  However, as Zednik (2011) has noted (see also Clark 1997 and Bechtel 1998), the differential equations on which dynamical explanations depend contain terms that permit interpretation. This is what turns a piece of pure mathematics into applied mathematics, which routinely is understood as describing causal processes (Sauer 2010). As an instance of applied (rather than pure) mathematics, The Lotka Volterra equations, for instance, do indeed explain the dynamics of predator-prey populations when their terms are taken to refer to predation rate and reproductive rate. The equations reveal how predation affects the size of the prey population, and how depletion in the prey population affects the size of the predator population, and how reproduction restores the prey population. So, Spivey may be right that the “stuff” of minds consists in brains, bodies, and environments, but this does not preclude the differential equations that describe these interactions from being explanatory. They are explanatory because they describe how brains, bodies, and environments interact and the consequences ensuing from these interactions.