I don't believe Houshalter was referring to proving Friendliness (or something along those lines); my impression is that he was talking about implementing an AI, in which case neural networks, while "scruffy", should be considered a legitimate approach. (Of course, the "scruffiness" of NN's could very well affect certain aspects of Friendliness research; my relatively uninformed impression is that it's very difficult to prove results about NN's.)

If you can prove anything interesting about a system, that system is too simple to be interesting. Logic can't handle uncertainty, and doesn't scale at all to describing/modelling systems as complex as societies, brains, AIs, etc.