When I was invited to read this paper I felt not only honoured but particularly pleased to be given the opportunity to set forth for your criticism the views I have come to hold concerning the complex of problems centred round the use of Bayes's theorem. For what body of people has for longer been engaged in the application of the mathematical doctrine of probabilities to the affairs of life? And so, what body could be better fitted to judge the merits and the faults of any attempt to clarify the principles of the subject? It is no accident that the original publication of Bayes's famous paper was brought about by the author of the Northampton Life Table; and in the modern period, in dealing with the criticisms of Bayes's postulate stemming from Boole, the credit for a major advance is shared between Sir Harold Jeffreys and Mr Wilfred Perks, independent originators of the theory of invariant prior distributions. And, to anticipate a point I shall develop in more detail later on, it appears to me that the experience of actuaries in the formation of categories as, for instance, by occupational group, as abstainers or non-abstainers, and so on, can be highly relevant to the effective use of Bayes's theorem in many wider contexts; and an examination of the principles underlying the formation of categories should improve our insight into problems of statistical inference in general.