The CBC can be supported in various ways, employing different theories of computation. This chapter introduces representationalist theories of computation that might be used to ground the CBC, identify what motivates them, and raises concern about such theories. It focuses on the prospect of grounding the CBC in non-representational theories of computation. The chapter articulates the alternative possibility to the CBC – namely, that computation may depend on semantically-laden cognition and not the other way around. It examines a reversed rival of the CBC – that avoids the problems encountered by both representational and non-representational causal-mechanistic theories of computation and which is consistent with the known facts about how minds and brains work. Some defenders of the CBC embrace representational theories of computation. Representational theories of computation propose that computations are always and everywhere operations over symbols and that symbols have both representational and syntactic properties essentially.