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.