It is commonplace to remark that probability lies at the root of actuarial science. It is equally commonplace that there has been—and still is—considerable dispute over the definition of probability and that such dispute is usually of little consequence in practical calculations. This being so, some may wonder why I have chosen to ventilate once again the philosophical problems which encompass the concept of probability and which commonly bedevil discussions of what is meant by propositions of the form ‘The probability of x is y’ or ‘A is more probable than B’. The solutions which may be offered to this type of problem are not likely to affect the amount of a surrender value or the contribution scale of a pension scheme. On occasion they may affect the answers to estimation problems or decisions based upon significance tests, although even here the differences between the results yielded by alternative methods of approach are commonly negligible.

Medical and social progress over the past 50 years has resulted in a large increase in the expectation of life, and this, together with a declining birthrate, has caused an increase in the proportion of old persons in the population. In 1901 less than 5% of the population of England and Wales was aged 65 and over; by 1949 the estimated percentage had increased to 11% and must inevitably increase still further in the future. A result of this is that more and more attention is being given to diseases of old age and in fact a new specialized branch of medicine, geriatrics, seems to have arisen. Heart diseases form by far the largest group of causes of death in old age and in 1949 were the certified cause of death in 37% of the deaths in England and Wales at ages 65 and over (Table 1). Even in the age-group 55-59 heart disease was responsible for 24% of all deaths in 1949.