This may be old news to you, but if you are interested in what Russel and Goedel had to say, you should also look at Turing and Church. Its really amazing how these guys were all discovering the same stuff at (roughly) the same time. In fact, Turings halting problem can be extended to say precisely what Goedels incompleteness says- but its much much more accessible. There are plenty of texts in computability theory that are written on a pretty approachable level that will take you through Turing Machines and into the halting problem, and the discuss the import of it. I can look some up if you are interested.

Davin L.