Subsymbolic Computation Theory for the Human Intuitive Processor

The classic theory of computation initiated by Turing and his contemporaries provides a theory of effective procedures — algorithms that can be executed by the human mind, deploying cognitive processes constituting the conscious rule interpreter. The cognitive processes constituting the human intuitive processor potentially call for a different theory of computation. Assuming that important functions computed by the intuitive processor can be described abstractly as symbolic recursive functions and symbolic grammars, we ask which symbolic functions can be computed by the human intuitive processor, and how those functions are best specified — given that these functions must be computed using neural computation. Characterizing the automata of neural computation, we begin the construction of a class of recursive symbolic functions computable by these automata, and the construction of a class of neural networks that embody the grammars defining formal languages. 1 Effective Procedures vs. Intuitive Cognitive Processes What is the set of functions computable by human intuition? Intuitive cognitive processes contrast with conscious rule interpretation [9], the mental processes enabling a clerk to take a list of English instructions and carry out a complex mathematical calculation by consciously interpreting those instructions one after another. Less mundanely, the Entscheidungsproblem also concerns the capabilities of conscious rule interpretation: Turing’s 1936 paper [14] and other classic works provide a theory of the set of functions computable by human conscious rule interpretation, i.e., by effective procedures. Other notions of computation yielding different sets of computable functions derive from alternative conceptions of ‘machine’ in the sense of physical artifact (e.g., differential analyzer, optical or quantum computer). But it is a natural biological system, the brain, that motivates the conception of computation of interest here. Within one stream of cognitive science [10], models of the brain and models of mental processes converged around 30 years ago upon a class of computational systems for modeling intuition, a class known variously as ‘connectionist’, ‘parallel distributed processing’, or ‘abstract neural network’ computational architectures [7]. Since the dawn of modern cognitive science in the middle of the 20th century, many cognitive scientists have treated intuition as formally identical with conscious rule interpretation, but inaccessible to consciousness [10]. Within this