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This chapter examines four triviality arguments: arguments from Ian Hinckfuss, John Searle, Hilary Putnam, and David Chalmers. The arguments are of varying strength, scope, and plausibility. Despite the differences, I argue that they succeed in ruling out a classical “mapping” theory of computational implementation. This theory takes isomorphism between a formal computational model and a physical system to be a sufficient condition for implementation. More sophisticated theories depart from a classical mapping account but defeat triviality arguments only at cost. Focusing our attention on performance with respect to the triviality arguments allows costs associated with a theory of implementation to be measured. I conclude by tentatively proposing a theory that aims to minimize cost: pluralism about computational implementation. Triviality arguments should be welcomed. They provide powerful and informative constraints on viable theories of computational implementation.
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