ABSTRACT
INTRODUCTION In Chapters 2 and 3 we concentrated on the potential of connectionism to tackle some of the computational and empirical discrepancies between logicism and some important properties of human cognition. We noted that there are problems for logicism, both at the computational, algorithmic, and implementational levels. In this pivotal chapter we move away from the implementational level and concentrate on the computational and algorithmic levels of explanation in considering the prospects for a logicist theory of everyday, defeasible inference. We focus on two issues. First, at the computational level, we assess the completeness* (see Chapter 1) of extensions of logic to capture defeasible inference. Second, at the algorithmic level, we look in detail at the computational tractability of these extensions of logic. These issues were raised in passing in Chapters 2 and 3, but here form the focus of discussion. We again take Fodor and Pylyshyn’s characterisation (see our opening quote) as a paradigm of logicist cognitive science against which our arguments are explicitly directed. However, in this chapter we argue that these arguments apply more generally to a large class of theories in cognitive science. In the next chapter, we consider the generality of our arguments by examining a range of possible attempts to deal with the problems that we raise. We will argue that these are not successful, and conclude that the implications of our arguments are very general.
