Integrating computation into the mechanistic hierarchy in the cognitive and neural sciences

It is generally accepted that, in the cognitive sciences, there are both computational and mechanistic explanations. We ask how computational explanations can integrate into the mechanistic hierarchy. The problem stems from the fact that implementation and mechanistic relations have different forms. The implementation relation, from the states of an abstract computational system (e.g., an automaton) to the physical, implementing states is a homomorphism mapping relation. The mechanistic relation, however, is that of part/whole; the explanans in a mechanistic explanation are components of the explanandum phenomenon. Moreover, each component in one level of mechanism is constituted and explained by components of an underlying level of mechanism. Hence, it seems, computational variables and functions cannot be mechanistically explained by the medium-dependent properties that implement them. How then, do the computational and implementational properties integrate to create the mechanistic hierarchy? After explicating the general problem (section 2), we further demonstrate it through a concrete example, of reinforcement learning, in cognitive neuroscience (sections 3 and 4). We then examine two possible solutions (section 5). On one solution, the mechanistic hierarchy embeds at the same levels computational and implementational properties. This picture fits with the view that computational explanations are mechanism sketches. On the other solution, there are two separate hierarchies, one computational and another implementational, which are related by the implementation relation. This picture fits with the view that computational explanations are functional and autonomous explanations. It is less clear how these solutions fit with the view that computational explanations are full-fledged mechanistic explanations. Finally, we argue that both pictures are consistent with the reinforcement learning example, but that scientific practice does not align with the view that computational models are merely mechanistic sketches (section 6)