Much work in confirmation theory is directed towards finding or interpreting a function, c, taking on hypotheses and evidence as its arguments and returning a value by which the degree of support of the evidence for the hypothesis can be assessed. Confirmation functions are generally thought of as probability functions. That is, c(H,E) is thought to obey the axioms of probability theory, where H is an hypothesis and E the evidence being considered. A difficulty with this approach is that the various problems of induction, including Hume's and Goodman's, militate against construing any confirmation function as a probability function. To date, no satisfactory probability function has been found which addresses the general problem of ampliative inference and which is immune to the standard objections of the Humean or Goodmanian type.

These sorts of considerations suggest it would be promising to examine, as candidates for an acceptable confirmation function, functions which are not probability functions.