This paper is an investigation of variable binding as it occurs in dynamic predicate logic (DPL) as opposed to classical predicate logic (CPL). We begin by addressing a troubling conceptual problem, namely that the established notion of syntactic dynamic binding does not correspond to any well-defined notion of semantic dynamic binding. We solve this problem by conservatively re-engineering Groenendijk and Stokhof’s (1991) original semantics for DPL in such a way that the equivalence of the ensuing notion of semantic binding with the extant notion of syntactic binding can be established. We then compare this notion of dynamic binding to its counterpart in CPL. To this end, we invoke the previously invisible syntactic structure that emerges when one refines the common syntax of CPL and DPL in such a way as to render all syntactic operations both categorematic and binary branching. This allows us to formulate a general schema describing the variable binding behaviors of both logics, the only difference consisting in the value of a schematic parameter. Since binary branching and categorematicity are necessary for a semantics whose only semantic operation is unary functional application, our analysis reveals that, in a dynamic semantics of this kind, it is not (just) quantifier phrases, but rather arbitrarily complex operators that act as variable binders. The analysis also suggests that, despite first appearances, dynamic binding is not a counterexample to the principle that operators can only bind variable occurrences that lie within their syntactic scopes.
