a constructive process.
Conscious thought, however, seems different. People love to deconstruct (splitting problems into smaller pieces, division of labor), but we seem to be very bad at the constructive part.
Some are better than others - some are trying harder than others - but we're none of us big picture thinkers, in the same way that we're big picture see-ers or big picture hear-ers. (I can't quantify constructive ability, so I'm just calling it a feeling.) For example, despite all the analysis we do of human affairs, we can't answer a simple question like what will be the state of the world in 100 years? What are we moving towards?
What do you think about that?
* This exchange reminds me of a description in Wired Magazine of the difference between program designers and program developers. Designers are usually female, talkative, vegetarian and live in lofts. Developers are always male, eat only fast food, live at work and don't speak at all except to say, You're wrong about that.