The epistemology of conceptual clustering: KBG, an implementation

Abstract

This paper analyzes differences between a numeric and symbolic approach to inductive inference. It shows the importance of existing structures in the acquisition of further knowledge, including statistical confirmation. We present a new way of looking at Hempel's paradox, in which both existing structures and statistical confirmation play a role in order to decrease the harm it does to learning. We point out some of the most important structures, and we illustrate how uncertainty does blur but does not destroy these structures. We conclude that pure symbolic as well as pure statistical learning is not realistic, but the integration of the two points of view is the key to future progress, but it is far from trivial. Our system KBG is a first-order logic conceptual clustering system; thus it builds knowledge structures out of unrelated examples. We describe the choices done in KBG in order to build these structures, using both numeric and symbolic types of knowledge. Our argument gives us firm grounds to contradict Carnap's view that induction is nothing but uncertain deduction, and to propose a refinement to Popper's “purely deductive” view of the growth of science. In our view, progressive organization of knowledge plays an essential role in the growth of new (inductive) scientific theories, that will be confirmed later, quite in the Popperian way.