The Multiple-Computations Theorem and the physics of singling out a computation

The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in outline why Putnam?s result, and likewise the more restricted result we call the Multiple-Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why non-reductive approaches to solving the multiple-computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that non-physical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam?s unrestricted result by appealing to systems with certain kinds of input and output states, as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviourism. We conclude with some remarks about the non-physical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables.