In this paper we discuss the status of three compelling questions, which impinge on parameter theory:
a. What are the actual parameters of UG?
b. What is the form of a possible parameter?
c. How are parameter values distributed in space and time?
With respect to the first question, we present the guidelines of a heuristic methodology to discover the parameters of UG, Modularized Global Parametrization, first proposed by Longobardi (2003). Building on the potential of such an approach, we pursue a Minimalist critique of the general form of parameters and sketch the programmatic lines of a Principles&Schemata model of UG. To address the third problem, we begin to investigate the implications of a parametric approach for the study of phylogenetic relationships among languages and, more broadly, of cognitive approaches to the study of history.
