We introduce symbolic dynamics to cognitive scientists with the aim of furthering constructive debate on representation. Symbolic dynamics is a mathematical framework in which both continuous and discrete states of a system can be considered jointly. We discuss a number of theoretical implications this framework has for cognitive science, and offer some consideration of the way in which it might be employed for comparing or conciliating discrete and continuous representational theories. Symbolic dynamics may thus serve as a common, level playing field for debate in theories of cognitive representation.