Such a limit would be worth knowing about. But I see no reason to assume that limit exists in the absence of evidence, particularly as our tools and reasoning are improving all the time.
We can be pretty sure there is a limit. We're physical creatures in a (roughly) deterministic world, so ultimately we're bound by Rice's theorem just as computers are.
Can the human brain in principle be simulated by a (deterministic) algorithm? Seems to me the answer is obviously yes, as we are 'merely' extremely complex machines whose operation is governed by deterministic physical laws. If you agree, you are forced to agree that we are bound by Rice's theorem.
Whether it's ever likely to be a practical problem, is another matter.
edit: We already know there are mathematically interesting numbers so enormous they cannot be represented in our universe, let alone computed by humans or our machines. That's not really the kind of practical limit we're interested in, but it still shows a limit of a sort. TREE(3) for instance.
My perspective on results like Rice's theorem is that they tell us that the Turing machine formalism can express incomprehensible programs. I don't see that as a convincing argument that there are important or useful programs that we cannot comprehend; rather I see it as a demonstration the Turing machine model is broad, and an argument that we should look for stricter models that still admit all the programs we care about (probably based on some form of typed lambda calculus).
> My perspective on results like Rice's theorem is that they tell us that the Turing machine formalism can express incomprehensible programs.
I'm afraid I don't know what you're saying here.
> I don't see that as a convincing argument that there are important or useful programs that we cannot comprehend
I don't see that there's any way to contest it. The only way to deny that we are bound by Rice's theorem, is to deny that the human mind is algorithmic. This presumably requires the denial of determinism, which is fairly absurd.
If you're not following my argument, I'd be happy to rephrase it.
> an argument that we should look for stricter models that still admit all the programs we care about (probably based on some form of typed lambda calculus).
That offers no escape. We're still bound by Rice's theorem. Perhaps it will never be a practical issue, but the fact remains.
> If you're not following my argument, I'd be happy to rephrase it.
I'm not following what it is that you think Rice's theorem tells us.
Rice's theorem says that nontrivial properties of Turing machine programs are undecidable, i.e. for a given property, there will be Turing-machine programs for which we can't tell whether they have that property or not.
That doesn't tell us anything about what is possible for programs, or put any limits on programs that we do understand. It just says that in the Turing machine model there must exist programs that we don't understand. Fine. Who cares?
