This implies that the combinatorial space of possible grammars is large. If it isn't, then the structure of the universe would imply a narrow set of possible wo

This implies that the combinatorial space of possible grammars is large. If it isn't, then the structure of the universe would imply a narrow set of possible workable grammars. The combinatorial space of languages is obviously infinite, but is this so for grammars? If not then you would expect many languages to share the same grammars. Seems analogous to the same question about mathematics. Are there many different possible arithmetics? No. There are infinitely many ways to express arithmetic symbolically but there is only one arithmetic. 2 + 2 never equals 5.