Notes on the Doctrine of Chances

Abstract

On reperusing this article after the lapse of a full general ion, it strikes me as making two points that were worth making. The better made of the two had been still better made ten years before in my three articles in the Journal of Speculative Philosophy Vol. 2.¹ This point is that no man can be logical whose supreme desire is the well-being of himself or of any other existing person or collection of persons. The other good point is that probability never properly refers immediately to a single event, but exclusively to the happening of a given kind of event on any occasion of a given kind. So far all is well. But when I come to define probability, I repeatedly say that it is the quotient of the number of occurrences of the event divided by the number of occurrences of the occasion. Now this is manifestly wrong, for probability relates to the future; and how can I say how many times a given die will be thrown in the future? To be sure I might, immediately after my throw, put the die in strong nitric acid, and dissolve it, but this suggestion only puts the preposterous character of the definition in a still stronger light. For it is plain that, if probability be the ratio of the occurrences of the specific event to the occurrences of the generic occasion, it is the ratio that there would be in the long run, and has nothing to do with any supposed cessation of the occasions. This long run can be nothing but an endlessly long run; and even if it be correct to speak of an infinite ‘number,’ yet (infinity divided by infinity) has certainly, in itself, no definite value.