Theory of Probability

5The Evaluation of Probabilities

5.1 How should Probabilities be Evaluated?

In order to say something about this subject without running the risk of being misunderstood, it is first of all necessary to rule out the extreme dilemma that a mathematical treatment often poses: that of either saying everything, or of saying nothing. As far as the evaluation of probabilities is concerned, one would be unable to avoid the dilemma of either imposing an unequivocal criterion, or, in the absence of such a criterion, of admitting that nothing really makes sense because everything is completely arbitrary.

Our approach, in what follows, is entirely different. We shall present certain of the kinds of considerations that do often assist people in the evaluation of their probabilities, and might frequently be of use to You as well. On occasion, these lead to evaluations that are generally accepted: You will then be in a position to weigh up the reasons behind this and to decide whether they appear to You as applicable, to a greater or lesser extent, to the cases which You have in mind, and more or less acceptable as bases for your own opinions. On other occasions, they will be vaguer in character, but nonetheless instructive. However, You may want to choose your own evaluations. You are completely free in this respect and it is entirely your own responsibility; but You should beware of superficiality. The danger is twofold: on the one hand, You may think that the choice, being subjective, ...