I think people like Jerry Fodor define computation as the manipulation of logical symbols by some algorithm. The idea is that you use a standard functionalist analysis (see someone like Putnam 67) to analyze the inputs(X) and outputs(Y) of a cognitive system. So you have (schematically) something like: X->?->Y. Where the "?" defines the project of cognitive neuroscience (i.e. figuring out the physical instantiation of the manipulation of intercalated proteins & neurotransmitter). So, in this picture cognition is not a "state" that needs to be defined a priori but a "black-box" process that needs to be spelled out empirically. At bottom, stuff is continuous, not discrete.

But too much ink gets spilled over this philosophical issue. It seems much more fruitful to analyze the mind as a Turing machine (contentious) and apply computational complexity theory to define limits on human computation based on the hierarchy-- my two cents.