Consider the family of questions:
Does the kth Turing machine halt on input n?
A familiar diagonal argument shows that there is no Turing machine which can answer all n, k instantiations of this question6 Supposedly we humans can.7 Thus, following Gödel and Lucas, it is still argued (e.g., by Penrose [8] [9]) that there are things which we can do which no Turing machine can, so computationalism is false.
There are many ways to respond to this argument, but the transparent computationalist approach seems novel: reject the last step as a non sequitur. Even if Turing machines can't do everything humans can, that does not imply that computers can't. Humans can do more than Turing machines? Big deal: computers can do more than Turing machines can as well. For example, computers can take up space, consume energy, exert gravitational force on their neighbours, keep time, etc. Now it is true that traditional theory would have it that these properties are irrelevant to the computational properties of a system. But that is an odd position, since it is by virtue of such properties that a computer has the computational properties it has and gets any computational work done at all. And as computers become more entrenched and embedded in the real world, those ``non-computational" properties become more and more relevant to success or failure. The case of timing was discussed before, and this alone would be enough to allow one to conclude that computers can do more than Turing machines. Suppose the mass of the computer on the Pathfinder robot stabilises the movement of the robot to such an extent that the visual navigation algorithms implemented in the computer can actually work. Is the mass of the computer still irrelevant to the computational success of the processor? If these non-formal properties are relevant to designing and understanding computational systems, theoretical results about the limitations of disembodied automata will be seen as less and less relevant.
Despite the foregoing, I doubt that the resolution of the diagonalization objection really has much to do with the fact that humans and computers are embodied while Turing machines are not. Rather, I think diagonalization is something no entity can escape, be it abstract or concrete - including humans. Consider the person-halting problem: suppose we enumerate all persons, and all questions of English. Then, is there any person who can answer this question correctly for all values of n and k?
Is the kth person's answer to the nth question ``no"?
No, and for the same diagonalizing reasons as for the traditional halting problem. But notice that there is no non-question-begging argument against the possibility of a single Turing machine being able to answer all those questions. Since Turing machines are not mentioned in those questions, there is no way of tripping a Turing machine up on a case of contradictory self-reference. In short, transparency, although possible, is probably not the best solution here.