Knowledge, Understanding, and Computational Complexity

Searle’s arguments that intelligence cannot arise from formal programs are refuted by arguing that his analogies and thought-experiments are fundamentally flawed: he imagines a world in which computation is free. It is argued instead that although cognition may in principle be realized by symbol processing machines, such a computation is likely to have resource requirements that would prevent a symbol processing program for cognition from being designed, implemented, or executed. In the course of the argument the following observations are made: (1) A system can have knowledge, but no understanding. (2) Understanding is a method by which cognitive computations are carried out with limited resources. (3) Introspection is inadequate for analyzing the mind. (4) Simulation of the brain by a computer is unlikely not because of the massive computational power of the brain, but because of the overhead required when one model of computation is simulated by another. (5) Intentionality is a property that arises from systems of sufficient computational power that have the appropriate design. (6) Models of cognition can be developed in direct analogy with technical results from the field of computational complexity theory. Penrose [30] has stated . . . I am inclined to think (though, no doubt, on quite inadequate grounds) that unlike the basic question of computability itself, the issues of complexity theory are not quite the central ones in relation to mental phenomena. On the contrary, I intend to demonstrate that the principles of computational complexity theory can give insights into cognition. In 1980, Searle [36] published a critique of Artificial Intelligence that almost immediately caused a flurry of debate and commentary in academic circles. The paper distinguishes ∗Author’s address: Department of Computer Sciences, University of North Texas, P.O. Box 13886, Denton, TX 76203-3886, U.S.A. Electronic mail: [email protected].