Reasoning by Analogy in Inductive Logic

The best known examples of rational probability functions exclude the possibility of argument by analogy, and attempts to find alternative classes of functions have had limited success. In this paper we explicate a notion of similarity that derives from the sharing of identical properties and propose an Analogy Principle (AP) based on this notion. We then classify the probability functions that satisfy AP (in the presence of some other widely accepted principles of rationality) for languages with at most four mutually exclusive and jointly exhaustive outcomes (as in the Wheel of Fortune case) and show that there are no solutions to AP for larger languages. In light of this, we conclude by suggesting a modification of the principle and noting that it remains an open problem to provide the full classification of probability functions that satisfy it.