|The notion of parameters in UG as the source of cross-linguistic variation was introduced in the early 80’s, within the GB model (Chomsky 1981). Accordingly, many of the parameters proposed in subsequent work referred crucially to output conditions applying at levels of representation such as S-structure, made use of government vs. Spec-head agreement, or involved distinctions between components such as “overt syntax” vs. “LF-component”. With the elimination of all conceptually unnecessary levels of representation and machinery within the Minimalist Program (MP) framework (Chomsky 1995, 2001), the status of such parameters, and the clusters of cross-linguistic variation they capture, must be reassessed. A more general issue that has been, and continues being, of central interest is: what constitutes a possible parameter, i.e., what aspects/components of UG are subject to parameterization? An interesting, influential, but not unproblematic, proposal has been the “lexical parameterization” hypothesis, claiming that all parametric values are associated with individual lexical items, in particular, with individual functional elements. In addition to the lexicon, another uncontroversial area of cross-linguistic variation is the PF component. Within a strongly interface-oriented model of grammar such as the MP framework, it is expected that some cases of prima facie syntactic cross-linguistic variation actually will turn out to be attributable to variation in requirements of the PF interface. In the seminar, we will examine the status and sub-types of proposed parameters and the associated patterns of cross-linguistic variation, in light of minimalist models of the computational system (CS). The cases to be discussed specifically will involve “component” parameters, such as the Lexicon-Syntax parameter (Siloni 2002, Reinhart and Siloni 2005), overt/covert displacement parameters (earlier claimed to be S-structure-LF parameters) as proposed for Wh-movement and QR across languages, cross-linguistic variation in the syntax of Focus and (alleged) “Focus-movements”, as well as “word-order” and “configurationality” parameters. The course can be taken either as a seminar or as a non-seminar.