No computation without implementation? A potential problem for the single hierarchy view of physical computation

Abstract

The so-called integration problem concerning mechanistic and computational explanation asks how they are related to each other. One approach is that a computational explanation is a species of mechanistic explanation. According to this view, computational or mathematical descriptions are mechanism sketches or macroscopic descriptions that include computationally relevant and exclude computationally irrelevant physical properties. Some suggest that this results in a so-called single hierarchy view of physical computation, where computational or mathematical properties sit together in the same mechanistic hierarchy with the implementational properties. This view can be contrasted with a separate hierarchy view, according to which computational and physical descriptions have their own hierarchies which are related to each other via a bridging implementation relation. The single hierarchy view has been criticized for downplaying the explanatory value of computational explanations and not being hospitable to multiple realization of cognitive processes. In this paper, I argue that (1) the aforementioned criticisms fail, and (2) there might be a deeper problem with the single hierarchy view, which is that the single hierarchy view might collapse into a separate hierarchy view. The kind of abstraction used by the single hierarchy view does not seem to grant mathematical or computational descriptions but only more stripped physical or implementational descriptions.