Istvan Stephen Norman Berkeley

Berkeley [Minds Machines 10 (2000) 1] described a methodology that showed the subsymbolic nature of an artificial neural network system that had been trained on a logic problem, originally described by Bechtel and Abrahamsen [Connectionism and the mind. Blackwells, Cambridge, MA, 1991]. It was also claimed in the conclusion of this paper that the evidence was suggestive that the network might, in fact, count as a symbolic system. Dawson and Piercey [Minds Machines 11 (2001) 197] took issue with this latter claim. They described some lesioning studies that they argued showed that Berkeley’s (2000) conclusions were premature. In this paper, these lesioning studies are replicated and it is shown that the effects that Dawson and Piercey rely upon for their argument are merely an artifact of a threshold function they chose to employ. When a threshold function much closer to that deployed in the original studies is used, the significant effects disappear.

There is widespread belief that connectionist networks are dramatically different from classical or symbolic models. However, connectionists rarely test this belief by interpreting the internal structure of their nets. A new approach to interpreting networks was recently introduced by Berkeley et al. (1995). The current paper examines two implications of applying this method: (1) that the internal structure of a connectionist network can have a very classical appearance, and (2) that this interpretation can provide a cognitive theory that cannot be dismissed as a mere implementation.

Connectionist research first emerged in the 1940s. The first phase of connectionism attracted a certain amount of media attention, but scant philosophical interest. The phase came to an abrupt halt, due to the efforts of Minsky and Papert (1969), when they argued for the intrinsic limitations of the approach. In the mid-1980s connectionism saw a resurgence. This marked the beginning of the second phase of connectionist research. This phase did attract considerable philosophical attention. It was of philosophical interest, as it offered a way of counteracting the conceptual ties to the philosophical traditions of atomism, rationalism, logic, nativism, rule realism and a concern with the role symbols play in human cognitive functioning, which was prevalent as a consequence of artificial intelligence research. The surge in philosophical interest waned, possibly in part due to the efforts of some traditionalists and the so-called black box problem. Most recently, what may be thought of as a third phase of connectionist research, based on so-called deep learning methods, is beginning to show some signs of again exciting philosophical interest.

In 1988, Smolensky proposed that connectionist processing systems should be understood as operating at what he termed the `subsymbolic' level. Subsymbolic systems should be understood by comparing them to symbolic systems, in Smolensky's view. Up until recently, there have been real problems with analyzing and interpreting the operation of connectionist systems which have undergone training. However, recently published work on a network trained on a set of logic problems originally studied by Bechtel and Abrahamsen (1991) seems to offer the potential to provide a detailed, empirically based answer to questions about the nature of subsymbols. In this paper, a network analysis procedure and the results obtained using it are discussed. This provides the basis for an insight into the nature of subsymbols, which is surprising.

The notion of a ‘symbol’ plays an important role in the disciplines of Philosophy, Psychology, Computer Science, and Cognitive Science. However, there is comparatively little agreement on how this notion is to be understood, either between disciplines, or even within particular disciplines. This paper does not attempt to defend some putatively ‘correct’ version of the concept of a ‘symbol.’ Rather, some terminological conventions are suggested, some constraints are proposed and a taxonomy of the kinds of issue that give rise to disagreement is articulated. The goal here is to provide something like a ‘geography’ of the various notions of ‘symbol’ that have appeared in the various literatures, so as to highlight the key issues and to permit the focusing of attention upon the important dimensions. In particular, the relationship between ‘tokens’ and ‘symbols’ is addressed. The issue of designation is discussed in some detail. The distinction between simple and complex symbols is clarified and an apparently necessary condition for a system to be potentially symbol, or token bearing, is introduced