Consider catching a ball. We know how to design a robot that will catch a ball: it will be the hardware for moving an "arm" and a "hand" for the catching, as well as computer hardware and some software for the logic. The software will solve differential equations in order to predict where the ball will be, and when to move the "arm" and "hand" to the correct spot in order to catch it.
No one, as far as I know, argues that humans actually solve differential equations in their head when they catch a ball. They just... catch it. Perhaps with some failed attempts along the way, but as a part of growing up, we learned basic eye-hand coordination.
The notion that syntax and grammar as we have formalized it exist in our brains is the same as saying that differential equations exist in our brains. I find it much more likely that we innately have rough models for syntax, grammar, mechanical movement and object trajectories, but that it takes significant trial-and-error for us to tune those models until the point of competence. I think these models have to be at least partly statistical - otherwise, we wouldn't need to learn anything - and that while our formalisms may be nice approximations of what we do in our brains, I see no reason why they have to be exactly it.
By actually I meant solve them in the same way that you and I solve them; analytically, using our formalisms. Rather, I'm proposing that our brains are using some statistical model that gives results pretty damn close to what the analytical answers would be. And that something similar is true for syntax and grammar.
No one, as far as I know, argues that humans actually solve differential equations in their head when they catch a ball. They just... catch it. Perhaps with some failed attempts along the way, but as a part of growing up, we learned basic eye-hand coordination.
The notion that syntax and grammar as we have formalized it exist in our brains is the same as saying that differential equations exist in our brains. I find it much more likely that we innately have rough models for syntax, grammar, mechanical movement and object trajectories, but that it takes significant trial-and-error for us to tune those models until the point of competence. I think these models have to be at least partly statistical - otherwise, we wouldn't need to learn anything - and that while our formalisms may be nice approximations of what we do in our brains, I see no reason why they have to be exactly it.