Re: Cristopher Moore on Theorems From Physics?

It is critically important to distinguish between the objective landscape, the boolean functions as mathematical objects, and the syntactic landscape, the particular formal language we are using as a propositional calculus to denote and compute with those objects.  If we do hill-climbing, we must keep our feet on the objective territory, however much we rely on syntactic maps to narrate the travelogue.  (Many will be thinking of manifolds here.)  The object domain has a fixed structure but the conceptual clarity and computational efficiency of propositional calculi can very likely be improved indefinitely.