Two diametrically opposed positions on syntactic change have wide currency in the literature. The first is the classical position of mainstream formal linguistics. In this view, UG-based strategies lead to a dramatically rapid cascade of seemingly unrelated diachronic changes. The second view has been developed primarily in the context of functional linguistics and associated statistical approaches. In this way of looking at things, diachronic change is ‘fuzzy’, in the sense that syntactic categories and constructions undergo a gradual evolution. In this paper I argue that neither position is correct. Syntactic change is discrete and abrupt, as is maintained by most formal syntacticians. However, we must abandon the view that such change can be interpreted in terms of UG-provided parameters or cues.