Watson won't be able to assign a truth value to this gramatically correct sentence, but would it have the insight that it just stumbled upon a philosophical problem that's solved by narrowing the notion of truth it uses (Bertrand Russell).
In other words, a machine may not be able to examine itself in the way that humans can when certain problems arise.
Also, the limits of computation have been given an upper bound. If it's not computable by a Turing machine with a finite memory tape (or anything else that is mappable to a Turing machine with a finite memory tape), it's not computable by a physical computer.
Steve Yegge started exploring the metaphysics of computer programs before he stopped blogging; it makes for interesting reading.
(As far as I know, neurons can be approximated well enough by classical computers and you don't even need to go quantum, but that's another story.)
Am not going to argue whether a machine can "really" be alive, "really" be self-aware. Is a virus self-aware? Nyet! How about oyster? I doubt it. A cat? Almost certainly. A human? Don't know about you tovarishch, but I am. Somewhere along evolutionary chain from macromolecule to human brain self-awareness crept in. Psychologists assert it happens automatically whenever a brain acquires certain very high number of associational paths. Can't see it matters whether paths are protein or platinum.
By a physical Turing equivalent computer. True. The breakthrough will come when we'll be able to overcome the damnation of step-by-step-ness (which is the primitive expression of causality).
It already happens for 1/0 answers.