The dynamical hypothesis states that cognitive systems are dynamical systems. While dynamical systems play an important role in many cognitive phenomena, the dynamical hypothesis as stated applies to every system and so fails both to specify what makes cognitive systems distinct and to distinguish between proposals regarding the nature of cognitive systems. To avoid this problem, I distinguish several different types of dynamical systems, outlining four dimensions along which dynamical systems can vary: total-state versus partial-state, internal versus external, macroscopic versus (...) microscopic, and systemic versus componential, and illustrate these with examples. I conclude with two illustrations of partial-state, internal, microscopic, componential dynamicism. (shrink)