An influential view in (philosophy of) cognitive science is that computation in cognitive systems is semantic, conceptually depending on representation: to compute is to manipulate representations. I argue that accepting the non-semantic teleomechanistic view of computation lays the ground for a promising alternative strategy, in which computation helps to explain and naturalise representation, rather than the other way around. I show that this computation-based approach to representation presents six decisive advantages over the semantic view. I claim that it can improve the two most influential current theories of representation, teleosemantics and structural representation, by providing them with precious tools to tackle some of their ma...