We first explore the challenge of enriching the concept of interfaces between syntax, semantics and pragmatics: it  is largely fixed,  innate and governed by simpliciity (economy).   Variation lies within modules, not across them.          Then we argue: Grammar  can provide notations for thought, (Chomsky (2014)) for instance,  through an extension of X-bar theory  to mathematics which demonstrates what a unifying notation for Cognitive Science can look like.    The formalism of Generative grammar may also  carry implications for political ideology and our view  of personal integrity.

We argue that the acquisition path and  actual acquisition evidence is the strongest source of insight for deep principles.  Topics will include (briefly): ellipsis, quantification, wh-movement, recursion, Speech Acts, and the ingredients of False Belief reasoning.     The experiments lead to specific suggestions for how linguistic theory can make the leap into the classroom, and inform our approach to multilingualism. dialects and language disorders.