Piccinini:

"The mapping account says, roughly, that a computing system is a concrete system such that there is a computational description that maps onto a physical description of the system. If any mapping is acceptable, it can be shown that almost every physical system implements every computation (Putnam 1988, Searle 1992). This trivialization result can be avoided by putting appropriate restrictions on acceptable mappings; for instance, legitimate mappings must respect causal relations between physical states (Chrisley 1995, Chalmers 1996, Copeland 1996, Scheutz 2001).

Still, there remain mappings between (many) computational descriptions and any physical system. Under the mapping account, everything performs at least some computations. This still strikes some as a trivialization of computationalism. Furthermore, it doesn"t do justice to computer science, where only relatively few systems count as performing computations. Those who want to restrict the notion of computation further have to look beyond the mapping account of computation."

"Putnam's proposal, and its historical importance, was analyzed in detail in Piccinini forthcoming b. According to Putnam (1960, 1967,1988), a system is a computing mechanism if and only if there is a mapping between a computational description and a physical description of the system. By computational description, Putnam means a formal description of the kind used in computability theory, such as a Turing Machine or a finite state automaton. Putnam puts no constraints on how to find the mapping between the computational and the physical description, allowing any computationally identified state to map onto any physically identified state. It is well known that Putnam's account entails that most physical systems implement most computations. This consequence of Putnam's proposal has been explicitly derived by Putnam (1988, pp. 95-96, 121-125) and Searle (1992, chap. 9)."

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