On the Probability of past vs. Future Events

Abstract

It is not unusual to come across the apparently entirely reasonable attitude that there is some intrinsically important distinction to be drawn between the probability of a past event and the probability of a future event. The nature of the problem. is beautifully limned in the following quotation': If I ask, 'What is the probability that I shall die within a year?' I can get a numerical answer which, for example, will satisfy the life insurance comnpanies. But if I ask, 'What is the probability that Hitler is dead?' my question is meaningless; his present state of aliveness or deadness may be unknown, but it is certainly a fact capable of being certainly known by somebody, and thus is not a matter of probability. This may be regarded as fairly representative of the orthodox (i.e., non-Bayesian) view. Let us examine these two questions more carefully in the form: 1) What is the probability that I shall die within 18 years? 2) What is the probability that Hitler died 18 years ago ? Prima facie, it certainly sounds ridiculous to ask for the probability that Hitler died 18 years ago: he either did die or he didn't, tout court. And in this respect question (2) appears to be fundamentally different from question (1) it appears, indeed, to be nonsense. Closer examination, however, will disclose that this is not quite so simply the case.