Chapter 5 is devoted specifically to the history of the head-complement parameter. The first explicit proposals in this respect are found in Graffi (1980), Stowell (1981), and Travis (1984). Then, attention is focused on Kayne’s (1994) Linear Correspondence Axiom and its contribution to the crisis of the head-complement parameter. After considering Chomsky’s (1995a, 1995b) Bare Phrase Structure theory, the discussion turns to the two current main hypotheses about head directionality: on the one hand, that linearization applies in the PF component, as proposed by Richards (2004, 2008); on the other hand, that linear order is determined within narrow syntax, as put forth by Biberauer and Roberts (2015) and Roberts (2019). The chapter ends with a review of Donati and Branchini’s (2013) experimental perspective on linearization, which supports the idea that linear order is part of externalization rather than narrow syntax.

Chapter 6 draws the conclusions of the historical review conducted in the previous chapters and critically reconsiders the notion of parameter, reevaluating both its role in Generative Grammar and its theoretical status. First, concerning Linearization parameters like the ones responsible for overt vs. covert wh-movement and head directionality, it is argued that linguistic variation can be attributed to PF-interface conditions having a disambiguating effect on a specific set of syntactic representations which cannot meet bare output conditions. Second, considering Roberts’s (2019) reformulation of argument-drop, verb movement, and V2 as instances of head movement, it is argued that Chomsky’s (2021a) extra-syntactic account of head movement suggests the possibility of developing a unified theory overcoming the duality between the ‘syntactic parameters’ accounting for the emergence of null arguments and verb movement on one side and Linearization parameters on the other. Lastly, the possibility that variation can arise in the narrow syntax is also considered, followed by some final remarks on the latest views on parametric variation in connection with current minimalist assumptions.