Computation as Implementation

Abstract

Many accounts of computation associate it with the implementation of some abstract structure such as an automaton, algorithm, or program. This chapter focuses on David Chalmers’s account. Chalmers develops an account of implementation as a response to the so-called triviality results, which indicate that every physical object performs every computation, and he goes on to identify computation with implementation. The chapter presents a nuanced approach to Chalmers’s account. On the positive side, it suggests that his notion of implementation successfully circumvents the dire consequences of the triviality results. Additionally, it agrees that the implementation of some formalism is necessary for computing. On the negative side, it argues that implementation (in Chalmers’s sense) is not sufficient for computation. Many physical systems—such as rocks, stomachs, and hurricanes—do not compute, even when they implement a formalism of some sort.