""AI representatives" no more have their own paradigm of the limits of computability than they have their own paradigm of what it is for a number to be prime. Computability and (un)decidability are objectively defined concepts in mathematical logic and computer science and to demonstrate that a function is computable or that a problem is decidable or undecidable is (once again) no different in kind that proving that a given number is prime. "Simple problem[s] of everyday experience" will typically not have any bearing on questions of computability and (un)decidability. Of course, there might be analogies of these notions in everyday experience — but they are typically not going to be the same concepts."
I do not doubt that the above are objectively defined concepts. Yet with any concept that are created from verbs, or operations if you like, I have the suspicion that to compute or to decide are operations just as to add or to multiply, etc. I believe that separating data and instructions is not a matter of difference of viewpoints, but a difference in materialization. And the fact that a digital computer has been devised with that semantic structure suggest that the duality of form and content is not the same dichotomy as data and instruction.
Ferenc