One of the central issues in cognitive science is the nature of human representations. We argue that symbolic representations are essential for capturing human cognitive capabilities. We start by examining some common misconceptions found in discussions of representations and models. Next we examine evidence that symbolic representations are essential for capturing human cognitive capabilities, drawing on the analogy literature. Then we examine fundamental limitations of feature vectors and other distributed representations that, despite their recent successes on various practical problems, suggest (...) that they are insufficient to capture many aspects of human cognition. After that, we describe the implications for cognitive architecture of our view that analogy is central, and we speculate on roles for hybrid approaches. We close with an analogy that might help bridge the gap. (shrink)

It is shown how mathematical discoveries such as De Moivre's theorem can result from patterns among the symbols of existing formulae and that significant mathematical analogies are often syntactic rather than semantic, for the good reason that mathematical proofs are always syntactic, in the sense of employing only formal operations on symbols. This radically extends the Lakatos approach to mathematical discovery by allowing proof-directed concepts to generate new theorems from scratch instead of just as evolutionary modifications to some existing theorem. (...) The emphasis upon syntax and proof permits discoveries to go beyond the limits of any prevailing semantics. It also helps explain the shortcomings of inductive AI systems of mathematics learning such as Lenat's AM, in which proof has played no part in the formation of concepts and conjectures. (shrink)

Conventional behaviors develop from practice for regularly occurring problems of coordination within a community of actors. Reusing and extending conventional methods for coordinating behavior is the task of everyday reasoning.The computational model presented in the paper details the emergence of convention in circumstances where there is no ruling body of knowledge developed by prior generations of actors within the community to guide behavior. The framework we assume combines social theories of cognition with human information processing models that have been developed (...) within Cognitive Science. The model presented reflects both elements of the framework. Conventional behaviors are partially coded in the predisposition of participants in a joint activity to expect certain points of coordination to develop during the course of the activity. The expected points of coordination that are commonly assumed form a design for an activity. Because of uncertainty, interruptions, and numerous other opportunities to get off‐track and out‐of‐synch, the participants must work jointly and continuously to achieve conventional coordination.One feature of the model is that the community improves its performance despite the fact that individual actors reason independently about their experiences. Another important feature of the model is that the mechanisms for improving behavior are tied to the memory function of individual actors. A third important feature is that the social interaction among the participants simplifies and drives the everyday reasoning processes. An analysis of a large set of computational experiments supports the theoretical position that is developed regarding everyday reasoning and convention. (shrink)