I thought the same, then saw you wrote first. It's not crass to believe that an author, wanting to express an idea, may not want to drive away an audience for the idea.

Sure you can, if you have arbitrarily long but still finite time. (Think recursive versus recursively enumerable sets.)

When he says "can't", he doesn't mean it's impossible, he means it's infeasible. There are no techniques for doing it fast enough that anyone has to worry about it being done.