Induction by enumeration

Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by E. M. Gold (1967, Inform. and Control 10, 447-474)). The concept is less easily interpreted within the first-order paradigm discussed by K. T. Kelly (1996, "The Logic of Reliable Inquiry," Oxford Univ. Press, New York) and E. Martin and D. Osherson (1998, "Elements of Scientific Inquiry," MIT Press, Cambridge, MA), in which the scientist's data amount to the basic diagram of a structure. We formulate two kinds of enumerative induction that are appropriate to the first-order paradigm and analyze their potential for discovery. Among other results, it is shown that one form of enumerative induction achieves maximum inductive competence.