Confirmation theory

The result of a test of a general hypothesis can be positive, negative or neutral. The first, qualitative, task of confirmation theory is to explicate these types of test result. However, as soon as one also takes individual hypotheses into consideration, the interest shifts to the second, quantitative, task of confirmation theory: probabilistically evaluating individual and general hypotheses in the light of an increasing number of test results. This immediately suggests conceiving of the confirmation of an hypothesis as increasing its probability due to new evidence.

Rudolf Carnap initiated a research programme in quantitative confirmation theory by designing a continuum of probability systems with plausible probabilistic properties for the hypothesis that the next test result will be of a certain kind. This continuum of inductive systems has guided the search for optimum systems and for systems that take analogy into account.

Carnapian systems, however, assign zero probability to universal hypotheses. Jaakko Hintikka was the first to reconsider the confirmation of such hypotheses and using Carnap’s continuum for this purpose has set the stage for a whole spectrum of inductive systems of this type.