The bigger problem with the SW, as many have noted, is that Gödel will never hava a chance to screw up the works, because he only talks about the incompleteness of CONSISTENT sets of axioms. Getting consistency in the SW's vast network of RDF metadata will be a monumental problem, and ANYTHING can be proven in with an inconsistent set of axioms (as my poor remaining neurons dimly recall my higher education).
So, at best the SW will have to employ some heuristics for finding useful axioms to feed into a logical inference engine. Whether this is worth the cost is another matter.
Yep, I think you've got it here - there won't be one single set of axioms in one inference engine, so the analysis in these terms falls flat. To get the kind of system doing things even vaguely like TimBL talks of, there are going to have to be heuristics liberally scattered throughout the system - after all, there are human nodes in there too.
If I want to book an appointment with an appropriate therapist at 9am in the morning, I should be aware that there's at least a 1% chance of getting a pizza at 10am instead
The sw will of course also provide new ways of talking about what we saw on television (or heard on the radio) last night ;-)