Reminds me of this puzzle (http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29#Example). In fact, just read the whole page, it's good stuff, and mentions Pinker.
This is why it's always seemed to silly to me to try to axiomitize logic. Either you already "implement" logic, in which case it's unneccessary, or you don't, in which case you're a rock and there's no point in dealing with you.
I think this also has deeper implications for the philosophy of math -- the desire to fully axiomitize is still deeply ingrained despite Goedel, but in some ways this seems like a more fundamental challenge. You can write down as many rules as you want for string manipulation, but the realization of those rules in actual manipulation remains ineffable on paper.
I noticed that as well. Subtle indeed.