Three primary research questions guide the core of these papers. (A) Methodologically, how can broadly defined mathematical/cognitive principles guide linguistic investigation? (B) To what extent do general mathematical principles apply linguistic domains? What principles guide computation at different levels of linguistic structure (phonology, metrical structure, syntax)? (C) How is the computational domain defined? In these manuscripts, Vergnaud’s goal is not to radically depart from the Minimalist Program within generative grammar, but rather to take the underlying goal of the generative program and bring it to an even more general scientific level. The themes of and in this book reflect his goal of scientific progress in linguistics, and he has opened the doors to new exploration of old empirical problems in linguistics that may, someday, have deeper biological and physical explanations through the theory presented in this publication.