Towards a General Theory of Auxiliary Concepts and Definability in First-Order Theories

There is a fairly extensive philosophical and methodological literature dealing with the role of auxiliary (‘theoretical’) terms in scientific theories. In this literature, logical and foundational ideas play a surprisingly small role, despite the wealth of results concerning definability and related concepts which logicians have established. Virtually the only non-trivial result cited is Craig’s (general) elimination theorem, and the purpose in bringing it up is all too often to deny its relevance. The possible importance of Craig’s less general, but in certain respects more informative, interpolation theorem has not caught the fancy of philosophers of science, whose store of systematic logical results and techniques seems to be often rather restricted.