According to his own lights, X is ignorant of the truth value of h if and only if both the truth and falsity of h are serious possibilities from his point of view. Thus experimenter X is ignorant concerning the superiority of therapy A over therapy B when it is possible as far as he knows that therapy A is superior and it is also possible that it is not. Alternatively stated, X is ignorant if he suspends judgement concerning the truth values of these alternatives.

Similarly, investor Y is ignorant concerning the yield of a given portfolio of stocks and bonds when several hypotheses specifying different yields are possibly true, as far as he is concerned, no two of them are possibly both true, and at least one of them must be true.

In these cases and countless others, possibility is what I call ‘serious’ possibility according to an agent at a time. Perhaps it would be helpful to call it subjective possibility in analogy to subjective probability. Evaluations of truth-value-bearing hypotheses with respect to probability are evaluations with respect to a factor which determines risks and expectations in a sense best understood by reference to decision theories where risk and expectation are fundamental, as for example in ‘Bayesian’ decision theories, which enjoin rational agents to maximize expected utility.

It is axiomatic in such theories that rational agents may assign subjective probability other than 0 to hypothesis h only if the truth of h is a serious possibility according to X – i.e., only if the truth of h is a serious or subjective possibility according to X.