Abstract

Philosophers became interested in computation because it promised a novel solution to an old problem: How to be a materialist about the mind without eliminating mental content. Similarly, the working hypothesis of many cognitive scientists is that systems are cognitive in virtue of computing appropriate functions. The abstract notion of computation developed by Turing and others, however, entails that computing systems, taken by themselves, do not determine what functions they compute. ;The main contention of this study is that physical computing systems, as opposed to the abstract computing machines they implement, do determine what functions they compute. The function computed by a system, however, does not reside in its environment; instead, it is defined over the interface that allows the system to interact with that environment. ;After a brief introductory chapter, I rehearse in Chapter 2 the fundamental concepts of the theory of computable functions, and I describe the salient features of abstract computing machines. Then, in Chapter 3, I provide an account of the implementation of an abstract computing machine by a physical system. Throughout that chapter I rebut a number of philosophical objections that have been raised against the very possibility of physical computation. ;In Chapter 4, I sort out a number of issues that directly bear on the account of physical computation I develop in Chapter 5. There I argue that physical computation is automated function composition, and I show that computing systems are always causally connected to the function they compute, and the computed function supervenes on the system that computes it. ;I then discuss, in Chapter 6, two potential problems with my account. precludes the computation of abstract functions. This constitutes a shortcoming, of course, only if abstract functions can be computed at all, and I argue that it is far from obvious that they can. will be unacceptable to those who want the computed function to be located in a system's environment. But the environmentalist approach, I argue, does not provide us with a viable account of computation. I conclude by drawing out the implications of my account of computation for the nature of the relationship between computing systems and their environment.