ABSTRACT
In this chapter we turn to a problem in the philosophy of probability which, though intriguing, is perhaps of secondary importance. It is the question of whether we can introduce probabilities for single, unrepeated events. The problem is perhaps most easily seen in terms of the frequency theory. We therefore introduce probabilities for attributes which appear in a long sequence of events: an empirical collective. Now does it make sense to ascribe a probability to the appearance of the attribute on a single event of the sequence as well as in the whole sequence? We can, for example, speak validly of ‘the probability of heads in this sequence of tosses’. Can we also speak of ‘the probability of heads on the next toss’ granted that ‘the next toss’ is an individual event which will never be repeated in the course of nature? Of course we have replaced collectives by sets of repeatable conditions, but, as usual, a corresponding problem arises in the new approach. Granted that we introduce probabilities for a set of repeatable conditions, can we also introduce them for particular instances of these conditions? It is interesting to note that von Mises explicitly denies the validity of such probabilities of single events. The example he considers is the probability of death. We can certainly introduce the probability of death before 80 in a sequence of, say, 40-year-old English non-smokers. But can we consider the probability of death before 80 for an individual person? Von Mises says ‘No’ (1928, p. 11):
We can say nothing about the probability of death of an individual even if we know hiscondition of life and health in detail. The phrase ‘probability of death’, when it refers to a single person has no meaning at all for us. This is one of the most important consequences of our definition of probability….
