to the Mind Edited by

mental elements arise from a physical substrate, and interact causally with the physical world? Approaches to answering these fundamental questions can be derived from the hypothesis that the mind/ brain is a computer: for computers are well understood, physically realized abstract systems that can be endowed with unbounded competence, and whose function can respect epistemic constraints. The answers to the fundamental questions differ, however, depending on the kind of computer the mind/brain is alleged to be: a symbolic computer, a connectionist computer, or some mixture of the two. (1) V A R I E T I E S OF C O M P U T A T I O N : A L T E R N A T I V E C O M P U T A T I O N A L A B S T R A C T I O N S Different types of computation provide different kinds of computational abstractions to serve the role of mentalist theoretical constructs. These abstractions, which will be denoted ‘a’, can be considered in light of the following criteria for assessing their adequacy in meeting the needs of cognitive theory. Desiderata for Mentalist Abstracta a Computational suficiency: a must be part of a system with sufficient computational power to compute classes of functions possessing the basic characteristics of cognitive functions. Frequently attested such characteristics include: unbounded competence or ‘productivity’; recursion; systematicity; Turing Universality; structure-sensitivity; concept and language learnability; statistical sensitivity. Empirical adequacy: a must enable the construction of accounts of human competence and performance which explain the empirical facts of human cognition acknowledged by C o G NITIVE P S Y C H O L O G Y , linguistics (see CHOMSKY), etc. COMPUTATIONAL MODELS OF’ M I N D (3) Phgsical [neural] realizability: a must be realizable in a physical [neural] system These criteria together pose the central paradox of cognition. On the one hand, especially in higher cognitive domains like reasoning and language, cognition seems essentially a matter of structure processing. On the other hand, in perceptual domains, and in the details and variance of human performance, cognition seems very much a matter of statistical processing; and the underlying neural mechanisms seem thoroughly engaged in numerical processing. Thus these criteria seem on the one hand to demand computational abstractions a which provide symbolic structure processing, and on the other, abstractions a which provide numerical and statistical processing. And, indeed, contemporary cognitive theory relies on two types of computation, one addressing the structural, the other the numerical/ statistical, side of the central paradox. Symbolic Computation and the Clas Computational Theory of Mind In symbolic computation, the a provided are symbols (asym) and According to the classical computational theory of mind, MENTAL R E P R E S E N T A T I O N S are symbol structures, and mental processes consist in the manipulation of these representations according to symbolic algorithms, based on symbolic rules. The symbolic computational abstractions fare admirably with respect to the structural side of the criteria of computational sufficiency and empirical adequacy. Physical computers demonstrate the physical realizability of symbolic computation. But the statistical side of computational sufficiency and empirical adequacy are essentially ignored by pure symbolic computation, and little if any insight has arisen from the symbolic theory concerning whether, and how, it can be effectively neurally realized. Local Connectionist Computation ‘Local connectionist models’ are connectionist networks in which each unit corresponds to a symbol or symbol structure (perhaps an entire proposition). Typically, the connections in such networks, and the computations performed in each connectionist unit, are carefully hand-constructed to implement specific symbolic rules. The abstractions provided by this computational framework are the individual unit’s activity (aind-act) and the individual connection (aind.cnx). These function very much like the symbol and rule of symbolic computation. Indeed, this kind of connectionism has strong affinities to traditional symbolic computation. It is the kind of network proposed by McCulloch and Pitts (1943; reprinted in Boden, 1990) which historically contributed to the development of symbolic computation; it is intimately related to contemporary research in the design of algorithms with ‘fine-grained parallelism’. It offers some of the same kinds of computational sufficiency as symbolic computation, but with significant limitations. These networks often employ units which are discrete-state machines, with discrete messages passed along connections. However, genuine numerical processing can also be used: certain kinds of statistical inference can then be performed. Neural realizability has been a main driving force -in much of this research, through Jerome Feldman’s ‘100 step rule’: these networks are typically designed to perform their computations in roughly the same number of steps or ‘cycles’ available to neurons 100. The plausibility of these networks as simplified neural models depends on the hypothesis that symbols and rules are more or less localized to individual neurons and synapses (see Feldman’s article in Nadel et al., 1989, which includes references on local connectionist models). PDP Connectionist Computation and un Eliminativist Theory A different style of connectionist modelling is the ‘parallel distributed processing (PDP)’ approach. Here, the computational abstractions offered to replace symbols and rules are patterns of numerical activity over groups of units (apat.act), and patterns of weights