[philosophus]

Not quite. We can compute any determinate process, perhaps. (Although as Gödel‎ showed, self-reference introduces computational paradoxes even in closed, limited, artificial, formal systems: how do we compute "this statement is false?") You seem to believe that consciousness is essentially computation, and perhaps you're right. You may be wrong though -- the nature of consciousness is one of the trickiest, most intractable problems. It's an open question. Again as with Gödel‎, self-reference introduces problems. If we believe that consciousness is a mechanical/chemical operation without innate intelligence, then any statement about consciousness is itself a product of a certain balance of chemicals in the brain only. So the whole idea of getting to the truth about such things is a pointless endeavor.

"does not mean that a computer can understand itself" -- not sure I entirely agree here either. My computer seems pretty good at understanding itself: right now it's telling me its internal temperature, what programs it's running, CPU and memory utilization, and so forth. In fact, it probably understands itself much better than I do -- at billions of computations per second, I certainly can't keep up. I'm being cute, yes, but I'm also suggesting you seem to implicitly accept that there's a certain type of self-understanding or consciousness that computers don't have, but living beings (in particular, humans) do. Whereas before you said your brain is just a computer ... ?

[nmc]

Let us make a distinction, shall we?

Determination is not an issue. Any non-deterministic Turing machine has an equivalent deterministic Turing machine.

Consciousness is an issue. Indeed, if consciousness is pure computation, then its self-referencing character make it vulnerable to Gödel's incompletude theorem. However, maybe consciousness is more than mere computation — maybe it cannot be reduced to an axiomatic system. Anyway, as far as neuroscience goes, I think consciousness mostly remains a philosophical debate.

* * *

You misinterpreted my sentence. What I meant is: "universal computation is not, in itself, a proof that a computer can understand itself". This relates to my above remark: maybe consciousness is not pure computation.

Also, a system monitoring its own status is not necessarily understanding itself.