The missing link: Implementation and realization of computations in computer and cognitive science

The notion of computation has attracted researchers from a wide range of areas, cognitive psychology being one of them. The analogy underlying the (metaphorical) usage of "computer" in cognitive psychology can be succinctly summarized by saying that the mind is to the brain as the program is to the hardware. Two main assumptions are buried in this analogy: (1) that the mind can somehow be understood computationally, and (2) that the same kind of relation-the implementation relation-that obtains between programs and computer hardware obtains between minds and brains too. While the first assumption has led to fertile research, the second remained mainly at the level of an assumption.; Recently our understanding of the implementation relation has been challenged by claims of Putnam and Searle (both of which are examined in detail) that every physical system can be viewed as implementing every computation. If this were true, then computation would hardly be an appropriate notion for describing mental processes.; Many people have attacked these claims by finding flaws in the respective arguments, some have even attempted positive accounts of what it means for a physical system to implement a computation (e.g., Chalmers or Copeland). While these positive accounts can avoid most of the problems with the intuitive notion of implementation (as pointed out by Searle and Putnam), it is argued that they still do not get at the heart of their criticisms, namely the formation of physical state types. To overcome these problems, a positive account of implementation and physical realization of computations is developed which does not depend on the notion of physical state, but rather develops the notion of implementation as a series of abstractions over the physical peculiarities of the implementing system.