Anna Wierzbicka's 'natural semantic metalanguage' (NSM) theory has given rise to a new approach to investigating the fundamentals of syntax. The central idea is that all languages share an irreducible core which consists of a set of universal semantic primitives with certain universal combinatorial (i.e. syntactic) properties. This paper outlines a series of hypotheses about the universal syntax of semantic primitives--hypotheses which are tested in the individual language studies which comprise the rest of the volume. Topics include: the valency options and complementation possibilities of primitive predicates such as and , the grammar of temporal and locative primitives (such as ), and of the conditional ( ...) and counterfactual ( ... ) constructions.