Interesting paper, thanks for linking. I think this is slightly tangential to the Norvig-Chomsky controversy though. What Mumford is saying is that probability

Interesting paper, thanks for linking. I think this is slightly tangential to the Norvig-Chomsky controversy though. What Mumford is saying is that probability and statistics is a more useful basis for modelling natural phenomena than classical logic. I don't think Chomsky would disagree with this! What he disagrees with is the idea (also raised by Mumford) that merely reproducing surface-level aspects of a given natural phenomenon (like human language) with no insight or understanding is sufficient for a scientific theory. It isn't sufficient: one also has to show that the theory cannot produce phenomena that are not natural, and give some insight into what's going on. In fact, it's not even necessary: Galileo advanced physics by imagining a frictionless plane. This doesn't and can't exist in the real world, but it helps us understand what does happen in the real world. As an example, Mumford talks about how particle filters work much better than any "classical AI" technique for certain tracking tasks. This is true, and particle filters are still important in engineering for this reason, but it's not a theory of how humans accomplish this for the simple reason that particle filters can just as happily do other things that humans don't/can't.